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<p>INTRODUCTION TO THERMAL ANALYSIS</p><p>Hot Topics in Thermal Analysis and Calorimetry</p><p>Volume 1</p><p>Series Editor:</p><p>Judit Simon, Budapest University of Technology and Economics, Hungary</p><p>Introduction</p><p>to Thermal Analysis</p><p>Techniques and Applications</p><p>Edited by</p><p>Michael E. Brown</p><p>Chemistry Department,</p><p>Rhodes University,</p><p>Grahamstown, South Africa</p><p>KLUWER ACADEMIC PUBLISHERS</p><p>NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW</p><p>eBook ISBN: 0-306-48404-8</p><p>Print ISBN: 1-4020-0472-9</p><p>©2004 Kluwer Academic Publishers</p><p>New York, Boston, Dordrecht, London, Moscow</p><p>Print ©2001 Kluwer Academic Publishers</p><p>All rights reserved</p><p>No part of this eBook may be reproduced or transmitted in any form or by any means, electronic,</p><p>mechanical, recording, or otherwise, without written consent from the Publisher</p><p>Created in the United States of America</p><p>Visit Kluwer Online at: http://kluweronline.com</p><p>and Kluwer's eBookstore at: http://ebooks.kluweronline.com</p><p>Dordrecht</p><p>CONTENTS</p><p>Preface to the First Edition, Chapman & Hall, London, 1988 ix</p><p>About the First Edition of this Book</p><p>Preface to the Second Edition</p><p>1. INTRODUCTION</p><p>1.1 Definition and History</p><p>Thermal Analysis Instruments</p><p>References</p><p>1.2</p><p>2. THERMAL EVENTS</p><p>2.1</p><p>2.2</p><p>2.3</p><p>2.4</p><p>2.5</p><p>2.6</p><p>Introduction</p><p>The Solid State</p><p>Reactions of Solids</p><p>Decomposition of Solids</p><p>Reaction with the Surrounding Atmosphere</p><p>Solid-Solid Interactions</p><p>References</p><p>3. THERMOGRAVIMETRY (TG)</p><p>3.1</p><p>3.2</p><p>3.3</p><p>3.4</p><p>3.5</p><p>3.6</p><p>3.7</p><p>3.8</p><p>3.9</p><p>Introduction</p><p>The Balance</p><p>Heating the Sample</p><p>The Atmosphere</p><p>The Sample</p><p>Temperature Measurement</p><p>Temperature Control</p><p>Sample Controlled Thermal Analysis (SCTA)</p><p>Calibration</p><p>Presentation of TG Data</p><p>Automation of TG</p><p>Thermomagnetometry (TM)</p><p>Interpretation of TG and DTG Curves</p><p>Applications of Thermogravimetry (TG)</p><p>Applications of Thermomagnetometry (TM)</p><p>References</p><p>3.10</p><p>3.11</p><p>3.12</p><p>3.13</p><p>3.14</p><p>3.15</p><p>x</p><p>xi</p><p>1</p><p>4</p><p>11</p><p>13</p><p>13</p><p>14</p><p>15</p><p>16</p><p>16</p><p>17</p><p>19</p><p>19</p><p>21</p><p>24</p><p>26</p><p>26</p><p>28</p><p>29</p><p>36</p><p>37</p><p>40</p><p>43</p><p>44</p><p>46</p><p>49</p><p>52</p><p>v</p><p>vi</p><p>4. DIFFERENTIAL THERMAL ANALYSIS (DTA) AND</p><p>DIFFERENTIAL SCANNING CALORIMETRY (DSC)</p><p>Classical DTA4.1</p><p>4.2</p><p>4.3</p><p>4.4</p><p>4.5</p><p>4.6</p><p>4.7</p><p>4.8</p><p>4.9</p><p>Calorimetric DTA or heat-flux DSC</p><p>Differential Scanning Calorimetry (DSC)</p><p>Comparison of the Principles of DTA and DSC</p><p>Modulated Temperature Differential Scanning Calorimetry (mt-DSC)</p><p>Sample Containers and Sampling</p><p>Quantitative Aspects of DTA and DSC curves</p><p>Interpretation of DSC and DTA curves</p><p>Determination of Phase Diagrams</p><p>General Applications of DSC and DTA</p><p>Automation</p><p>References</p><p>4.10</p><p>4.11</p><p>5.</p><p>5.1</p><p>5.2</p><p>5.3</p><p>5.4</p><p>5.5</p><p>5.6</p><p>5.7</p><p>5.8</p><p>5.9</p><p>5.10</p><p>References</p><p>THERMOPTOMETRY</p><p>Introduction</p><p>Thermomicroscopy</p><p>Thermophotometry</p><p>Thermoluminescence</p><p>Combination of Thermomicroscopy with DSC (or DTA)</p><p>Combination of Thermomicroscopy with TG</p><p>Other techniques combined with Thermomicroscopy</p><p>Some Applications of the techniques of Thermoptometry</p><p>Electron Microscopy</p><p>Micro Thermal Analysis</p><p>6. THERMOMECHANOMETRY</p><p>Definitions and scope</p><p>Thermodilatometry</p><p>Thermomechanical Analysis (TMA)</p><p>Dynamic Mechanical Analysis (DMA)</p><p>References</p><p>6.1</p><p>6.2</p><p>6.3</p><p>6.4</p><p>7. COMBINATION OF THERMAL ANALYSIS TECHNIQUES</p><p>7.1</p><p>7.2</p><p>Principles</p><p>Equipment</p><p>References</p><p>129</p><p>130</p><p>137</p><p>105</p><p>106</p><p>112</p><p>120</p><p>127</p><p>102</p><p>91</p><p>92</p><p>92</p><p>94</p><p>95</p><p>96</p><p>97</p><p>97</p><p>98</p><p>99</p><p>55</p><p>57</p><p>57</p><p>58</p><p>61</p><p>64</p><p>65</p><p>76</p><p>78</p><p>80</p><p>88</p><p>89</p><p>8. EVOLVED GAS ANALYSIS (EGA)</p><p>vii</p><p>139</p><p>139</p><p>141</p><p>143</p><p>144</p><p>147</p><p>148</p><p>152</p><p>154</p><p>8.1</p><p>8.2</p><p>8.3</p><p>8.4</p><p>8.5</p><p>8.6</p><p>8.7</p><p>8.8</p><p>Basic Principles</p><p>Evolved Gas Detection (EGD)</p><p>Mass Spectrometry (MS)</p><p>Fourier Transform Infrared (FTIR) Spectroscopy</p><p>Gas Chromatography (GC)</p><p>Special-purpose Detectors</p><p>Applications of EGA</p><p>Pulsed Gas Thermal Analysis</p><p>References</p><p>9. LESS-COMMON TECHNIQUES</p><p>9.1</p><p>9.2</p><p>9.3</p><p>9.4</p><p>9.5</p><p>References</p><p>157</p><p>157</p><p>164</p><p>172</p><p>177</p><p>178</p><p>Introduction</p><p>Emanation Thermal Analysis (ETA)</p><p>Thermosonimetry (TS) and Thermoacoustimetry</p><p>Thermoelectrometry (or Thermoelectrical Analysis, TEA)</p><p>Miscellaneous Techniques</p><p>10. REACTION KINETICS FROM THERMAL ANALYSIS</p><p>10.1</p><p>10.2</p><p>10.3</p><p>10.4</p><p>10.5</p><p>10.6</p><p>Introduction</p><p>Heterogeneous reactions</p><p>Formulation of the problem</p><p>Kinetic Analysis of Isothermal Data</p><p>Kinetic Analysis of Nonisothermal Data</p><p>The influences of various parameters on the shapes of theoretical thermal</p><p>analysis Curves</p><p>The Compensation Effect</p><p>Complex reactions</p><p>Prediction of Kinetic Behaviour</p><p>Kinetic Standards</p><p>Kinetic Test Data</p><p>Publication of Kinetic Results</p><p>Conclusions</p><p>References</p><p>11. PURITY DETERMINATION USING DSC</p><p>Introduction11.1</p><p>11.2</p><p>11.3</p><p>11.4</p><p>11.5</p><p>11.6</p><p>References</p><p>Phase equilibria</p><p>The DSC melting curve</p><p>Corrections</p><p>Step methods</p><p>Conclusions</p><p>10.10</p><p>10.11</p><p>10.12</p><p>10.13</p><p>10.7</p><p>10.8</p><p>10.9</p><p>181</p><p>182</p><p>183</p><p>194</p><p>195</p><p>200</p><p>204</p><p>205</p><p>206</p><p>206</p><p>207</p><p>209</p><p>209</p><p>211</p><p>215</p><p>217</p><p>219</p><p>221</p><p>224</p><p>224</p><p>226</p><p>viii</p><p>12. CONCLUSIONS</p><p>The Range of Thermal Analysis</p><p>The Future of Thermal Analysis</p><p>References</p><p>APPENDICES</p><p>A. LITERATURE</p><p>A.1</p><p>A.2</p><p>A.3</p><p>A.4</p><p>A.5</p><p>Books</p><p>Conference Proceedings</p><p>Journals</p><p>Nomenclature</p><p>Manufacturer’s Literature</p><p>B. MAJOR SUPPLIERS OF THERMAL ANALYSIS EQUIPMENT</p><p>Choosing Thermal Analysis Equipment</p><p>Major Suppliers of Thermal Analysis Equipment</p><p>DATA PROCESSING IN THERMAL ANALYSIS</p><p>Introduction</p><p>Data processing</p><p>Spreadsheets and database packages</p><p>Algorithms</p><p>References</p><p>C.1</p><p>C.2</p><p>C.3</p><p>C.4</p><p>C.</p><p>D. INTRODUCTORY EXPERIMENTS</p><p>D.1</p><p>D.2</p><p>Differential Scanning Calorimetry (DSC)</p><p>Thermogravimetry (TG)</p><p>245</p><p>245</p><p>246</p><p>E. EXAMPLE EXAMINATION QUESTIONS</p><p>EXPLANATION OF THE SYMBOLS USED IN THE TEXT</p><p>INDEX 255</p><p>251</p><p>247</p><p>12.1</p><p>12.2</p><p>229</p><p>229</p><p>230</p><p>231</p><p>231</p><p>235</p><p>236</p><p>237</p><p>237</p><p>238</p><p>238</p><p>238</p><p>241</p><p>241</p><p>241</p><p>242</p><p>242</p><p>244</p><p>The aim of this book is, as its title suggests, to help someone with little or no knowledge of</p><p>what thermal analysis can do, to find out briefly what the subject is all about, to decide</p><p>whether it will be of use to him or her, and to help in getting started on the more common</p><p>techniques. Some of the less-common techniques are mentioned, but more specialized texts</p><p>should be consulted before venturing into these areas.</p><p>This book arose out of a set of notes prepared for courses on thermal analysis given at</p><p>instrument workshops organized by the S.A. Chemical Institute. It has also been useful for</p><p>similar short courses given at various universities and technikons. I have made extensive use</p><p>of the manufacturers' literature, and I am grateful to them for this information. A wide variety</p><p>of applications has been drawn from the literature to use as examples and these are</p><p>acknowledged in the text. A fuller list of the books, reviews and other literature of thermal</p><p>analysis is given towards the back of this book. The ICTA booklet 'For Better Thermal</p><p>Analysis' is also a valuable source of information.</p><p>I am particularly grateful to my wife, Cindy, for typing the manuscript, to Mrs Heather</p><p>Wilson for the line drawings, and to Professor David Dollimore of the University of Toledo,</p><p>Ohio, for many helpful suggestions.</p><p>PREFACE TO THE FIRST EDITION, CHAPMAN & HALL, LONDON, 1988</p><p>Michael E. Brown</p><p>Grahamstown 1987</p><p>ix</p><p>“... a readable basic textbook covering material rarely seen in general analytical texts, at a</p><p>level where the reader may gain an adequate overview of the information to be obtained</p><p>from the various methods. (...) This book is a valuable starting point for those wishing to</p><p>explore the field.”</p><p>“Brown’s work is a convenient and easy-to-read first book for those intending to use</p><p>thermal analysis methods; it is a practical help in getting started.”</p><p>“...an excellent, well-balanced, notably clear and thoroughly up-to-date introduction to the</p><p>various techniques and methods of Thermal Analysis...”</p><p>“This excellent monograph in the field of thermal analysis does exactly what its title</p><p>suggest. (...) Any student of thermal analysis would be well recommended to obtain a</p><p>copy.”</p><p>“This is a book that many people will use and about which the author has a right to be</p><p>proud. I have already started using it in teaching undergraduate and graduate courses and in</p><p>planning laboratory experiments.”</p><p>ABOUT THE FIRST EDITION OF THIS BOOK...</p><p>x</p><p>Peter C. Uden, University of Massachusetts</p><p>in Journal of the American Chemical Society (1990)</p><p>György Pokol</p><p>in Journal of Thermal Analysis (1990)</p><p>Slade Warne, University of Newcastle (Australia)</p><p>in Canadian Mineralogist (1989)</p><p>F.W. Wilburn</p><p>in NATAS</p><p>from effects such as thermomolecular</p><p>flow or convection (Section 3.4.). To check that the mass-loss is real, it is advisable to rerun</p><p>the sample, which should then produce a type (i) curve, unless the carrier gas contained</p><p>moisture or was very readily readsorbed on the sample at the lower temperature.</p><p>Type (iii) curves: represent decomposition of the sample in a single stage. The curve may be</p><p>used to define the limits of stability of the reactant, to determine the stoichiometry of the</p><p>reaction, and to investigate the kinetics of reaction (see Chapter 10).</p><p>Type (iv) curves: indicate multi-stage decomposition with relatively stable intermediates.</p><p>Again, the temperature limits of stability of the reactant and of the intermediates can be</p><p>determined from the curve, together with the more complicated stoichiometry of reaction.</p><p>Type (v) curves: also represent multi-stage decomposition, but in this example stable</p><p>intermediates are not formed and little information on all but the stoichiometry of the overall</p><p>reaction can be obtained. It is important to check the effect of heating rate on the resolution</p><p>of such curves. At lower heating rates, type (v) curves may tend to resemble type (iv) curves</p><p>more closely, while at high heating rates both type (iv) and type (v) curves may resemble type</p><p>(iii) curves and hence the detail of the complex decomposition is lost.</p><p>Type (vi) curves: show a gain in mass as a result of reaction of the sample with the surrounding</p><p>atmosphere. A typical example would be the oxidation of a metal sample.</p><p>Type (vii) curves: are not often encountered. The product of an oxidation reaction decomposes</p><p>again at higher temperatures (e.g.,</p><p>Resolution of the individual stages of more complex TG curves can be improved by</p><p>examining the derivative DTG curves (Figure 3.14).</p><p>44</p><p>the magnetic field with the balance mechanism is avoided by use of long suspension wires and</p><p>suitable magnetic screening. Some applications of TM are described below.</p><p>3.13 Interpretation of TG and DTG Curves</p><p>45</p><p>46</p><p>Applications of TG are limited, to some extent, in that not all of the thermal events, listed in</p><p>Chapter 2, are accompanied by changes in mass. For desorption, decomposition and oxidation</p><p>processes, however, much valuable information can be obtained from TG alone. Much of the</p><p>earlier work in TG was on the accurate definition of conditions for drying or ignition of</p><p>analytical precipitates [62]. Examples of TG curves for and for [63]</p><p>are given in Figures 3.15 and 3.16. The mass losses define the stages, and the conditions of</p><p>temperature (and surrounding atmosphere) necessary for preparation of the anhydrous</p><p>compounds, or intermediate hydrates, can be established immediately. At higher temperatures,</p><p>the sulfates will decompose further. Knowledge of the thermal stability range of materials</p><p>provides information on problems such as the hazards of storing explosives, the shelf-life of</p><p>drugs and the conditions for drying tobacco and other crops. By using an atmosphere of air or</p><p>oxygen, the conditions under which oxidation of metals and degradation of polymers become</p><p>catastrophic can be determined.</p><p>3.14 Applications of Thermogravimetry (TG)</p><p>47</p><p>TG curves for more complex materials, such as minerals and polymers, are not always</p><p>immediately interpretable in terms of the exact reactions occurring. Such curves can, however,</p><p>be used for "fingerprint" purposes. The TG curve obtained on a given apparatus, under</p><p>specified conditions, is compared with a bank of reference curves accumulated on the apparatus</p><p>concerned. Some sets of reference curves have been published [64] but, as mentioned earlier,</p><p>comparison is best when curves from the same instrument are available.</p><p>The reactions corresponding to the mass losses can best be determined, or confirmed, by</p><p>simultaneous evolved gas analysis (EGA) (Chapter 9). For example, in Figure 3.15, the</p><p>appearance of traces of and in the evolved gases would indicate the onset of</p><p>sulfate decomposition. A complementary technique, such as hot-stage microscopy (HSM)</p><p>(Chapter 5) may provide information on the mechanism of dehydration or decomposition, by</p><p>showing up the formation and growth of decomposition nuclei, or progress of the</p><p>reactant/product interface inwards from crystal surfaces.</p><p>A very routine application of TG is the proximate analysis of coal [65-67] which involves</p><p>stepwise temperature increases as well as changes in the gaseous atmosphere as indicated in</p><p>Figure 3.17.</p><p>48</p><p>When the process occurring is clearly defined, e.g. the stoichiometric dehydration of a</p><p>definite hydrate, the kinetics of the reaction can be determined from the TG curves (or from a</p><p>series of isothermal curves of mass-loss against time, obtained at different temperatures).</p><p>Details of some of the kinetic analyses that have been suggested are given in Chapter 10.</p><p>Values of activation energies, obtained in this way, have been used to extrapolate to conditions</p><p>of very slow reaction at low temperatures (in predicting shelf-lives of materials, resistance to</p><p>weathering, and in estimating rates of natural processes, e.g. petroleum genesis over geological</p><p>times) and to very fast reaction at high temperatures (behaviour of propellants and explosives).</p><p>In addition to the use of a thermobalance for magnetic susceptibility measurements, as</p><p>mentioned above, a thermobalance may also be used to measure the vapour-pressure of a</p><p>sample, e.g. a metal, by determining the rate of mass-loss through a calibrated orifice in a</p><p>Knudsen cell; for accurate density measurements; for determining surface areas by adsorption,</p><p>and for particle-size analysis by sedimentation.</p><p>49</p><p>3.15 Applications of Thermomagnetometry (TM)</p><p>The major applications of TM have been to ferromagnetic samples where the magnetic effects</p><p>are strongest. For example, TM has been used [68] to examine the spinel phases formed during</p><p>the thermal decomposition of siderite The TM and TG curves shown in Figure 3.18</p><p>for siderite samples heated in nitrogen, show the onset of decomposition at around 400°C. As</p><p>the wustite (FeO) originally formed is oxidized by evolved magnetite is formed.</p><p>The apparent mass gain in the TM curve occurs as the magnetite nuclei grow and crystallize.</p><p>When the temperature rises beyond the Curie point of magnetite, the TM trace coincides with</p><p>the TG trace in the absence of a magnetic field. In oxygen, the wustite is oxidized so rapidly</p><p>to haematite that the strongly magnetic spinel phase never has a chance to form. The conditions</p><p>for optimization of the formation of the ferrite from decomposition of the NiFe citrate</p><p>have also been determined through use of TM [69].</p><p>A novel use of TM is to study reactions in sealed systems [70], e.g. corrosion, provided</p><p>that there is at least one ferromagnetic reactant or product. Figure 3.19 shows the apparatus</p><p>used and the results obtained for the corrosion of carbon steel in an ammoniated EDTA</p><p>solution.</p><p>Another application is in the determination of pyrite in coal [65],usually in combination with</p><p>EGA. The residual ash from normal proximate analysis is heated in a reducing atmosphere</p><p>in the presence of a magnetic field (see Figure 3.17). From the apparent changes in</p><p>mass, as the is reduced to Fe and the product is cooled, the pyrites content can be</p><p>calculated [65].</p><p>50</p><p>51</p><p>52</p><p>References</p><p>A.W. Czanderna and S.P. Wolsky, “Microweighing in Vacuum and Controlled</p><p>Environments”, Elsevier, Amsterdam, 1980.</p><p>C.J. Keattch and D. Dollimore, “An Introduction to Thermogravimetry”,</p><p>Heyden, London, 2nd Edn, 1975.</p><p>P.K. Gallagher, “Handbook of Thermal Analysis and Calorimetry”, Vol.1, (Ed. M.E.</p><p>Brown), Elsevier, Amsterdam, 1998, Ch.3.</p><p>P.K. Gallagher, “Thermal Characterization of Polymeric Materials”, (Ed. E.A. Turi),</p><p>Academic Press, San Diego, 2nd Edn, 1997, Ch.1.</p><p>J.P. Termeulen, F.J. Van Empel, J.J. Hardon, C.H. Massen and J.A. Poulis,</p><p>“Prog. Vacuum Microbalance Techniques”, Vol.1, (Eds T. Gast and E. Robens),</p><p>Heyden, London, 1972, p.41.</p><p>F. Boersma and F.J. Van Empel, “Prog. Vacuum Microbalance Techniques”,</p><p>Vol.3,</p><p>(Eds C. Eyraud and M. Escoubes), Heyden, London, 1975, p.9.</p><p>D.E. Henderson, M.B. DiTaranto, W.G. Tonkin, D.J. Ahlgren, D.A. Gatenby</p><p>and T.W. Shum, Anal. Chem., 54 (1982) 2067.</p><p>V.B. Okhotnikov and N.Z. Lyakhov, J. Solid State Chem., 53 (1984) 161.</p><p>J.C.A. Offringa, C.G. de Kruif, P.J. van Ekeren and M.G.H. Jacobs,</p><p>J.Chem. Thermodyn. (1983) 681.</p><p>B.J. Mulder, J.Phys.E : Sci.Instrum., 17 (1984) 119.</p><p>E. Steinheil, “Prog. in Vacuum Microbalance Techniques”, Vol.1, (Eds T. Gast</p><p>and E. Robens), Heyden, London, 1972, p.1 11.</p><p>A. Kishi, K. Takaoka and M. Ichihasi, Proc. 5th ICTA, (Ed. H. Chihara), Heyden,</p><p>London, 1977, p.554.</p><p>A. Maesono, M. Ichihasi, K. Takaoka and A. Kishi, Proc. 6th ICTA, (Ed. H.G.</p><p>Wiedemann), Birkhauser, Basel, 1980, Vol.1, p.195.</p><p>E. Karmazin, R. Barhoumi, P. Satre and F. Gaillard, J.Thermal Anal., 30</p><p>(1985) 43; 29 (1984) 1269.</p><p>E. Karmazin, R. Barhoumi and P. Satre, Thermochim. Acta, 85 (1985) 291.</p><p>P. Cielo, J. Thermal Anal., 30 (1985) 33.</p><p>E. Robens, Vacuum, 35 (1985) 1.</p><p>S. Inderijarso, J.S. Oklany, A. Millington, D. Price and R. 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Robens), Heyden, London,</p><p>1972,p.l81.</p><p>J.W. Schurman, C.H. Massen and J.A. Poulis, “Prog. Vacuum Microbalance</p><p>Techniques”, Vol.1, (Eds T.Gast and E. Robens), Heyden, London, 1972, p.189.</p><p>M.G.C. Cox, B. McEnaney and V.D. Scott, “Prog. Vacuum Microbalance</p><p>Techniques”, Vol.2, (Eds S.C. Bevan, S.J. Gregg and N.D. Parkyns), Heyden,</p><p>London, 1973, p.27.</p><p>H.R. Oswald and H.G. Wiedemann, J. Thermal Anal., 12 (1977) 147.</p><p>V.V. Boldyrev, M. Bulens and B. Delmon, “The Control of the Reactivity of Solids”,</p><p>Elsevier, Amsterdam, 1979.</p><p>“Manual on the Use of Thermocouples in Temperature Measurement”, American</p><p>Society for Testing and Materials, ASTM Special Technical Publication 470A, 1974.</p><p>H. Dean Baker, E.A. Ryder and N.H. Baker, “Temperature Measurement in</p><p>Engineering”, Vol.2, Omega Press, Stamford, 1975, Ch.1.</p><p>D. Chen and D. Dollimore, Thermochim. Acta, 272 (1996) 75.</p><p>R.L. Blaine, Proc. 25th NATAS, (Ed. R.J. Morgan), 1997, p.485.</p><p>R.L. Blaine and B.K. Hahn, J. Thermal Anal., 54 (1998) 695.</p><p>M. Reading, in “Handbook of Thermal Analysis and Calorimetry, Vol. 1,</p><p>(Ed. M.E. Brown), Elsevier, Amsterdam, 1998, Ch.8.</p><p>J. Rouquerol, Bull. Soc. Chim. Fr., (1964) 31.</p><p>J. Paulik and F. Paulik, Anal. Chim. Acta, 56 (1971) 328.</p><p>J. K. Arthur and J. P. Redfern, J. Therm. Anal., 38 (1992) 1645.</p><p>F. Paulik and J. Paulik, Thermochim. Acta, 100 (1986) 23.</p><p>J. Rouquerol, Thermochim. Acta, 144 (1989) 209.</p><p>O. Toft Sorensen, Thermochim. Acta, 50 (1981) 163.</p><p>P.K. Gallagher, in “Handbook of Thermal Analysis and Calorimetry”,</p><p>Vol. 1, (Ed. M.-E. Brown), Elsevier, Amsterdam, 1998, Ch.4.</p><p>P. S. Gill, S. R. Sauerbrunn, and B. S. Crowe, J. Therm. Anal.,</p><p>38(1992)255.</p><p>S.R. Sauerbrunn, P.S. Gill and B.S. Crowe, Proc. 5th ESTAC, (1991) O-6.</p><p>J. Rouquerol, F. Rouquerol, P. Llewellyn, M. Pijolat, M/Soustelle and V. Bouineau,</p><p>Proc. 12th ICTAC (2000), paper O.14, in press.</p><p>P. A. Barnes, G. M. B. Parkes, and E. L. Charsley, Anal. Chem.,</p><p>66 (1994) 2226.</p><p>J. Rouquerol and M. Ganteaume, J. Thermal Anal., 11 (1977) 201.</p><p>P.A. Barnes and G.M.B. Parkes, Proceedings of the 6th Int. Symp.</p><p>on the Scientific Bases for the Preparation of Catalysts, Louvain-la-Neuve,</p><p>(Ed. G. Poncelet et al.), (1995) 859.</p><p>S.D. Norem, M.J. O'Neill and A.P. Gray, Thermochim. Acta, 1 (1970) 29.</p><p>54</p><p>48.</p><p>49.</p><p>50.</p><p>51.</p><p>52.</p><p>53.</p><p>54.</p><p>55.</p><p>56.</p><p>57.</p><p>58.</p><p>59.</p><p>60.</p><p>61.</p><p>62.</p><p>63.</p><p>64.</p><p>65.</p><p>66.</p><p>67.</p><p>68.</p><p>69.</p><p>70.</p><p>P.D. Garn, O. Menis and H.G. Wiedemann, Proc. 6th ICTA, (Ed. H.G.</p><p>Wiedemann), Vol.1, Basel, 1980, p.201.</p><p>A.R. McGhie, Thermochim. Acta, 55 (1983) 987.</p><p>A.R. McGhie, J. Chiu, P.G. Fair and R.L. Blaine, Thermochim. Acta, 67</p><p>(1983)241.</p><p>M.E. Brown, T.T. Bhengu and D.K. Sanyal, Thermochim. Acta, 242</p><p>(1994) 141.</p><p>P.K. Gallagher, Z. Zhong, E.L. Charsley, S.A. Mikhail, M. Todoki, K.</p><p>Tanaguchi and R.L. Blaine, J. Thermal Anal., 40 (1993) 1423.</p><p>B.J. Weddle, S.A. Robbins and P.K. Gallagher, Pure Appl. Chem., 67</p><p>(1995) 1843.</p><p>E.M. Gundlach and P.K. Gallagher, J. Thermal Anal., 49 (1997) 1013.</p><p>C.M. Earnest, “Compositional Analysis by Thermogravimetry”, (Ed. C.M. Earnest),</p><p>ASTM, Philadelphia, 1988, STP 997, p.1.</p><p>E.J. Millett, J. Phys. E., Sci. Instr., 9 (1976) 794.</p><p>J.M. Ferguson, P.M. Livesey and D. Mortimer, “Prog. Vacuum Microbalance</p><p>Techniques”, Vol.1, (Eds T. Gast and E. Robens), Heyden, London 1972, p.87.</p><p>P.K. Gallagher, J. Thermal Anal., 49 (1997) 33.</p><p>S. St.J. Warne and P.K. Gallagher, Thermochim. Acta, 110 (1987) 269.</p><p>S. St.J. Warne, Thermochim. Acta, 192 (1991) 19.</p><p>P.K. Gallagher, Thermochim. Acta, 214 (1993) 1.</p><p>C. Duval, “Inorganic Thermogravimetric Analysis”, Elsevier, Amsterdam,</p><p>2nd Edn., 1963.</p><p>H.G. Wiedemann, J. Thermal Anal., 12 (1977) 147.</p><p>G. Liptay (Ed.), “Atlas of Thermoanalytical Curves”, Vol.1 (1971), Vol.2</p><p>(1973), Vol.3 (1974), Vol.4 (1975), Vol.5 and Cumulative Index</p><p>(1976), Heyden, London.</p><p>D. Aylmer and M.W. Rowe, Proc. 7th ICTA, (Ed. B. Miller), Wiley, Chichester,</p><p>1982, Vol.2, p. 1270.</p><p>S. St.J. Warne, “Thermal Analysis in the Geosciences”, (Eds W. Smykatz-Kloss</p><p>and S. St.J. Warne), Springer-Verlag, Berlin, 1991, p.62-83.</p><p>H.G. Wiedemann, R. Riesen, A. Boiler and G. Bayer, “Compositional Analysis by</p><p>Thermogravimetry”, (Ed. C.M. Earnest), ASTM, Philadelphia, 1988, STP 997,</p><p>p.227.</p><p>P.K. Gallagher and S. St.J. Warne, Thermochim Acta, 43 (1981) 253.</p><p>H. Tzehoval and M. Steinberg, Israel J. Chem., 22 (1982) 227.</p><p>R.G. Charles, Proc. 7th ICTA, (Ed. B. Miller), Wiley, Chichester, 1982, Vol.1, p264.</p><p>Birkhäeuser,</p><p>DIFFERENTIAL THERMAL ANALYSIS (DTA)</p><p>AND</p><p>DIFFERENTIAL SCANNING CALORIMETRY (DSC)</p><p>4.1 Classical DTA [1,2]</p><p>Differential thermal analysis, DTA, is the simplest and most widely used thermal analysis</p><p>technique. The difference in temperature, between the sample and a reference material is</p><p>recorded while both are subjected to the same heating programme. In 'classical' DTA</p><p>instruments, represented schematically in Figure 4.1., a single block with symmetrical cavities</p><p>for the sample and reference is heated in the furnace. The block is chosen to act as a suitable</p><p>heat-sink, and a sample-holder of low thermal conductivity is included between the block and</p><p>the sample to ensure an adequate differential temperature signal during a thermal event.</p><p>Should an endothermic thermal event positive, such as melting) occur in the sample, the</p><p>temperature of the sample, will lag behind the temperature of the reference, which</p><p>follows the heating programme. If the output from the thermocouples, is recorded</p><p>against (or the furnace temperature, the result will be similar to Figure 4. l(c)). If an</p><p>exothermic process negative such as oxidation) occurs in the sample, the response will be</p><p>in the opposite direction. Since the definition of as is rather arbitrary, each DTA</p><p>curve should be marked with either the endo or exo direction. The negative peak, shown in</p><p>Figure 4.1(c), is called an endotherm and is characterized by its onset temperature. The</p><p>temperature at which the response is at a maximum distance from the baseline, is often</p><p>reported but is very dependent upon the heating rate, used in the temperature programme and</p><p>factors such as the sample size and the thermocouple position. The area under the endotherm</p><p>(or exotherm) is related to the value of the enthalpy change, for the thermal event (for a</p><p>more detailed interpretation, see Section 4.7).</p><p>The reference material should have the following characteristics:</p><p>(i) It should undergo no</p><p>thermal events over the operating temperature range. (ii) It should not react with the sample</p><p>holder or thermocouple, (iii) Both the thermal conductivity and the heat capacity of the</p><p>reference should be similar to those of the sample. Alumina, and carborundum, SiC,</p><p>have been extensively used as reference substances for inorganic samples, while for organic</p><p>compounds, especially polymers, use has been made of octyl phthalate and silicone oil.</p><p>Both solid samples and reference materials are usually used in powdered form. The</p><p>particle-size and the packing conditions influence results. A common technique for matching</p><p>the thermal properties of the sample to those of the reference, is to use the reference material</p><p>55</p><p>56</p><p>as a diluent for the sample. There must obviously be no reaction of the sample with the</p><p>reference material.</p><p>The furnace system is usually purged with an inert gas and the possibilities of atmosphere</p><p>control are similar to those discussed for TG (Chapter 3).</p><p>57</p><p>4.2 Calorimetric DTA or heat-flux DSC [3]</p><p>In 'calorimetric' DTA, (also known as Boersma DTA), the sample and reference, in similar</p><p>holders, usually flat pans, are placed on individual thermally conducting bases. The</p><p>thermocouple junctions are attached to these bases and are thus not directly in the sample or</p><p>reference material. This configuration has the advantage that the output signal is less</p><p>dependent upon the thermal properties of the sample (see above), but response is slower (see</p><p>Figure 4. l(b)).</p><p>The temperature range of DTA depends on the materials used for the furnace windings and</p><p>for the thermocouples.</p><p>4.3 Differential Scanning Calorimetry (DSC) [4-8]</p><p>In power-compensated differential scanning calorimetry (pc-DSC), the aim is to maintain the</p><p>sample and a reference material at the same temperature throughout the</p><p>controlled temperature programme. Any difference in the independent supplies of power to</p><p>the sample and the reference is then recorded against the programmed (reference) temperature.</p><p>The apparatus is shown schematically in Figure 4.2(a), and an example of a resulting DSC</p><p>curve in Figure 4.2(b). There are many similarities between DSC and DTA, including the</p><p>superficial appearance of the thermal analysis curves obtained, but the principle of</p><p>power-compensated DSC is distinctly different to that of heat-flux DSC (see Sections 4.2 and</p><p>4.4).</p><p>Thermal events in the sample thus appear as deviations from the DSC baseline, in either an</p><p>endothermic or exothermic direction, depending upon whether more or less energy has to be</p><p>supplied to the sample relative to the reference material. Again, these directions should be</p><p>clearly marked on the record, to avoid later confusion. In DSC, endothermic responses are</p><p>usually represented as being positive, i.e. above the baseline, corresponding to an increased</p><p>transfer of heat to the sample compared to the reference. Unfortunately this is exactly the</p><p>opposite convention to that usually used in DTA, where endothermic responses are represented</p><p>as negative temperature differences, below the baseline, as the sample temperature lags behind</p><p>the temperature of the reference.</p><p>The operating temperature range of power-compensated DSC instruments is generally more</p><p>restricted than that of DTA instruments. The Perkin-Elmer DSC-7, for example, has a</p><p>maximum temperature of 726°C (999 K). Low temperature attachments are available for</p><p>extending the operating range of the DSC to as low as -175°C. At low temperatures the</p><p>instrument has to be protected from moisture condensation.</p><p>58</p><p>4.4 Comparison of the Principles of DTA and DSC [3,9,10]</p><p>A schematic diagram of a differential thermal apparatus is given in Figure 4.3 together with</p><p>definitions of the terms needed for comparison of classical DTA, heat-flux DSC and</p><p>power-compensated DSC.</p><p>59</p><p>For an ideal instrument, the heat capacities and thermal resistances would be matched, i.e.</p><p>and Note that and It is further assumed</p><p>that and that heat flow is governed by Newton's law:</p><p>Heat flow to the sample side, heats both (i) the sample monitoring station and (ii) the sample:</p><p>also</p><p>so</p><p>and</p><p>Similar expressions hold for the reference side.</p><p>Classical DTA</p><p>Thermocouples are in the sample and in the reference material so that and i.e.</p><p>The signal then is:</p><p>and depends upon the difference in heat capacities, the heating rate and the thermal resistance,</p><p>R. R is difficult to determine as it depends on both the instrument and the properties of the</p><p>sample and the reference.</p><p>Power-compensated DSC</p><p>The power is varied to make Thus and i.e. there is no thermal</p><p>resistance. The signal is then:</p><p>is of similar form to classical DTA, except that R depends only on the instrument and not on</p><p>the characteristics of the sample.</p><p>The signal:</p><p>Heat-flux DSC</p><p>The conditions are that:</p><p>Applying Newton's law:</p><p>60</p><p>61</p><p>4.5 Modulated Temperature Differential Scanning Calorimetry (MTDSC or mt-DSC)</p><p>Modulated Temperature Differential Scanning Calorimetry (mt-DSC according to the newest</p><p>nomenclature proposals, Chapter 1, and usually referred to as MTDSC) is a technique [2,6,11 -</p><p>16] in which the conventional linear heating programme is modulated by superimposing a sine</p><p>wave (or other periodic waveform, see below) of small amplitude on the linear rise. Portions</p><p>of each cycle then involve heating while other portions involve cooling. The overall trend,</p><p>however, remains a linear change in average temperature with time. The resultant heat flow</p><p>signal is analyzed to separate the response to the perturbation from the response to the</p><p>underlying heating programme.</p><p>The modulated heating programme may, for example, be of the form:</p><p>where is the starting temperature, the heating rate, B the amplitude of the modulation and</p><p>its angular frequency where is the frequency).</p><p>The contributions to the resulting heat flow can be written in the form [2]:</p><p>where is the heat flow into the sample, is the heat capacity of the sample and f(t,T)</p><p>is the heat flow arising as a consequence of a “kinetically hindered” event [2]. The form of</p><p>f(t,T) will be different for different types of process.</p><p>Combination of equations (1) and (2) gives:</p><p>The total or underlying signal is where F(t,T) is the average of f(t,T) over</p><p>the interval of at least one modulation, and the cyclic signal is</p><p>where D is the amplitude of the kinetically hindered response to the temperature</p><p>modulation. Both and D will be slowly varying functions of time and temperature but can</p><p>be considered effectively constant over the duration of a single modulation. f(t,T) can also give</p><p>rise to a cosine contribution.</p><p>The kinetically hindered responses are usually assumed to show Arrhenius-type behaviour.</p><p>The cosine response of f(t,T) can be made negligible by adjusting the frequency of modulation</p><p>and the underlying heating rate, to ensure that there are many cycles over the course of the</p><p>transition. The amplitude of the temperature modulation is usually restricted to a degree or less</p><p>so that the kinetic response can be considered to be linear.</p><p>4.5.1 Introduction</p><p>62</p><p>4.5.2 Alternative modulation functions and methods of analysis</p><p>Some workers and manufacturers (Perkin-Elmer and Mettler-Toledo) have preferred a square</p><p>wave or a sawtooth modulation. In some cases they have proceeded with a Fourier transform</p><p>analysis and taken the first Fourier coefficient (Perkin-Elmer). This then gives equivalent</p><p>results to the use of a sine wave with a FT analysis [2],</p><p>Use of a square wave (Mettler-Toledo) ensures that a steady state is achieved over the</p><p>isothermal plateau. Because dT/dt is zero, the signal during this portion must be a</p><p>non-reversing contribution. The difference between the maxima and the minima generated by</p><p>the modulation, i.e. the amplitude, gives a measure of the reversing signal. An alternative is</p><p>to use equal positive and negative heating rates, with a longer duration being given to the</p><p>positive or negative portions in order to provide a net heating or cooling rate. The sum of the</p><p>maxima and minima in the heat</p><p>flow produced by this modulation [2], provides a measure of</p><p>the non-reversing component (where F(t,T) is assumed not to change during the modulation).</p><p>Again the difference between them is a measure of the reversing signal. The disadvantage of</p><p>these approaches is that there is only one point per modulation obtained using only part of the</p><p>data, with the intervening data being lost. This severely compromises accuracy and resolution.</p><p>4.5.3 Advantages of mt-DSC [2]</p><p>Use of mt-DSC with appropriate frequencies and amplitudes of modulation allows separation</p><p>of reversing processes, such as glass transitions, from non-reversing processes such as</p><p>relaxation endotherms, or cure reactions. Baseline curvature on the cyclic signal is generally</p><p>very low, thus making it easier to distinguish between baseline effects and real transitions. The</p><p>signal-to-noise ratio of the cyclic measurement of heat capacity is generally greater, because</p><p>all drift or noise at frequencies other than that of the modulation is ignored by the Fourier</p><p>transform analysis. Resolution of processes can be improved because very low underlying</p><p>heating rates can be used.</p><p>The signals derived from a MTDSC experiment (see Figure 4.4) are: (i) the average or</p><p>underlying signal, equivalent to conventional DSC; (ii) the in-phase cyclic component from</p><p>which can be calculated, and (iii) the out-of-phase signal, D. can be multiplied by the</p><p>heating rate, to give (iv) the reversing contribution to the underlying heat flow. Subtraction</p><p>of (iv) from the underlying signal (i) gives (v) the non-reversing heat flow.</p><p>63</p><p>64</p><p>4.6 Sample Containers and Sampling</p><p>At temperatures below 500°C (773 K) samples are usually contained in aluminium sample pans.</p><p>One type of pan has lids which may be crimped (Figure 4.5.) into position, while for volatile</p><p>samples, pans and press are available which enables a cold-welded seal, capable of</p><p>withstanding 2-3 bar (220-300 kPa) pressure, to be made. The use of aluminium pans above</p><p>500°C will result in destruction of the DSC sample holder, so it is essential to ensure that the</p><p>hardware or software of the instrument will limit the maximum temperature which may be used</p><p>by an operator unless he or she has specifically overridden the limit.</p><p>65</p><p>For temperatures above 500°C, or for samples which react with the Al pans, gold or graphite</p><p>pans are available. Glass sample holders are sometimes suitable. The reference material in</p><p>most DSC applications is simply an empty sample pan.</p><p>The sample-holder assembly is purged by a gas which may be inert or reactive as desired.</p><p>(The high thermal conductivity of helium makes it unsuitable for thermal measurements</p><p>although it has advantages for evolved gas analysis (see later)).</p><p>Dense powders or discs, cut out of films with a cork borer, are ideal samples. Low density</p><p>powders, flocks or fibres may be prepacked in a small piece of degreased aluminium foil to</p><p>compress them. A small syringe is used for filling pans with liquid samples. When volatile</p><p>products are to be formed on heating the sample, the pan lid should be pierced. This is also</p><p>necessary when reaction with the purge gas is being investigated.</p><p>If the total mass of the sample + pan + lid is recorded before and after a run, further</p><p>deductions on the processes occurring can be made from any change in mass.</p><p>4.7 Quantitative Aspects of DTA and DSC Curves</p><p>4.7.1 Characteristics of a DSC Curve [8]</p><p>Some characteristic terms are used to describe a measured DSC curve (see Figure 4.6).</p><p>66</p><p>The zero line is the curve measured with the instrument empty, i.e. without samples and</p><p>without sample containers (crucibles), or with the sample containers (crucibles) empty.</p><p>The (interpolated) baseline is the line constructed in such a way that it connects the</p><p>measured curve before and after a peak, as if no peak had developed. A peak in the curve</p><p>appears when the steady state is disturbed by some production or consumption of heat by</p><p>the sample. Peaks associated with endothermic processes are plotted upwards (positive</p><p>direction of heat addition to the system). Some transitions, such as glass transitions, lead</p><p>to changes in the shape of the DSC curve, rather than to distinguishable peaks.</p><p>The characteristic temperatures of a DSC curve are defined as follows [8]:</p><p>Initial peak temperature: The peak begins where the curve of measured values begins</p><p>to deviate from the baseline.</p><p>Extrapolated peak onset temperature: Where the line drawn through the almost linear</p><p>section of the ascending peak slope intersects the baseline.</p><p>Peak maximum temperature: Where the difference between the DSC curve and the</p><p>interpolated baseline is a maximum. This not necessarily the absolute maximum of the</p><p>DSC curve.</p><p>Extrapolated peak completion temperature: Where the line through the descending peak</p><p>slope intersects the baseline.</p><p>Final peak temperature: Where the DSC curve returns to the baseline.</p><p>4.7.2 The Baseline</p><p>The features of interest in DTA or DSC curves are the deviations of the signal from the</p><p>baseline, and the baseline is not always easy to establish. Initial displacements of the</p><p>baseline itself from zero, result from mismatching of the thermal properties of the sample</p><p>and the reference material and asymmetry in the construction of sample and reference</p><p>holders. In severe cases this may cause a sloping baseline, which may require electrical</p><p>compensation. After a thermal event, the response will not return to the original baseline</p><p>if the thermal properties of the high-temperature form of the sample are different from</p><p>those of the low-temperature form. Many different procedures for baseline construction</p><p>have been suggested (Figure 4.7) and may be incorporated in the software supplied with</p><p>an instrument.</p><p>It should be immediately obvious whether a DSC or DTA feature is a peak or a</p><p>discontinuity, provided that the baseline can be established with certainty. Whether a peak</p><p>is in the exothermic or endothermic direction should be ascertained by comparison with a</p><p>known melting (endothermic) peak. If there is any suggestion from initial runs that any of</p><p>the features involve overlapping peaks, then further experiments should be done in which</p><p>the sample mass and the heating rate are varied to see whether the individual peaks can be</p><p>resolved.</p><p>67</p><p>4.7.3 Measurement of enthalpy changes [18]</p><p>Once a satisfactory baseline has been defined, the area of the endotherm or exotherm is</p><p>determined by numerical integration. The measured area, A, is assumed to be proportional</p><p>to the enthalpy change, for the thermal event represented.</p><p>The glass transition in polymers (see Figure 4.8.) is accompanied by an abrupt changes</p><p>in position of the baseline resulting from the change in heat capacity on going from the</p><p>glassy to rubber-like states. The enthalpy change, for such transitions is zero, which</p><p>is often regarded as the criterion for a second-order transition, but Wunderlich [ 17] has</p><p>emphasized that the glass transition is time dependent and hence is not at thermodynamic</p><p>equilibrium.</p><p>where is the sample mass and K is the calibration factor. This factor has to be</p><p>determined by relating a known enthalpy change to a measured peak area. Usually the</p><p>melting of a pure metal, such as indium, is used for calibration.</p><p>68</p><p>The procedure for the determination of the enthalpy change for a process occurring in the</p><p>sample, is then to determine:</p><p>and to use this value in</p><p>where A is the area and subscripts c and s refer to calibrant and sample, respectively. Note</p><p>that the heating rate used in the temperature programme does not enter into the</p><p>calculations, but, in precise work, should be the same for sample and calibrant.</p><p>The calibration factor, K, contains contributions from the geometry and thermal</p><p>conductivity of the sample/reference system and is thus specific to a particular instrument</p><p>under one set of operating conditions. For power-compensated DSC, the proportionality</p><p>constant, K, is virtually independent of temperature, while for DTA or heat-flux DSC, the</p><p>value of K is markedly dependent upon</p><p>temperature, so that calibrations have to be carried</p><p>out over the full operating temperature range of the instrument. Compensation for the</p><p>temperature dependence of the calibration factor is, however, now usually built into the</p><p>hardware or software of heat-flux DSC instruments.</p><p>The melting point of the standard used for the enthalpy calibration above is usually used</p><p>at the same time to calibrate the temperature output of the instrument.</p><p>69</p><p>4.7.4 Calibration materials</p><p>Certified reference materials (CRM) are available from some national laboratories, mainly</p><p>the UK Laboratory of the Government Chemist (LGC) and the US National Institute of</p><p>Standards and Technology (NIST) [18]. Table 4.1. lists the transition temperatures and</p><p>enthalpies of materials recommended as standards [18],</p><p>Ideally, the thermal properties of the standard including its transition temperature, should</p><p>be as close as possible to those of the sample under consideration. The calibrant should</p><p>[18] also be available in high purity at low cost, be easy to handle and of low toxicity and</p><p>be chemically and physically stable. The transition of interest should be readily reversible.</p><p>Enthalpy (and specific heat capacity ) data should be known to an order of magnitude</p><p>better than the DSC reproducibility. Enthalpies of fusion or transition are not generally</p><p>known to better than let alone the desired [18]. Richardson and Charsley [18]</p><p>have described experimental procedures in detail. Some important recommendations are</p><p>that, for melting transitions, the sample should have been premelted to give a thin layer</p><p>between the pan and its lid; samples should be of minimum size consistent with an</p><p>adequate signal and should be reweighed at the end of a run to guard against any possible</p><p>vaporization. Most of the molten metals listed in Table 4.1 will react with aluminium pans.</p><p>Cammenga et al. [19] have discussed sample/pan compatibilities.</p><p>Other reference materials and potential calibrants are described in the detailed review by</p><p>Richardson and Charsley [18]. The International Confederation for Thermal Analysis</p><p>and Calorimetry (ICTAC) reference materials mainly feature solid/solid transitions.</p><p>Round-robin comparisons show wide uncertainties in the averaged onset temperatures</p><p>(Table 4.2) and in determinations of enthalpy changes. ICTAC has a new programme to</p><p>recertify most of these materials, which should therefore be considered to be secondary,</p><p>or working, standards.</p><p>4.7.5 Measurement of heat capacity</p><p>DSC can also be used to measure heat capacities of materials. Because heat capacity</p><p>values are fundamental to thermodynamics, this is an important feature.</p><p>Where is the heat capacity at constant pressure.</p><p>70</p><p>71</p><p>In the absence of a sample, i.e. with empty pans in both holders of Figure 4.9(a), the DSC</p><p>baseline should be a horizontal line. A sloping baseline may be observed when the sample</p><p>and reference holders have different emissivities, i.e., if the amount of energy lost by</p><p>radiation does not vary in the same way with for both sample and reference. This could</p><p>occur for a black sample and a shiny reference, so a sloping baseline is often an indication</p><p>that the sample-holder assembly should be cleaned by heating in air to high temperatures,</p><p>with aluminium pans removed.</p><p>72</p><p>When a sample is introduced, the DSC baseline is displaced in the endothermic direction</p><p>and the displacement, is proportional to the total heat capacity, of the sample. (The</p><p>total heat capacity = mass x specific heat capacity). This is illustrated in Figure 4.9(a).</p><p>where is the heating rate and B the calibration factor. The value of B is determined using</p><p>a standard substance [18], e.g. sapphire, scanned under similar conditions to the sample</p><p>(see Figure 4.9(b)). Although the technique is simple in principle, Suzuki and Wunderlich</p><p>[20] have shown that a great deal of care is necessary to get accurate and reproducible</p><p>results. Because of the proportionality of the DSC response to the heat capacity of the</p><p>sample, a shift in baseline after a transition is common (Figure 4.9(c)) and the baseline has</p><p>to be estimated as shown in Figure 4.7 or by more elaborate procedures [21].</p><p>4.7.6 Measurement of thermal conductivity</p><p>Thermal conductivity, is an important physical property, particularly with the present</p><p>emphasis on the efficient use of energy. Numerous methods for measuring thermal</p><p>conductivity have been published and dedicated commercial instruments are available.</p><p>Several papers have been published [22-25] in which heat-flux DSC instruments have been</p><p>used to measure thermal conductivity. An advantage of using DSC is that specific heat</p><p>capacities, can be measured in the same instrument and hence, if density values, are</p><p>available or can be measured, thermal diffusivities, D, can be calculated from the</p><p>relationship, Chiu and Fair [22] have described an attachment for the</p><p>DuPont 990 DSC cell, (Figure 4.10), which allows for measurement of thermal</p><p>conductivity ofa sample (in cylindrical form) without modification ofthe basic instrument.</p><p>The temperature at the bottom of the sample is measured via the output of the DSC,</p><p>while the temperature at the top of the sample is measured with a separate</p><p>thermocouple in the contact rod. The heat input for the sample is also provided by the</p><p>DSC. The cell is calibrated with a sample of known thermal conductivity. The output of</p><p>the DSC operating in the normal mode is used as the baseline. With the sample in position,</p><p>the DSC cell is brought to the desired measurement temperature, and when the DSC</p><p>output is steady with time, the temperature difference across the sample, and the</p><p>recorder displacement, are determined. The sample is then replaced by a calibrant, e.g.</p><p>a standard glass, and the correspondingquantities, and are determined. The thermal</p><p>conductivity of the sample, is then calculated from:</p><p>where is the length and d the diameter of the sample (subscript s) and calibrant (subscript</p><p>c) as specified. A sample length of 10 to 25 mm is recommended and a precision of better</p><p>than 3% is claimed. Sircar and Wells [23] have used the above method in studying</p><p>elastomer vulcanizates, and Hillstrom [24], a very similar system, for determining the</p><p>thermal conductivity of explosives and propellants.</p><p>73</p><p>74</p><p>Two identical cylinders of sample (1-3 mm high, 2-4 mm diameter) are then placed on the</p><p>so that:</p><p>Hakvoort and van Reijen [25] using a DuPont 910 DSC, replaced the temperature sensor</p><p>on the top of the sample by a disc of pure gallium or indium metal (see Figure 4.11(a)).</p><p>The temperature at the top of the sample during the melting of the metal is then fixed at the</p><p>melting point, of the metal. The y-output scale calibration factor C for the</p><p>instrument is first determined by melting a weighed sample of the metal placed directly on</p><p>the sensor, without a sample pan, and measuring the DSC signal, y, with time. The heat of</p><p>melting, is given by:</p><p>75</p><p>sample and reference positions of the DSC (with silicone grease if necessary). A disc of</p><p>the metal to be melted (10 to 40 mg and diameter similar to that of the sample) is placed on</p><p>top of the cylinder on the sample side and the sensor temperature, and the DSC signal,</p><p>y are recorded with time as the cell is heated at constant rate. During the melting of the</p><p>metal, the top of the sample cylinder remains at constant temperature, while the lower</p><p>side temperature, increases at constant rate. The DSC plot obtained is shown in Figure</p><p>4.11(b). Two quantities are determined: the slope of the plot of against time,</p><p>and the slope of the DSC curve, Combining these quantities,</p><p>The thermal conductivity, is then calculated from [4]:</p><p>where A is the cross-sectional area of the sample cylinder and h its height.</p><p>Boddington et al. [26] have carried out a more elaborate modification of a Stanton</p><p>Redcroft DTA model 673 for measurement of the thermal diffusivity of pyrotechnic</p><p>compositions.</p><p>76</p><p>4.8 Interpretation of DSC and DTA curves</p><p>At the heart of all thermal analysis experiments lies the problem of correlating the features</p><p>recorded with the thermal events taking place in the sample. Some aspects of this</p><p>correlation for TG results have been discussed in Section 3.8. DSC or DTA provides</p><p>different information and if simultaneous measurements are not possible, the results of</p><p>parallel experiments, using different techniques such as TG and DSC or DTA, under</p><p>conditions (e.g. sample mass, heating rate, atmosphere) as closely matched as possible, are</p><p>most valuable.</p><p>Once the main features of the DTA or DSC curve have been established, and baseline</p><p>discontinuities have been examined, attention can be directed at the correlation of the</p><p>endothermic or exothermic peaks with thermal events in the sample.</p><p>A useful procedure is to test whether the event being monitored is readily reversible on</p><p>cooling and reheating, or not. Exothermic processes are not usually readily reversible, if</p><p>at all, in contrast to melting and many solid-solid transitions.</p><p>The melting endotherms for pure substances are very sharp (i.e. they occur over a narrow</p><p>temperature interval) and the melting point, is usually determined, as shown in Figure</p><p>4.2(b), by extrapolation of the steeply rising, approximately linear, region of the endotherm</p><p>back to the baseline. For impure substances the endotherms are broader and it is possible</p><p>to estimate the impurity content (up to a maximum of about 3 mole %) from the detailed</p><p>shape of the melting endotherm (see Chapter 11).</p><p>TG and EGD or EGA information is invaluable at this stage in distinguishing between</p><p>irreversible or slowly-reversible phase transitions and decompositions. Quantitative mass</p><p>losses and detailed EGA may, in addition, lead to determination of the stoichiometry of</p><p>decomposition. Account must naturally be taken of the gaseous atmosphere surrounding</p><p>the heated sample. Dehydration may be found to be reversible on cooling in a moist</p><p>atmosphere before reheating, and carbonate decompositions are usually reversible in</p><p>atmospheres. Comparison of features observed, under otherwise similar conditions, in inert</p><p>and oxidising atmospheres is valuable. TG results may show increases in mass</p><p>corresponding to reaction of the sample with the surrounding atmosphere.</p><p>It cannot be over emphasised that as many additional techniques available, such as</p><p>hot-stage microscopy, conventional elemental analysis, X-ray diffraction (XRD) and the</p><p>many types of spectroscopy, should be used to confirm suggested interpretations of TA</p><p>features recorded. Table 4.3 summarises the overall interpretation procedure, but this</p><p>should NOT be followed blindly. There is no substitute for experience built up by running</p><p>samples with well-documented behaviour on your own instrument, and also examining the</p><p>almost legal-type of "proof" of events provided by more-conscientious authors (spurred on</p><p>by more-demanding editors).</p><p>77</p><p>78</p><p>4.9 Determination of phase diagrams</p><p>It is not always easy to detect accurately by eye the onset and completion of melting of</p><p>binary or more complicated systems. The records obtainable from DSC and DTA runs,</p><p>under carefully defined sample conditions, and slow heating and cooling rates so that</p><p>equilibrium is approached, provide a more accurate way of establishing the phase diagram</p><p>for the melting and solubility behaviour of the system under consideration.</p><p>In a binary system of immiscible solids and their completely miscible liquids, with the</p><p>well-known phase diagram shown in Figure 4.12 (e.g. the benzoic acid/naphthalene system</p><p>[27,28] or the triphenylmethane/trans-stilbene system [29]), the melting curves of the pure</p><p>components A and B (with melting points and are readily obtained, using DSC</p><p>or DTA, and should be sharply defined. The melting behaviour ofmixtures ofA and B will</p><p>depend upon the histories ofthe mixtures and, in this discussion, it will be assumed that the</p><p>mixtures have been prepared in completely molten form initially (without any volatilization</p><p>or oxidation [30]).</p><p>A DSC or DTA record of the slow cooling of such a molten mixture of composition</p><p>(mole fraction) initially at temperature in Figure 4.12, would show no deviation from the</p><p>baseline until temperature when solid B begins to crystallize in an exothermic process.</p><p>This exotherm is not sharp but tails off as crystallization becomes complete (see Figure</p><p>4.13). The area under this exotherm will depend upon the amount of B present in the</p><p>sample of the mixture. As the temperature of the mixture falls further, the eutectic</p><p>temperature, is reached and solid A crystallizes in a sharp exotherm (Figure 4.13). If</p><p>the composition had been chosen to be that corresponding to point E, the DSC or DTA</p><p>record would have shown only a single sharp exotherm as the eutectic composition</p><p>solidified. At low concentrations of A, and similarly at low concentrations of B, the</p><p>formation of the eutectic may be difficult to detect and hence to distinguish from the</p><p>formation of solid solutions [30].</p><p>79</p><p>If the mixture, whose cooling curve is shown in Figure 4.13, were to be reheated slowly,</p><p>the DSC or DTA record should ideally be the endothermic mirror image of that shown.</p><p>The use of the heating rather than the cooling curve avoids problems of supercooling.</p><p>Ideally then, the DSC or DTA traces should be readily relatable to the phase diagram, as</p><p>illustrated schematically in Figure 4.14.</p><p>80</p><p>The area under the peak for the eutectic melting is a simple function of concentration (see</p><p>Figure 4.15) and such a curve may be used to determine the composition of an unknown</p><p>mixture, e.g. an alloy [31].</p><p>Pope and Judd [30] give an example of a more complicated phase diagram, with</p><p>incongruently and congruently melting compounds and solid solution, eutectic and liquidus</p><p>reactions, while Eysel [32] discusses the even more complex system. A</p><p>variety of systems, including ternary systems and phase studies under high pressure, is</p><p>discussed by Gutt and Majumdar [33], and the theoretical background is covered by Sestak</p><p>[34]. The phase diagrams for the ternary Ge-Sb-Bi system [35] and the complicated Te</p><p>system, with 17 phase regions [36], serve as illustrations of how successful such</p><p>studies can be. Combination of DTA with thermomicroscopy can provide additional</p><p>information over a more limited temperature range.</p><p>4.10 General applications of DTA and DSC</p><p>The results obtained using DTA and DSC are qualitatively so similar that their applications</p><p>will not be treated separately. It should be noted that DTA can be used to higher</p><p>temperatures than DSC (max 725°C) but that more reliable quantitative information is</p><p>obtained from DSC.</p><p>Although DTA and DSC curves may be used solely for "fingerprint" comparison with sets</p><p>of reference curves, it is usually possible to extract a great deal more information from the</p><p>curves, such as the temperatures and enthalpy changes for the thermal events occurring.</p><p>As an example, the DSC curve for is shown in Figure 4.16 for comparison</p><p>with the TG curve given in Figure 3.10. Note the increase in of dehydration per mole</p><p>of removed.</p><p>81</p><p>The shape of the melting endotherm can be used to estimate the purity of the sample. The</p><p>procedure is discussed in detail in Chapter 11.</p><p>Detection of solid-solid phase transitions, and due measurement of for these</p><p>transitions, is readily done by DSC or DTA. A low temperature attachment permits the</p><p>range of samples which can be examined, to be extended, as shown by the DSC curve for</p><p>carbon tetrachloride in Figure 4.17. Satisfactory operation as low as -175°C has been</p><p>achieved. Condensation of atmospheric moisture can cause problems and has to be</p><p>reduced. Redfern [39] has reviewed some of the cooling systems available and has</p><p>discussed some low-temperature applications.</p><p>Application of thermal analysis to the study of polymers has been most rewarding [38].</p><p>A DSC curve for a typical organic polymer is shown in Figure 4.18. Most solid polymers</p><p>are formed by rapid cooling to low temperatures (quenching) from the melt and are thus</p><p>initially in the glassy state. The transition from a glass to a rubber, the glass transition, is</p><p>accompanied</p><p>by a change in heat capacity, but no change in enthalpy The</p><p>transition thus appears on the DSC curve as a discontinuity in the baseline (see Figure 4.19)</p><p>at the glass-transition temperature, As the temperature is slowly increased, the polymer</p><p>may recrystallise giving the exotherm shown, before melting occurs. At higher</p><p>temperatures the polymer may decompose (degrade) or oxidise depending upon the</p><p>surrounding atmosphere.</p><p>82</p><p>83</p><p>The degradation or oxidation of polymers can be studied using DSC in the isothermal</p><p>mode. Figure 4.20 shows the effect of stabilizers on the oxidation of polyethylene at</p><p>200°C. The crystallisation of polymers can also be studied using isothermal DSC. Several</p><p>approaches are possible. The molten polymer may be cooled rapidly to a temperature in</p><p>the crystallisation range, and the crystallisation from the liquid observed, or the temperature</p><p>may be raised from ambient so that crystallisation from the rubber-like state is observed.</p><p>Re-use of plastic waste is obviously most desirable, but is hampered by the problems of</p><p>identification, sorting and collection. DSC may aid in identification of the constituents of</p><p>the scrap, as illustrated in Figure 4.21. An example is given in Figure 4.22 of the use of</p><p>DSC in testing for completeness of curing of epoxy resins. The second scan shows no</p><p>residual exotherm but indicates the glass-transition temperature for the cured resin.</p><p>84</p><p>85</p><p>The behaviour of liquid crystals is of practical importance because of the optical</p><p>phenomena which occur at the transition points, and their proposed role in biological</p><p>processes. Instead of going directly from solid to liquid at a sharp melting point, liquid</p><p>crystals form several mesophases between solid and liquid states. The compounds which</p><p>display this behaviour, generally have large asymmetric molecules with well-separated</p><p>polar and non-polar regions. In the smectic mesophase molecules are aligned and tend to</p><p>form similarly aligned layers; while in the cholesteric mesophase the orientation of the</p><p>molecular axes shifts in a regular way from layer to layer, and in the nematic mesophase</p><p>molecules are aligned, but layers are not formed (see Figure 4.23). Changes from one</p><p>mesophase to another can be detected using DSC, and the enthalpies of transition</p><p>evaluated, as shown for cholesteryl myristate in Figure 4.24.</p><p>DSC can also be used to study the liquid vapour and solid vapour transitions [39,40]</p><p>and to measure the enthalpies of vaporisation and of sublimation. In open sample pans</p><p>these changes are spread out over too wide a temperature interval for an accurate baseline</p><p>to be determined. The rate of escape of vapour is reduced by partial sealing of the pan.</p><p>This sharpens up the trace as shown in Figure 4.25.</p><p>86</p><p>87</p><p>Structural changes in fats and waxes also show up clearly, making the technique (with low</p><p>temperature attachments) ideal for food chemistry (see Figure 4.26).</p><p>88</p><p>4.11 Automation</p><p>Robotic systems for handling several samples without operator intervention are available.</p><p>The Perkin-Elmer accessory enables 48 samples to be run consecutively on their DSC. The</p><p>system, shown in Figure 4.27, has a removable sample carousel and a pneumatically</p><p>controlled sampling arm. The arm, under computer control, automatically selects any</p><p>desired sample from the carousel, places it in the DSC sample holder and closes the cover.</p><p>The sample is then subjected to programmed treatment as desired. On completion of this</p><p>treatment, the sample is removed from the DSC and replaced in the carousel. The sequence</p><p>in which the samples are handled and their individual treatments can be programmed and</p><p>the data obtained are stored. The system is obviously at its most efficient when used for</p><p>quality control with one procedure applied to many similar samples.</p><p>89</p><p>References</p><p>R.C. Mackenzie, (Ed.), "Differential Thermal Analysis", Vols 1 and 2,</p><p>Academic Press, London, 1969.</p><p>P.J. Haines, M. Reading and F.W. Wilburn, “Handbook of Thermal Analysis and</p><p>Calorimetry”, Vol.1, (Ed. M.E. Brown), Elsevier, Amsterdam, 1998, Ch.5.</p><p>J. Sestak, V. Satava and W.W. Wendlandt, Thermochim. Acta, 7 (1973) 372.</p><p>J.L. 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Hillstrom, Thermal Conductivity, 16 (1979) 483.</p><p>G. Hakvoort and L.L. van Reijen, Thermochim. Acta, 93 (1985) 371;</p><p>85 (1985) 319.</p><p>T. Boddington, P.G. Laye and J. Tipping, Comb. Flame, 50 (1983) 139.</p><p>M.J. Visser and W.H. Wallace, DuPont Thermogram, 3 (2) (1966) 9.</p><p>T. Daniels, "Thermal Analysis", Kogan Page, London, 1973, p.119.</p><p>J.L. McNaughton and C.T. Mortimer, "Differential Scanning Calorimetry",</p><p>Perkin-Elmer Order No.L-604 (Reprinted from IRS, Phys. Chem. Ser.2, Vol.10,</p><p>Butterworths, 1975), p.28.</p><p>M.I. Pope and M.D. Judd, "Differential Thermal Analysis", Heyden, London,</p><p>1980, p.53.</p><p>R.L. Fyans, Perkin Elmer Instrument News, 21 (1) (1970) 1.</p><p>W. Eysel, Proc. 3rd ICTA,(Ed. H.G. Wiedemann), Birkhauser Verlag, Basel,</p><p>Vol.2 (1971) 179.</p><p>W. Gutt and A.J. Majumdar, "Differential Thermal Analysis", (Ed. R.C.</p><p>Mackenzie), Academic, London, 1972, Vol.2, p.79.</p><p>J. Sestak, "Thermophysical Properties of Solids", Comprehensive Analytical</p><p>Chemistry, Vol.XIID, (Ed. G. Svehla), Elsevier, Amsterdam, 1984, p. 109.</p><p>S. Surinach, M.D. Baro and F. Tejerina, Proc. 6th ICTA, (Ed. H.G. Wiedemann),</p><p>Birkhauser Verlag, Basel, Vol.1 (1980) p. 155.</p><p>Z. Boncheva-Mladenova and V. Vassilev, Proc. 6th ICTA, (Ed. W. Hemminger),</p><p>Birkhauser Verlag, Basel, Vol.2 (1980) p.99.</p><p>J.P. Redfern, "Differential Thermal</p><p>Analysis", (Ed. R.C. Mackenzie),</p><p>Academic, London 1972, Vol.2, p.119.</p><p>E.A. Turi (Ed.), “Thermal Characterization of Polymeric Materials”,</p><p>2nd Edn, Vols 1 and 2, Academic Press, San Diego, 1997.</p><p>T. Daniels, "Thermal Analysis", Kogan Page, London, 1973, p. 132.</p><p>J.L. McNaughton and C.T. Mortimer, "Differential Scanning Calorimetry",</p><p>Perkin-Elmer Order No.L-604 (Reprinted from IRS, Phys. Chem. Ser.2, Vol. 10,</p><p>Butterworths, 1975), p. 19.</p><p>21.</p><p>22.</p><p>23.</p><p>24.</p><p>25.</p><p>26.</p><p>27.</p><p>28.</p><p>29.</p><p>30.</p><p>31.</p><p>32.</p><p>33.</p><p>34.</p><p>35.</p><p>36.</p><p>37.</p><p>38.</p><p>39.</p><p>40.</p><p>THERMOPTOMETRY</p><p>5.1 Introduction</p><p>Thermoptometry (also referred to as thermo-optical analysis, TOA) is a group of</p><p>techniques in which optical properties of a sample are measured as a function of</p><p>temperature [1]. Under this heading, the major technique is thermomicroscopy, i.e. direct</p><p>observation of the sample. Other techniques involve measurement of total light reflected</p><p>or transmitted (thermophotometry), light of specific wavelength(s) (thermospectrometry),</p><p>refractive index (thermorefractometry), or emitted light (thermoluminescence).</p><p>Wiedemann and Felder-Casagrande [2] have recently reviewed these techniques and also</p><p>dealt with their historical development, including the important role of W.J. McCrone [3]</p><p>in the development and popularisation of thermomicroscopy. Wendlandt’s book [4]</p><p>contains an excellent chapter and there is also useful information in references [5,6].</p><p>Gallagher’s chapter in reference [7] contains much recent information.</p><p>To the above techniques must now be added the more recent developments of scanning</p><p>tunnelling microscopy and atomic force microscopy that have led to the new field of</p><p>Micro Thermal Analysis described in section 5.10 below.</p><p>91</p><p>It is interesting that the most obvious property of a material, i.e. its outward appearance,</p><p>is often not examined or monitored during the heating process and yet can provide so</p><p>much reliable first-hand evidence of the processes occurring. Other thermal analysis</p><p>techniques give results which have to be associated by inference with thermal events and</p><p>some processes such as sintering, decrepitation and creeping and foaming of melts are</p><p>only really detectable by direct observation.</p><p>The apparatus required for thermomicroscopy [2] (a schematic diagram is given in Figure</p><p>5.1(a)) consists of a microscope with a hot and/or cold stage, a sample holder, gaseous</p><p>atmosphere control (including, perhaps, vacuum pumps), light sources and a system for</p><p>recording and processing visual observations, as well as the temperature of the sample.</p><p>The main requirement for the microscope is that suitable heat-resistant objective lenses</p><p>of adequate focal length are available. Controlled temperature stages for microscopes are</p><p>readily available [2,7] and can cover the temperature range from -180°C up to 3000°C,</p><p>allowing for study of a wide range of problems, especially phase studies. Some stages are</p><p>designed to allow combination with other measurement techniques such as DSC or TG</p><p>(see below). Stages have to be as thin as possible to enable them to fit between the</p><p>microscope’s objective lens and the microscope table. Allowance may have to be made</p><p>for heating by the illuminating source, or heat filters may be necessary. Movement of the</p><p>sample holder is essential so that different regions of the sample can be examined and so</p><p>that blocking of the view of the sample by some sublimation and condensation on the</p><p>cover plate can be temporarily overcome. Sapphire glass sample pans are recommended</p><p>[2]. Standard photographic equipment or video cameras can be used for recording</p><p>observations. Many software packages are available for different types of image analysis.</p><p>Sawyer and Grubb [8] have reviewed the use of themomicroscopy in the study of</p><p>polymers, where overlapping transitions, such as melting and degradation or crystallization</p><p>and melting, can lead to ambiguities of interpretation. Kuhnert-Brandstatter’s book [9]</p><p>is a classic on the thermomicroscopy of pharmaceuticals.</p><p>5.2 Thermomicroscopy</p><p>92</p><p>5.3 Thermophotometry</p><p>In thermophotometry, provision is made for measurement of the intensity of the light</p><p>reflected or transmitted by the sample (a schematic diagram is given in Figure 5.1(b)). If</p><p>samples are viewed in transmitted light using crossed polars, the only light transmitted is</p><p>that arising from rotation of the plane of polarization of the light, caused by changes in the</p><p>crystalline structure of the sample. Melting or the formation of an isotropic structure</p><p>results in complete extinction of the light.</p><p>93</p><p>94</p><p>5.4 Thermoluminescence</p><p>The technique involving measurement of light actually being emitted by the sample is</p><p>known as thermoluminescence, TL [1,4]. TL arises from the annealing of defects in the</p><p>solid sample as the temperature is raised. The defects are present in the sample on account</p><p>of its previous thermal history, or through irradiation of the sample. TL has been used</p><p>in radiation dosimetry, archaeological dating, geological activity and evaluation of</p><p>catalysts, etc.. A simple model of the TL process, descriptions of apparatus and</p><p>discussion of applications are given in reference [4]. One version of a system used for TL</p><p>is illustrated in Figure 5.2 [10].</p><p>Nuzzio [11] has described the modification of a DuPont 990 Thermal Analyzer for TL</p><p>measurements. The light-measuring system included filters to absorb heat and to minimize</p><p>the black-body radiation encountered at temperatures above 400°C. A reference light</p><p>source was used for calibration. TL measurements could be made under isothermal or</p><p>increasing temperature conditions. Arrangements for measurements under reduced</p><p>pressures are also described.</p><p>Manche and Carroll [12] modified a Perkin-Elmer DSC-1B for simultaneous TL and</p><p>DSC, using a matched pair of optical fibres mounted directly above each calorimeter cup.</p><p>An example of the use of TL in the authentication and characterization of medieval</p><p>pottery sherds is provided by the study of Miliani et al. [13] with their TL results</p><p>illustrated in Figure 5.3.</p><p>95</p><p>Some polymers when heated in air or oxygen exhibit a low-level light emission that is</p><p>called oxyluminescence (or chemiluminescence) [4]. The intensity of the light is</p><p>proportional to the concentration of oxygen in contact with the polymer surface and the</p><p>presence of stabilizers decreases the intensity. Such measurements can thus provide</p><p>valuable insights into the oxidative degradation of polymers (and many other organic</p><p>compounds). Vigorous redox reactions between oxidizing groups and reducing ligands</p><p>in coordination compounds may also be accompanied by light emission [4,14,15].</p><p>5.5 Combination of Thermomicroscopy with DSC (or DTA)</p><p>If visual examination can be combined with a quantitative measurement such as DSC or</p><p>DTA, even more meaningful results can be obtained. The Mettler system [2] (see Figure</p><p>5.4) has a heat-flux DSC sensor built from thin-film thermopiles deposited on a special</p><p>glass disc. The sample is placed in a sapphire crucible and a similar but empty crucible</p><p>is used as a reference. Sample illumination is by transmitted (normal or polarized) light.</p><p>The temperature range is from room temperature to 300°C.</p><p>Sommer and Jochens [16] have described a micro-thermal analysis system based on the</p><p>use of a thermocouple as both specimen holder and heating source. The system is easily</p><p>and cheaply constructed and is particularly useful in phase studies of non-metallic</p><p>samples.</p><p>96</p><p>Charsley et al. [17-19] have made excellent use of hot-stage microscopy for determining</p><p>the ignition temperatures of pyrotechnic compositions. The sample was contained</p><p>between two microscope cover glasses which rested on a heating block, within an</p><p>atmosphere-controlled chamber. The block contained a sapphire window for light</p><p>transmission, and a platinum resistance thermometer for measurement of the temperature</p><p>and control of the heating or cooling programme. Provision for cooling with liquid</p><p>nitrogen gave an overall temperature range of -180°C to 600°C. The intensity of the</p><p>transmitted light</p><p>was measured using a silicon photodetector.</p><p>Haines and Skinner [20] modified a DSC to carry out simultaneous measurements of the</p><p>intensity of light reflected from the sample. Changes in the surface of the sample may not</p><p>be accompanied by measurable enthalpy changes, but may show up clearly through</p><p>changes in reflectance. A binocular microscope was used so that one eyepiece could be</p><p>used for photographing the actual appearance of the sample, while the photodetector was</p><p>used on the other eyepiece. The sample was in either an open DSC pan, or else a mica</p><p>window was crimped into the pan. Changes in the intensity of the reflected light are</p><p>cumulative so that the curves recorded are related to DSC curves as integral to derivative.</p><p>Figure 5.5 is a schematic diagram of a Mettler simultaneous thermomicroscopy-TG system</p><p>[2], The sample holder for microscopy is attached to a balance by an aluminium oxide</p><p>capillary. Otherwise the equipment is closely similar to that in Figures 5.1 and 5.4.</p><p>5.6 Combination of Thermomicroscopy with TG</p><p>97</p><p>The review by Wiedemann and Felder-Casagrande [2] contains some magnificent examples</p><p>of the power of microscopic techniques in investigating a wide variety of problems. The</p><p>micrographs produced are often works of art in their own right Problems tackled so</p><p>successfully by Wiedemann and his coworkers include the dehydration and hydration of</p><p>gypsum, to form the industrially important hemihydrate, known</p><p>as Plaster of Paris [23]; the formation of nuclei of graphite on the surfaces of natural</p><p>diamonds [24]; the oxidation of graphite flakes [25]; phase transitions in the</p><p>series of solid solutions [26]; and polymorphism [27], glass transitions [28] and</p><p>crystallization in a variety of organic compounds, including explosives [29],</p><p>Pharmaceuticals [27] and liquid crystals [30].</p><p>An example of the results obtained by Haines and Skinner [20] on heating is shown</p><p>in Figure 5.6. The phase transition from orthorhombic, phase II, to trigonal, phase I, at</p><p>128°C and melting at 335°C show up clearly. The phase transition at 128°C for did</p><p>5.8 Some applications of the techniques of Thermoptometry</p><p>Gallagher [7] has described some additional combinations of techniques. These include</p><p>microscopy and X-ray diffraction [21], and DSC combined with an FTIR microscope [22].</p><p>5.7 Other techniques combined with Thermomicroscopy</p><p>98</p><p>Many of the kinetic studies of mechanisms of decomposition of solids invoke processes</p><p>of formation and growth of product nuclei. These speculations can often be confirmed or</p><p>refuted using thermomicroscopy. Use of scanning electron microscopy (SEM), rather than</p><p>optical microscopy, has the advantages of greater magnification and much increased depth</p><p>of field as well as providing the possibility of energy-dispersive X-ray analysis of the</p><p>sample. There are, however, additional problems in the necessity for operating under</p><p>vacuum and the effect of the electron beam on the sample. Recent developments [7] have</p><p>led to instruments called environmental SEMs which can operate at pressures as high as 70</p><p>torr and have hot stages capable of operating at 1000°C and above.</p><p>5.9 Electron Microscopy</p><p>Matzakos and Zygourakis [31] coupled microscopy with TG to obtain a record on video</p><p>of the pyrolysis of coal at high heating rates</p><p>Manche and Carroll [12] tested their TL system using mixtures of LiF and LiF is</p><p>a well-known and extensively-studied thermoluminescent material and was used as</p><p>the temperature and calorimetric standard and does not normally exhibit</p><p>thermoluminescence. Ground mixtures were pressed into discs and the discs were</p><p>irradiated with X-rays. The sample discs, with a preheated disc of LiF as reference, were</p><p>heated in the modified DSC. The results obtained are shown in Figure 5.7. Areas under</p><p>the glow curves and the DSC endotherms were measured and were shown to be linear</p><p>functions of the mass fraction of the individual salts.</p><p>99</p><p>The development of scanning tunnelling microscopy (STM) [32] and atomic force</p><p>microscopy (AFM) [33] has made it possible to scan the topography of a solid surface at</p><p>resolutions down to the scale of individual atoms. Both STM and AFM use extremely fine</p><p>probe tips which are moved across the sample in a regular</p><p>sensors are used to determine the three-dimensional position ofthe probe tip. The elevation</p><p>scanning pattern. Piezoelectic</p><p>(z-direction) of the tip is related to the actual features of the surface over which it is moved</p><p>in the x and y directions. In AFM a very small force is maintained to keep the probe tip in</p><p>contact with the surface as it traverses, without digging into it. In STM the surface has to</p><p>be conducting and a small constant tunnelling current is maintained between the probe and</p><p>the surface. The probe then rides at less than 1 nm above the surface. The tunnelling</p><p>current depends upon both the surface topography and the local electronic states on the</p><p>surface. Examination of the same surface using both techniques ca</p><p>relationships between topographical features and electronic inhomogeneities.</p><p>n reveal any</p><p>In MicroThermal Analysis [34-40] thermal analysis is performed on specimens,</p><p>or regions of specimens, as small as The sensor is a very fine, pointed platinum</p><p>wire mounted on the tip of an atomic force microscope probe (see Figures 5.8 and 5.9). The</p><p>sample, or sample region, is heated at a linear rate by passing a current through the wire and</p><p>the resistance of the wire is used simultaneously to measure the sample temperature.</p><p>Because of the small thermal mass of the sensor, heating rates up to 25°C/s can be used. The</p><p>imaging capabilities of the AFM are used to map the surface area of interest (see, for</p><p>5.10 Micro Thermal Analysis</p><p>100</p><p>example, Figure 5.10) and to select regions for subsequent thermal analysis. The use of a</p><p>controlled temperature stage [35] allows the entire sample to be heated or cooled and a</p><p>thermal probe is then not necessary. Standard AFM contact or non-contact probes can then</p><p>be used to produce very high resolution images.</p><p>101</p><p>102</p><p>Various TA methods are possible. Micro differential thermal analysis involves comparison</p><p>of the temperature difference of, or the difference in power supplied to, the sample with</p><p>respect to a reference. If the probe is loaded with a small force, so that it can penetrate into</p><p>a melted specimen, micro thermomechanical analysis is possible (see Chapter 6). The use</p><p>of sinusoidal temperature programmes has led to some modulated techniques. The</p><p>configuration can be used to pyrolyse selected areas of the sample by rapidly heating</p><p>the probe to 600-800°C. The evolved gases can be absorbed in a suitable sampling tube</p><p>placed near to the probe and analysed later by GC-MS [36].</p><p>Micro thermal analysis has been mainly used qualitatively for identification ofthe material</p><p>being examined, e.g. multi-layer films [34], pharmaceuticals [37] and polymer blends [38].</p><p>Temperature calibration [41] is more difficult than in the macro TA versions because the</p><p>calibrant comes into direct contact with the platinum sensor, so that metals like indium, tin,</p><p>and zinc are not suitable, and organic compounds and polymers have been used. The sensor</p><p>is easily cleaned after the experiment by heating in air. Powdered organic materials need</p><p>to be formed into larger crystals by recrystallization from the melt. The recommended [41 ]</p><p>calibrants and their melting temperatures are: biphenyl (69.3°C); benzil (94.5 °C); benzoic</p><p>acid (122.4 °C); diphenylacetic acid (147.3 °C); anisic acid (183.3 °C), and 2-</p><p>chloroanthraquinone (209.6 °C). Suitable crystals with smooth flat surfaces can be fixed</p><p>to the sample mounts using double-sided tape. A two-point calibration procedure is</p><p>recommended [41].</p><p>The DTA response for polymers is different to that for pure organic compounds because</p><p>the organic melt tend to shrink away from the hot probe and lose contact, but the less-</p><p>mobile polymer materials remain in contact. For polymer studies, calibration</p><p>using Nylon</p><p>6, Nylon 6,6 or polyethylene terephthalate is recommended [41]. Use of polymer films</p><p>simplifies the calibration procedure.</p><p>The precision of temperature measurement depends on the heating rate. The higher</p><p>heating rates (600 to 1500°C/min) gave better precision than lower rates (120 to 480°C/min)</p><p>[41].</p><p>By controlling the temperature of the tip of the probe [42], the heat flow from the tip</p><p>to the surface of the sample can be used to map the thermal transport properties of the</p><p>surface. Such measurements have important applications in microelectronics, cellular</p><p>biology, polymer science, etc. Calibration is carried out using hard materials of known</p><p>thermal conductivity [42].</p><p>References</p><p>1 .</p><p>2.</p><p>3.</p><p>4.</p><p>W. Hemminger and S.M. Sarge, “Handbook of Thermal Analysis and Calorimetry”,</p><p>Vol.1, (Ed. M.E. Brown), Elsevier, Amsterdam, 1998, Ch.1.</p><p>H.G. Wiedemann and S. Felder-Casagrande, “Handbook of Thermal Analysis and</p><p>Calorimetry”, Vol.1, (Ed. M.E. Brown), Elsevier, Amsterdam, 1998, Ch.10.</p><p>W.C. McCrone, “Fusion Methods in Chemical Microscopy”, Wiley, New York,</p><p>1957; Proc. 1st ESTA, (Ed. D. Dollimore), Heyden, London, 1976, p.63;</p><p>J.H. Kilbourn and W.C. McCrone, Microscope, 33 (1985) 73; W.C. McCrone,</p><p>J.H. Andreen and S.-M. Tsang, Microscope, 41 (1993) 161.</p><p>W.W. Wendlandt, “Thermal analysis”, Wiley, New York, 3rd Edn, 1986, Ch.9.</p><p>103</p><p>5.</p><p>6.</p><p>7.</p><p>8.</p><p>9.</p><p>10.</p><p>11.</p><p>12.</p><p>13.</p><p>14.</p><p>15.</p><p>16.</p><p>17.</p><p>18.</p><p>19.</p><p>20.</p><p>21.</p><p>22.</p><p>23.</p><p>24.</p><p>25.</p><p>26.</p><p>27.</p><p>28.</p><p>29.</p><p>30.</p><p>31.</p><p>32.</p><p>33.</p><p>34.</p><p>35.</p><p>E.L Charsley, in “Thermal Analysis - Techniques and Applications”, (Eds E.L</p><p>Charsley and S.B. Warrington), Royal Society of Chemistry, Cambridge, 1992, p.68.</p><p>P.J. Haines, “Thermal Methods of Analysis”, Blackie, Glasgow, 1995, p. 186.</p><p>P.K. Gallagher, in “Thermal Characterization of Polymeric Materials”, (Ed. E.A.</p><p>Turi), Academic Press, New York, 2nd Edn, 1997, Ch.1.</p><p>L.C. Sawyer and D.T. Grubb, “Polymer Microscopy”, Chapman and Hall, New</p><p>York, 1987.</p><p>M. Kuhnert-Brandstatter, “Thermomicroscopy in the Analysis of Pharmaceuticals”,</p><p>Pergamon, Oxford, 1971.</p><p>T. Hatakeyama and Zhenhai Liu, “Handbook of Thermal Analysis”, Wiley,</p><p>Chichester, 1998, p.30.</p><p>D.B. Nuzzio, Thermochim. Acta, 52 (1982) 245.</p><p>E.P. Manche and B. Carroll, Anal. Chem., 54 (1982) 1236.</p><p>C. Miliani, N. Forini, A. Morresi, A. Romani and S. Spigarelli, Thermochim. Acta,</p><p>321 (1998) 191.</p><p>W.W. Wendlandt, “The State-of-the-Art of Thermal Analysis”, NBS Spec.</p><p>Tech. Publ. S80, (Eds O.Menis, H.L. Rook and P.D. Garn), 1980, p.219.</p><p>W.W. Wendlandt, Thermochim. Acta, 35 (1980) 247; 39 (1980) 313.</p><p>G. Sommer and P.R. Jochens, Minerals Sci. Eng., 3 (1971) 3.</p><p>E.L. Charsley, A.C.F. Kamp and J.A. Rumsey, Thermochim. Acta, 92 (1985) 285.</p><p>E.L. Charsley and A.C.F. Kamp, Proc. 3rd ICTA, (Ed. H.G. Wiedemann),</p><p>Birkhauser, Basel, 1971, Vol.1, p.499.</p><p>E.L. Charsley and M.R. Ottaway, Proc. 1st ESTA, (Ed. D. Dollimore), Heyden,</p><p>London, 1976, p.444.</p><p>P.J. Haines and G.A. Skinner, Thermochim. Acta, 59 (1982) 343.</p><p>M. Epple and H.K. Cammenga, Ber. Bunsenges. Phys. Chem., 96 (1992) 1774.</p><p>S. Lin, C.M. Liao and R.C. Liang, Polym. J. (Tokyo), 27 (1995) 201.</p><p>H.G. Wiedemann and M. Rossler, Thermochim. Acta, 95 (1985) 145.</p><p>H.G. Wiedemann and G. Bayer, Z. Anal. Chem., 276 (1975) 21.</p><p>H.G. Wiedemann and A. Reller, Thermochim. Acta, 271 (1996) 163.</p><p>H.G. Wiedemann and G. Bayer, J. Thermal Anal., 30 (1985) 1273.</p><p>H.G. Wiedemann, J. Thermal Anal., 40 (1993) 1031.</p><p>H.G. Wiedemann, G. Widmann and G. Bayer, Assignment of the Glass Transition,</p><p>ASTM STP 1249, (Ed. R.J. Seyler), American Society for Testing and Materials,</p><p>Philadelphia, 1994.</p><p>H.G. Wiedemann and G. Bayer, Thermochim. Acta, 85 (1985) 271.</p><p>J. Cheng, Y. Jin, G. Liang, B. Wunderlich and H.G. Wiedemann, Mol. Cryst. Liq.</p><p>Cryst., 213 (1992) 237.</p><p>A.N. Matzakos and K. Zygourakis, Rev. Sci. Instr., 64 (1993) 1541.</p><p>G. Binnig and H. Rohrer, Helv. Phys. Acta, 55 (1982) 726.</p><p>G. Binnig,, C.F. Quate and C. Gerber, Phys. Rev. Lett., 56 (1986) 930.</p><p>D.M. Price, M. Reading, A. Caswell, A. Hammiche and H.M. Pollock, Microscopy</p><p>Anal., 65 (1998) 17.</p><p>M. Reading, D.M. Price, H.M. Pollock and A. Hammiche, Amer. Lab., 30( 1) (1999)</p><p>13.</p><p>104</p><p>A. Hammiche, M. Reading, H.M. Pollock and D.J. Hourston, Rev. Sci. Instr., 67</p><p>(1996) 4268.</p><p>D.Q.M. Craig, R.G. Royall, M. Reading, D.M. Price, T.J. Lever and J. Furry, Proc.</p><p>26th NATAS, (1998) 610.</p><p>M. Reading, D.L. Hourston, M. Song, H.M. Pollock and A. Hammiche, Amer. Lab.,</p><p>30(1) (1998) 13.</p><p>T.J. Lever and D.M. Price, Amer. Lab., 30(16) (1998) 15.</p><p>D.M. Price, M. Reading and T.J. Lever, J. Thermal Anal. Calorim., 56 (1999) 673.</p><p>R.L. Blaine, C.G. Slough and D.M. Price, Proc. 28th NATAS, (2000) 883.</p><p>D.M. Price, M. Reading, A. Hammiche and H.M. Pollock, Proc. 28th NATAS,</p><p>(2000) 586.</p><p>39.</p><p>40.</p><p>41.</p><p>42.</p><p>36.</p><p>37.</p><p>38.</p><p>105</p><p>6.1 Definitions and scope</p><p>THERMOMECHANOMETRY</p><p>As described in Chapter 1, several Special Techniques have been developed from the</p><p>Primary Technique known as Thermomechanometry [1]. These are listed and defined in</p><p>Table 6.1. No standard accepted nomenclature exists at present so the various alternatives</p><p>in use are given.</p><p>106</p><p>6.2 Thermodilatometry</p><p>6.2.1 Principles</p><p>Measurement of the thermal expansion of solids and liquids is a classical physical</p><p>technique known as dilatometry. When special emphasis is put on recording such</p><p>dimensional changes as a function of temperature, during a controlled temperature</p><p>programme, the technique is labelled thermodilatometry [1,2] and is one of the special</p><p>techniques derived from thermomechanometry. For solids, we can distinguish between</p><p>linear and volume expansion, and instruments for measuring the length of a solid sample</p><p>as a function of temperature are the most common.</p><p>Most solids expand on heating. Exceptions include vitreous silica and ZnS at low</p><p>temperatures. The change in a linear dimension, L, with T is given by:</p><p>where is the length at and the length at and is the coefficient of linear</p><p>expansion. Over a small temperature interval, is approximately constant for many</p><p>materials, so the dilation:</p><p>The value of is related to the structure and type of bonding in the solid. In general,</p><p>strong bonding results in low values of so the order of expansion coefficients is usually:</p><p>covalent and ionic materials</p><p>Notes (1989)</p><p>David Dollimore, University of Toledo</p><p>in Analytical Chemistry (1989)</p><p>Preparation of this Second Edition has made me very aware of how many things have changed</p><p>since 1987. The greatest changes have been in the tasks that can now be comfortably handled</p><p>by computers and their ever-growing range of accessories. The availability of sophisticated</p><p>word processing and graphics packages, plus scanners and excellent printers, has, however,</p><p>resulted in much greater responsibility being thrust upon authors for the preparation of camera-</p><p>ready copy, a phrase that now causes scientists to leave their lab benches and become</p><p>permanently attached to their computer screens. The number of people that the author can now</p><p>blame for any remaining mistakes (although my wife, Cindy, has done her utmost to track</p><p>these down) has decreased drastically to one!</p><p>In this Edition, relatively small sections of the First Edition have withstood the changes of</p><p>14 years. One of the most embarrassing parts of the First Edition, that has now disappeared</p><p>without trace, is the Appendix of lots of programs written in Applesoft BASIC. Would that</p><p>I had had the advice of Professor Bernhard Wunderlich in advance of the appearance of that</p><p>Edition.</p><p>A sad aspect of the intervening years has been the death of Professor David Dollimore,</p><p>whose helpful comments were acknowledged in the First Edition. My many collaborations</p><p>with Dr Andrew Galwey of Belfast have continued and many of the aspects of Chapter 10 on</p><p>kinetics owe a great deal to discussions with him over the years. I also am grateful to Mr</p><p>Emmanuel Lamprecht and Dr Cheryl Sacht for commenting on some of the chapters.</p><p>This Edition will undoubtedly be criticized, even more than the First, by nomenclature</p><p>purists. I have tried to indicate the complexity and unresolved nature of the nomenclature</p><p>question and have made much, but certainly not exclusive, use of the logical scheme developed</p><p>by Dr Wolfgang Hemminger and his ICTAC Nomenclature Committee. Instrument</p><p>manufacturers have, however, had a large (and uncontrollable) part in the development of</p><p>nomenclature and this is taken into account.</p><p>What will any future edition look like? The range of information on the Internet and the ease</p><p>with which this information can be updated is impressive, but an alarming prospect for “old-</p><p>timers”.</p><p>Michael E. Brown</p><p>Grahamstown 2001</p><p>xi</p><p>PREFACE TO THE SECOND EDITION</p><p>What do bread and chocolate, hair and finger-nail clippings, coal and rubber, ointments</p><p>and suppositories, explosives, kidney stones and ancient Egyptian papyri have in</p><p>common? Many interesting answers could probably be suggested, but the connection</p><p>wanted in this context is that they all undergo interesting and practically important changes</p><p>on heating.</p><p>The study of the effect of heat on materials obviously has a long history, from man's</p><p>earliest attempts at producing pottery, extracting metals (about 8000 BC) and making glass</p><p>(about 3400 BC) through the philosophical discussions of the alchemists on the elements</p><p>of fire, air, earth and water, to early work on the assaying of minerals (about 1500 AD),</p><p>followed by the development of thermometry and calorimetry [1,2]. Only in the late 19th</p><p>century did experiments on the effect of heat on materials become more controlled and</p><p>more quantitative. Much of this work depended upon the development of the analytical</p><p>balance which has its own interesting history [3,4]. Some milestones in the development</p><p>of thermal measurements are given in Table 1.1.</p><p>Excellent accounts of the basic, but difficult, concepts of “heat” and “temperature” and</p><p>the development of temperature scales have been given by Wunderlich [5] and by Schuijff</p><p>[6]. A detailed thermodynamic background to thermal analysis and calorimetry has been</p><p>provided by van Ekeren [7]. In very brief summary, heat is one of the forms in which</p><p>energy can be transferred. Such transfer requires a temperature difference and three</p><p>mechanisms of transfer have been identified: conduction, convection and radiation. The</p><p>laws of thermodynamics deal with thermal equilibrium (zeroth), conservation of energy</p><p>(first), direction of spontaneous processes including heat transfer (second), and the</p><p>reference point for entropy measurements (third).</p><p>To provide useful qualitative and quantitative information on the effect of heat on</p><p>materials, experiments have to be carefully planned, and use is often made of sophisticated</p><p>equipment. The following formal definition of thermal analysis was originally provided</p><p>by the International Confederation for Thermal Analysis and Calorimetry (ICTAC).</p><p>INTRODUCTION</p><p>1.1 Definition and History</p><p>1</p><p>A recent discussion of the above ICTAC definition by Hemminger and Sarge [8,9] points</p><p>out some of the difficulties and suggests some modification to:</p><p>Hemminger and Sarge [8,9] explain that: (a) “analysis” means much more than</p><p>“monitoring”; (b) in most experiments it is a change in a property, rather than the property</p><p>itself which is monitored and (c) it is the temperature of the sample’s environment (e.g.</p><p>a furnace), rather than the actual sample temperature which is programmed. A</p><p>“temperature alteration” includes: (i) a stepwise change from one constant temperature to</p><p>another; (ii) a linear rate of change of temperature; (iii) modulation of a constant or</p><p>linearly changing temperature with constant frequency and amplitude; and (iv)</p><p>uncontrolled heating or cooling. The direction of change may involve either heating or</p><p>cooling and the above modes of operation may be combined in any sequence. Isothermal</p><p>experiments, other than at ambient temperature, are included in this definition under mode</p><p>(i), where the first constant temperature is usually ambient temperature and the change is</p><p>to the desired isothermal experimental conditions. The temperature may also be</p><p>programmed to maintain a constant rate of reaction, such a mode is a sample-controlled</p><p>programme (Chapter 3).</p><p>Hemminger and Sarge [8,9] state that the qualification concerning the “specified</p><p>atmosphere” should not be part of the general definition, but is an operational parameter</p><p>similar to other parameters such as crucible material, etc. They also distinguish between</p><p>“thermoanalytical techniques” and “thermoanalytical methods”. The techniques are</p><p>characterized by the suffix “-metry”, while the more comprehensive methods, which</p><p>include the evaluation and interpretation of the measured property values, are indicated</p><p>by adding “analysis”. For example the technique of differential thermometry involves</p><p>measurement of the difference in temperature of a sample and some reference material,</p><p>but the interpretation of the observations made is part of the method of differential thermal</p><p>analysis.</p><p>2</p><p>PREVIOUS</p><p>THERMAL ANALYSIS (TA) refers to a group of techniques in which</p><p>a property of a sample is monitored against time or temperature while</p><p>the temperature of the sample, in a specified atmosphere, is</p><p>programmed.</p><p>NEW</p><p>THERMAL ANALYSIS (TA) means the analysis of a change in a</p><p>property of a sample, which is related to an imposed temperature</p><p>alteration.</p><p>The proposals of Hemminger and Sarge have yet to obtain official recognition (August</p><p>2001) and acceptance by the various bodies concerned with thermal analysis and</p><p>calorimetry. The proposals are described here because of their elegance as a logical</p><p>system. Practical nomenclature, however, is determined by general acceptance and factors</p><p>such as the role of journal editors in insisting on particular usage. Manufacturers also play</p><p>a significant role in the terms used in their patents, instrument manuals and application</p><p>sheets.</p><p>Because there are many properties of the sample which can be measured, the number of</p><p>techniques (and associated methods) is quite large. The main sample properties used and</p><p>the associated primary techniques are listed in Table 1.2. Absolute values of the sample</p><p>property may be recorded, or the difference in the property of the sample compared to the</p><p>same property of a reference material may be more convenient</p><p>to be as much as 20 000X. Calibration of the</p><p>LVDT is carried out, initially, using a micrometer screw gauge incorporated in the</p><p>measuring system.</p><p>Safety devices, to prevent damage caused by melting of the sample in the apparatus, are</p><p>often included. These are activated by rapid sample contractions and power to the furnace</p><p>is cut off immediately.</p><p>Expansion of a standard material can be used as a temperature indicator. Isothermal</p><p>measurements may be made to study creep or recrystallization processes in the sample (see</p><p>applications). Changes in volume of liquid samples, contained in a suitable cylinder, can</p><p>be converted into equivalent linear movement by means of a close-fitting piston attached</p><p>to a push-rod. A bleed valve on the cylinder ensures that no air is trapped in the liquid.</p><p>108</p><p>Linseis [3] has described a laser dilatometer based on the principle of a Michelson</p><p>interferometer. A schematic diagram is given in Figure 6.3. The laser beam is split, after</p><p>a 90° reflection, into two separate beams. The two beams are directed at reflectors</p><p>attached to the ends of the sample and reference materials. After total reflection, the</p><p>beams are recombined and the interference patterns are examined using photodiode</p><p>detectors and converted to measurements of expansion or shrinkage. These dilation</p><p>measurements are accurate to one quarter of the wavelength of the laser and involve no</p><p>mechanical connections with the sample, so very rapid changes of dimension can be</p><p>examined. The temperature range over which such an optical system can be used is also</p><p>much greater than for a mechanical system and it is suggested [3] that it will prove useful</p><p>in examining the expansion coefficients of superconducting materials at liquid helium</p><p>temperatures.</p><p>Karmazsin et al. [4] have suggested use of an optoelectronic transducer in place of a</p><p>LVDT. This has particular advantages for simultaneous thermodilatometric,</p><p>thermoconductimetric and thermomagnetometric measurements as LVDTs are sensitive</p><p>to electrical perturbations. A stabilized light source (Figure 6.4) illuminates two</p><p>photosensitive cells through two rectangular holes of a screen, which is attached to the</p><p>push-rods of the dilatometer. Movement of the screen alters the relative amount of light</p><p>received by the two cells. Dimensional variations down to m could be measured and</p><p>speed of response was about ten times that of a LVDT. Examples of simultaneous</p><p>measurements are given [4].</p><p>109</p><p>110</p><p>6.2.3 Interpretation of results</p><p>Values of the coefficient of expansion, may be determined from the slope of a curve</p><p>of L against T,because:</p><p>Alternatively, the time derivative of the dilation:</p><p>so</p><p>where the heating rate.</p><p>The engineering coefficient of expansion, is defined by:</p><p>where and are the lengths of the sample at and respectively.</p><p>Usually it is the discontinuities in the curve of L against T, rather than actual values of</p><p>which are of main interest in thermodilatometry, as these indicate occurrence of thermal</p><p>events in the sample. These discontinuities are discussed in the applications section</p><p>below.</p><p>6.2.4 Applications of thermodilatometry</p><p>A very practical application of TD is in the selection of suitable materials for use as</p><p>brake-linings [5]. Obviously a low coefficient of expansion, coupled with other qualities</p><p>such as wear-resistance and a suitable coefficient of friction, is desirable (Figure 6.5).</p><p>Wendlandt [6] has used TD to study the change in structure from octahedral to</p><p>tetrahedral in the cobalt (II) pyridine coordination compound, (Figure 6.6).</p><p>Another application of TD has been that of Gallagher [7] to the study of the kinetics of</p><p>sintering of powdered Chromindur alloys (Fe-Cr-Co), used in making high energy</p><p>magnets. Arrhenius-type plots of ln against 1/T showed two regions with different</p><p>activation energies. The values of the activation energies corresponded well with the</p><p>diffusion energies in the low-temperature face-centred cubic and the high-temperature</p><p>body-centred cubic phases.</p><p>111</p><p>112</p><p>TD has also been used [8] to study the sintering behaviour of kaolins and kaolinitic clays.</p><p>On heating, kaolin loses structural water at about 550°C and forms the metakaolin</p><p>structure. Above 960°C this converts to a spinel structure and then above 1100°C to</p><p>mullite. The mullite formed sinters at higher temperatures. These reactions are</p><p>accompanied by the shrinkages shown in Figure 6.7. The TD curves of kaolins and</p><p>kaolinitic clays may be used for their classification [8].</p><p>Other applications of TD include studies of the effects of additives on the shrinkage of</p><p>cellular concretes [9]; the defects in non-stoichiometric oxides [10]; the firing of ceramics</p><p>and the properties of alloys [11].</p><p>6.3 Thermomechanical Analysis (TMA)</p><p>{Static Force Thermomechanometry (sf-TM)}</p><p>6.3.1 Principles [2]</p><p>Static Force Thermomechanometry (or Static Force Thermomechanical Analysis, sf-TM A)</p><p>will be more easily recognised by its less systematic, but well-established name,</p><p>Thermomechanical Analysis (TMA).</p><p>Thermodilatometry is carried out by measuring expansion and contraction under</p><p>negligible loads. Further information of interest may be obtained by measuring the</p><p>penetration, i.e. the expansion or contraction of a sample while under compression, as a</p><p>function of temperature. Alternatively, the extension, i.e. the expansion or contraction of</p><p>a sample under tension, may be measured as a function of temperature. These techniques,</p><p>plus flexure and torsional measurements, are classified as thermomechanical analysis</p><p>(TMA) and are obviously of great practical importance in materials testing (see</p><p>applications).</p><p>113</p><p>6.3.2 Practical details</p><p>The apparatus used is based on that for thermodilatometry (Section 6.2). The principles</p><p>of penetration, extension, flexure and torsional measurements are illustrated in Figure 6.8.</p><p>114</p><p>Two main types of experiment are possible: (i) measurement of dilation with</p><p>temperature at a fixed load, or (ii) measurement of dilation with load at a fixed</p><p>temperature.</p><p>The Shimadzu TMA-50 instrument is illustrated in Figure 6.9. The overall measurement</p><p>range is mm about the zero position. The load range is</p><p>Temperature calibration of a TMA instrument can be done using a special sandwich</p><p>sample built up, as shown in Figure 6.10, from discs of pure metals, separated by alumina</p><p>discs. As the metals melt, the probe shows step-wise changes in length. The calibration</p><p>sample can obviously only be used once. Several different designs are available for the</p><p>probe, e.g. flat, pointed or rounded ends.</p><p>115</p><p>6.3.3 Stress-strain curves</p><p>Thermomechanical Analysis (TMA) (or, more precisely, Static Force</p><p>Thermomechanometry), as described above, involves measurement of the change of a</p><p>dimension of the sample as the load on the sample is increased, while the temperature is</p><p>held constant. This is effectively the determination of a stress-strain curve for the sample.</p><p>The load is related to the applied stress (force/area) and the change in dimension is related</p><p>to the strain (elongation/original length).</p><p>Different types of materials give different types of stress-strain curves and, of course, the</p><p>nature of the stress-strain curve for a given material will change as the temperature at</p><p>which the measurements are made is changed.</p><p>The two extremes of behaviour are elastic solids, which obey Hooke's law, i.e., that the</p><p>applied stress is proportional to resultant strain (but is independent of the rate of strain),</p><p>and liquids, which obey Newton's law, i.e., that the applied stress is proportional to rate</p><p>of strain (not the strain itself). Both laws only hold for small values of strain or rate of</p><p>strain.</p><p>For a sample under tension the tensile stress, and the tensile</p><p>strain, elongation/original length</p><p>Tensile Stress:</p><p>116</p><p>Hooke's law is</p><p>where E = Young's modulus (units: force/area). For an isotropic body (i.e. properties</p><p>independent of direction) the changes in length and in width are related by Poisson's ratio:</p><p>for which values range from 0.2 to 0.5.</p><p>Shear Stress:</p><p>For a sample</p><p>subjected to a shearing stress, the shear stress, and the</p><p>shear strain, Again, Hooke's law is where G is</p><p>the shear modulus. and for small so</p><p>6.3.4 Viscoelastic behaviour</p><p>The stresses applied to liquids are usually shear stresses and Newton's law for viscous</p><p>liquids is:</p><p>that is, the shear stress is proportional to the rate of shear strain, or:</p><p>where is the viscosity coefficient.</p><p>Compression: When a pressure is applied to a body of original volume, causing a</p><p>volume change, the stress, and the strain Hooke's law is</p><p>where B is the bulk modulus. The</p><p>compressibility of the sample is defined as</p><p>Of the three moduli, E, G and B, only two are independent. They are related via</p><p>Poisson's ratio:</p><p>or</p><p>117</p><p>Many polymers show behaviour intermediate between elastic solids and viscous liquids</p><p>and such materials are classified as viscoelastic. Shear of viscoelastic materials is</p><p>described by a combination of Hooke's and Newton's laws. Strains are additive, so when</p><p>the total shear stress is</p><p>Hence</p><p>When the shear strain is constant:</p><p>which rearranges to:</p><p>that is:</p><p>This means that at a fixed strain, if the initial stress is this will relax</p><p>exponentially with time. The relaxation time is</p><p>6.3.5 Stress-strain measurements on polymers</p><p>If a viscoelastic sample is subjected to a tensile force, applied at a uniform rate, and the</p><p>resultant elongation of the sample is measured, a curve of the form shown in Figure 6.11</p><p>(a) may be obtained. (The detailed shape will depend upon the rate of application of the</p><p>stress.) In the region OL, Hooke's law is obeyed and the slope gives Young's modulus,</p><p>E. Beyond the yield point, Y, viscous flow occurs until the maximum elongation is</p><p>achieved at the break point, B.</p><p>(Hooke’s law) and (Newton's law)</p><p>so</p><p>and</p><p>If at and at</p><p>or</p><p>118</p><p>The effects of temperature on the stress-strain curves are illustrated in Figure 6.11 (b).</p><p>As the temperature increases, (i) the modulus of elasticity, E, (i.e. slope of OL in Figure</p><p>6.11 (a)) decreases; (ii) the yield strength decreases; and (iii) the maximum elongation</p><p>generally increases.</p><p>6.3.6 Modulated-Temperature Themomechanical Analysis[13,14]</p><p>Application of a modulated-temperature programme to TMA [13,14] provides a method</p><p>for separating reversible processes such as thermal expansion from irreversible processes</p><p>such as the deformation arising from creep or dimensional changes arising from</p><p>orientational relaxations in solids. Depending upon the nature of the sample,</p><p>measurements can be made under tension (films and fibres) or compression (rods or</p><p>blocks). Data treatment is similar to that used in modulated-temperature DSC (see</p><p>Chapter 4).</p><p>119</p><p>6.3.7 Applications of TMA</p><p>TMA and TD measurements are often carried out on the same sample with the same</p><p>apparatus. Examples of both expansion and penetration measurements on neoprene rubber</p><p>[15] are given in Figure 6.12. The coefficient of linear thermal expansion, can be</p><p>determined from the slope of the expansion curve (see Section 6.2). Both the</p><p>glass-transition and melting show up clearly. Another example [15] is the use of</p><p>penetration measurements for testing polyethylene-coated paper (Figure 6.13). The</p><p>structural transition and the melting show up clearly even though the coating was very thin</p><p>(</p><p>and the furnace and</p><p>its associated temperature control system. The DMA 2980 has some new features</p><p>compared to the traditional design [22]. It uses a non-contact, direct-drive motor to</p><p>provide the stress over a wide dynamic range (0.0001 to 18 N). It also uses an optical</p><p>encoder, instead of the traditional linear variable differential transformer (LVDT, see</p><p>Figure 6.2). The typical resolution of an LVDT [22] is 1 part in 200 000, so to obtain 1</p><p>nm resolution, the maximum displacement would be 200 An optical encoder</p><p>measures displacement from the light diffraction patterns produced when one grating</p><p>moves relative to another stationary grating. The resolution [22] is 1 nm over the whole</p><p>displacement range of 25 mm, corresponding to 1 part in 25 000 000. This increased</p><p>resolution improves the precision of the measured parameters and allows very stiff</p><p>materials with very small oscillation amplitudes to be studied. With its cooling</p><p>attachment, the DMA 2980 covers a temperature range of -150 to 600°C.</p><p>122</p><p>123</p><p>124</p><p>Some of the clamping systems available for most DMA instruments are illustrated in</p><p>Figure 6.16 [2,20,23]. Clamps should have high stiffness, low mass and be easy to load</p><p>and adjust [22].</p><p>The sample, which is usually in film or fibre form, is clamped in the appropriate sample</p><p>holder. Although samples should ideally be rigid enough to be tested as a sheet or rod,</p><p>softer materials, such as thermosets or elastomers can be studied by using specially</p><p>designed supports [24]. With thin films, buckling deformation can be a problem. Toth</p><p>et al. [25] have developed a special sample clamp assembly which provides an arched</p><p>sample cross-section. Miller [26] describes a technique for characterizing organic</p><p>coatings by DMA by coating a multiple filament glass strand. The contribution of the</p><p>substrate alone is subtracted to give the contribution of the coating. A similar technique</p><p>using a thin steel strip as substrate can be used in examining the mechanical properties of</p><p>paints. Liquid samples can be supported on films or absorbed into papers or braids.</p><p>6.4.3 Applications of DMA</p><p>Changes in Young's modulus indicate changes in rigidity and hence strength of the sample.</p><p>Damping measurements give practical information on glass transitions, changes in</p><p>crystallinity, the occurrence of cross-linking, and also shows up the features of polymer</p><p>chains. The information obtained has been used in various very practical areas such as</p><p>studies of vibration dissipation, impact resistance and noise abatement.</p><p>at -95°C and 65°C. The lower temperature peak has been attributed to long chain</p><p>crankshaft relaxations in the amorphous phase and the higher temperature peak to similar</p><p>motion in the crystalline phase. The temperatures and relative sizes of the two peaks can</p><p>be related to the degree of crystallinity of the sample. The damping curve for branched</p><p>polyethylene (Figure 6.17 (b)) has features at -112°C, -9°C and 45°C. The -112°C and</p><p>45°C peaks are explained as above, while the -9°C peak is attributed to relaxations</p><p>in the amorphous phase.</p><p>125</p><p>Typical DMA results [27] on two different samples of polyethylene are shown in Figure</p><p>6.17 (a) and (b). The damping curve for linear polyethylene (Figure 6.17 (a)) shows peaks</p><p>126</p><p>The thermal behaviour of styrene-butadiene-rubber (SBR) is illustrated in Figure 6.18</p><p>[27,28]. Various formulations of SBR are used in tyre manufacture. Different</p><p>styrene-butadiene ratios may be used, or different butadiene isomers, or different additives</p><p>e.g. carbon black. A high cis-butadiene content lowers the glass transition temperature,</p><p>(to as much as -110°C compared to -50°C) giving greater flexibility at low</p><p>temperatures. The addition of carbon black (Figure 6.18 (c)) increases the modulus of</p><p>elasticity. The is also slightly increased. The complex damping curve at low</p><p>temperatures indicates polymer-carbon black interactions and may lead to adverse</p><p>properties e.g. heat build-up.</p><p>127</p><p>Huson et al. [24] have used the changes in height of DMA damping peaks as a measure</p><p>of the extent of vulcanisation in elastomer blends. Results agreed well with torque</p><p>rheometer measurements.</p><p>Gill [29] has given a general review of the application of DMA to polymer composites.</p><p>Toth et al. [25] have used DMA to study the effect of ageing on paper. Samples were</p><p>subjected to accelerated ageing at 100°C in air with 50% relative humidity and the DMA</p><p>curves of original and aged samples were recorded. The increased brittleness of the aged</p><p>samples showed up in the damping curves.</p><p>Schenz et al. [30] have designed a sample mold for preparing frozen aqueous solutions</p><p>for examination by DMA. The DMA technique was found to be very sensitive to</p><p>second-order transitions. Frozen dilute solutions of sucrose showed two glass transitions</p><p>at around -32°C, suggesting that as the solutions are frozen, tiny localised inclusions are</p><p>formed where the concentration differs from the bulk concentration. These inclusions</p><p>have a higher than that of the bulk solution. DSC was not sensitive enough to detect</p><p>these details.</p><p>Kaiserberger [31] has compared the performance of TMA, DMA and DSC for</p><p>determining the viscoelastic properties of polymers and concludes that DMA has superior</p><p>sensitivity in detecting phase transitions of second and higher order.</p><p>In addition to the references quoted already, there is some useful information on</p><p>applications of DMA to polymers in [32] and to food in [33].</p><p>References</p><p>W. Hemminger and S.M. Sarge, “Handbook of Thermal Analysis and</p><p>Calorimetry”, Vol.1, (Ed. M.E. Brown), Elsevier, Amsterdam, 1998, Ch.1.</p><p>R.E. Wetton, “Handbook of Thermal Analysis and Calorimetry”, Vol.1,</p><p>(Ed. M.E. Brown), Elsevier, Amsterdam, 1998, Ch.6.</p><p>M. Linseis, Proc. 4th ICTA, Vol.3, Heyden, London, 1975, p.913.</p><p>E. Karmazsin, P. Satre and M. Romand, Proc. 7th ICTA, Vol. 1, Wiley,</p><p>Chichester, 1982, p.337.</p><p>P.F. Levy, Proc. 4th ICTA, Vol.3, Heyden, London, 1975, p.3;</p><p>Int. Lab., Jan/Feb(1971)61.</p><p>W.W. Wendlandt, Anal. Chim. Acta, 33 (1965) 98.</p><p>P.K. Gallagher, Proc. 6th ICTA, Vol.1, Birkhaeuser, Basel, 1980, p. 13.</p><p>K.H. Schuller and H. Kromer, Proc. 7th ICTA, Vol.1, Wiley, Chichester,</p><p>1982, p.526.</p><p>O. Hoffman, Proc. 8th ICTA, Thermochim. Acta, 93 (1985) 529.</p><p>V.E. Shvaiko-Shvaikovsky, Proc. 8th ICTA, Thermochim. Acta, 93</p><p>(1985)493.</p><p>W. Hadrich, E. Kaiserberger and H. Pfaffenberger, Ind. Res. Dev.,</p><p>(Oct. 1981) 165.</p><p>J.M.G. Cowie, "Polymers: Chemistry and Physics of Modern Materials",</p><p>Intertext, New York, 1973, Ch.l2.</p><p>D.M. Price, Thermochim. Acta, 357/358 (2000) 23; 315 (1998) 11.</p><p>D.M. Price and G.M. Foster, J. Thermal Anal. Calorim., 56 (1999) 649.</p><p>3.</p><p>4.</p><p>6.</p><p>7.</p><p>8.</p><p>5.</p><p>2.</p><p>1.</p><p>9.</p><p>10.</p><p>11.</p><p>12.</p><p>13.</p><p>14.</p><p>128</p><p>P.F. Levy, Proc. 4th ICTA, Vol.3, Heyden, London, 1975, p.3; Int. Lab.,</p><p>Jan/Feb. (1971)61.</p><p>G. Widmann, Mettler Application No.3401 (1983).</p><p>R. Huggett, S.C. Brooks and J.F. Bates, Lab. Prac., 33 (11) (1984) 76.</p><p>J.A. Brydson, "Plastic Materials", Iliffe Brooks Ltd., London, 1969.</p><p>K.P. Menard, “Dynamic Mechanical Analysis - A Practical Introduction”,</p><p>CRC Press, Boca Raton, USA, 1999.</p><p>P.K. Gallagher in “Thermal Characterization of Polymeric Materials” (Ed. E.M.</p><p>Turi), Academic Press, New York, 2nd Edn, 1997, Ch. 1.</p><p>B. Wunderlich, “Thermal Analysis”, Academic Press, Boston, 1990, Ch.6.</p><p>J. Foreman and K. Reed, TA Instruments Thermal Analysis Technical Publication</p><p>TA-229.</p><p>R.E. Wetton, J.C. Duncan and R.D.L. Marsh, Amer. Lab., 25 (1993) 15.</p><p>M.G. Huson, W.J. McGill and P.J. Swart, J. Polym. Sci., Polym. Letters,</p><p>22 (1984)143.</p><p>F.H. Toth, G. Pokol, J. Gyore and S. Gal, Proc. 8th ICTA, Thermochim.</p><p>Acta, 93 (1985) 405; 80 (1984) 281.</p><p>D.G. Miller, Int. Lab., (March 1982) 64.</p><p>DuPont Instruments, Thermal Analysis Review, Dynamic Mechanical</p><p>Analysis, undated.</p><p>R.L. Hassel, DuPont Application Brief, TA68.</p><p>P.S. Gill, Ind. Res. Dev., (March 1983) 104.</p><p>T.W. Schenz, M.A. Rosolen, H. Levine and L. Slade, Proc. 13th NATAS,</p><p>1984, paper 12, p.57.</p><p>E. Kaiserberger, Proc. 8th ICTA, Thermochim. Acta, 93 (1985) 291.</p><p>J. Foreman, reprint from American Laboratory, January</p><p>1997, TA Instruments</p><p>TA-236.</p><p>Thermal Analysis Application Brief, TA Instruments TA-119.</p><p>16.</p><p>17.</p><p>18.</p><p>19.</p><p>15.</p><p>20.</p><p>21.</p><p>22.</p><p>23.</p><p>24.</p><p>25.</p><p>26.</p><p>27.</p><p>28.</p><p>29.</p><p>30.</p><p>31.</p><p>32.</p><p>33.</p><p>COMBINATION OF THERMAL ANALYSIS TECHNIQUES</p><p>7.1 Principles</p><p>A truly simultaneous thermal analysis technique involves measurements of two or more</p><p>of the properties in Table 1.1 on the same portion of the sample during a single</p><p>temperature programme [1,2]. Each of the properties may be monitored continuously, or</p><p>they may be sampled in a repetitive sequence to allow forthe requirements of data capture.</p><p>Simultaneous measurements must thus be distinguished from parallel measurements,</p><p>where different portions of the sample are examined using different instruments, and</p><p>concurrent measurements where different portions of the same sample, in different</p><p>containers, are held within a single furnace and are subjected to a common temperature</p><p>programme, Figure 7.1. This last option is also used in instruments designed for carrying</p><p>out one type of measurement on several samples. A simultaneous technique is usually</p><p>written as the two acronyms linked with a hyphen, e.g. TG-DTA.</p><p>129</p><p>130</p><p>Results of the thermal analysis of a given sample, under a specified set of conditions, on</p><p>a given instrument, are usually reasonably repeatable [3]. Agreement with the results on</p><p>another portion of the same sample, obtained using the same technique on an instrument</p><p>of a different make, or a similar instrument in a different laboratory, may be much less</p><p>reproducible. It is even more difficult to compare results of parallel measurements from</p><p>two or more independent thermal analysis techniques, e.g. TG and DTA. The advantages</p><p>of being able to relate results of different techniques are obvious. For example TG cannot</p><p>be used to detect melting, while melting and decomposition cannot be distinguished</p><p>unambiguously using DTA. A substance which melts with accompanying decomposition</p><p>must thus be studied using both TG and DTA (or DSC). There is usually a synergistic</p><p>effect in that the total amount of information about the sample that is obtained is greater</p><p>than the sum of the information obtained from the individual techniques. There are also</p><p>savings in time and amounts of sample, but generally the sensitivities of the individual</p><p>techniques are decreased on combination, because of compromises in instrumental design.</p><p>Some sophisticated techniques, such as power-compensated DSC, do not lend themselves</p><p>easily to simultaneous measurement of other properties.</p><p>Any of the basic TA techniques can be complemented by combination with evolved gas</p><p>analysis (EGA). Such combination usually has little effect on the sensitivity of the basic</p><p>technique. EGA is discussed in detail in Chapter 8.</p><p>7.2 Equipment</p><p>Pioneers in the use of simultaneous methods, based on their instrument called the</p><p>"Derivatograph", have been J. and F. Paulik [4]. The Derivatograph (Figure 7.2) is an</p><p>example of one of the first successful combinations, i.e. that of TG with DTA to give TG-</p><p>DTA. In the Derivatograph and some other instruments, the DTA reference material is</p><p>not weighed.</p><p>In the Netzsch STA 449 TG-DTA system (Figure 7.3) the whole DTA configuration,</p><p>together with its thermocouple leads, is incorporated into the balance suspension. A</p><p>variety of different sample modules for the Setaram TG-DTA/DSC system is shown in</p><p>Figure 7.4. A different approach is used in the Setaram simultaneous TG-DSC 111</p><p>(Figure 7.5) [5]. There is no mechanical contact of the TG sample pans with the detectors</p><p>of the DSC tubes. This is claimed not to affect the quantitative performance of the</p><p>detectors. The symmetrical configuration of the system and the absence of contact</p><p>problems are both factors in favour of accurate weighing (Chapter 3).</p><p>DTA may be combined with TMA by inserting thermocouples in the sample and in the</p><p>reference. The Mettler-Toledo TMA/SDTA840 is illustrated in Figure 7.6. DTA/DSC</p><p>and TG have all been very successfully combined with hot-stage microscopy by Mettler-</p><p>Toledo (see Chapter 5). Combination of X-ray diffraction with other TA techniques has</p><p>had some success [6-9]. The simultaneous DSC-XRD system used by Yoshida et al. [9]</p><p>is shown in Figure 7.7, and results of simultaneous DSC-wide-angle XRD measurements</p><p>[9] on the crystallization of hexatriacontane on cooling at 0.5 from the</p><p>melt are shown in Figure 7.8.</p><p>131</p><p>Some of the less-common properties, whose measurement is described in Chapter 9, have</p><p>been measured simultaneously with more conventional properties.</p><p>While dealing with simultaneous measurements, it is worth stressing the importance of</p><p>complementary techniques which can aid in identifying the thermal events occurring in</p><p>the sample. Complementary techniques include all forms of spectroscopy, X-ray and</p><p>electron diffraction, optical and electron microscopy and are limited only by the ingenuity</p><p>of the investigator.</p><p>132</p><p>133</p><p>134</p><p>135</p><p>136</p><p>137</p><p>References</p><p>W. Hemminger and S.M. Sarge,“Handbook of Thermal Analysis and</p><p>Calorimetry”, Vol.1, (Ed. M.E. Brown), Elsevier, Amsterdam, 1998, Ch.1.</p><p>J. Van Humbeeck, “Handbook of Thermal Analysis and Calorimetry”, Vol.1,</p><p>(Ed. M.E. Brown), Elsevier, Amsterdam, 1998, Ch.11.</p><p>R.L. Blaine, C.G. Slough and D.M. Price, Proc. 12th ICTAC, (2000), paper</p><p>O.19.</p><p>J. Paulik and F. Paulik, "Simultaneous Thermoanalytical Examinations</p><p>by means of the Derivatograph", "Wilson and Wilson's Comprehensive</p><p>Analytical Chemistry", Vol. XIIA, Elsevier, Amsterdam, 1981.</p><p>P. Le Parlouer, Proc. 8th ICTA, Thermochim. Acta, 92 (1985) 371.</p><p>P.K. Gallagher in “Thermal Characterization of Polymeric Materials” (Ed. E.M.</p><p>Turi), Academic Press, New York, 2nd Edn, 1997, Ch.1, p97.</p><p>R. Androsch, M. Stolp and H.-J. Radusch, Thermochim. Acta, 271 (1996) 1.</p><p>C. Wutz, M. Bark, J. Cronauer, R. Doehrmann and H.G. Zachmann,</p><p>Rev. Sci. Instr., 66 (1995)1303.</p><p>H. Yoshida, R. Kinoshita and Y. Teramoto, Thermochim. Acta, 264 (1995) 173.</p><p>5.</p><p>6.</p><p>7.</p><p>8.</p><p>9.</p><p>4.</p><p>3.</p><p>2.</p><p>1.</p><p>EVOLVED GAS ANALYSIS (EGA)</p><p>8.1 Basic Principles</p><p>8.2 Evolved Gas Detection (EGD)</p><p>EGD has the advantage that measurements of the single property selected for detection of</p><p>the gas (for example, thermal conductivity, see below) may be completely continuous and</p><p>hence are readily related to thermal analysis curves. The purge gas from the thermal</p><p>analysis equipment becomes the carrier for sweeping evolved gases to a detector (Figure</p><p>139</p><p>Many samples, on heating, release gases or vapour through desorption or decomposition.</p><p>This release is accompanied by thermal effects and, obviously, mass-losses, which,</p><p>themselves, can be detected by the appropriate thermal analysis technique, e.g. DTA or</p><p>DSC and TG, respectively. The thermal analysis technique does not, however, identify</p><p>the gas evolved and, for complex decompositions, such information is essential. It has</p><p>thus become fairly routine to couple the basic techniques already described with a system</p><p>for either detecting the evolution of gas (or gases) from the sample (evolved gas detection,</p><p>EGD) or, more satisfactorily, detecting and identifying the gases evolved (evolved gas</p><p>analysis, EGA) [1-4]. The apparatus for EGA will obviously be more complex than that</p><p>required for EGD. Gas-solid reactions can also be studied by determining the amounts of</p><p>products formed or reactant gas consumed. A novel technique on this principle is pulsed</p><p>(gas) thermal analysis [5] (see below).</p><p>In practice, the main techniques in current use for EGA are mass spectrometry (MS) or</p><p>Fourier transform infrared spectroscopy (FTIR). Because of the time intervals required</p><p>between sampling, gas chromatography (GC) (see below) has declined in usage. If the</p><p>evolved gas mixtures are so complex that preliminary separation is required, GC may be</p><p>used for the separation coupled with MS or FTIR for the analysis.</p><p>The main thermal analysis technique with which EGA has been coupled is</p><p>thermogravimetry (TG) and simultaneous techniques (see Chapter 7) are usually indicated</p><p>by hyphenation, for example TG-MS or TG-FTIR.</p><p>The practical</p><p>aspects of coupling EGA methods with TA instruments have been</p><p>discussed in considerable detail by Kaiserberger and Post [6]. The gas flow conditions</p><p>in the combined instruments have to be carefully examined and correlation of the two sets</p><p>of data obtained from the two techniques by suitable calibration is important. The</p><p>distribution of an evolved gas in the flow of purge gas depends [6] on the volume ratio,</p><p>the flow profile and the diffusion coefficients of the species involved. The distribution</p><p>broadens with increasing time of flow after mixing.</p><p>140</p><p>8.1). The detector should be as close as possible to the sample to decrease condensation</p><p>of vapours, secondary reactions in the gas phase, and time lags between thermal analysis</p><p>and EGD curves. The most commonly used detectors are those usually found in simpler</p><p>gas chromatographs, namely: (i) thermal conductivity detectors (TCD, or katharometers),</p><p>(ii) gas-density detectors, and (iii) ionization detectors. In addition, use has been made</p><p>of infrared radiometers.</p><p>For maximum sensitivity, the measured property, e.g. thermal conductivity, of the</p><p>evolved gas should differ markedly from that of the carrier (Table 8.1). and He have</p><p>very high thermal conductivities and argon very low, making them suitable carriers, but</p><p>their influence on the thermal effects being examined, must be determined because</p><p>artefacts have been observed [7]. Flame ionization detectors are particularly sensitive to</p><p>organic compounds, but do not respond to water vapour. Some separation of gas</p><p>mixtures is possible by carrying out several EGD runs with suitable cold traps (or even</p><p>specific absorbents) interposed between the sample and the detector. Alternatively, two</p><p>similar detectors may be used, one on either side of the trap.</p><p>141</p><p>8.3 Mass Spectrometry (MS)</p><p>Probably the most versatile and fastest means of repetitive gas analysis is mass</p><p>spectrometry, so the most obvious solution to the problem of identifying the gases evolved</p><p>from a thermal analysis instrument, is to replace the detector (Figure 8.1) by a mass</p><p>spectrometer. Emmerich and Kaiserberger [8] have long suggested that the capital already</p><p>invested in thermal analysis equipment warrants the further expense of adding a mass</p><p>spectrometer to get the maximum information per run.</p><p>The greatest obstacle to routine use of TA-MS has been that mass spectrometers require</p><p>high vacuum for their operation, while most thermal analysis experiments are carried out</p><p>at, or just above, atmospheric pressure. The coupling interface [6,9,10] (see Figure 8.2)</p><p>thus has to allow for the pressure differences in the TA and MS systems while transferring</p><p>a representative sample of the evolved gases from the TA system.</p><p>142</p><p>Problems that can arise include: (i) condensation of vapours in the sampling system -</p><p>attempts to decrease this by heating the system may promote secondary reactions; (ii) the</p><p>high concentration of carrier gas may swamp the smaller responses of evolved gases - He,</p><p>with its low mass number, is thus useful as a carrier. Particular problems encountered in</p><p>high-temperature studies have been discussed [11].</p><p>Roduit et al. [12] have examined the influence of mass transfer on the coincidence of TA</p><p>and MS curves. Quantitative calibration of TA-MS systems by injection of known</p><p>amounts of a calibration gas into the carrier gas stream, or by decomposition of a solid</p><p>sample with a simple stoichiometric reaction in the TG system, is discussed by</p><p>Maciejewski and Baiker [13]. They recommend that the use of helium as carrier gas</p><p>should be avoided wherever possible because its high diffusivity changes the shape of the</p><p>MS signal. Stability of the gas flow-rate is essential in quantitative measurements. The</p><p>problems of condensation of water vapour are also discussed.</p><p>Criado et al. [14] have calculated the expected EGA curves on the assumption that the</p><p>partial pressures of the gases generated during thermal decomposition of a sample are</p><p>proportional to the reaction rate. The apparent reaction order, n, approaches zero as the</p><p>efficiency of the mass-transfer through the system decreases, but the apparent activation</p><p>energy remains approximately constant.</p><p>Complete mass spectra may be recorded repetitively, or selected mass numbers may be</p><p>sampled using a suitably programmed system, or a single mass number may be monitored</p><p>continuously. The results of TA-MS may be presented as a plot of the total ion current</p><p>(the integral of the signal over the entire mass range scanned) against the temperature, or</p><p>of the intensity of a peak of fixed mass number against T (Figure 8.3).</p><p>143</p><p>In interpreting the results of MS studies, allowance has to be made for the fragmentation</p><p>patterns of the parent product molecules. Excessive fragmentation of the gas molecules</p><p>occurs in some cheaper quadrupole mass spectrometers which do not have a variable</p><p>ionization potential. Mixtures of and CO, for example, may then appear mainly as</p><p>and fragments.</p><p>Statheropoulos et al. [16] have discussed procedures for the evaluation of the</p><p>performance of a TG-MS system. These include monitoring the stability of the mass-flow,</p><p>the gas transfer delay, and any condensation of evolved gases. Sills and He [17] used the</p><p>oxidation of pyrite to determine transfer times.</p><p>8.4 Fourier Transform Infrared (FTIR) Spectroscopy</p><p>The potential use of Fourier transform infrared spectrometry (FTIR) for evolved gas</p><p>analysis was recognized by Liebman et al. [18], who remarked on the specificity and the</p><p>short measurement times required, as well as warning of the possibilities for interference</p><p>from the rotational-vibrational fine structure of spectra of small molecules such as</p><p>and TA-FTIR continues to grow in popularity with the wider availability of FTIR</p><p>spectrometers. The apparatus for evolved gas analysis by FTIR [1,19] requires (like most</p><p>simultaneous methods discussed in Chapter 7) that some compromises be made between</p><p>the ideal requirements for operation of the individual instruments. For example, high</p><p>144</p><p>heating rates and low carrier-gas flowrates will give greater concentrations of degradation</p><p>products in the gas analysis cell, but these conditions are not always the most suitable for</p><p>accurate thermal analysis. Secondary reactions between gaseous products are also</p><p>enhanced at low flow-rates, while high flow-rates can cause weighing problems in TG.</p><p>Kaiserberger and Post [6] deal with the coupling of TA equipment to FTIR</p><p>instrumentation. In contrast to TA-MS, the whole gas flow from the TA instrument</p><p>should pass through the gas cell of the FTIR instrument, so the transfer line should not</p><p>change the flow rate and pressure of the purge gas. The transfer time for the gas to reach</p><p>the FTIR cell is determined by the flow rate chosen for the TA system and the length of</p><p>the transfer line. Typically, transfer times will be a few seconds and flow will be laminar.</p><p>A gas cell used for FTIR spectroscopy is illustrated in Figure 8.4(c). The gas sampling</p><p>region of the TG is illustrated in Figure 8.4 (a). FTIR spectra over the full range of the</p><p>instrument can be recorded, or “windows” selected. The results of TA-FTIR experiments</p><p>can be presented in several ways. The most common form of presentation is as a plot of</p><p>the overall integrated intensity of the IR absorption as a function of temperature. This is</p><p>known as a Gram-Schmidt plot (see Figure 8.5(a)). The areas under these absorption</p><p>peaks are very dependent upon the nature of the species contributing to the absorption, so,</p><p>unlike DTG, DSC or DTA curves, the relative amounts of different species cannot be</p><p>directly inferred from Gram-Schmidt plots. Full or partial IR spectra (see Figure 8.5(b))</p><p>at points chosen along the TA curve can be examined and used to identify the species</p><p>being evolved at that stage.</p><p>Morgan [20] has described the use of non-dispersive (i.e. fixed wavelength) infrared</p><p>analyzers, coupled in series to a DTA apparatus, to measure the amounts of and</p><p>evolved by minerals and mineral mixtures. (See Figure 8.6.)</p><p>8.5 Gas Chromatography</p><p>(GC)</p><p>Another approach to EGA is to precede the detector (Figure 8.1) by a column of a suitable</p><p>adsorbent, i.e. to pass the evolved gases from the thermal analysis instrument through a</p><p>gas chromatograph [6]. Sampling, of course, now becomes intermittent because time has</p><p>to be allowed for the component of the gas mixture with the longest retention time, to be</p><p>eluted from the column, before the next sample is introduced. This is the main</p><p>disadvantage of GC because times required for adequate separations may be of the order</p><p>of several minutes. This means that only a few samplings may be possible during a rapid</p><p>thermal event, and some events may even be missed completely. The advantage of GC is,</p><p>however, that by suitable choice of column-packing material, most separations can be</p><p>achieved and retention times, once determined, provide a simple means of identification.</p><p>A multiple-loop gas sampling valve has been used [21 ] to overcome some of the sampling</p><p>problems. Collection of samples at selected time intervals is followed by later analysis on</p><p>the reasonable assumption that secondary reactions between evolved gases do not occur</p><p>in the sample loops.</p><p>145</p><p>146</p><p>147</p><p>The vast literature of gas-solid chromatography is available in deciding upon a suitable</p><p>set of analysis conditions for a given sample and its expected products. Two useful</p><p>references on the analysis of mixtures of the more commonly-encountered gases are the</p><p>books by Hachenburg [22] and Thompson [23].</p><p>A major disadvantage of TG-MS and TG-FTIR, when applied to samples such as</p><p>polymers which degrade to produce a variety of complex fragments simultaneously, is the</p><p>lack of separation of products before analysis. The resulting MS or FTIR data are then</p><p>very difficult to interpret. Lever et al. [24,25] have described the use of sorbent tubes, as</p><p>an alternative to cold traps, for condensing the gases for later analysis by GC-MS. The</p><p>suggested name for the technique is Evolved Gas Collection. The collection tube can be</p><p>coupled to the inlet of the GC-MS and the volatiles are thermally desorbed. A portion of</p><p>the gas can be readsorbed for further GC-MS experiments. Price et al. [26,27] have used</p><p>a similar technique in combination with a scanning thermal microscope (see also Chapter</p><p>5).</p><p>8.6 Special-purpose Detectors</p><p>There is no reason, in principle, why any means of analyzing gases should not be coupled</p><p>to a thermal analysis instrument, and there are reports of the use of absorbents and</p><p>volumetric methods for the determination of total amounts of evolved gases. Detailed</p><p>information on the evolution of each component with time is, however, most desirable.</p><p>Water-vapour is a very common product of thermal decompositions, as well as being a</p><p>product of the reduction of metal oxides with hydrogen, and special detectors have been</p><p>148</p><p>developed to monitor evolution of water, in addition to the use of non-dispersive infrared</p><p>analyzers described above [20]. Many of the common methods for determining the water</p><p>content of gases are not entirely suitable when the water content is varying fairly rapidly,</p><p>on account of slow and/or non-linear detector responses. For EGA the response of the</p><p>detector should also be selective for water as other products may be evolved</p><p>simultaneously.</p><p>Warrington and Barnes [28] have shown that an electrolytic hygrometer is suitable for</p><p>continuous water analyses. The hygrometer has two fine platinum wires wound closely,</p><p>but not in contact, on a PTFE former. The wires are coated with phosphoric acid and the</p><p>whole element is enclosed in a flow-through glass tube which may be coupled to the outlet</p><p>of a TA apparatus. At the start, the acid is electrolysed to dryness using a potential of 100</p><p>V between the two wires, and, in this state, there is then a negligible current between the</p><p>two wires. The acid coating absorbs any water from the gas stream passing through the</p><p>tube and this water is then electrolysed. The electrolysis current is proportional to the</p><p>water concentration in the gas. Precautions necessary to avoid spurious effects are</p><p>described [28], and the system was tested on the dehydration of several hydrates and the</p><p>decompositions of several carboxylic acids.</p><p>Gallagher et al. [29,30] developed an EGA system based on a Panametrics Model 700</p><p>Moisture Analyser in which the moisture content is determined from the dew point of the</p><p>gas stream and the flow rate. The relationship is non-linear and the computations are</p><p>described [29]. Allowance has to be made for background moisture in the gas stream and</p><p>for degassing of the TA apparatus as the temperature rises, as well as loss of moisture by</p><p>adsorption on cooler surfaces of the system.</p><p>Morgan [20] has described an electrolytic detector for analysis based on a fuel cell.</p><p>in the carrier gas diffuses through a semi-permeable membrane and is adsorbed on</p><p>a sensing electrode, producing a current in the circuit which is proportional to the partial</p><p>pressure of in the carrier gas. Calibration using a standard gas mixture is required.</p><p>Cote et al. [31 ] have discussed the use of solid electrolytes of for analysis of</p><p>and for The latter has been used in a study of the decomposition of</p><p>Chemical conversion agents have been suggested to simplify the final analysis, e.g. use</p><p>of to convert CO to and of to convert to for easier GC analysis.</p><p>The kinetic aspects of these processes introduce undesirable uncertainties in EGA.</p><p>New sensors are regularly being developed and reported in the literature. Some of these</p><p>will undoubtedly find application in EGA systems of the future.</p><p>8.7 Applications of EGA</p><p>Knaepen et al. [32] used TG coupled with MS and FTIR, as well as DSC, to study the</p><p>thermal decompositions of a range of hydrated strontium oxalates,</p><p>Their results are illustrated in Figure 8.7. The TG, DTG and DSC curves and the MS</p><p>traces for water CO and are shown. The initial endothermic process is dehydration,</p><p>while the higher temperature endothermic decomposition stages of the oxalate group give</p><p>rise to mixtures of CO and in different proportions as shown. Detailed</p><p>decomposition mechanisms were proposed [32].</p><p>149</p><p>150</p><p>151</p><p>Dei and Guarini [33] used DSC-FTIR to show that a small endothermic event that</p><p>precedes the main decomposition of commercial involves the simultaneous</p><p>evolution of water and This was interpreted as water-assisted decomposition of</p><p>portions of the surface to carbonate.</p><p>Raemaekers and Bart [34] have provided a comprehensive review of the applications of</p><p>TG-MS in polymer analysis, including the characterization of homopolymers, copolymers,</p><p>polymeric blends and composites, residual monomers, solvents, additives, and toxic</p><p>degradation products. When using TG-MS for degradation studies (see, for example,</p><p>Figure 8.8 [35]), slow heating rates are recommended so that kinetic factors can result in</p><p>some separation of the gaseous products. Polymer identification requires a higher mass</p><p>number range than needed for most degradation studies. The relative merits of electron</p><p>impact and chemical ionization techniques are discussed. For complex mixtures, tandem</p><p>mass spectrometers may be desirable.</p><p>152</p><p>Kettrup et al. [36] have described the design of a macro TA-MS system for use in the</p><p>analysis of samples of environmentally important materials, such as garbage, contaminated</p><p>soil, etc., where large samples are necessary to obtain representative results. Evolved</p><p>gases were also adsorbed on suitable resins for subsequent GC-MS. Reggers et al. [37]</p><p>have applied a number of TA - EGA techniques to a variety of waste materials.</p><p>Most of the references to the instrumental systems described above also give some</p><p>examples of their virtually unlimited applications. As a typical example of a practical</p><p>situation, information on the gaseous products, especially hazardous products such as</p><p>and HCN, formed during the degradation of polymers is essential for the safe use of</p><p>polymers in high temperature environments.</p><p>8.8 Pulsed Gas Thermal Analysis</p><p>Maciejewski et al. [5] have introduced</p><p>a technique which they have named pulse thermal</p><p>analysis (PTA). Because of possible ambiguity concerning the property of the system to</p><p>which the ‘pulse’ refers and hence possible confusion with one of the many variations of</p><p>modulated temperature techniques (see Chapter 4), the technique will be referred to here</p><p>as pulsed gas thermal analysis. Gallagher [3] has suggested the name ‘consumed gas</p><p>analysis’. The method is based on the injection of a known amount of gaseous reactant</p><p>into an inert carrier gas stream which then passes over or through a solid reactant in the</p><p>sample pan of a TG or DSC or DTA instrument. The changes in the composition of the</p><p>gas stream, as well as any mass (TG) and/or enthalpy changes (DSC or DTA) are</p><p>monitored and related to incremental extent of reaction resulting from each pulse of gas.</p><p>The reactions that can be studied include reduction and oxidation of solids and</p><p>heterogeneous catalytic processes on solid surfaces. The technique has the advantage that</p><p>the solid reactant can be brought to the desired temperature under an inert atmosphere</p><p>before the reactive gas is injected. Reaction thus takes place at a well-defined</p><p>temperature. The incremental amounts of reaction can be controlled by the amount of</p><p>reactant gas injected in a pulse.</p><p>As an example, Maciejewski et al. [5] used the isothermal reduction of CuO by</p><p>hydrogen at 450°C, see Figure 8.9. Each pulse extended the fractional reaction by 0.035.</p><p>The MS signal for water shows that the desorption of water produced during</p><p>CuO reduction is slow.</p><p>153</p><p>J. Mullens, “Handbook of Thermal Analysis and Calorimetry”, Vol.1, (Ed.</p><p>M.E. Brown), Elsevier, Amsterdam, 1998, Ch.12.</p><p>E. Kaiserberger (Ed.)”Coupling Thermal Analysis and Gas Analysis</p><p>Methods”, Special Issue of Thermochim. Acta, 295 (1997) 1-186.</p><p>P.K. Gallagher, “Thermal Characterization of Polymeric Materials”, (Ed. E.A.</p><p>Turi), Academic, San Diego, 2nd Edn, 1997, Ch. 1.</p><p>S.B. Warrington in “Thermal Analysis: Techniques and Applications”, (Eds</p><p>E.L. Charsley and S.B. Warrington ), Royal Society of Chemistry, Cambridge,</p><p>1992, p.84.</p><p>M. Maciejewski, C.A. Müller, R. Tschan, W.D. Emmerich and A. Baiker,</p><p>Thermochim. Acta, 295 (1997) 167.</p><p>E. Kaiserberger and E. Post, Thermochim. Acta, 295 (1997) 73.</p><p>A. Hallbrucker and E. Mayer, J. Thermal Anal., 35 (1989) 1733.</p><p>W.D. Emmerich and E. Kaiserberger, J. Thermal Anal., 17 (1979) 197;</p><p>Proc. 7th ICTA, Vol.1, (Ed. B. Miller) Wiley, Chichester, 1982, p.279.</p><p>G. Szekely, M. Nebuloni and L.F. Zerilli, Thermochim. Acta, 196 (1992) 511.</p><p>E. Kaiserberger and E. Post, Thermochim. Acta, 324 (1998) 197.</p><p>K. Jaenicke-Rossler and G. Leitner, Thermochim. Acta, 295 (1997) 133.</p><p>B. Roduit, J. Baldyga, M. Maciejewski and A. Baiker, Thermochim. Acta,</p><p>295 (1997) 59.</p><p>M. Maciejewski and A. Baiker, Thermochim. Acta, 295 (1997) 95.</p><p>J.M. Criado, C. Real, A. Ortega and M.D. Alcala, T. Thermal Anal., 36</p><p>(1990) 2531.</p><p>R.L. Schmid and J. Felshe, Thermochim. Acta, 59 (1982) 105.</p><p>M. Statheropolous, S. Kyriakou and N. Tzamtzis, Thermochim. Acta, 322</p><p>(1998) 167.</p><p>I.D. Sills and S. He, Thermochim. Acta, 339 (1999) 125.</p><p>S.A. Liebman, D.H. Ahlstrom and P.R. Griffiths, Appl. Spectrosc., 30</p><p>(1976) 355.</p><p>W.M. Groenewoud and W. de Jong, Thermochim. Acta, 286 (1996) 341.</p><p>D.J. Morgan, J. Thermal Anal, 12 (1977) 245.</p><p>J.H. Slaghuis and P.M. Morgan, Thermochim. Acta, 175 (1991) 135.</p><p>H. Hachenburg, "Industrial Gas Chromatographic Trace Analysis", Heyden,</p><p>London, 1973.</p><p>B. Thompson, "Fundamentals of Gas Analysis by Gas Chromatography",</p><p>Varian, Palo Alto, 1977.</p><p>T.J. Lever, D.M. Price and S.B. Warrington, Proc. 28th NATAS, (2000) 720.</p><p>D. Roedolf, T.J. Lever, D.M. Price and K. Schaap, Proc. 12th ICTAC, (2000)</p><p>paper PI-9.</p><p>D.M. Price, M. Reading, T.J. Lever, A. Hammiche and H.M. Pollock, Proc.</p><p>12th ICTAC, (2000) paper O-20.</p><p>D.M. Price, M. Reading and R.M. Smith, Proc. 28th NATAS, (2000) 705.</p><p>154</p><p>1.</p><p>2.</p><p>3.</p><p>4.</p><p>References</p><p>5.</p><p>6.</p><p>7.</p><p>8.</p><p>9.</p><p>10.</p><p>11.</p><p>12.</p><p>13.</p><p>14.</p><p>15.</p><p>16.</p><p>17.</p><p>18.</p><p>19.</p><p>20.</p><p>21.</p><p>22.</p><p>23.</p><p>24.</p><p>25.</p><p>26.</p><p>27.</p><p>S.B. Warrington and P.A. Barnes, Proc. 6th ICTA, Vol.1, (Ed. H.G.</p><p>Wiedemann), Birkhaeuser Verlag, Basel, 1980, p.327.</p><p>P.K. Gallagher, E.M. Gyorgy and W.R. Jones, J. Thermal Anal.,</p><p>23 (1982) 185.</p><p>P.K. Gallagher and E.M. Gyorgy, Proc. 6th ICTA, Vol.1, (Ed. H.G.</p><p>Wiedemann), Birkhaeuser Verlag, Basel, 1980, p. 113.</p><p>R. Cote, C.W. Bale and M. Gauthier, J. Electrochem. Soc., 131 (1984) 63.</p><p>E. Knaepen, J. Mullens, J. Yperman and L.C. van Poucke, Thermochim. Acta,</p><p>284 (1996) 213.</p><p>L. Dei and G.G.T. Guarini, J. Thermal Anal., 50 (1997) 773.</p><p>K.G.H. Raemaekers and J.C.J. Bart , Thermochim. Acta, 295 (1997) 1.</p><p>J. Mullens, R. Carleer, G. Reggers, M. Ruysen, J. Yperman and L.C. Van</p><p>Poucke, Bull. Soc. Chim. Belg., 101 (1992) 267.</p><p>A. Kettrup, G. Matuschek, H. Utschick, Ch. Namendorf and G. Bräuer,</p><p>Thermochim. Acta, 295 (1997) 119.</p><p>G. Reggers, M. Ruysen, R. Carleer and J. Mullens, Thermochim. Acta, 295</p><p>(1997)107.</p><p>155</p><p>28.</p><p>29.</p><p>30.</p><p>31.</p><p>32.</p><p>33.</p><p>34.</p><p>35.</p><p>36.</p><p>37.</p><p>LESS-COMMON TECHNIQUES</p><p>Some of the techniques of thermal analysis, based on the monitoring of less-obvious</p><p>properties of a sample and often requiring more specialized equipment, are grouped, for</p><p>convenience, under the heading of less-common techniques [1], These techniques include</p><p>Emanation Thermal Analysis (ETA), Thermoelectrometry and Thermosonimetry. A few</p><p>interesting techniques that are difficult to classify are described at the end of this Chapter,</p><p>under Miscellaneous.</p><p>9.1 Introduction</p><p>9.2 Emanation Thermal Analysis (ETA) [1-10]</p><p>9.2.1 Introduction</p><p>Emanation thermal analysis (ETA) involves the measurement of the release of inert (and</p><p>usually radioactive) gas from an initially solid sample, while the temperature of the</p><p>sample, in a specified atmosphere, is programmed. The rate of release of gas is used as</p><p>an indication of the changes taking place in the sample. Comparison of ETA results with</p><p>those from thermogravimetry (TG) and evolved gas analysis (EGA) provides information</p><p>about the microstructure of the sample.</p><p>Most of the solids to be studied do not naturally contain inert gas and the solubility of</p><p>inert gases in inorganic solids is small. The inert gases are trapped at lattice imperfections</p><p>and these defects can serve as both traps and diffusion pathways. The migration of inert</p><p>gases in solids is discussed in reference [3].</p><p>9.2.2 Sample preparation</p><p>There are several techniques for incorporating inert gas in a solid sample. These</p><p>techniques can be divided broadly into two groups: (A) techniques for introducing the</p><p>parent nuclide of the inert gas, e.g.</p><p>(see Figure 9.1) or (B) techniques for introducing the inert gas itself. Labelling with</p><p>parent nuclide gives a sample which is stable for longer as far as a source of inert gas is</p><p>concerned. Gas is being formed continuously and will not all be lost in a single run on the</p><p>sample. The recoil mechanism associated with the release of the inert gas has to be taken</p><p>into account. The following methods have been used:</p><p>157</p><p>158</p><p>A1: Coprecipitation of parent isotopes. The disintegration process ensures a random</p><p>distribution of the products.</p><p>A2: Impregnation of the sample with a solution of parent isotope. This method is used</p><p>when coprecipitation is not possible. Parent atoms are distributed only on the surface.</p><p>Disintegration results in penetration of the daughter atoms into crystallites but, unless the</p><p>crystallites are small, the distribution is non-uniform. The distribution may be improved</p><p>by annealing the sample.</p><p>A3: Nuclear reactions may be used to produce the parent nuclide or the inert gas, e.g.,</p><p>159</p><p>B1: Ion bombardment is a common method of implanting inert gas atoms in solids. The</p><p>ions may be generated in vacuum using an electrical discharge or a microwave plasma.</p><p>The quantity of gas absorbed depends on the gas used, the energy of bombardment and the</p><p>nature of the solid.</p><p>B2: Diffusion at high temperature and/or pressure is also sometimes possible. is</p><p>usually used. (Solids labelled with are called kryptonates. years for</p><p>B3: Crystallization or sublimation</p><p>of the sample in an inert gas atmosphere may be more</p><p>effective in incorporating the gas.</p><p>9.2.3 Apparatus for measurement of gas release</p><p>ETA is usually carried out in conjunction with other TA techniques, e.g. NETZCH</p><p>markets ETA/DTA/EGA apparatus. Carrier gas, at an accurately controlled flow-rate is</p><p>used to carry released gas to suitable counting chambers. Rn, an , requires a</p><p>scintillation counter, or an ionization chamber or semi-conductor detector, while Geiger</p><p>counters are used for Kr, Xe and Ar For experiments lasting a long time</p><p>compared with the half-life of the inert gas used, the decay of the measured gas should be</p><p>taken into account. A typical ETA apparatus is shown schematically in Figure 9.2.</p><p>160</p><p>9.2.4 Rate of gas release</p><p>Details of the gas release are very dependent upon the way in which the sample was</p><p>originally labelled. Release may involve either bulk or defect diffusion. There may also</p><p>be recoil ejection. The emanating power, E, is defined as:</p><p>where is the release rate and is the formation rate. may be</p><p>measured by dissolution of the sample in acid or other solvent and measurement of the gas</p><p>released.</p><p>It is of interest that TG and EGA curves obtained during release of gaseous products of</p><p>thermal decomposition may not correlate exactly with ETA curves. Beckman and Balek</p><p>[8] have used gas percolation theory to model gas release during ETA experiments. Their</p><p>latest model [8] for the sample consists of three solid components with different gas</p><p>diffusion coefficients and extends their earlier two-component model [7]. The initial solid</p><p>reactant has a low diffusion coefficient, as does the final, stable product. The solid</p><p>intermediate is highly disordered and permeable. The initial distribution of inert gas in the</p><p>sample is not assumed to be uniform, whereas the formation of gaseous products by</p><p>thermal decomposition is assumed to be uniform. The total emanating power of the</p><p>sample is taken to be the sum of the values for the three individual components.</p><p>During the initial stages of reaction [8], isolated clusters of the intermediate phase are</p><p>totally surrounded by reactant but, later, these clusters become interconnected allowing</p><p>gaseous products to migrate. The intermediate phase converts to the final product and, in</p><p>the final stages of decomposition, isolated clusters of residual reactant and/or intermediate</p><p>phase can be totally surrounded by stable product.</p><p>Isothermal gas-release curves for the three-component model were calculated [8] (see</p><p>Figure 9.3) for different proportions of each of the three components. The shapes of the</p><p>curves are strongly dependent upon the values of and as well as upon the rate</p><p>coefficient for the thermal decomposition reaction and a structural relationship factor [8].</p><p>This makes ETA a sensitive, although possibly difficult to interpret, means of exploring</p><p>microstructural changes during solid state reactions.</p><p>161</p><p>9.2.5 Applications of ETA</p><p>One of the major uses of ETA is in the characterization of powders. Emanating power</p><p>is related to surface area and hence changes in grain size and the occurrence of sintering</p><p>during heating may be detected.</p><p>Figure 9.4 shows a series of isothermal ETA curves for NiO samples, prepared from the</p><p>carbonate. These curves, obtained in a nitrogen atmosphere, were used [3] to determine</p><p>the kinetic parameters for sintering of the samples. The apparent activation energy of</p><p>was decreased to when a similar series of runs were done in oxygen.</p><p>Phase changes also show up as changes in emanating power, e.g. the orthorhombic to</p><p>rhombohedral phase transition of at 128°C is seen in Figure 9.5.</p><p>162</p><p>Solid-gas reactions have also been studied [1], e.g. the oxidation of labelled metals or</p><p>reduction of labelled oxides. ETA and EGA curves are in good agreement. Information</p><p>on solid-liquid reactions, e.g. the hydration of cement, has been obtained. In both</p><p>solid-gas and solid-liquid reactions the formation of a layer of solid product may hinder</p><p>emanation.</p><p>163</p><p>For solid-solid reactions such as spinel formation [3,5], e.g.,</p><p>with ZnO labelled with the emanation of the individual components is checked first.</p><p>ETA traces for the reaction are shown in Figure 9.6. The oxides interact in a series of</p><p>stages. Product begins to form by surface diffusion between 250 and 400°C as shown by</p><p>the increased emanation (curve 3). The DTA and thermodilatometry (TD) curves (curves</p><p>2 and 1 in Figure 9.6) show no changes at these temperatures. Sharp changes in all of the</p><p>curves in Figure 9.3 are observed at 670 to 700°C. The exotherm on the DTA curve is</p><p>small, but the increased emanation (curve 3) shows up clearly. This corresponds to</p><p>interaction by volume diffusion. The reaction is complete by about 800°C. The dilation</p><p>shown in curve 1 is suggested [3] to be caused by the formation of a very finely powdered</p><p>product which sinters at higher temperatures. The ETA curve during the second heating</p><p>of the reaction mixture (curve 4) shows that reaction was complete during the first heating.</p><p>The reactivities of different preparations of have been compared using this</p><p>technique [3],</p><p>164</p><p>The main drawback about ETA is that preparation and handling of samples requires all</p><p>the usual radiochemical facilities and precautions. The amounts used in samples are so</p><p>small that evolved gas, after dilution with carrier, does not form a hazard. Inert gases are</p><p>not incorporated biologically and the decay products are stable, so hazards are reduced.</p><p>9.3 Thermosonimetry (TS) and Thermoacoustimetry</p><p>9.3.1 Introduction</p><p>In thermosonimetry (TS), sound waves emitted by a sample (acoustic emission) [11,12]</p><p>are measured as a function of temperature during a controlled heating programme. The</p><p>sounds emitted arise from the release of thermal stresses in the sample, e.g., movement of</p><p>dislocations, generation and propagation of cracks, nucleation of new phases, relaxation</p><p>processes and discontinuous changes in physical properties. At the glass transition</p><p>temperature, a discontinuous change in free volume generates elastic waves which cause</p><p>an acoustic effect. The limit of detection of a burst of acoustic emission has been</p><p>estimated [11] as about 1 fJ and the frequencies involved range from audio to several</p><p>MHz. The stress-relief processes described above are not generally detectable by the more</p><p>conventional thermal analysis techniques, on account of their low energy, and thus TS may</p><p>be used, amongst other applications (see below), to assess radiation damage, defect</p><p>content and the degree of annealing of samples. It is also a sensitive technique for</p><p>detecting the mechanical events associated with dehydration, decomposition, melting, etc.</p><p>[13,14].</p><p>In thermoacoustimetry, the characteristics of imposed acoustic waves after passing</p><p>through a sample, are measured as a function oftemperature while the sample is subjected</p><p>to a controlled temperature programme.</p><p>9.3.2 Apparatus for thermosonimetry</p><p>The sounds are emitted as mechanical vibrations prior to and during thermal events in the</p><p>sample. This sonic activity in the sample is picked up and transmitted by means of a</p><p>specially adapted stethoscope. The mechanical waves are converted to electrical signals</p><p>by conventional piezoelectric transducers. The stethoscope is made of fused silica (up to</p><p>1000°C), or ceramics or noble metals for higher temperatures. The sample is held in the</p><p>sample head which acts as an acoustic transformer and is connected via a transmitting rod</p><p>to a piezoelectric sensor, fixed on a heavy recoil foundation and a seismic mount to</p><p>prevent interference from external noise. A schematic diagram of the apparatus [15,16]</p><p>is shown in Figure 9.7. The properties of the transducer may vary with temperature, so</p><p>the waveguiding system is used to transmit the acoustic emissions from the heated sample</p><p>to the transducer at ambient temperature. Contact surfaces must be well polished and thin</p><p>films of silicone oil improve signal transfer. Direct insertion of a thermocouple in the</p><p>sample can cause severe mechanical damping, so the thermocouple</p><p>is usually placed as</p><p>close as possible to the sample without actually touching it.</p><p>165</p><p>Simultaneous TS - DTA measurements have been reported [17-20]. Such a system has</p><p>been used [18] to examine the transitions in the ICTAC standards. Lee et al. [21] have</p><p>combined thermodilatometry and TS.</p><p>9.3.3. Interpretation</p><p>The output from a thermosonimetry experiment consists of a rapid cascade of decaying</p><p>signals, which may be recorded as: (i) the number of signals of peak amplitude greater</p><p>than a set threshold value in a given time; or (ii) the time for which the signal amplitude</p><p>exceeds the threshold value; or (iii) the number of times that signals pass through a chosen</p><p>voltage level in a positive direction; or (iv) the root-mean-square amplitude level (energy);</p><p>or (v) as a set of frequencies. The Nyquist theorem requires that the sampling frequency</p><p>should be at least twice that of the maximum frequency component present in the signal.</p><p>Because chemical acoustic emission usually occurs in bursts, continuous recording of high</p><p>frequency data is usually replaced by data acquisition only when the signal exceeds a set</p><p>threshold. Choice of this threshold relative to the background noise is discussed by Wade</p><p>et al. [22].</p><p>Frequency distributions of the TS signals are obtained [18] by timing the intervals</p><p>between the amplitude components of the decaying signal. The time intervals are</p><p>converted into pulse heights which are fed to a multi-channel analyzer to give a display</p><p>of the frequency distribution.</p><p>Wentzell and Wade [23] investigated (i) the reproducibility of power spectra from a</p><p>given chemical system; (ii) the dependence of the spectra on the transducer used; and (iii)</p><p>whether the information obtained in the spectra was sufficient to distinguish amongst the</p><p>different processes which could be occurring. They found that reproducibility of spectra</p><p>obtained with the same transducer was good, but that reproducibility between transducers</p><p>was not as good. Transducer response remained reasonably constant over several months</p><p>of use.</p><p>Relationships have been sought between the frequency distributions and the processes</p><p>occurring in the sample. In the simplest case, frequency distributions can be used as</p><p>'fingerprints' of sample origin. Detailed interpretation is complex and empirical pattern</p><p>recognition methods have been suggested [24,25]. Wentzell et al. [24] evaluated possible</p><p>descriptors obtained from AE signals for use in characterizing the processes giving rise</p><p>to the signals. Descriptors were grouped into four categories: (i) those associated with</p><p>the absolute magnitude of the signal; (ii) those related to the rate of decay of the signal;</p><p>(iii) those measuring the central tendency of the power spectrum, and (iv) those</p><p>characterizing the dispersion of the power spectrum. The conclusion reached [24] was</p><p>that "acoustic emission will present a challenge to modern pattern recognition methods",</p><p>and the subtlety of the information obtainable was emphasized.</p><p>Although interpretation of power spectra is complicated by distortion of the acoustic</p><p>signal by instrumental factors, the main features of the spectra could be associated [23]</p><p>with fundamental processes occurring in the systems examined, e.g., bubble release was</p><p>associated with low frequencies and crystal fracture with high frequencies.</p><p>The particle size, mass, chemical nature and form (e.g., single crystals, powder) of the</p><p>sample all affect the TS signal and the TS curves also vary with the resonance frequency</p><p>of the piezoelectric sensor [19]. The resonance frequencies of the sensors used by</p><p>Shimada [19] were 140 kHz, 500 kHz, 1 MHz and 1.5 MHz. For power spectra, a</p><p>wideband sensor (300 kHz to 2 MHz) was used.</p><p>166</p><p>9.3.4 Apparatus for thermoacoustimetry</p><p>In the apparatus used by Mraz et al. [26], a pair of lithium niobate transducers are in</p><p>contact (under a constant pressure of about 300 kPa) with opposite faces of the sample</p><p>(Figure 9.8). One transducer induces the incident acoustic signal and the other detects the</p><p>transmitted signal. Thermal expansion of the sample during the heating programme is</p><p>monitored continuously with a linear variable differential transformer (LVDT), so that</p><p>changes in sample dimensions can be allowed for in the calculations. Arrangements are</p><p>made for atmosphere control around the sample.</p><p>167</p><p>The incident signal is generated by a pulse generator. The transmitted signal received</p><p>by the second transducer is inverted and amplified and an attenuated version of the driving</p><p>pulse is added to this output signal. This summation procedure enables detection of the</p><p>first-arrival times of both the compressional (P) and shear (S) waves. The velocities of</p><p>the P and S waves and hence the various elastic moduli are then computed at set</p><p>temperature intervals, and the final result is a plot of velocity or modulus against</p><p>temperature. The instrument was calibrated with an aluminium standard for which the P</p><p>and S wave velocities were accurately known.</p><p>The apparatus described by Kasap and Mirchandan [27] (Figure 9.9) operates from room</p><p>temperature to 350°C. The sample is loaded between two identical glass rods, one of</p><p>which is stationary and the other vertically movable. Transducers and thermocouples are</p><p>attached to the rods and not the sample.</p><p>168</p><p>Samples are in the form of sheets or pellets. Blank experiments are carried out with the</p><p>two glass rods in contact. The ultrasonic transit time through the sample is obtained from</p><p>the time delay between the through signal and the echo signal. The through signal travels</p><p>the length of both rods plus the sample length. The echo signal travels the length of the</p><p>top rod and back, allowance also has to be made for travel time through the coupling</p><p>regions at the interfaces. Absolute determination of the ultrasonic velocity is usully</p><p>unnecessary - only the variation with temperature. The use of the through and echo</p><p>signals eliminates the influence of temperature variations in the glass rods.</p><p>The change in attenuation, of the ultrasonic waves with temperature is obtained by</p><p>measuring the peak-to-peak amplitude of the through signal, at temperature T and</p><p>relating it to the value at a reference temperature,</p><p>(where is the path length through the sample). Kasap and Mirchandan [27] illustrated</p><p>the operation of their system with curves of and of against T (where is the</p><p>ultrasonic velocity at T) for various materials exhibiting glass transitions. The</p><p>plots showed distinct changes in slope at while the plots showed peaks. The</p><p>features of the thermoacoustic curves were clearly related to DSC and microhardness</p><p>measurements.</p><p>169</p><p>Ravi Kumar et al. [28] have given a detailed description of the thermoacoustical</p><p>parameters of polymers.</p><p>9.3.5 Applications of thermosonimetry and thermoacoustimetry</p><p>TS curves are usually used in combination with other thermoanalytical results to</p><p>characterize a sample. TS curves on kaolins [ 15] show two regions of increased activity</p><p>(Figure 9.10). Comparing results obtained by TS with those obtained by TG and DTA,</p><p>these regions have been identified as dehydroxylation (500-600°C) followed by</p><p>recrystallisation (980-985°C) to the metakaolin structure. TS examination of the thermal</p><p>decomposition of a powdered sample of brucite [15], suggested that</p><p>dehydroxylation occurs in a stepwise fashion with successive bursts of reaction as the</p><p>sample breaks up. The barrier effect which has to be overcome was not identified.</p><p>The frequency distributions obtained [18] on heating samples of (a) and</p><p>(b) to their transition temperatures of 582°C and 299°C, respectively, are shown in Figure</p><p>9.11. The pre-transition activity in involves release of included fluid, while that</p><p>in corresponds to generation of micro-cracks. The frequency distribution for</p><p>shows fewer low frequency components. Frequency distributions for the</p><p>dehydration steps in are qualitatively similar to those of again</p><p>through the fluid loss processes. A combined TS - DTA study of [17] identified</p><p>the two regions of increased</p><p>acoustic activity with the phase transition (orthorhombic to</p><p>cubic) (200 to 340°C) and melting accompanied by decomposition (560 to 660°C). The</p><p>onset ofthe lower temperature TS peak was well below the transition temperature (298 ° C)</p><p>indicating that mechanical changes occur in the sample particles prior to the transition.</p><p>Solidification of the KCl product of decomposition was detectable by TS but not on the</p><p>DTA curve.</p><p>170</p><p>In a series of further papers, Shimada et al. [16,17] showed that the low temperature TS</p><p>signals decreased with decreasing sample mass, which confirmed that acoustic emission</p><p>was from the whole sample and not just from particles in contact with the sample holder.</p><p>Resolution of the peaks in the higher temperature signal was better at low sample masses.</p><p>The low temperature peak decreased with particle size and was undetected below 75 µm</p><p>diameter particles. Optical and scanning electron microscopy showed that the low</p><p>temperature TS peak results from fracture of large particles and/or release of liquid from</p><p>their surfaces. behaves similarly, but TS curves for were</p><p>complicated by dehydration in two steps (55 to 80 °C and 155 to 200 °C). The DTA curve</p><p>for [16] showed melting at 340 to 380°C and two successive exotherms due to</p><p>decomposition (540 to 610°C). The TS curve showed four main peaks. The first two</p><p>(360 to 480°C and 485 to 520°C) arise from post-melting events, while the last two (530</p><p>to 570°C and 570 to 620°C) correspond to the decomposition stages</p><p>KCl. The first two TS peaks were shown by high temperature microscopy to be related</p><p>to the formation and evolution of gas bubbles in the melt.</p><p>The phase transitions ( orthorhombic trigonal 128 °C; trigonal on cooling</p><p>124°C) occurring on heating and cooling powdered and single crystal samples of</p><p>were also investigated [20] using simultaneous TS - DTA, supported by microscopy. The</p><p>phase has useful ferroelectric properties. The transition was affected by the</p><p>temperature from which the samples were cooled. This observation was interpreted as</p><p>resulting from annealing of defects formed by the transition. The TS signals for the</p><p>transition were stronger than for the or transitions</p><p>Lee et al. [21] have used TS - dilatometry to study the phase II phase III transition of</p><p>hexachloroethane in great detail. Agreement between integrated acoustic emission and the</p><p>dilatometric plots was good. Emission was less intense during heating than during</p><p>cooling, on account of supercooling. Different acoustic 'signatures' for the processes of</p><p>nucleation and of growth could not be assigned.</p><p>171</p><p>Thermoacoustimetry has been used [26] to distinguish between grades of oil shales.</p><p>Both the P and the S wave velocities decrease with increasing temperature and with</p><p>increasing organic content (Figure 9.12). Results are very reproducible. Discontinuities</p><p>and peaks in the plots are related to loss of water and decomposition of some hydrocarbon</p><p>fractions. Thermoacoustimetry has also been used [29], in combination with DTA, to</p><p>examine the characteristics of synthetic fibres (Figure 9.13). The increases in signal occur</p><p>firstly at the glass-transition temperatures and then prior to melting. The glass fibre shows</p><p>no changes in this temperature range.</p><p>172</p><p>9.4 Thermoelectrometry (or Thermoelectrical Analysis, TEA )</p><p>9.4.1 Introduction</p><p>The main electrical properties of the sample which may be measured as a function of</p><p>temperature are dc or ac conductance, capacitance and dielectric properties [30,31].</p><p>Measurements may be made in the presence or absence of an electric field, for example,</p><p>measurement of the emf generated when two dissimilar metal electrodes are in contact</p><p>with the sample during a heating programme, is known as thermovoltaic detection, TVD</p><p>[31]. After a sample has been exposed to a static electric field, measurements may be</p><p>made of the thermally stimulated discharge current, TSDC. Dielectric analysis measures</p><p>changes in properties of the sample as it is subjected to a periodic field [31] and in</p><p>dielectric thermal analysis, DETA, the sample is also subjected to a temperature</p><p>programme.</p><p>Most thermoelectrometry studies are carried out simultaneously with other techniques,</p><p>especially DTA. TG studies on the decomposition of solids have also been carried out in</p><p>the presence of applied electrical fields.</p><p>9.4.2 Apparatus</p><p>There is an excellent and comprehensive review of all aspects of thermoelectrometry in</p><p>the book by Wendlandt [30]. Gallagher [31] has reviewed the apparatus developed for</p><p>thermoelectrometry and Bidstrup Allen [32] has provided a detailed theoretical</p><p>background to dielectric measurements.</p><p>A DSC cell that has been modified [33] for simultaneous measurements of dc</p><p>conductance is shown in Figure 9.14. The DSC cell base is insulated from the rest of the</p><p>cell with a thin glass slide. A thin piece of asbestos was used in the reference position to</p><p>compensate for the heat capacity of the sample. Platinum foil was used to form an</p><p>electrical connection from the bottom of the sample to the top of the reference.</p><p>Glass-insulated platinum wire electrodes contact the tops of the sample and the reference.</p><p>The current through the sample was recorded as a function of temperature. The</p><p>dimensions of the sample were then used to calculate the resistivity. Sample surfaces were</p><p>coated with colloidal graphite to overcome contact resistance. The sensitivity of the DSC</p><p>was reduced considerably by the presence of the glass slide.</p><p>173</p><p>Dielectric thermal analysis, DETA, involves measurements of both the capacitance and</p><p>the conductance of the sample as functions of time, temperature and frequency. The</p><p>capacitance is a measure of the material’s ability to store charge, while the conductance</p><p>is a measure of the ease of transfer of charge.</p><p>Four major properties are reported during dielectric analysis: the permittivity (also</p><p>called the dielectric constant); the loss factor the dissipation factor, tan and</p><p>the ionic conductivity The permittivity, which measures the alignment of dipoles,</p><p>and the loss factor, which represents the energy required to align dipoles and move ions,</p><p>both provide valuable information about molecular motion. As in most TA techniques, it</p><p>is the changes in these properties that accompany thermal events in the sample that are</p><p>usually of more interest than absolute values of the electrical properties.</p><p>A sample cell for concurrent dielectric measurement and DTA [34] is illustrated in</p><p>Figure 9.15. A coaxial-type two terminal electrode configuration is used. The inner</p><p>electrode is a silver rod positioned symmetrically with respect to the outer electrode, which</p><p>is a thin silver foil pressed against the walls of the cavity in the nickel block. The sample</p><p>may be a liquid, a powder or a machined solid. Approximately 500 mg of sample is</p><p>required. A separate smaller (50 mg) sample is used for concurrent DTA. The sample is</p><p>connected to the inverting input of an operational amplifier, configured as a</p><p>current-to-voltage converter with capacitive feedback. The measured phase-shift and</p><p>attenuation of this network can be related [34] to the dielectric properties of the sample.</p><p>The apparatus can be operated in two modes: either using a continuous range of</p><p>frequencies (50 Hz to 1 MHZ) at selected temperatures, or over a continuous range of</p><p>temperatures at selected frequencies. Changes in the dielectric properties of the sample,</p><p>brought about by phase transitions or chemical reactions are better resolved using the</p><p>second mode. The instrument was calibrated with standard organic liquids.</p><p>The TA Instruments DEA 2970 Dielectric Analyzer is shown in Figure 9.16. It consists</p><p>of a sensor and a ram/furnace assembly. Different shapes of ceramic sensors can be</p><p>mounted in the ram/furnace assembly, which provides the controlled experimental</p><p>conditions (heating, cooling, atmosphere and applied force). The ram is driven by a</p><p>stepper motor and can apply a constant force or maintain a constant distance between</p><p>plates, based upon the information fed back from the force transducer</p><p>to measure, or the rate of</p><p>change of the sample property with temperature (or time) may be of interest (derivative</p><p>measurements). Further techniques (and methods) derived from those in Table 1.2. are</p><p>listed in Table 1.3. Care is needed in interpreting the new terminology in terms of the</p><p>familiar older names, particularly in the manufacturers’ literature. When the pressure of</p><p>the atmosphere in the apparatus is above ambient, the abbreviated technique is sometimes</p><p>prefaced by HP for “high pressure”, e.g. HPDTA.</p><p>The range of samples is enormous, limited usually, but not necessarily, to initially solid</p><p>substances. Studies on liquids provide less information of interest and studies on gases</p><p>are not usually included under thermal analysis. The temperature programme to which the</p><p>sample is subjected is most often a constant heating (or cooling) rate and the atmosphere</p><p>is usually an inert gas, but studies in reactive gases also provide a wealth of information.</p><p>Like most techniques based on relatively simple principles, the interpretation of results</p><p>is not always as straightforward and, hence, it is important to combine information from</p><p>several techniques whenever possible.</p><p>3</p><p>4</p><p>The establishment of the International Confederation of Thermal Analysis (ICTA) in</p><p>Aberdeen in 1965 and its growth and influence are important factors in the history of</p><p>thermal analysis and are fascinatingly described, from personal experience, by Dr Robert</p><p>Mackenzie [10]. ICTA became ICTAC in 1992 by adding Calorimetry to its title.</p><p>1.2 Thermal Analysis Instruments</p><p>All thermal analysis instruments have features in common. These are illustrated in Figure</p><p>1.1. The sample, contained in a suitable sample pan or crucible, is placed in a furnace and</p><p>subjected to some desired temperature programme. During this procedure, one or more</p><p>properties of the sample are monitored by use of suitable transducers for converting the</p><p>properties to electrical quantities such as voltages or currents. The variety of the</p><p>techniques to be discussed stems from the variety of physical properties that can be</p><p>measured and the variety of transducers that can be used.</p><p>Measurements are usually continuous and the heating rate is often, but not necessarily,</p><p>linear with time. The results of such measurements are thermal analysis curves and the</p><p>features of these curves (peaks, discontinuities, changes of slope, etc.) are related to</p><p>thermal events in the sample. (“Thermogram” is not a recommended term for a thermal</p><p>analysis curve, because of its medical usage.) The thermal events which may be detected</p><p>are described in Chapter 2.</p><p>5</p><p>6</p><p>7</p><p>8</p><p>9</p><p>10</p><p>References</p><p>R.C. Mackenzie, Thermochim. Acta, 73 (1984) 249, 307; 92 (1985) 3; 148</p><p>(1989) 57; J. Thermal Anal., 40 (1993) 5, Israel J. Chem., 22 (1982) 203.</p><p>J.O. Hill (Ed.), "For Better Thermal Analysis and Calorimetry", 3rd Edn,</p><p>ICTA, 1991.</p><p>C.J. Keattch and D. Dollimore, "An Introduction to Thermogravimetry",</p><p>Heyden, London, 2nd Edn, 1975.</p><p>R. Vieweg, "Progress in Vacuum Microbalance Techniques", Vol. 1, (Eds T</p><p>Gast and E. Robens), Heyden, London, 1972, p.l.</p><p>B. Wunderlich, “Thermal Analysis”, Academic Press, Boston, 1990.</p><p>A. Schuijff, “Calorimetry and Thermal Analysis of Polymers”, (Ed. V.B.F.</p><p>Mathot), Hanser Publishers, Munich, 1994, Ch.l.</p><p>P.J. van Ekeren, “Handbook of Thermal Analysis and Calorimetry”, Vol.1, (Ed.</p><p>M.E. Brown), Elsevier, Amsterdam, 1998, Ch.2.</p><p>W. Hemminger and S.M. Sarge, “Handbook of Thermal Analysis and</p><p>Calorimetry”, Vol.1, (Ed. M.E. Brown), Elsevier, Amsterdam, 1998, Ch.l.</p><p>W. Hemminger, Recommendations of the ICTAC Nomenclature Committee,</p><p>ICTAC NEWS, December 1998, p.106-122.</p><p>R.C. Mackenzie, J. Thermal Anal., 40 (1993) 5.</p><p>11</p><p>1.</p><p>2.</p><p>3.</p><p>4.</p><p>5.</p><p>6.</p><p>7.</p><p>8.</p><p>9.</p><p>10.</p><p>THERMAL EVENTS</p><p>The main characteristic feature of the solid state is the relatively ordered arrangement of the</p><p>constituent atoms, molecules or ions. Just as the concept of an “ideal gas” is useful in</p><p>describing the behaviour of real gases, the concept of a “perfect solid” or “perfect crystal” is</p><p>useful as the reference point for real solids. A perfect (crystalline) solid has a completely</p><p>ordered arrangement of its constituents, while real solids have imperfections of many kinds.</p><p>When the order present is marginally greater than for liquids, but considerably less than in a</p><p>perfect crystal, the substance is sometimes referred to as a “non-crystalline solid”. When</p><p>liquids composed of complex molecules or ions (e.g. sucrose or silicates and a vast number of</p><p>organic polymers) are cooled rapidly a glass may be formed. A glass resembles a solid in many</p><p>of its physical properties, e.g. rigidity, but differs in that the constituents do not show the</p><p>regular (lattice) arrangement of a crystalline solid. Glasses are thus examples of non-</p><p>crystalline solids. They do not melt at a sharply-defined temperature, but soften over a</p><p>temperature interval. This transition from the rigid glassy state to a more flexible form is known</p><p>as the glass transition and the temperature interval over which this change occurs, known as</p><p>the glass transition temperature, [6], is of tremendous importance in the practical use of</p><p>polymers.</p><p>Crystalline solids may be classified according to the dominant bonding forces between the</p><p>constituents in the crystal, i.e. as molecular, covalent, ionic or metallic crystals [2,7].</p><p>In molecular crystals the identity of each individual molecule is preserved. The van der Waals</p><p>attractive forces between molecules, which give the solid its coherence, are weak compared</p><p>with the (usually covalent) bonds between the atoms comprising each molecule. On heating,</p><p>most molecular solids melt without chemical changes of the constituents. Some compounds</p><p>may be unstable because of molecules with considerable internal strains or containing several</p><p>reactive groups, as in many explosives, and decomposition may occur at temperatures below</p><p>2.2 The Solid State</p><p>The sample referred to in the definition of thermal analysis in Chapter 1, is very often in the</p><p>solid state, at least at the start of the investigation. The thermal behaviour of liquids can also</p><p>be studied using special techniques (see below), but gases are not normally the principal</p><p>reactants in thermal analysis experiments.</p><p>2.1 Introduction</p><p>13</p><p>the melting point. The size and shape of the constituent molecule has a very marked effect on</p><p>the order possible when molecules are packed closely together. Large molecules</p><p>(macromolecules), especially non-linear and relatively rigid molecules, seldom form very</p><p>ordered arrangements. Thermal analysis has played an important role in exploring the properties</p><p>of such high-polymers [6,8],</p><p>In covalent crystals, each constituent atom is linked to its neighbours through directed</p><p>covalent bonds. The crystal structure is determined by the arrangement in space of these bonds.</p><p>Such solids are hard and have high melting points, e.g. diamond, silicon carbide, etc.</p><p>In ionic crystals, ions of opposite charge are packed as efficiently as possible, subject to the</p><p>additional influence of thermal energy. Because of the non-directional nature of electrostatic</p><p>forces, the structures adopted are determined by: (i) the relative numbers of cations and anions,</p><p>(ii) the relative sizes of positive and negative ions and (iii) the ionic shapes. Molecules of water</p><p>(or solvent) of crystallization, may be incorporated in the crystal structure. Dehydration usually</p><p>precedes decomposition but some overlap of these processes may occur.</p><p>Metals (and alloys) are usually close-packed arrangements of similar sized spheres. Each atom</p><p>has a high coordination number. The valence electrons from each atom have freedom to</p><p>migrate in an applied field so that metals are good conductors of electricity, e.g., copper, iron,</p><p>lead, etc.</p><p>In many crystalline substances there may be several bond types, e.g. the vast number of</p><p>coordination compounds. Loss of water from a crystal containing a hydrated cation involves</p><p>the rupture of coordinate bonds and the associated hydrogen bonds.</p><p>14</p><p>and the linear</p><p>variable differential transformer (LVDT). The high sensitivity of DEA makes it able to</p><p>detect transitions that are not visible using other TA techniques, for example, the final</p><p>stages of polymer cure.</p><p>174</p><p>9.4.3 Applications of thermoelectrometry</p><p>Electrical conductivity measurements are useful in detecting the appearance of liquid</p><p>phases in the reactions between initially solid reactants. It is also possible to monitor the</p><p>loss of chemisorbed OH groups in quantities too small to be detected by TG. Changes in</p><p>electrical conductivity during heating have also been attributed to changes in</p><p>concentrations of crystal defects.</p><p>Measurements of resistivity against temperature for polymers [33] show sharp drops in</p><p>resistivity at about the glass-transition temperature. The formation of conductive carbon</p><p>chains by cross-linking and cyclization within the polymer can be detected by the gradual</p><p>decrease of resistivity with increasing temperature. Such processes are not shown up by</p><p>TG or DSC. A curve for PVC is shown in Figure 9.17, with the glass transition and the</p><p>region of dehydrochlorination marked. Thermoelectrometry is also useful in studying the</p><p>effect of carbon black additives on the properties of polymers [33].</p><p>175</p><p>176</p><p>The thermal decomposition of oil shales has been shown [34], using thermoelectrometry,</p><p>to be a two-step process involving the breakdown of an outershell polar bridge</p><p>(180-350°C) and cleavage of an inner naphthenic structure (350-500°C).</p><p>AC electrical conductivity measurements (up to 350°C) on the Group l metal and</p><p>ammonium perchlorates [34] showed that identical charge conduction mechanisms</p><p>attributed to movement of interstitial cations were present in all these salts.</p><p>Changes in the dielectric constant of a material with temperature can arise from changes</p><p>in molecular orientation brought about by phase transitions or chemical reactions. A curve</p><p>of dielectric constant against temperature for has the same form as the</p><p>TG curve (see Chapter 3). The curve for (120-200°C) shows a peak at about</p><p>165°C, of a form similar to that observed in the DTA curve, for the order-disorder crystal</p><p>transition. This peak is attributed to Debye relaxation behaviour as N atoms diffuse along</p><p>the b-axis in the crystal. Comparing the two curves, it was proposed that removal of</p><p>from the copper sulphate crystals is a very fast diffusion process, so no dielectric</p><p>relaxation is observed. Thus significant additional information is provided by the</p><p>dielectric measurements. Extension of the above studies [35] to include another known</p><p>order-disorder ferroelectric crystal, showed that there was an</p><p>endothermic DTA peak at 105°C with accompanying mass loss showing removal of</p><p>Curves of dielectric constant against temperature show that prior to the dehydration, the</p><p>molecules are involved in diffusion, similar to the order-disorder transition in</p><p>but escape of the leads to an ordered anhydrous compound.</p><p>The power of DETA in separating multiple transitions is illustrated for</p><p>polymethylmethacrylate (PMMA) [36] in Figure 9.18. A series of curves of loss factor</p><p>against temperature at different frequencies shows that the transition (which involves</p><p>motion in long segments of the main polymer chain) and the transition (which involves</p><p>rotation of short-chain ester side groups) become more clearly separated as the test</p><p>frequency is decreased.</p><p>177</p><p>9.5 Miscellaneous Techniques</p><p>Mandelis [37] has reviewed photothermal applications in the thermal analysis of solids.</p><p>Thermal waves may be optically induced in solid samples by modulated irradiation. The</p><p>thermal waves then interact with the sample before being detected by suitable sensors.</p><p>Acoustic waves may be simultaneously induced and then detected. Details of the theory</p><p>and experimental techniques are given in the review [37]. Applications include accurate</p><p>measurement of thermal transport properties such as thermal conductivity, difffusivity and</p><p>effusivity and, indirectly, specific heat capacity. Use of these techniques can add</p><p>significantly to the information obtainable from other thermal analysis techniques,</p><p>particularly in determining the mechanisms of phase transitions.</p><p>A recent paper by Parkes and co-workers [38] describes a new technique of microwave</p><p>thermal analysis (their suggested abbreviation is MWTA). The advantages of such a</p><p>technique are that the microwave radiation heats by direct molecular interaction rather than</p><p>conduction or convection as in conventional heating and so temperature gradients in the</p><p>sample are decreased. The uniformity of heating can improve the resolution of thermal</p><p>events. MWTA depends upon changes in the dielectric properties of the sample and the</p><p>information obtained is complementary to other techniques.</p><p>Epple and Cammenga [39] have illustrated the use of temperature�resolved X�ray</p><p>diffractometry in thermal analysis. The structural information provided is not accessible</p><p>through thermoanalytical techniques and is essential in the formulation of mechanisms for</p><p>solid state reactions. Speyer [40] gives a useful case study of the complementary use of</p><p>X�ray diffractometry in examining fusion in glass preparation.</p><p>178</p><p>References</p><p>V. Balek and M.E. Brown in “Handbook of Thermal Analysis and Calorimetry”,</p><p>Vol.1 (Ed. M.E. Brown), Elsevier, Amsterdam, 1998, Ch. 9.</p><p>V. Balek, Thermochim. Acta, 22 (1978)1; 7th ICTA, Vol.1,</p><p>Wiley, New York, 1982, p.371; Thermochim. Acta, 110 (1987) 222.</p><p>V. Balek and J. 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E.A.</p><p>Turi), Academic, San Diego, 2nd Edn, 1997, pp. 168�177.</p><p>W.W. Wendlandt, “Thermal Analysis”, Wiley, New York, 3rd Edn, 1986,</p><p>pp.734�739.</p><p>K. Lonvik and co�workers, 4th ICTA (1975) Vol.3, p1089; 6th ICTA (1980)</p><p>Vol.2, p313; 7th ICTA (1982) Vol.1, p306; J. Therm. Anal., 25 (1982) 109;</p><p>Thermochim. Acta, 72 (1984)159,205; 110 (1987) 253; 214 (1993) 51.</p><p>S. Shimada, Thermochim. Acta, 163(1990)313; 196 (1992) 237;</p><p>200 (1992) 317; 255(1995)341; J. Thermal Anal, 40 (1993) 1063.</p><p>S. Shimada and R. Furuichi, Bull. Chem. Soc. Jpn, 63 (1990) 2526;</p><p>Thermochim. Acta, 163 (1990) 313.</p><p>G.M. Clark, 2nd ESTA (1981) p85; Thermochim. Acta, 27 (1978) 19.</p><p>S. Shimada, Y. Katsuda and R. Furuichi, Thermochim. Acta, 183 (1991) 365;</p><p>184(1991)91.</p><p>1.</p><p>2.</p><p>3.</p><p>4.</p><p>5.</p><p>6.</p><p>7.</p><p>8.</p><p>9.</p><p>10.</p><p>11.</p><p>12.</p><p>13.</p><p>14.</p><p>15.</p><p>16.</p><p>17.</p><p>18.</p><p>19.</p><p>179</p><p>S. Shimada, Y. Katsuda and M. Inagaki, J. Phys. Chem., 97 (1993) 8803.</p><p>O. Lee, Y. Koga and A.P. Wade, Talanta, 37 (1990) 861.</p><p>A.P. Wade, K.A. Soulsbury, P.Y.T. Chow and I.H. Brock, Anal. Chim. Acta,</p><p>246(1991)23.</p><p>P.D. Wentzell and A.P. Wade, Anal. Chem., 61 (1989) 2638.</p><p>P.O. Wentzell, O. Lee and A.P. Wade, J. Chemomet., 5 (1991) 389.</p><p>I.H. Brock, O. Lee, K.A. Soulsbury, P.D. Wentzell, D.B. Sibbald and A.P.</p><p>Wade, Chemomet. Intell. Lab. Syst, 12 (1992) 271.</p><p>T. Mraz, K. Rajeshwar and J. Dubow, Thermochim. Acta 38 (1980) 211.</p><p>S.O. Kasap and V. Mirchandan, Meas. Sci. Technol., 4 (1993) 1213.</p><p>M. Ravi Kumar, R.R. Reddy, T.V.R. Rao and B.K. Sharma, J. Appl. Polym.</p><p>Sci., 51(1994)1805.</p><p>P.K. Chatterjee, 4th ICTA, (Ed. I Buzas), Heyden, London, 1974, Vol. 3, p835.</p><p>W.W. Wendlandt, “Thermal Analysis”, Wiley, New York, 3rd Edn, 1986, pp.697-</p><p>733; Thermochim. Acta, 73 (1984) 89.</p><p>P.K. Gallagher, “Thermal Characterization</p><p>of Polymeric Materials”, (Ed. E.A.</p><p>Turi), Academic Press, San Diego, 2nd Edn, 1997, Ch.1.</p><p>S.A. Bidstrup Allen in “Handbook of Thermal Analysis and Calorimetry”, Vol.1</p><p>(Ed. M.E. Brown), Elsevier, Amsterdam, 1998, Ch. 7.</p><p>A.K. Sircar, T.G. Lombard and J.L. Wells, Thermochim. Acta, 37 (1980) 315.</p><p>K. Rajeshwar and co-workers, Thermochim. Acta, 33 (1979) 157;</p><p>26 (1978) 1; Anal. Chem., 51 (1979) 1149; Nature (London),</p><p>287 (1980) 131; J. Chem. Phys., 72 (1980) 6678; J. Phys. Chem.</p><p>Solids, 41 (1980)271; Phys. Status Solidi, 58 (1980)245.</p><p>A. Bristoti, I.R. Bonilla and P.R. Andrade, J. Thermal Anal., 9 (1976)</p><p>93; 8 (1975) 387.</p><p>TA Instruments Brochure TA-057B: The DEA 2970 Dielectric Analyzer.</p><p>A. Mandelis, J. Thermal Anal, 37 (1991) 1065.</p><p>G.M.B. Parkes, P.A. Barnes, G. Bond and E.L. Charsley, Thermochim. Acta,</p><p>356 (2000) 85.</p><p>M. Epple and H.K. Cammenga, J. Thermal Anal., 38 (1992) 619.</p><p>R.F. Speyer, “Thermal Analysis of Materials”, Marcel Dekker, New York, 1994,</p><p>Ch.5.</p><p>20.</p><p>21.</p><p>22.</p><p>23.</p><p>24.</p><p>25.</p><p>26.</p><p>27.</p><p>28.</p><p>29.</p><p>30.</p><p>31.</p><p>32.</p><p>33.</p><p>34.</p><p>35.</p><p>36.</p><p>37.</p><p>38.</p><p>39.</p><p>40.</p><p>REACTION KINETICS FROM THERMAL ANALYSIS</p><p>The main reasons for measuring rates of reactions are: (i) to obtain information about the</p><p>reaction mechanism, which may prove useful in modifying the course of that reaction or</p><p>in predicting the behaviour of similar, as yet untested, reactions; and/or (ii) to determine</p><p>values of the kinetic parameters (see below) for the reaction of interest, which may allow</p><p>rates of reaction under conditions of reaction different from those for which the</p><p>measurements were made, to be calculated by interpolation or (with less certainty)</p><p>extrapolation.</p><p>These two aims are seldom unrelated, because the reaction mechanism, which is used</p><p>here in the sense of the detailed chemical steps involved, can usually only be inferred from</p><p>the overall picture constructed from the results of the mathematical side of kinetic analysis</p><p>(the kinetic model) and as much complementary evidence (e.g., spectroscopy, chemical</p><p>and structural analysis, etc.) as possible.</p><p>The rate of a general homogeneous reaction of the form:</p><p>10.1 Introduction</p><p>is conventionally measured by following the decrease in concentration of reactant A or the</p><p>increase in concentration of either product B or C at constant temperature. A rate equation</p><p>of the form:</p><p>Rate = k f(concentrations of reactants & products) (T constant)</p><p>is then determined from experiment. The rate coefficient, k, is a function of temperature,</p><p>usually assumed to be given by the Arrhenius equation [1]:</p><p>where T is the temperature in kelvin, and the Arrhenius parameters, E the activation</p><p>energy and A the pre-exponential or frequency factor, can be determined by carrying out</p><p>a series of experiments over a range of different but constant temperatures. An Arrhenius</p><p>plot is a plot of ln k (or log k) against 1/T.</p><p>In thermal analysis experiments, the reactions studied are almost invariably</p><p>heterogeneous reactions involving at least one initially solid reactant [2,3] and the reaction</p><p>temperature is usually being continuously increased or decreased according to some set</p><p>181</p><p>(usually linear) programme. The rate equations which are likely to apply in heterogenous</p><p>reactions are considerably different from those familiar in homogeneous kinetics (see</p><p>below) and programmed temperature experiments require a different approach to kinetic</p><p>analysis, often referred to in general as nonisothermal kinetics (NIK). The principles</p><p>developed for NIK analysis have been applied to homogeneous kinetics, but because of</p><p>the influence of thermal analysis techniques and their main use in the study of initially</p><p>solid samples, the emphasis has been on heterogeneous systems.</p><p>Vyazovkin [4] has given an excellent review, from an historical perspective, of the extent</p><p>to which the concepts of homogeneous kinetics have influenced the language and practice</p><p>of heterogeneous kinetics. One of the most limiting concepts has been that of a single-step</p><p>reaction. Real solid-state reactions occur in multiple steps that will usually have different</p><p>kinetic parameters, e.g. formation and growth of nuclei. As a result of this</p><p>oversimplification, the kinetic models currently in use for solid-state reactions (and</p><p>described in detail below) are in many ways similar to the “ideal gas law” that has long</p><p>been used for describing the behaviour of real gases with varying degrees of success.</p><p>Better descriptions are needed, but the quality of the data being analysed has got to</p><p>warrant the effort.</p><p>Another limiting concept [4] has been the assumption that the Arrhenius parameters, E</p><p>and A, are constants and do not depend upon the extent of reaction . The methods of</p><p>kinetic analysis developed by Vyazovkin and others, described below, have enabled this</p><p>assumption to be checked and it is shown not to hold in many solid-state reactions.</p><p>Much effort has been directed at obtaining kinetic information from the results of</p><p>thermal analysis experiments [5]. A brief history of the development of nonisothermal</p><p>kinetic analysis has been given [6] and contributions to the field continue to appear in the</p><p>current literature. In this introductory account only the main approaches will be outlined.</p><p>More detail can be found in various reviews [5, 7-9]. Most methods of analysis are</p><p>referred to by the names of their proposers and it becomes an impossible feat of memory</p><p>to associate them with their mathematical principles.</p><p>Garn [10] expressed some initial reservations concerning the nonisothermal approach.</p><p>These included problems of measurement of sample temperature when allowance has to</p><p>be made for heat transfer from the furnace to the outer regions of the sample and then into</p><p>the sample; the self-cooling or self-heating of the sample during reaction, and the removal</p><p>of evolved product gases from the vicinity of the sample and the influence of these</p><p>products on the rate of reaction when the reaction has a high degree of reversibility. Many</p><p>of these reservations, however, are applicable to solid state kinetics in general.</p><p>182</p><p>10.2 Heterogeneous reactions</p><p>When a solid sample is heated, one of the many possible changes which it may undergo,</p><p>is decomposition (see Table 2.1). Information on the kinetics and mechanisms of solid</p><p>decompositions is of both practical and theoretical importance [3,4]. For a heterogeneous</p><p>reaction of the type:</p><p>183</p><p>the concept of reactant (or product) concentration does not play the significant role that</p><p>it does in homogeneous reactions and the progress of reaction has to be measured in some</p><p>other way. Usually the fractional reaction, is, defined in terms of the change in mass</p><p>of the sample where m is the mass at that stage, is the initial mass</p><p>and the mass of the sample when reaction is complete), or equivalent definitions in</p><p>terms of amounts of gas evolved or heat absorbed or evolved.</p><p>has to be carefully defined in relation to the reaction stoichiometry. Serious problems</p><p>of definition may arise if the composition of the products varies with the extent of</p><p>reaction, or if the gaseous products of a reversible reaction are not being effectively and</p><p>completely removed from the neighbourhood of the sample, or if the reactant melts or</p><p>sublimes.</p><p>Several other factors, which have no analogy in homogeneous reactions, have to be taken</p><p>into account when solids are involved as reactants and/or products. These include</p><p>possible variations in properties with direction (anisotropy) in the crystal structure of a</p><p>single pure solid, as well as the presence of numerous impurities and structural defects,</p><p>such as surfaces, edges, dislocations and point defects, in any real solid sample. Although</p><p>such features form only a small proportion of the mass of a solid, they have marked effects</p><p>on many of the physical properties and, especially, thermal stability [11].</p><p>Numerous observations confirm that decomposition of solid reactants generally is</p><p>initiated at defective regions of the crystal such as the surface or, more specifically, points</p><p>of emergence of dislocations at the surface.</p><p>Nuclei of solid product, B, are thus formed,</p><p>the gaseous product escapes (sometimes with difficulty) and the resulting disruption</p><p>causes strain in the neighbouring regions of unreacted A, resulting in growth of the nuclei</p><p>(see Figure 10.1). The shape of these nuclei will be governed by the crystal structure, in</p><p>that decomposition in some directions will occur more readily than in others. The detailed</p><p>geometry of the processes of nucleation and growth [12,13] leads to specific predictions</p><p>of the rate at which the product gas is evolved. In addition to considering the geometry</p><p>of the reactant/product interface, account has to be taken of the chemical reactions taking</p><p>place at or near the interface and physical processes such as diffusion and heat transfer.</p><p>10.3 Formulation of the problem</p><p>10.3.1 Introduction</p><p>A kinetic study thus involves measurement of either as a function of time, t, at constant</p><p>temperature, or as a function of temperature, T, which is increased according to some</p><p>heating programme (usually linear), The isothermal method, against t,</p><p>corresponds to the conventional curve of concentration against t familiar from</p><p>homogeneous kinetics, while the dynamic method, i.e. measurement of against T, is the</p><p>basis of thermal analysis, see Figures 10.2 and 10.3.</p><p>184</p><p>10.3.2 Conversion functions and reaction models</p><p>Kinetic analysis of both isothermal and dynamic results involves attempting to relate the</p><p>experimentally observed t or T values with values predicted for a limited set of</p><p>models [3,4] based on processes of nucleation and growth (see Figure 10.1), diffusion or</p><p>some simpler geometrical forms of progress of the reactant/product interface.</p><p>In the literature, there is considerable ambiguity in the use of the term reaction</p><p>mechanism. Sometimes it has the meaning, common to homogeneous kinetics, of</p><p>describing the chemical steps by which reactants are converted to products. Often,</p><p>however, the term is used to describe the rate equation and, by implication, the geometrical</p><p>or other model on which the rate equation is based. In homogeneous kinetics, one would</p><p>not imply that the fact that the experimental data could be described by, for example, a</p><p>second-order rate equation revealed much about the mechanism other than the possibility</p><p>of control by a bimolecular reaction step. The chemical nature of such a step would be</p><p>referred to as the reaction mechanism. In solid state reactions, information on the</p><p>chemical steps involved can be very difficult to obtain and many kinetic studies do not</p><p>proceed beyond identification of the most appropriate rate equation (or kinetic model)</p><p>from a rather limited selection.</p><p>The expressions derived from these models can all be written in their integral forms (at</p><p>constant T):</p><p>The reproducibility of the sets of t or T data under fixed conditions of isothermal</p><p>temperature, or at a constant heating-rate, needs to be examined, including any influence</p><p>of the sample mass on the data. Some experimental techniques may produce relatively</p><p>noisy t or T traces and some smoothing of the data may be advisable. The extent of</p><p>mathematical smoothing can always be monitored, while the smooth experimental traces</p><p>from other measurement techniques may contain an unknown amount and type of</p><p>instrumental damping.</p><p>Krís and Sesták [14] have pointed out that both and T may vary with position in the</p><p>sample and that heat and mass transport effects are seldom taken into consideration, even</p><p>in DTA where the real temperature deviation from the programmed temperature is</p><p>recorded [15].</p><p>185</p><p>or differential forms:</p><p>where and are known as conversion functions (see Table 10.1 and Figures 10.2,</p><p>and 10.3).</p><p>What constitutes the most acceptable description of the experimental t or T data is</p><p>still a matter of debate. At least two main aspects need to be considered: (i) the purely</p><p>mathematical "fit" of the experimental data to the relationship between and t, and</p><p>186</p><p>187</p><p>188</p><p>189</p><p>t or and required by the functions listed in Table 10.1, together with the range</p><p>of across which this expression satisfactorily represents the data (whether the fit varies</p><p>with temperature is also important) and (ii) the evidence in support of the kinetic model</p><p>upon which the conversion function is based, obtained by complementary techniques such</p><p>as optical and electron microscopy, spectroscopy, etc.</p><p>190</p><p>191</p><p>10.3.3 The Effect of Temperature</p><p>The effect of temperature is introduced through use of the Arrhenius equation (see</p><p>above) so that:</p><p>The validity of applying the Arrhenius equation to heterogeneous reactions has been</p><p>questioned [10,16], but the parameters E and A do have practical value even if their</p><p>theoretical interpretation is difficult [17]. Laidler [1] has described alternative empirical</p><p>functions that have been proposed and concludes that they have no significant advantages.</p><p>For reversible reactions, the rate of reaction will depend on the partial pressure, p, of the</p><p>gaseous product. The rate equation should thus include allowance for this, in terms of</p><p>some function h(p)</p><p>This complication is usually ignored and this may be justifiable when working in vacuum</p><p>or with a strong flow of inert gas through the sample.</p><p>For dynamic measurements, the usual approach is to write:</p><p>where is the heating rate. The heating rate is usually maintained constant,</p><p>although other programmes have been considered [18,19]. Reading et al. [20] have</p><p>developed a technique referred to as constant rate thermal analysis (CRTA) (see Chapter</p><p>3) in which the the sample is heated in such a way that reaction takes place at constant</p><p>rate, and Ortega et al. [21] have extended this idea to control the temperature so that the</p><p>reaction proceeds at a constantly increasing rate (acceleration).</p><p>A temperature-jump or step-wise programme has also been suggested [22,23] in which,</p><p>during a single experiment, the temperature is rapidly changed ("jumped") from one value</p><p>to another and the rates at the two (or more) temperatures are measured and used to</p><p>calculate Arrhenius parameters for that particular value. This method assumes that</p><p>does not change significantly during the time taken to measure the two rate values.</p><p>Modulated temperature DSC (see Chapter 4), in which the programmed temperature</p><p>follows small regular oscillations, is a relatively new technique for distinguishing</p><p>reversible and irreversible contributions to the thermal behaviour of samples and kinetic</p><p>applications are beginning to appear.</p><p>The relationship between and is one of the areas of controversy [24-28] but</p><p>if the above procedure is accepted, and most treatments proceed on that basis, then:</p><p>192</p><p>Separating variables:</p><p>10.3.4 The Temperature Integral</p><p>Use of equation (10.2) obviously involves evaluation of the temperature integral:</p><p>The problem is simplified by introducing the variable so that:</p><p>Then equation (10.2) becomes:</p><p>Tables of values of the integral p(x) have been provided [29,30]. A lot of attention has</p><p>been directed at finding suitable approximations for the above temperature integrals</p><p>[5,6,31-33]. Gorbachev [34] has suggested that there is little value in trying to find more</p><p>accurate approximations considering the nature of the original T data. The three main</p><p>approaches to evaluation of the temperature integral [31 ] are : (i) use of numerical values</p><p>of p(x); (ii) use of series approximations for p(x), and (iii) use of approximations to</p><p>obtain an expression which can be integrated [5], for example, Doyle's approximation [35]</p><p>(for x > 20) is:</p><p>Integrating between the limits, at and at</p><p>(because</p><p>193</p><p>Flynn [36] has commented that the computer power now available has decreased the need</p><p>for approximations.</p><p>10.3.5 The "Inverse Kinetic Problem" (IKP)</p><p>The unknowns are thus A, E and the form of the conversion function, either or .</p><p>(Note that there is no standardization on this terminology and in some papers and</p><p>are used in exactly the opposite sense to that given here.) Often, following homogeneous</p><p>kinetics, is taken to be so that n,</p><p>the apparent "order of reaction", becomes</p><p>the third unknown. A more general conversion function, suggested by Sestak and</p><p>Berggren [37] is:</p><p>which increases the number ofunknowns, but allows for all the usual models of solid state</p><p>reactions. The unknowns then have to be determined from experimental measurements</p><p>which can be converted to values of and/or at temperatures T, obtained at a set</p><p>heating rate</p><p>Militký and Sesták [38] have expressed the "inverse kinetic problem" (IKP) as the</p><p>necessity to determine up to six unknown constants, b1, b2, b3, d1, d2 and d3 in the</p><p>expression</p><p>The simpler form of the Arrhenius equation, i.e. b2 = 0, is generally used because a</p><p>temperature dependent term in the pre-exponential factor [39,40] only adds a further</p><p>adjustable parameter. When d3 is zero, is the Sesták-Berggren</p><p>equation (see above), or if the Prout-Tompkins or Austin-Rickett equation</p><p>results (see Table 10.1).</p><p>It is also usually assumed that a single rate expression, or applies over a wide</p><p>range of values and that the values of the Arrhenius parameters, A</p><p>and E, are constant over at least that range. If the rate expression and/or the Arrhenius</p><p>parameters vary with i.e. the reaction mechanism changes (see below), the kinetic</p><p>analysis becomes more complicated. Budrugeac and Segal [41] have, for example, used</p><p>the assumption that E may be a function of of the form:</p><p>where and are constants, together with the assumption of a compensation</p><p>relationship (see below) between E and A. This effectively introduces four more</p><p>adjustable parameters.</p><p>Before proceeding further with the kinetic analysis of nonisothermal data, the simpler</p><p>and more conventional isothermal approach will be outlined.</p><p>194</p><p>10.4 Kinetic Analysis of Isothermal Data</p><p>The main approaches which have been used in kinetic analysis of isothermal data for</p><p>decompositions and other reactions of solids are listed below [2,3]. These are all based</p><p>on the initial assumption that a single conversion function and a single set of Arrhenius</p><p>parameters, A and E, apply over the full range of It is always necessary to watch for</p><p>any indications, such as curved Arrhenius plots, that may indicate that these assumptions</p><p>are not valid.</p><p>(i) The linearity of plots of (from Table 10.1) against time is determined,</p><p>(ii) Plots of against measured values of reduced-time are compared with similar plots</p><p>calculated for the rate equations in Table 10.1. Measured time values are corrected by</p><p>subtraction of the induction period to onset of the main reaction (also including the time</p><p>required to heat the reactant to temperature, T ). Experimental time values, can</p><p>then be scaled by the reduced-time factor, where is the time at</p><p>which and Plots of measured values of against for all</p><p>experiments including those at different isothermal temperatures, should then all fall on</p><p>a single curve. This composite curve can be compared with the calculated curve for each</p><p>conversion function from Table 10.1. Such calculated curves are expressed in the form,</p><p>and deviations for each point can be determined. Comparisons</p><p>of the magnitudes, and variations with of these differences are then used to identify the</p><p>rate equation giving the most acceptable kinetic fit to the data and its range of</p><p>applicability. Any systematic change in the shape of the curve with temperature</p><p>can be identified during preparation of the composite curve. The magnitude of is</p><p>proportional to the rate coefficient at temperature T, so that the reciprocals of the time</p><p>scaling factors can be used as quantitative measures of k to calculate the activation energy,</p><p>without the necessity for identifying the kinetic model [42]. The reference value of is</p><p>not always selected at 0.50 because this often corresponds to the region of maximum rate</p><p>and, hence, this choice introduces error into the determination of . When there is an</p><p>initial reaction, or uncertainty in the length of the induction period, it may be appropriate</p><p>to use two common points for the scaling, for example [43] at and</p><p>at Other aspects of analysis by the reduced-time method have been</p><p>discussed by Jones et al. [44].</p><p>(iii) Plots of measured values of against either or t are compared with similar</p><p>curves calculated for the rate equations in Table 10.1.</p><p>(iv) The linearity of plots of against (fromTable 10.1.) is determined. Various</p><p>standard statistical criteria, e.g. the correlation coefficient, r; the standard error of the</p><p>slope of the regression line, or the standard error of the estimate of from are</p><p>used to quantify the deviation of a set of experimental points from the calculated</p><p>regression line. The use of a single parameter to express the deviation of the data from</p><p>the least-squares line does not, however, reveal whether deviations are systematic or</p><p>approximately random. The magnitudes and directions of such deviations and their</p><p>variations with can, however, be useful [42] in identifying the most appropriate rate</p><p>equation, and plots of residuals, against time have been</p><p>recommended. Each kinetic model within similar groups may then be associated with the</p><p>alternative model with which it is most likely to be confused. Note that high values of the</p><p>195</p><p>correlation coefficient, r, are obtained on analysis using the incorrect expression, even</p><p>over the wide range When the range used in the analysis is shortened</p><p>[42] to distinguishability becomes even more difficult.</p><p>Once a satisfactory fit has been obtained for a rate equation, the value</p><p>of k and its standard error, may be determined from the slope of the plot. If the form</p><p>of the conversion function does not change with temperature, the values of k at a</p><p>series of isothermal temperatures, T, can be used in a conventional Arrhenius plot to</p><p>calculate values for E and A.</p><p>10.5 Kinetic Analysis of Nonisothermal Data</p><p>10.5.1 Introductory Comments</p><p>The changes in experimental conditions on going from isothermal to programmed</p><p>temperature measurements are neither minor nor trivial. The “warm up” period required</p><p>to reach isothermal conditions is a well-known source of kinetic distortion, but</p><p>experiments at different heating rates can result in different temperature gradients in the</p><p>samples which unless corrected for may also lead to erroneous kinetic conclusions. There</p><p>has also been extensive discussion [45,46] of the applicability under nonisothermal</p><p>conditions of the Avrami-Erofeev (or JMAEK) equation (see Table 10.1), which is based</p><p>on a model that includes contributions from the distinct processes of nucleation and of</p><p>product growth which may have very different temperature dependences.</p><p>10.5.3 The uniqueness of experimentally determined kinetic parameters</p><p>After years of debate about whether the form of or and the magnitudes of E and</p><p>A can be obtained from measurements from a single programmed temperature</p><p>experiment, Criado et al. [48] clearly showed that the same TG curve could be generated</p><p>using three different kinetic models with different Arrhenius parameters. This is</p><p>illustrated in Figure 10.4.</p><p>10.5.2 Classification of Methods</p><p>The traditional classification of methods used in the analysis ofthe nonisothermal kinetic</p><p>data has usually been to distinguish differential methods, based on use of equation (10.1),</p><p>from integral methods, based on use of equation (10.2). Vyazovkin and Lesnikovich [47]</p><p>criticized this conventional classification because it refers to the type of experimental data</p><p>used. They suggested instead a classification based on the method of calculation of the</p><p>kinetic parameters, which involves either “discrimination”, i.e. identification of the</p><p>kinetic model or or a “non-discriminatory” method. An alternative name for</p><p>non-discriminatory methods is “model-free methods”, but this tends to give the</p><p>unfortunate and incorrect impression that the kinetic model or is not necessary</p><p>for characterization of a reaction. The best description is as “isoconversional methods”</p><p>and these extremely effective and highly recommended methods are described in more</p><p>detail below.</p><p>Methods involving discrimination can be further sub-divided</p><p>into methods of “analysis”,</p><p>where a single model is sought to describe the experimental data, or methods of</p><p>“synthesis”, where several models are combined to give a better description of the data.</p><p>196</p><p>Agrawal [49] had earlier discussed some of the problems of the uniqueness of the derived</p><p>parameters. Non-unique kinetic parameters may be an explanation for some reported,</p><p>apparent compensation effects (see below).</p><p>Vyazovkin and Lesnikovich [47,50,51] emphasize that all inverse problems have</p><p>ambiguous solutions that arise from attempts to determine too many unknown constants</p><p>from limited data, or when a set of experimental data can be alternatively described by</p><p>different formal models and kinetic constants.</p><p>Málek [52] has given an excellent account of the correlation between kinetic parameters</p><p>and the kinetic models from which they are derived. As a consequence of the correlation</p><p>between E and A (the so-called “compensation effect” (see below)) a TA curve can be</p><p>described by a kinetic model and an associated apparent E value, instead of the true model</p><p>and true E value, where:</p><p>and the multiplying factor, F, is characteristic of the true kinetic model. Values of such</p><p>factors are given.</p><p>197</p><p>10.5.4 Isoconversional Methods [4,7,53-58]</p><p>In retrospect, it is interesting to note how much effort was put into attempts to extract</p><p>kinetic parameters from experiments at a single heating-rate. Since the clear</p><p>demonstrations, described above, of the non-uniqueness of such kinetic parameters, papers</p><p>based on such methods continue to appear. When data from several dynamic experiments</p><p>at different heating rates, are available (and this should become the only acceptable</p><p>norm for kinetic investigations using TA techniques, other than sets of data at a</p><p>series of different but constant temperatures, or constant-rate studies) the approach is</p><p>usually to temporarily eliminate the unknown form of the model or by comparing</p><p>measurements made at a common value of under the different heating-rate conditions.</p><p>Such methods of kinetic analysis have been classified as “isoconversional”, or “model</p><p>free”, or “non-discriminatory” (see above), and much of their development and promotion</p><p>is due to Vyazovkin and co-workers [4,7,53-58]. To avoid discarding potentially</p><p>significant information, the parameters obtained from the initial stages of the</p><p>isoconversional methods should be used with the original data to determine the conversion</p><p>function (kinetic model), which Sesták [59] regards as the major goal of kinetic studies,</p><p>although this is sometimes not done. Maciejewski [60] has clearly shown that a reaction</p><p>must be described by, at very least, a complete kinetic triplet (E, A and or</p><p>Knowledge of only one of the Arrhenius parameters, such as a value for E, is insufficient</p><p>to characterise the kinetics of a reaction. More complex reactions may require several sets</p><p>of kinetic triplets for complete characterization.</p><p>Isoconversional methods are based upon the assumption that the rate of reaction at a</p><p>constant extent of reaction, is only a function of the temperature:</p><p>where the subscript indicates the values at that extent of reaction. From integration of</p><p>equation (10.3):</p><p>A plot of ln against is the basis of the Friedman [61] method. Vyazovkin</p><p>[53] points out that, like other differential methods, measurements of instantaneous rates</p><p>are very sensitive to experimental noise, and recommends use of an integral method, based</p><p>on a more general form of integration of equation (10.2):</p><p>where T(t) is the heating programme. For linear heating programmes, use of one of the</p><p>many approximations for the temperature integral (see discussion above) leads to</p><p>relationships of the form:</p><p>198</p><p>Plots of against are the basis of the methods of Flynn and Wall [62] and</p><p>Ozawa [63]. Vyazovkin [53] has discussed the various comparisons that have been made</p><p>between Friedman’s differential method and the Flynn, Wall and Ozawa integral method.</p><p>Because of differences that may arise, Vyazovkin has suggested and tested an “advanced”</p><p>isoconversional approach where integration is carried out over small intervals of [53].</p><p>A main advantage of isoconversional methods is identified [53] as being the calculation</p><p>of consistent activation energies which are in good agreement with values from isothermal</p><p>experiments. Variations of E with extent of reaction, are usually an indication of a</p><p>complex conversion function. A disadvantage of the approach is that the value of A</p><p>cannot be determined without knowledge of the model A good guide to the</p><p>adequacy of a kinetic analysis is the ability to reconstruct a set of calculated - time or</p><p>curves for comparison with the experimental data.</p><p>In summary then, classification of methods of kinetic analysis as either differential or</p><p>integral methods is not ofgreat practical use because data can be transformed readily from</p><p>one form to the other by use of numerical methods of differentiation and integration.. The</p><p>isoconversional approach eliminates the need to identify the rate equation, or kinetic</p><p>model, during the initial stages of a kinetic analysis. The values of the Arrhenius</p><p>parameters for many reactions are relatively insensitive to the rate equation applicable,</p><p>but for a complete analysis the values of A and E obtained in this first stage may then be</p><p>used in identifying the conversion function.</p><p>Several approaches involve use of the second derivative of equation (10.1), or the</p><p>version with with respect to temperature [7,31 ] or with respect to time</p><p>[31], in spite of the problems of obtaining accurate values of second derivatives. Using</p><p>gives:</p><p>and, because this second derivative must be zero at the inflexion point of a TG curve or</p><p>the maximum of a DSC peak::</p><p>from which E may be calculated if n is known and and are measured</p><p>[64]. Combining equations (10.5) and (10.6) gives:</p><p>and, because is a constant for a given value of n, the Kissinger [65] method of</p><p>obtaining a value for E is to plot 1n against for a series of experiments at</p><p>different heating rates, The slope of such a plot is -E/R.</p><p>199</p><p>Augis and Bennett [66] have modified the Kissinger treatment for use with the Avrami</p><p>- Erofe'ev model, which applies in so many solid-state reactions. They plot</p><p>against where is the initial temperature at the start of the heating programme,</p><p>instead of against Elder [67] has generalized the Kissinger treatment</p><p>to make is applicable to the full range of kinetic models. The generalized equation is:</p><p>where m is the temperature exponent of the preexponential term in the modified Arrhenius</p><p>equation and is often taken as zero, and</p><p>This correction term was found to be relatively small, but helps in distinguishing between</p><p>similar models. The values of E obtained were not very sensitive to incorrect choice of</p><p>model.</p><p>The Ozawa treatment [63] is also applicable to derivative curves and is similar to the</p><p>Kissinger method. is plotted against and the slope of this plot is again -E/R.</p><p>Van Dooren and Muller [68] studied the effects of sample mass and particle-size on the</p><p>determination of kinetic parameters from DSC runs using the methods of Kissinger and</p><p>of Ozawa. It was found that both sample mass and particle size could influence the values</p><p>of the kinetic parameters, but the extent of these effects varied from one substance</p><p>examined to another. The two methods gave similar values for E with slightly lower</p><p>precision for the Kissinger method. It was suggested that temperatures at (half</p><p>conversion) should be used in place of</p><p>The “non-parametric kinetics (NPK)” method [69] of Serra, Nomen and Sempere is</p><p>based on the usual assumption that the reaction rate can be expressed as a product of two</p><p>independent functions, and h(T). h(T), the temperature dependence, need not be of</p><p>the Arrhenius-type. The reaction rates, measured from several experiments at</p><p>different heating-rates, are organised as an n x m matrix whose rows correspond to</p><p>different (constant) degrees of conversion, and whose columns correspond (by</p><p>interpolation) to different (constant) temperatures.</p><p>The NPK method then uses the</p><p>Singular Value Decomposition (SVD) algorithm [70] to decompose matrix A into the two</p><p>vectors a and b. These vectors can then be further analysed by examining the resulting</p><p>plots of rate against (to determine the kinetic model) and of rate/ against temperature</p><p>(to check on Arrhenius-type behaviour and to determine Arrhenius parameters when</p><p>appropriate). The NPK method uses a large number of points and a wide range of</p><p>temperatures. This is a model-free method in the sense that it allows for isolating the</p><p>temperature dependence of the reaction rate (and, therefore, the activation energy) without</p><p>making any assumptions about the reaction model.</p><p>200</p><p>10.6 The influences of various parameters on the shapes of theoretical thermal</p><p>analysis curves</p><p>With there being so many parameters in equations (10.1) or (10.2), it is useful to see what</p><p>effect varying one of these parameters at a time has on the shape of a TG or DSC curve</p><p>[5,6,31,71]. The most fundamental variable is the form of the conversion function</p><p>or (see Table 10.1). The shapes of the theoretical isothermal time curves for</p><p>various model conversion functions [2,3,5,72] are shown in Figure 10.3. It is not always</p><p>an easy task to distinguish amongst the models, even under isothermal conditions [73].</p><p>The shapes of these curves are, of course, considerably altered under nonisothermal</p><p>conditions and theoretical temperature curves [31,67] for the various models are given</p><p>in Figure 10.5. (These curves were constructed using the Doyle approximation [29] for</p><p>the temperature integral, p(x), see below.) The models based on apparent order of reaction,</p><p>n, (even if fractional) i.e. F1, F2, R2 and R3, Figure 10.5(b), are difficult to distinguish</p><p>at low values of Distinguishability improves for higher orders at higher values of</p><p>The diffusion models, D2, D3 and D4, give generally lower onset temperatures and flatter</p><p>curves (Figure 10.5(c)) than the nth-order group, while the Avrami-Erofeev models have</p><p>higher onset temperatures and steeper curves. Figure 10.6 shows the differential curves</p><p>corresponding to the integral curves given in Figure 10.5.</p><p>The next sets of comparisons are done with a fixed model and this is used to examine</p><p>the influence of the other variables, the heating rate the activation energy, E, and the</p><p>pre-exponential factor, A. Elder [67] has provided similar curves and Zsakó [71] has</p><p>shown similar influences for the first-order (F1) model. Although the F1 model is not a</p><p>very realistic representation, it is often assumed to apply as an approximation. Figure</p><p>10.7 shows the regular effect on the theoretical contracting-volume R3 curve, of doubling</p><p>the heating rate in the range Changing the pre-exponential factor by</p><p>factors of ten in the range to also affects mainly the onset</p><p>temperature and the acceleratory position of the curves, Figure 10.8, with the remaining</p><p>segments being almost parallel. Very similar behaviour is observed for curves with the</p><p>activation energy increasing in steps of in the range 90 to as</p><p>shown in Figure 10.9. The overall shape of the thermal analysis curve is thus determined</p><p>by the conversion function, or applying, while the position of this curve on the</p><p>temperature axis is determined by the values of E, A and, to a lesser extent, the heating rate</p><p>201</p><p>202</p><p>203</p><p>204</p><p>10.7 The Compensation Effect</p><p>Sometimes, for a series of closely related, but not identical reactions, the experimental</p><p>Arrhenius parameters, determined by similar procedures, have been reported to conform</p><p>to an equation of the form:</p><p>where a and b are constants. This is known as " a compensation effect"[2,3,74,75]</p><p>because the decrease in reaction rate resulting from an increase in activation energy, E, is</p><p>offset by an increase in the magnitude of ln A. This is also known as the isokinetic effect</p><p>because, for the set of (A, E) values that fit equation (10.5), there exists a temperature,</p><p>at which all rate coefficients are equal. For many reactions, the value of is at, or within,</p><p>the temperature ranges of the kinetic measurements exhibiting the compensation</p><p>behaviour. A similar effect has also been observed for a series of closely related, but not</p><p>identical, experiments on a single chemical reaction, where the differences in the</p><p>experimental conditions, including the physical state and history of the solid reactant, may</p><p>result in a relationship of the form of equation (10.5) between the apparent Arrhenius</p><p>parameters.</p><p>A huge volume of literature [75] has grown around this seemingly simple relationship.</p><p>None of the many theoretical explanations [74] suggested for compensation behaviour has</p><p>received general acceptance. There are good reasons for suspecting that many reported</p><p>instances of compensation effects may be computational artefacts [76-81].</p><p>205</p><p>10.8 Complex reactions</p><p>The behaviour of any real, initially-solid sample is going to be considerably more</p><p>complex than the idealized description given above. The success that has been achieved</p><p>using this limited set of models can only be attributed to an averaging effect over the</p><p>variety of processes occurring at the molecular level. When some of these processes have</p><p>very different kinetic characteristics, none of the models may provide an adequate</p><p>description of the experimental results.</p><p>There are several useful indicators ofthe possible occurrence of complex reactions [49].</p><p>From the experimental side, a lack of correspondence between DSC and DTG results</p><p>indicates that the rate of change of enthalpy is not directly proportional to the rate of mass</p><p>loss. Experiments at different heating rates also show up complexities.</p><p>Another important indication is the dependence of the value obtained for E upon the</p><p>extent of reaction, [81]. It is thus essential to use a method of kinetic analysis that</p><p>allows such a dependence to be detected. In isothermal studies, the occurrence ofcomplex</p><p>reactions may be detected by Arrhenius plots that are curved or give two linear regions</p><p>[81]. The shapes of plots of against reduced-time also vary systematically with</p><p>temperature.</p><p>The contributions to complex reactions are most easily separated when the activation</p><p>energies of the individual reactions are considerably different. Reactions with low E</p><p>values dominate the kinetics at low temperatures and slow heating rates, while those with</p><p>high E values dominate at high temperatures and high heating rates. At the isokinetic</p><p>temperature the rates of the participating reactions are equal.</p><p>Elder [82] has modelled several multiple reaction schemes, including mutually</p><p>independent concurrent first-order reactions, competitive first-order reactions, mutually</p><p>independent n-th order reactions, and mutually independent Avrami-Erofeev models with</p><p>n = 2 or 3.</p><p>Vyazovkin and Lesnikovich [81] have discussed the identification of the type of</p><p>complex process encountered in nonisothermal experiments by examination of the shape</p><p>of the curve of the dependence of the apparent value of E on found by isoconversional</p><p>methods. Concurrent reactions are characterized by an increasing dependence of E on</p><p>but detailed shapes are dependent on the ratios of the contributing rates. A decreasing</p><p>dependence of E on was found for intermediate reversible processes [81].</p><p>Contributions from individual reactions with similar E values are not separable by</p><p>changing the heating rate, so deconvolution has to be attempted by mathematical methods</p><p>[83]. Many such methods proposed in the literature are restricted to RO models. Criado</p><p>et al. [83] proceed on the basis of summing the individual contributions. The overall</p><p>reacted fraction is defined as:</p><p>where is the fraction ofthe total mass loss due to contributing reaction i (with Arrhenius</p><p>parameters, and A method is then presented which uses non-linear optimization</p><p>combined with a version of the Kissinger method to deconvolute up to 15 contributing</p><p>processes.</p><p>206</p><p>Ozawa and Kanari [84] have also discussed the kinetic analysis of competitive reactions</p><p>for which measurements of the extents of conversion</p><p>and rates of production of individual</p><p>products are required. Suitable data could be obtained by combining evolved gas analysis</p><p>with TG or DSC.</p><p>Vyazovkin [85] has treated the problem of a reaction complicated by diffusion as</p><p>consecutive reactions involving the formation of a surface layer followed by diffusion</p><p>through that layer.</p><p>10.9 Prediction of kinetic behaviour</p><p>An important practical aspect of kinetic studies is the prediction of kinetic behaviour</p><p>under conditions other than those used in the original experimental measurements [86],</p><p>for example, the estimation of shelf-lives of drugs under normal storage conditions, from</p><p>accelerated tests at higher temperatures. For predictions to be reasonably reliable, the</p><p>values of the kinetic parameters, E, A and the forms of the conversion functions, (or</p><p>should not vary with T. The precision of the estimates of E and A also needs to be</p><p>known [87]. Vyazovkin and Linert [87] and Maciejewski [60] have described some of</p><p>the implications of attempting to predict kinetic behaviour when the kinetic model</p><p>or has been incorrectly chosen (such as when non-unique kinetic triplets have been</p><p>determined by single heating-rate experiments), and when the reactions are complex.</p><p>Flynn [88] has reviewed the prediction of service lifetimes of polymeric materials, at</p><p>lower temperatures, from decomposition parameters obtained at relatively high</p><p>temperatures. Reasons for the failure of predictions are discussed. These include</p><p>extrapolation beyond temperatures at which phase changes (and accompanying changes</p><p>of physical properties) occur.</p><p>10.10 Kinetics Standards</p><p>Attempts to find a reaction which could serve as a standard for comparison of kinetic</p><p>measurements have not been successful. The major requirements for such a reaction have</p><p>been specified by Gallagher [89] as: (i) an irreversible reaction taking place in a single</p><p>stage, with (ii) a low value of the enthalpy of reaction, to minimize self-heating or self-</p><p>cooling effects; (iii) the temperature range required for reaction to proceed at a slow, but</p><p>measurable rate should not be too low, so as to avoid large temperature calibration errors;</p><p>(iv) there should be no reaction of the sample with the surrounding atmosphere; (v) no</p><p>dependence of reaction on the method of sample preparation, pretreatment or particle size</p><p>and distribution; and (vi) the changes to be measured to follow the course of reaction, e.g.,</p><p>mass, amounts of evolved gases, enthalpy change, should be large, to permit the use of</p><p>207</p><p>small samples. Some of these requirements are not compatible with each other, so</p><p>compromises are necessary.</p><p>The dehydration of lithium sulfate monohydrate as a kinetic standard was suggested,</p><p>but ruled out [89], because: (i) the reaction is reversible at low temperatures, and (ii) is</p><p>moderately endothermic; (iii) the reaction takes place at temperatures below 3 70 K and TG</p><p>instruments are difficult to calibrate accurately in this range; (iv) rates of the reaction are</p><p>very dependent upon particle-size and prehistory; (v) overall dehydration involves several</p><p>rate processes, e.g., chemical reaction, diffusion, recrystallization, and the rate-</p><p>determining step may not remain the same during the course of experiments; and (vi) the</p><p>overall rate of dehydration is influenced by the presence of water vapour in the</p><p>surrounding atmosphere.</p><p>Sbirrazzuoli et al. [90] have proposed and discussed an electronic means of simulating</p><p>DSC signals according to set kinetic laws for comparison with experimental results.</p><p>10.11 Kinetic Test Data</p><p>It is also useful to be able to test different methods of kinetic analysis on a “reference”</p><p>data set. Isothermal and nonisothermal data sets have been provided [91]and the kinetic</p><p>analysis of these data sets by a variety of volunteer participants, using computational</p><p>methods of their choice, has been discussed in considerable detail [92]. Some of the sets</p><p>are actual experimental results for the thermal decompositions of ammonium perchlorate</p><p>and calcium carbonate. The data sets 7 and 8 (illustrated in Figures 10.10 and 10.11,</p><p>respectively) were simulated using a system of two equally-weighted, parallel, first-order</p><p>reactions:</p><p>The Arrhenius parameters of the individual steps were taken to be.</p><p>The kinetic results produced from data sets 1 -4 are discussed by Maciejewski [60] and</p><p>for data sets 5-8 by Vyazovkin [93]. There is ample computational machinery available</p><p>for testing the “goodness-of-fit” of experimental data to the limited set of kinetic</p><p>equations. Provided that the methods of kinetic analysis are computationally sound, they</p><p>should be seen as complementary. Confidence in the resulting parameters is vastly</p><p>increased if similar values are obtained using different approaches It is a considerable</p><p>advantage to remove the influence of the kinetic model from the kinetic analysis while</p><p>estimating the Arrhenius parameters, but a full kinetic analysis should consider the</p><p>problems of identification of the function or functions (however complex these may turn</p><p>out to be) which determine the extent of reactant conversion. The introduction of</p><p>additional kinetic parameters to improve the goodness of fit can only be justified if they</p><p>can be given some physical significance.</p><p>208</p><p>The emphasis on computational aspects of kinetic analysis has not been matched by</p><p>effort put into better planning of experiments and the difficulties of interpretation of</p><p>results.</p><p>209</p><p>10.12 Publication of Kinetic Results</p><p>The final and very important stage of any research project is the reporting of kinetic results</p><p>in written form [5]. Some of the essential information that should be provided in such</p><p>reports includes: (1) the reasons for undertaking the research; (2) a review of the relevant</p><p>literature, especially work by other authors; (3) complete description of the materials used</p><p>(supplier, method of preparation or manufacture, structural information and particle sizes</p><p>and distributions, analytical results including purity and the nature and concentrations of</p><p>any impurities, reactant pretreatment); (4) full details of the equipment and methods used</p><p>and their calibration (calibration materials and procedures, heating rates, base-line</p><p>corrections; dimensions, geometry and material of the reactant container; pressures, flow</p><p>rates and purities of all gases). (5) The stoichiometry of the reaction(s) to which the</p><p>kinetic measurements refer and, hence, the basis of definition of the extent of reaction,</p><p>need to be specified (analysis of the residual solid product may be necessary). (6) The</p><p>reproducibility of the data measured for kinetic analysis should be specified. (7) The</p><p>methods used for determining the kinetic parameters by fitting the data to kinetic</p><p>expressions should be recorded, including the criteria for acceptability of fit, and the range</p><p>of fit of the equations considered. Some of the commercially available programs for</p><p>kinetic analysis do not even specify the algorithms on which they are based, while other</p><p>packages use kinetic expressions restricted to the reaction order (RO) type. (8)</p><p>Characterization of a reaction by a complete and unique kinetic triplet is essential. Such</p><p>a triplet cannot be estimated from experiments done at a single heating-rate, so the many</p><p>published methods based on this unacceptable approach should be abandoned in favour</p><p>of isoconversional methods on data obtained at different heating rates. (It is interesting</p><p>that no one would contemplate complete kinetic analysis of a single isothermal</p><p>experiment.) (9) Values of the Arrhenius parameters, E and A, reported should also</p><p>include their standard errors. The number of significant figures used to report numerical</p><p>values (± errors) must be realistic. (10) Results obtained should be discussed critically and</p><p>interpreted in the context of all relevant work, including citation of related studies by other</p><p>workers. Advances should be explained and discussed realistically and directions for</p><p>possible future advances should be indicated.</p><p>10.13 Conclusions</p><p>Two reasons given [5] for possible failure of a method of kinetic analysis are: (i) the</p><p>approximations used may not be valid, and (ii) the model used in deriving the mathematics</p><p>may not take into account physically real factors of the experiment such as the heat</p><p>transfer and atmosphere control problems.</p><p>Arguments about the relative value of non-isothermal and isothermal methods of kinetic</p><p>analysis are generally unproductive. The complementary use of the two approaches can</p><p>provide valuable insights into the processes occurring, provided that the experimenter is</p><p>critically aware of the shortcomings and limitations of each approach. Vyazovkin and</p><p>Lesnikovich [47] point out that the kinetic parameters calculated from isothermal data are</p><p>210</p><p>not very dependent upon the kinetic model chosen, while the opposite is true for non-</p><p>isothermal methods. Thus, ideally, one could determine the Arrhenius parameters from</p><p>isothermal measurements and the kinetic model from nonisothermal measurements.</p><p>The use of derivative methods avoids the need for approximations to the temperature</p><p>integral (discussed above). Measurements are also not subject to cumulative errors and</p><p>the often poorly-defined boundary conditions for integration do not appear in the</p><p>calculation [62]. Numerical differentiation of integral measurements normally produces</p><p>data which require smoothing before further analysis. Derivative methods may be more</p><p>sensitive in determining the kinetic model [94], but the smoothing required may lead to</p><p>distortion [95].</p><p>The reported lack of agreement amongst kinetic parameters calculated from the same set</p><p>of experimental data using different methods of mathematical analysis [5,93,96] is</p><p>disturbing. The set of models from which the ‘best model’ is to be chosen has been</p><p>criticized [47] as being is too limited. Even if the set does not contain the true model, one</p><p>of the set is probably going to appear to be the ‘best model’ for lack of alternatives.</p><p>Modification of the models in attempts to account for all the features of real processes,</p><p>however, generally results in an increased number of adjustable parameters, for which</p><p>physical interpretations are difficult to find. Vyazovkin and Lesnikovich [97] have</p><p>suggested that different aspects of the real process may be best described by a synthesis</p><p>of individual features of ideal models from the existing set.</p><p>Vyazovkin and Lesnikovich [47] have warned against the practice of forcing the model</p><p>to be of the reaction order (RO) type where the value of n may not possess physical</p><p>significance. They have also shown [50] that the Avrami - Erofeev model is equivalent</p><p>to linear combinations of some of the other formal models and hence may serve as a</p><p>generalized description. Coincidence of the parameters calculated by alternative methods</p><p>confirms only the equivalence of the methods of calculation and not the validity of the</p><p>parameters obtained.</p><p>The use of non-linear regression methods [98-105], where minimum deviation between</p><p>experimental and theoretical data is sought, is preferable to methods that involve</p><p>linearization of the appropriate rate equation [47], usually through a logarithmic</p><p>transformation which distorts the Gaussian distribution of errors.</p><p>As a final word, it is essential that a complete kinetic triplet be determined to characterize</p><p>a reaction. Such a complete and unique set cannot be determined from experiments done</p><p>at a single heating rate.</p><p>211</p><p>References</p><p>1.</p><p>2.</p><p>3.</p><p>K.J. Laidler, J. Chem. Educ., 49 (1972) 343; 61 (1984) 494.</p><p>M.E. Brown, D. Dollimore and A.K. 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Acta, 337 (1999) 1 1 1 .</p><p>PURITY DETERMINATION USING DSC</p><p>11.1 Introduction</p><p>Measurements of the depression of the melting point [1] of a sample are often used to</p><p>determine its purity [2]. Melting endotherms, recorded using differential scanning</p><p>calorimetry (DSC), are routinely used to recognize the occurrence of melting and to</p><p>measure the melting temperature of the sample. With a bit more effort, as discussed</p><p>below, it is possible to determine the purity ofthe sample by analyzing, in detail, the shape</p><p>of the melting endotherm. There is no need to have a high-purity sample of the substance</p><p>under investigation for comparison, although a sample of any very pure material, such as</p><p>indium metal, is needed to determine the thermal performance of the particular instrument</p><p>being used. Because such materials are used, in any case, to calibrate the instrument for</p><p>temperature and enthalpy measurements, this last requirement is readily achievable.</p><p>Calculations are based on the assumptions that solid solutions are not formed and that the</p><p>melt is an ideal solution. Melting must not be accompanied by decomposition or</p><p>sublimation. The assumptions made apply only to relatively pure (>98%) materials.</p><p>The practical aim ofpurity determinations is usually to decide whether or not the sample</p><p>meets certain specifications, determined by the intended further uses of the sample.</p><p>Special Technical Publication 838 of the ASTM [3] is an important source of information</p><p>on purity determination. In it, a review by Brennan and co-workers [4] outlines the history</p><p>of the DSC method and emphasizes A.P. Gray's pioneering work in this area.</p><p>The melting endotherm for a pure substance recorded on a DSC is illustrated in Figure</p><p>11.1. is the melting point of the sample and the area ABC is proportional to the</p><p>enthalpy of fusion, of the sample. The presence of an impurity in the sample (the</p><p>solvent) generally lowers the melting point of the solvent and also broadens the melting</p><p>range, giving a broader DSC endotherm as illustrated in Figure 11.2 (inset). From</p><p>endotherms such as illustrated in Figures 11.1 and 11.2, melting points and enthalpies of</p><p>fusion may readily be determined. In suitable cases, as mentioned above, an estimate of</p><p>the purity of a compound can be obtained, from analysis of the detailed shape of its</p><p>melting endotherm, e.g., Figure 11.2, without reference to compounds containing known</p><p>amounts of impurities.</p><p>215</p><p>216</p><p>217</p><p>11.2 Phase equilibria</p><p>The simplest system to consider is that in which the impurity forms an ideal solution in the</p><p>melt, i.e. a eutectic system. If the impurity is labelled, in the customary way, as</p><p>component 2 and the solvent as component 1, then for equilibrium (at constant pressure)</p><p>between pure 1 in the solid and 1 in the solution (or "melt") at activity there must be</p><p>equality of the chemical potentials of 1 in the two phases:</p><p>(where the superscript ° refers to standard conditions, i.e. unit activities). Differentiating</p><p>equation (11.1) with respect to temperature, T:</p><p>and because (where the bar represents a molar quantity)</p><p>so equation (11.2) on rearranging, becomes:</p><p>because and Integrating equation (13.3) between the limits</p><p>at (because solid solutions are not formed) and at T= T, assuming that</p><p>is independent of temperature over the range:</p><p>or</p><p>From equation (11.1)</p><p>218</p><p>For an ideal solution (the mole fraction of 1). Hence</p><p>For a dilute solution, i.e. small values of</p><p>Equation (11.4) forms the basis of melting-point depression calculations, as follows. At</p><p>the melting point of the impure sample:</p><p>If is small, and Also where m is the</p><p>molality of the solute and the molar mass of the solvent. Hence:</p><p>where is termed the cryoscopic constant.</p><p>Only when the sample is completely melted, i.e. at is the mole fraction of</p><p>impurity in the liquid, the same as that in the original sample, From the phase</p><p>diagram for a simple eutectic system (Figure 11.3) it may be seen that the value is the</p><p>minimum value which attains. At (see Figure 11.3), when the fraction of sample</p><p>that has melted, F, is less than unity, the composition of the melt is closer to that of the</p><p>eutectic, i.e., When melting commences, the first liquid has the eutectic</p><p>composition.</p><p>If F is the fraction melted at temperature T, then, assuming a linear initial segment of the</p><p>liquidus curve (Figure 11.3), and using equation (11.4):</p><p>Rearrangement yields:</p><p>If F can be determined at various temperatures, T, a plot of T against l/F should yield a</p><p>are known, can be determined from the measured slope</p><p>of the line. The DSC</p><p>curve is capable of providing values of F at temperatures T for use in such a plot.</p><p>straight line, provided that is independent of temperature. If the values of and</p><p>11.3 The DSC melting curve</p><p>The DSC measures the thermal energy per unit time, dH/dt, transferred to or from the</p><p>sample as the temperature of the sample holder, T, is changed at a constant rate,</p><p>Thus the output from the DSC is directly proportional to the heat capacity of the</p><p>system, dH/dT.</p><p>For an absolutely pure compound with zero melting range, dH/dt would become infinite</p><p>at the melting point, For an impure compound, dH/dT is finite and is a function of T.</p><p>When the fraction melted, F, is zero, the heat capacity of the sample is that of the solid</p><p>mixture, and when F = 1 the heat capacity of the sample is that of the ideal solution.</p><p>Intermediate behaviour is obtained as follows:</p><p>dF/dT is obtained from equation (11.6) as:</p><p>219</p><p>220</p><p>It is also assumed that, because of the restriction to consideration of ideal eutectic systems</p><p>and to the formation of ideal solutions on melting, that:</p><p>and therefore:</p><p>Combining these results:</p><p>Equation (11.9) then gives the variation of the heat capacity ofthe sample during melting</p><p>as a function of T. The upper limit of the melting process is (when F = 1).</p><p>Therefore, equation (11.7) becomes:</p><p>The lower limit of the melting process is when i.e. the heat</p><p>capacity of the sample is approximately constant. In the idealized DSC curves given in</p><p>Figs. 11.1 and 11.2, it has been assumed that the heat capacity of the liquid just above the</p><p>melting temperature is the same as that of the solid at lower temperatures (i.e., both equal</p><p>to</p><p>Equation (11.9) can be written as:</p><p>so that, within the limits of the assumptions made above, the heat capacity during melting</p><p>depends only on the mole fraction of impurity, and the temperature relative to the</p><p>melting point of the pure substance,</p><p>Because dH/dt is proportional to dH/dT, plots of dH/dT against T represent the initial</p><p>part of an idealized DSC melting curve. Such curves for phenacetin and for benzamide,</p><p>with values of from 0.0050 to 0.3000, have been given by Marti et al. [5,6].</p><p>The real DSC melting curve, because of factors such as thermal lag, which is discussed</p><p>in more detail below will look more like the curve in Figure 11.2, inset. The total area</p><p>under the curve, i.e. area ABC, is proportional to the enthalpy of fusion, . The actual</p><p>value of can be obtained by calibration of the instrument with a standard of known</p><p>(Figure 11.1). The feature sought for the present discussion, the fraction of the</p><p>sample melted, F, at temperature T, is obtained directly from the fractional area under the</p><p>curve, i.e. F = area ADE/area ABC. The range of F values used in practice is usually</p><p>restricted to 0.1</p><p>2.3 Reactions of Solids</p><p>When a single pure solid substance, A, is heated in an inert atmosphere, the resultant increase</p><p>in molecular, atomic or ionic motion may lead to changes in crystal structure, sintering, melting</p><p>or sublimation [1,2]. Some substances may decompose forming new molecular fragments,</p><p>some or all of which may be volatile at the temperatures reached.</p><p>In a perfect solid at zero kelvin the constituent units, whether they be atoms, molecules or ions,</p><p>form a completely and perfectly ordered three-dimensional array. This structural arrangement</p><p>is the result of the interaction of the bonding forces amongst the units (and the zero-point</p><p>energy). At higher temperatures, thermal energy results in increased vibration and rotation of</p><p>the constituents. These motions, although random, are limited in extent and each constituent</p><p>remains in the vicinity of its original site.</p><p>As a solid is heated, the amplitudes of the vibrations of the lattice constituents are increased</p><p>and eventually a temperature will be reached where one (or more) of the following changes will</p><p>occur, (i) Phase transition: a new arrangement of constituents may become more stable than</p><p>the original [3,4]. (ii) Melting: When sufficient energy becomes available, the forces of</p><p>attraction between constituents become insufficient to maintain the ordered arrangement of the</p><p>solid and the system relaxes to the more disordered arrangement of constituents in a liquid [5].</p><p>For some complex molecules the change from solid to liquid may occur in stages. The</p><p>structures of intermediate order are known as liquid crystals. (iii) Sublimation: When the</p><p>kinetic energy of the constituents increases very rapidly, direct transition to the disordered</p><p>arrangement of a gas may occur, without the intermediate formation of a liquid phase, (iv)</p><p>Thermal decomposition: When the bonding forces within constituent molecules or ions are</p><p>weaker than those between the atoms constituting these units, increasing the temperature may</p><p>result in bond redistribution and the formation of products chemically different from the</p><p>reactant. Such chemical processes are referred to as thermal decomposition (or crystolysis) [2].</p><p>These processes, some of which are reversible, are represented symbolically in Table 2.1</p><p>below. It is not unusual for melting or sublimation to occur concurrently with thermal</p><p>decomposition. During thermal decompositions that are accompanied by melting, the reaction</p><p>usually proceeds more rapidly in the liquid than in the crystalline state.</p><p>In any real crystal of A there will be imperfect regions [2,7] within which the constituents are</p><p>more reactive than in the bulk of the solid. The crystal surfaces are very important regions of</p><p>relative imperfection on account of the less symmetrical bonding in these regions. At a suitably</p><p>high temperature, decomposition can be initiated by redistribution of the bonding within</p><p>15</p><p>2.4 Decomposition of Solids</p><p>Numerous examples of such decompositions exist, e.g.</p><p>Decomposition of a single pure solid substance A may be represented [1,2] as:</p><p>imperfect regions. These initially isolated regions of product, still embedded in a matrix of</p><p>original reactant, are usually sufficiently mobile to reorganize into nuclei of product phase B.</p><p>Mechanisms of nucleation are discussed in references [1,2]. Part of the surface of the product</p><p>solid remains in contact with the crystal from which it was formed and this reactive</p><p>reactant/product interface is important in discussions of solid state decomposition mechanisms</p><p>[1,2]. Further decomposition results from either the formation of further nuclei, or through the</p><p>growth of the existing nuclei by addition of further product across the reactant/product</p><p>interface. Growth cannot continue indefinitely and nuclei eventually impinge on each other so</p><p>that growth ceases along areas of contact, or growth may cease if contact is lost between</p><p>product and the remaining reactant.</p><p>16</p><p>2.5 Reaction with the Surrounding Atmosphere</p><p>The sample may react with the surrounding atmosphere [9], e.g.</p><p>The decomposition of organic polymers in inert atmospheres to produce fragments of lower</p><p>molecular mass is called thermal degradation and is usually an endothermic process, in contrast</p><p>to the (exothermic) oxidation in air or oxygen. Very rapid exothermic reactions can lead to self-</p><p>sustaining combustion or, in the extreme, explosion.</p><p>2.6 Solid-Solid Interactions</p><p>When more than one solid substance is present initially, there are correspondingly more</p><p>possibilities for interaction on heating. New phases, such as solid solutions or eutectic</p><p>mixtures, may form, as well as new compounds formed by addition or double decomposition</p><p>reactions [10], e.g.</p><p>The above changes are nearly always accompanied by enthalpy changes, and sometimes also</p><p>by changes in mass (see Table 2.1), so they may be studied using one or more of the thermal</p><p>analysis techniques introduced in Chapter 1 and described in greater detail in the following</p><p>chapters.</p><p>M.E. Brown, D. Dollimore and A.K. Galwey, “Reactions in the Solid State”,</p><p>Comprehensive Chemical Kinetics, Vol.22, Elsevier, Amsterdam, 1980.</p><p>A.K. Galwey and M.E. Brown, “Thermal Decomposition of Ionic Solids",</p><p>Elsevier, Amsterdam, 1999.</p><p>C.N.R. Rao and K.J. Rao, “Phase Transitions in Solids”, McGraw-Hill, New</p><p>York, 1978.</p><p>J.W. Christian, “Transformations in Metals and Alloys”, Pergamon, Oxford,</p><p>1965; Vol. l, 2nd Edn, 1975.</p><p>A.R. Ubbelohde, “Melting and Crystal Structure”, Clarendon, Oxford, 1965;</p><p>“The Molten State of Matter”, Interscience, New York, 1978.</p><p>B. Wunderlich, “Thermal Analysis”, Academic, San Diego, 1990, p.95.</p><p>A.R. West, "Solid State Chemistry and its Applications", Wiley, Chichester, 1984,</p><p>Ch.12.</p><p>E.A. Turi (Ed.), “Thermal Characterization of Polymeric Materials”, 2nd Edn, Vols 1</p><p>and 2, Academic, San Diego, 1997.</p><p>J. Szekely, J.W. Evans and H.Y. Sohn, "Gas-Solid Reactions", Academic,</p><p>New York, 1976.</p><p>H. Schmalzried, "Solid State Reactions", Verlag Chemie, Weinheim, 2nd</p><p>Edn, 1981.</p><p>17</p><p>References</p><p>1.</p><p>2.</p><p>3.</p><p>4.</p><p>5.</p><p>6.</p><p>7.</p><p>8.</p><p>9.</p><p>10.</p><p>THERMOGRAVIMETRY (TG)</p><p>3.1 Introduction</p><p>Measurements of changes in sample mass with temperature (thermogravimetry, see Table 1.2)</p><p>are made using a thermobalance (sometimes referred to as a thermogravimetric analyzer).</p><p>(Note that mass is a measure of the amount of matter in a sample, whereas weight refers to the</p><p>effect of the gravitational force on a mass and thus varies from one geographical location to</p><p>another.) A thermobalance is a combination of a suitable electronic microbalance with a</p><p>furnace, a temperature programmer and computer for control, that allows the sample to be</p><p>simultaneously weighed and heated or cooled in a controlled manner, and the mass, time,</p><p>temperature data to be captured. The balance should be in a suitably enclosed system so that</p><p>the nature and pressure of the atmosphere surrounding the sample can be controlled (see Figure</p><p>3.1). Care is usually taken to ensure that the balance mechanism is maintained at, or close to,</p><p>ambient temperature, in an inert atmosphere.</p><p>3.2 The Balance</p><p>Several types of balance mechanism are possible [1-4]. Null-point weighing mechanisms are</p><p>favoured in TG as they ensure that the sample remains in the same zone of the furnace</p><p>irrespective of changes in mass. Various sensors have been used to detect deviations of the</p><p>balance beam from the null-position, e.g. in the Cahn RG electrobalance (Figure 3.2.) an</p><p>electro-optical device has a shutter attached to the balance beam. The shutter partly blocks the</p><p>light path between a lamp and a photocell. Movement of the beam alters the light intensity on</p><p>the photocell and the amplified output from the photocell is used to restore the balance to its</p><p>null-point and, at the same time, is a measure of the mass change. The restoring mechanism</p><p>is electromagnetic. The beam has a ribbon suspension and a small coil at the fulcrum, located</p><p>in the field of a permanent magnet. The coil exerts a restoring force on the beam proportional</p><p>to the current from the photocell.</p><p>is less than</p><p>225</p><p>Garn et al. [16-18] have discussed the problems that arise when there is appreciable solid</p><p>solubility. They used NMR to detect the solidus and compared DSC and NMR results.</p><p>They showed that lack of thermal equilibrium is not a principal source of error in the</p><p>method and also found that the measured impurity content is sometimes dependent upon</p><p>the nature of the impurity as well as its concentration. McGhie [19] has provided a very</p><p>useful discussion of the melting behaviour of solid solutions, using a system consisting</p><p>of 0 to 20% anthracene in 2,3-dimethyl naphthalene as an example. The normal DSC</p><p>method is invalid for such systems.</p><p>Wiedemann [20] has described the use of simultaneous DSC-thermomicroscopy (see</p><p>Chapter 5)for purity detemination. The addition of thermomicroscopy allows the various</p><p>stages of melting to be photographed to show the changes that occur. Flammersheim et</p><p>al. [21] have discussed the correction of DSC curves for the broadening of peaks caused</p><p>by the particular apparatus.</p><p>Purity determinations by thermal measurements are competitive [22] with other</p><p>techniques in terms of accuracy, precision, and ease of measurement, and, in many cases,</p><p>e.g. for crystalline organic compounds, are superior.</p><p>226</p><p>References</p><p>1.</p><p>2.</p><p>3.</p><p>4.</p><p>5.</p><p>6.</p><p>7.</p><p>8.</p><p>9.</p><p>10.</p><p>11.</p><p>12.</p><p>13.</p><p>14.</p><p>15.</p><p>16.</p><p>17.</p><p>18.</p><p>19.</p><p>20.</p><p>P.W. Atkins, “Physical Chemistry”, Oxford University Press, Oxford, 6th Edn,</p><p>1998, p.179.</p><p>M.E. Brown, J. Chem. Educ., 56 (1979) 310.</p><p>R.L. Blaine and C.K. Schoff (Eds), “Purity Determinations by Thermal Methods”,</p><p>ASTM Special Technical Publication 838, American Society for Testing and</p><p>Materials, Philadelphia, 1984.</p><p>W.P. Brennan, M.P. Divito, R.L. Fyans and A.P. Gray, in “Purity Determinations</p><p>by Thermal Methods”, (Eds R.L. Blaine and C.K. Schoff), ASTM Special</p><p>Technical Publication 838, American Society for Testing and Materials,</p><p>Philadelphia, 1984, p.5.</p><p>E.E. Marti, Thermochim Acta, 5 (1973), 173.</p><p>E.E. Marti, O. Heiber, W. Huber and G. Tonn, Proc. 3rd ICTA, (Ed. H.G.</p><p>Weidemann), Birkhauser Verlag, Basel, 1971, Vol.3, p.83.</p><p>Thermal Analysis Newsletters, Nos.5 and 6, Perkin-Elmer Corporation,</p><p>Norwalk, Connecticut (undated).</p><p>A.P. Gray and R.L. Fyans, Thermal Analysis Application Study No. 10,</p><p>Perkin-Elmer, Norwalk, 1973.</p><p>D.L. Sondack, Anal. Chem., 44 (1972) 888.</p><p>H. Staub and W. Perron, Anal. Chem., 46 (1974) 128.</p><p>J. Zynger, Anal. Chem., 47 (1975) 1380.</p><p>S.A. Moros, in “Purity Determinations by Thermal Methods”, (Eds R.L. Blaine</p><p>and C.K. Schoff), ASTM Special Technical Publication 838, American Society</p><p>for Testing and Materials, Philadelphia, 1984, p.22.</p><p>J.E. Hunter III and R.L. Blaine, in “Purity Determinations by Thermal Methods”,</p><p>(Eds R.L. Blaine and C.K. Schoff), ASTM Special Technical Publication 838,</p><p>American Society for Testing and Materials, Philadelphia, 1984, p.39.</p><p>J.P. Elder, in “Purity Determinations by Thermal Methods”, (Eds R.L. Blaine and</p><p>C.K. Schoff), ASTM Special Technical Publication 838, American Society for</p><p>Testing and Materials, Philadelphia, 1984, p.50.</p><p>A.A. Raskin, J. Thermal Anal., 30 (1985) 901.</p><p>P.D. Garn, B. Kawalec, J.J. Houser and T.F. Habash, Proc. 7th ICTA, Vol.2,</p><p>Wiley, Chichester, 1982, p.899.</p><p>B. Kawalec, J.J. Houser and P.D. Garn, J. Thermal Anal., 25 (1982) 259.</p><p>T.F. Habash, J.J. Houser and P.D. Garn, J. Thermal Anal., 25 (1982) 271.</p><p>A.R. McGhie, in “Purity Determinations by Thermal Methods”, (Eds R.L. Blaine</p><p>and C.K. Schoff), ASTM Special Technical Publication 838, American Society</p><p>for Testing and Materials, Philadelphia, 1984, p.61.</p><p>H.G. Wiedemann, R. Riesen and G. Bayer, in “Purity Determinations by Thermal</p><p>Methods”, (Eds R.L. Blaine and C.K. Schoff), ASTM Special Technical</p><p>Publication 838, American Society for Testing and Materials, Philadelphia, 1984,</p><p>p.107.</p><p>227</p><p>21.</p><p>22.</p><p>H.J. Flammersheim, N. Eckhardt and W. Kunze, Thermochim. Acta, 187 (1991)</p><p>269.</p><p>C.K. Schoff, in “Purity Determinations by Thermal Methods”, (Eds R.L. Blaine</p><p>and C.K. Schoff), ASTM Special Technical Publication 838, American Society</p><p>for Testing and Materials, Philadelphia, 1984, p. 141.</p><p>CONCLUSIONS</p><p>12.1 The Range of Thermal Analysis</p><p>In the preceding Chapters, only a few selected examples have been given of the vast</p><p>number of applications of thermal analysis. To get a better idea of the range of</p><p>applications over all branches of inorganic, organic, physical and industrial chemistry,</p><p>metallurgy, polymer science, glass and ceramic science, food science, biology, geology,</p><p>pharmacy, medicine, agriculture and engineering, it is worth scanning the contents pages</p><p>of some of the proceedings of the International Conferences on Thermal Analysis and</p><p>Calorimetry (ICTAC), as well as the biennial reviews in Analytical Chemistry (detailed</p><p>references are given in Appendix A), or any issue of the major journals in the field:</p><p>Thermochimica Acta and the Journal of Thermal Analysis and Calorimetry.</p><p>As suggested in the opening paragraphs of this book, there are very few materials which</p><p>will not show interesting changes on heating. The materials studied have ranged from</p><p>kidney stones to synthetic diamonds, and from ancient papyri to the latest polymers and</p><p>ceramics for very specialized applications. Maximum information can only be obtained</p><p>by combining the results of the use of several different (preferably simultaneous) thermal</p><p>analysis techniques with other complementary measurements. The information so obtained</p><p>has been used to solve old problems and to develop new processes for the future.</p><p>12.2 The Future of Thermal Analysis</p><p>Reading and colleagues, who have been so active at the forefront of developments in many</p><p>areas of Thermal Analysis, have published their views of “Thermal Analysis for the</p><p>Century” [ 1 ]. They identify three major problems with current thermal methods: the long</p><p>time required for measurements; the small size of samples, and the averaged nature of the</p><p>information obtained. Reading and co-workers have made very considerable contributions</p><p>to this third problem by their role in the development of modulated temperature DSC (see</p><p>Chapter 4) that has allowed reversible and irreversible processes to be separated. The</p><p>introduction of modulated techniques has been a major advance in TA [2] and has been</p><p>followed by another very promising new direction, that of micro thermal analysis (see</p><p>Chapter 5), also resulting from the creativity and skill of Reading and his colleagues.</p><p>Much of the future of TA lies in the further development of these techniques [3] and the</p><p>applications that will arise as the equipment required becomes more readily available.</p><p>Special issues of both Thermochimica Acta [4] and the Journal of Thermal Analysis and</p><p>Calorimetry [5] have surveyed the field of TA at the beginning of a new millennium.</p><p>229</p><p>230</p><p>The limited information available from the original basic techniques of TG, DSC/DTA,</p><p>TMA and DMA on their own is inadequate for the full solution of most problems in</p><p>materials science. TG will have to be operable in highest resolution mode with some form</p><p>of evolved gas analysis (MS or FTIR) being essential. Information on the effects of</p><p>modulating the temperature (or other parameters) during examination of a sample is also</p><p>becoming essential. The various spin-off techniques from atomic force microscopy will</p><p>permit the real heterogeneous nature of materials to be explored.</p><p>Mathot [6] has surveyed the development of thermal analysis and calorimetry in recent</p><p>years and has sounded a warning about the lack of attention paid by educational</p><p>institutions to analytical science in general and to training in the techniques of thermal</p><p>analysis and calorimetry in particular. He forecasts a decreasing competence level of users</p><p>of the techniques. To counteract this, Mathot suggests that efforts should be made to: use</p><p>present capabilities to the full; improve existing equipment; develop new equipment (and</p><p>not leave this entirely to the manufacturers); decrease the “black-box” nature of much of</p><p>the hardware and software so that users are aware of, and understand,</p><p>what they are doing;</p><p>and improve data measurement, processing and presentation. The key to doing this relies</p><p>on the education provided by institutions, manufacturers and national and international</p><p>thermal analysis and calorimetry societies.</p><p>References</p><p>1.</p><p>2.</p><p>3.</p><p>4.</p><p>5.</p><p>6.</p><p>M. Reading, D.J. Hourston, M. Song, H.M. Pollock and A. Hammiche,</p><p>Amer. Lab., January 1998, 13.</p><p>B. Wunderlich, Thermochim, Acta, 355 (2000) 43.</p><p>D.M. Price, M. Reading,, A. Hammiche and H.M. Pollock,</p><p>J. Thermal Anal. Calorim., 60 (2000) 723.</p><p>W. Hemminger (Ed.), Thermochimica Acta, Vol. 355 (2000).</p><p>M.E. Brown, N. Koga, J. Malek and J. Mimkes (Eds), Journal of Thermal</p><p>Analysis and Calorimetry, Vol. 60, No. 3, (2000).</p><p>V.B.F. Mathot, Thermochim. Acta, 355 (2000) 1.</p><p>APPENDIX A: THE LITERATURE OF THERMAL ANALYSIS</p><p>An introduction to the vast literature of thermal analysis is given below. See also</p><p>Hemminger and Sarge in Chapter 1 of Volume 1 of the Handbook of Thermal Analysis</p><p>& Calorimetry (Ed. M.E. Brown), Elsevier, Amsterdam, 1998.</p><p>A.1 Books</p><p>R.L. Blaine and C.K. Schoff (Eds), Purity Determinations by Thermal Methods,</p><p>ASTM Special Technical Publication 838, American Society for Testing and</p><p>Materials, Philadelphia, 1984.</p><p>A. Blazek, Thermal Analysis, Van Nostrand Reinhold, London, 1972.</p><p>M.E. Brown (Ed.), Handbook of Thermal Analysis and Calorimetry, Vol.1, Principles</p><p>and Practice, Elsevier, Amsterdam, 1998.</p><p>E.L. Charsley and S.B. Warrington (Eds.), Thermal Analysis: Techniques and</p><p>Applications, Royal Society of Chemistry, Cambridge, 1992, 296 pp.</p><p>T. Daniels, Thermal Analysis, Kogan Page, London, 1973.</p><p>J.W. Dodd and K.H. Tonge, Thermal Methods: Analytical Chemistry by Open</p><p>Learning, Wiley, Chichester, 1987, 337 pp.</p><p>C. Duval, Inorganic Thermogravimetric Analysis, 2nd Rev. Edn, Elsevier,</p><p>Amsterdam, 1962.</p><p>C.M. Earnest, Thermal Analysis of Clays, Minerals and Coals, Perkin-Elmer, Norwalk,</p><p>1984.</p><p>G.W. Ehrenstein, G. Riedel and P. Trawiel, Praxis der Thermischen Analyse von</p><p>Kunstoffen, Hanser, 1998.</p><p>J.L. Ford and P. Timmins, Pharmaceutical Thermal Analysis: Techniques and</p><p>Applications, E. Horwood, Chichester, 1989, 313 pp.</p><p>P.D. Garn, Thermoanalytical Methods of Investigation, Academic Press, New York,</p><p>1965.</p><p>P.J. Haines, Thermal Methods of Analysis: Principles, Applications and Problems,</p><p>Blackie Academic and Professional, London, 1995, 286 pp.</p><p>V.R. Harwalkar and C.-Y. Ma (Eds.), Thermal Analysis of Foods, Elsevier, London,</p><p>1990, 362 pp.</p><p>231</p><p>232</p><p>F. Hatakeyama and F. X. Quinn, Thermal Analysis: Fundamentals and Applications to</p><p>Polymer Science, Wiley, Chichester, 1994, 158 pp.</p><p>T. Hatakeyama and Zhenhai Liu, Handbook of Thermal Analysis, Wiley, Chichester,</p><p>1998.</p><p>K. Heide, Dynamische thermische Analysenmethoden, Deutscher Verlag für</p><p>Grundstoffindustrie, Leipzig, 2nd Edn, 1982, 311 pp.</p><p>W.F. Hemminger and H.K. Cammenga, Methoden der Thermischen Analyse,</p><p>Springer, Berlin, 1989, 299 pp.</p><p>G. Höhne, W. Hemminger and H.-J. Flammersheim, Differential Scanning Calorimetry</p><p>- An Introduction for Practitioners, Springer, Berlin, 1996, 222 pp.</p><p>C.J. Keattch and D. Dollimore, An Introduction to Thermogravimetry, 2nd Edn,</p><p>Heyden, London, 1975, 164 pp.</p><p>R.B. Kemp (Ed.), Handbook of Thermal Analysis and Calorimetry, Vol.4, From</p><p>Macromolecules to Man, Elsevier, Amsterdam, 1999, 1032 pp.</p><p>H. Kopsch, Thermal Methods in Petroleum Analysis, Wiley, New York, 1995.</p><p>W. Lodding (Ed.) Gas Effluent Analysis, Arnold, London, 1976, 220 pp.</p><p>C. Lu and A.W. Czanderna (Eds), Applications of Piezoelectric Quartz Crystal</p><p>Microbalances, Elsevier, Amsterdam, 1984.</p><p>R.C. Mackenzie (Ed.), Differential Thermal Analysis, Vol.1 and 2, Academic Press,</p><p>London, 1969.</p><p>J.L. McNaughton and C.T. Mortimer, Differential Scanning Calorimetry,</p><p>Perkin-Elmer Order No.: L-604 (Reprinted from IRS; Phys. Chem. Ser.2</p><p>(1975) Vol.10, Butterworths), 44 pp.</p><p>E. Marti, H.R. Oswald and H.G. Wiedemann (Eds), Angewandte chemische</p><p>Thermodynamik and Thermoanalytik, Birkhauser Verlag, Basel, 1979.</p><p>V.B.F. Mathot (Ed.), Calorimetry and Thermal Analysis of Polymers, Carl Hanser,</p><p>München, 1994, 369 pp.</p><p>K.P. Menard, Dynamic Mechanical Analysis - A Practical Introduction, CRC Press,</p><p>Boca Raton, USA, 1999, 208 pp.</p><p>233</p><p>O. Menis, H.L. Rook and P.D. Garn (Eds), The State-of-the-Art of Thermal</p><p>Analysis, NBS Special publication 580, 1980.</p><p>R.Sh. Mikhail and E. Robens, Microstructure and Thermal Analysis of Solid Surfaces,</p><p>Wiley, Chichester, 1983, 496 pp.</p><p>F. Paulik, Special Trends in Thermal Analysis, Wiley, Chichester, 1995, 459 pp.</p><p>M.I. Pope and M.D. Judd, Differential Thermal Analysis, Heyden, London, 1977.</p><p>A.T. Riga and C.M. Neag, Materials Characterization by Thermomechanical Analysis,</p><p>American Society for Testing and Materials, Philadelphia, 1991.</p><p>M.P. Sepe, Thermal Analysis of Polymers, Rapra Review Report No. 95, RAPRA,</p><p>1997.</p><p>W. Smykatz-Kloss, Differential Thermal Analysis, Applications and Results in</p><p>Mineralogy, Springer-Verlag, New York, 1974.</p><p>W. Smykatz-Kloss and S.St.J. Warne (Eds.), Thermal Analysis in the Geosciences,</p><p>Springer, Berlin 1991, 379 pp.</p><p>R.F. Speyer, Thermal Analysis of Materials, Marcel Dekker, New York, 1994, 285 pp.</p><p>J.W. Stucki, D.L. Bish and F.A. Mumpton (Eds), Thermal Analysis in Clay Science,</p><p>Clay Minerals Society, 1990.</p><p>D.N. Todor, Thermal Analysis of Minerals, Abacus Press, Tunbridge Wells, 1976.</p><p>E. A. Turi (Ed.), Thermal Characterization of Polymeric Materials, Academic Press,</p><p>New York, 2nd Edn., 1996.</p><p>W.W. Wendlandt, Thermal Analysis, 3rd Edn., Wiley, New York 1986, 814 pp.</p><p>W.W. Wendlandt and L.W. Collins (Eds), Thermal Analysis (Benchmark</p><p>Papers in Analytical Chemistry), Dowden, Hutchinson & Ross, Stroudsbourg,</p><p>USA, 1976.</p><p>234</p><p>W.W. Wendlandt and J.P. Smith, Thermal Properties of Transition Metal</p><p>Ammine Complexes, Elsevier, Amsterdam, 1967.</p><p>G. Widmann, R. Riesen, Thermal Analysis. Terms, Methods, Applications, Hüthig,</p><p>Heidelberg, 1986, 131 pp.</p><p>C.L. Wilson and D.W. Wilson (Eds), Comprehensive Analytical Chemistry,</p><p>Elsevier, Amsterdam.</p><p>Vol.XIIA: Simultaneous Thermoanalytical Examinations by Means of the</p><p>Derivatograph, J. Paulik and F. Paulik, 1981, 277 pp.</p><p>Vol.XIIB: Biochemical and Clinical Applications of Thermometric and</p><p>Thermal Analysis, N.D. Jesperson (Ed), 1982.</p><p>Vol.XIIC: Emanation Thermal Analysis and other Radiometric Emanation</p><p>Methods, V. Balek and J. Tolgyessy, 1983, 304 pp.</p><p>Vol.XIID: Thermophysical Properties of Solids, J. Sestak, 1984, 440 pp.</p><p>S.P. Wolsky and A.W. Czanderna (Eds), Microweighing in Vacuum and</p><p>Controlled Environments, Elsevier, Amsterdam, 1980.</p><p>B. Wunderlich, Thermal Analysis, Academic Press, Boston, 1990, 450 pp.</p><p>Videotapes</p><p>The University of York Electronics Centre, York, England, has produced 3 videotapes</p><p>of about 25 minutes each, entitled “Thermal Analysis: An Introduction to Principles</p><p>and Practice”, for commercial distribution.</p><p>Computer-assisted Courses</p><p>ATHAS (Advanced Thermal Analysis System) is a group founded by Professor B.</p><p>Wunderlich at the University of Tennessee. This site offers computer-assisted courses.</p><p>web.utk.edu/~athas/</p><p>Many more sites of interest can be found by following the links from the ICTAC</p><p>website at www.ictac.org</p><p>235</p><p>A.2 Conference Proceedings</p><p>The proceedings of the International and European Congresses on Thermal Analysis</p><p>and Calorimetry (ICTAC and ESTAC) are valuable sources.</p><p>236</p><p>A.3 Journals</p><p>The Journal of Thermal Analysis & Calorimetry(Kluwer) and Thermochimica Acta</p><p>(Elsevier) are the main English language specialist journals, although results of thermal</p><p>analyses appear in many other journals, especially Analytical Chemistry, Talanta,</p><p>Analytica Chimica Acta, International Laboratory, Laboratory Practice, Analyst, and the</p><p>many polymer journals.</p><p>At two-year intervals, the journal Analytical Chemistry publishes reviews including</p><p>detailed references. Analytical Chemistry, 72 (2000) 27R; 70 (1998) 27R; 68 (1996)</p><p>63R; 66 (1994) 17R; 64 (1992) 147R; 62 (1990) 44R; 60 (1988) 274R; 58 (1986) 1R; 56</p><p>(1984) 250R; 54 (1982) 97R; 52 (1980) 106R; 50 (1978) 143R; 48 (1976) 341R; 46</p><p>(1974)</p><p>451R; 44 (1972) 513R; 42 (1970) 268R; 40 (1968) 380R; 38 (1966) 443R; 36</p><p>(1964) 347R and earlier reviews on DTA.</p><p>Both Thermochimica Acta and the Journal of Thermal Analysis and Calorimetry have</p><p>published special issues on a variety of themes and in honour of leading thermal analysts.</p><p>Much valuable information can also be found in the proceedings of the conferences of</p><p>national societies, especially those of the North American Thermal Analysis Society</p><p>(NATAS). Many such proceedings are now published as special issues of the Journal</p><p>of Thermal Analysis and Calorimetry or Thermochimica Acta (see below).</p><p>237</p><p>The two references below are of particular historical value:</p><p>R.C. Mackenzie, A History of Thermal Analysis, Thermochim. Acta, 73 (1984), 251 -</p><p>367.</p><p>W.W. Wendlandt, The Development of Thermal Analysis Instrumentation 1955 - 1985,</p><p>Thermochim. Acta, 100 (1986), 1 - 22.</p><p>A.4 Nomenclature</p><p>The International Confederation for Thermal Analysis and Calorimetry (ICTAC) has</p><p>published several recommendations for the standardizing and reporting of results of</p><p>thermal analysis. Nomenclature is always evolving, as discussed in Chapter 1, as new</p><p>techniques are introduced and existing techniques are modified. To follow part of this</p><p>evolution, the following references are suggested. For the latest recommendations it is</p><p>probably wise to consult the ICTAC website and also follow any links from there to</p><p>organizations such as ASTM.</p><p>R.C. Mackenzie, Talanta, 16 (1969) 1227; Pure Appl. Chem., 37 (1974) 439; Talanta,</p><p>19 (1972) 1079;J. Therm. Anal., 8 (1975); Thermochim. Acta., 28 (1979) 1 and 46 (1981)</p><p>333.</p><p>See also The Metrication of Thermal Analysis or Conversion to SI Units, R.L. BLAINE,</p><p>Thermochim. Acta, 26 (1978) 217-228.</p><p>R.C. Mackenzie, Nomenclature in Thermal Analysis, in: Treatise on Analytical Chemistry</p><p>(P.J. Elving, Ed.), Part 1, Vol. 12, Wiley, New York, 1983, pp. 1- 16.</p><p>International Confederation for Thermal Analysis: For Better Thermal Analysis and</p><p>Calorimetry, 3rd Ed. (J.O. Hill, Ed.), 1991.</p><p>A.5 Manufacturer's Literature</p><p>The major manufacturers provide extensive information on thermal analysis, most of</p><p>which can be downloaded from their websites (see Appendix B).</p><p>APPENDIX B: MAJOR SUPPLIERS OF THERMAL ANALYSIS EQUIPMENT</p><p>Choosing Thermal Analysis EquipmentB.1</p><p>A bewildering array of equipment is available to anyone starting out in thermal analysis and</p><p>selecting a suitable system is not an easy decision. It is advisable first to visit the websites of</p><p>the suppliers (see below), or collect the pamphlets and specifications of most systems from the</p><p>suppliers and then attempt to make a preliminary selection by considering the following</p><p>factors:</p><p>(1) What types of sample are going to be examined both immediately and as far as can be</p><p>predicted, in the future?</p><p>(2) What sort of information on the sample is required, e.g. thermal stability, glass-transitions,</p><p>percentage crystallinity, mechanical properties, details of gases evolved etc.?</p><p>(3) Over what temperature ranges are the changes that are of interest likely to occur?</p><p>Answers to the above questions can be used to eliminate definitely unsuitable systems.</p><p>Unless there are very special requirements such as extreme ranges of temperature, or use of</p><p>very corrosive atmospheres or strongly exothermic or even explosive samples, there will</p><p>usually still be a wide choice of instruments. Prices related to budget available will obviously</p><p>be a further restriction, and modular systems, which can be added to, are attractive.</p><p>A most important question to be answered before choosing a system, is the training and</p><p>service available from the suppliers. This involves seeking out other users and checking on</p><p>their experiences. At the same time it is worth checking on the prices of spares and</p><p>accessories (which can be ridiculously high). Even the best equipment (which need not be the</p><p>most expensive) will be difficult to operate and maintain if the local agents cannot provide</p><p>informed and rapid service.</p><p>B.2 Major Suppliers of Thermal Analysis Equipment</p><p>These are listed (in alphabetical order) in the Table following. Because of rapid changes in</p><p>the market, it is recommended that a search be done if any difficulties are encountered in</p><p>accessing a website. It is also possible to follow links from the ICTAC website at</p><p>www.ictac.org</p><p>238</p><p>Major Suppliers of Thermal Analysis Equipment (in alphabetical order)</p><p>239</p><p>Company Address Website</p><p>Cahn (see Thermo Cahn)</p><p>Haake (see Thermo Haake)</p><p>Linseis GmbH</p><p>Mettler-Toledo Instrumente AG</p><p>Netzch-Geratebau GmbH</p><p>Perkin-Elmer Corporation</p><p>Polymer Laboratories</p><p>Seiko (see Thermo Haake)</p><p>Setaram</p><p>Shimadzu Corporation</p><p>TA Instruments</p><p>Thermo Cahn</p><p>Thermo Haake</p><p>Vielitzerstrasse 43, www.linseis.com</p><p>8672 Selb, FRG</p><p>CH-8606 Greifensee, Switzerland www.mt.com</p><p>P O Box 1460, www.netzsch.com</p><p>D-8672 Selb, Germany</p><p>761 Main Avenue,</p><p>Norwalk, Connecticut 06856, USA</p><p>www.instruments.perkinelmer. com</p><p>Essex Road, Church Stretton ,</p><p>SY6 6AX, England</p><p>7, rue de l'Oratoire, F-69300</p><p>Caluire, France</p><p>1, Nishinokyo Kuwabaracho,</p><p>Nakagyou-ku, Kyoto 604-8511,</p><p>Japan</p><p>109 Lukens Drive, New Castle,</p><p>DE 19720, USA</p><p>5225 Verona Rd, Madison,</p><p>WI 5371, USA</p><p>Dieselstr.4, Karlsruhe</p><p>BW 76227, Germany</p><p>www.setaram.com</p><p>www.shimadzu.com</p><p>www.shimadzu.co.jp</p><p>www.tainst.com</p><p>www.cahn.com</p><p>www.thermohaake.com</p><p>APPENDIX C: DATA PROCESSING IN THERMAL ANALYSIS</p><p>C.1 Introduction</p><p>Wendlandt [1] and Wunderlich [2] have dealt with some of the historical aspects of the</p><p>impact of microcomputers on the field of thermal analysis. Changes have been so rapid</p><p>that methods and equipment described in papers published even a few years ago (including</p><p>the first edition of this book) have generally become obsolete and the trend will continue</p><p>with developments such as the Internet, etc..</p><p>The manufacturers of thermal analysis equipment offer both the hardware and the</p><p>software necessary to carry out most thermal analyses, with a high degree of automation,</p><p>and to calculate the usual parameters from the captured data. These systems are generally</p><p>specific to the particular manufacturer's equipment and the software may be difficult, or</p><p>even impossible to modify for one's own requirements. Some calculations, such as the</p><p>derivation of kinetic parameters under nonisothermal conditions (see Chapter 10), are</p><p>areas of controversy and continuing development and it is necessary to know the approach</p><p>and the algorithms being used in such software before any significance can be attached</p><p>to the output. In this brief appendix, some of the basic procedures involved in data</p><p>processing are outlined. A more detailed discussion is given in reference [3].</p><p>The data processing required for thermal analysis in general, and especially for DSC and</p><p>DTA, bears many resemblances to that developed for gas chromatography, e.g. the</p><p>establishment of and correction of the signal for the baseline; detection of onset of peaks,</p><p>peak maxima and the return to the baseline; resolution of overlapping peaks and</p><p>determination of areas under peaks by numerical integration. The routines required for</p><p>TG usually involve smoothing and numerical differentiation, buoyancy corrections, and</p><p>possibly polynomial regression. All of the above procedures are well documented. Other</p><p>more specialized procedures, such as kinetic analysis under nonisothermal conditions</p><p>(Chapter 10), determination of purity by detailed analysis of the shape of melting</p><p>endotherms (Chapter 11), the determination of glass-transition temperatures and of heat</p><p>capacities, are usually available from the manufacturers, or may be carried out by</p><p>importing data files into spreadsheet packages.</p><p>C.2 Data processing</p><p>The sequence of operations in the capture and processing of data from thermal analysis</p><p>experiments is usually: (1) data capture and storage; (2) display of data for preliminary</p><p>examination; (3) manipulation of the data: (a) baseline correction, (b) smoothing, (c)</p><p>scaling; (4) processing of the data: (a) numerical differentiation, (b) peak integration;</p><p>(5) other calculations,</p><p>e.g., (a) kinetic analysis, (b) purity determination, etc.</p><p>Data capture, storage and display are too hardware-specific for discussion to be useful.</p><p>Baseline correction and scaling are usually fairly straightforward to understand from the</p><p>options available in the software provided.</p><p>241</p><p>242</p><p>C.3 Spreadsheet and database packages [5-10]</p><p>The availability of powerful spreadsheet packages, such as Microsoft Excel and Corel</p><p>Quatro, has virtually removed any necessity for the writing or use of dedicated software.</p><p>Reich and co-workers have published a series of papers on the use of spreadsheets [4-6]</p><p>and databases [7-9] for kinetic analyses of thermal analysis results. These papers also</p><p>show how the power of such packages continues to improve.</p><p>C.4 Algorithms</p><p>Smoothing of data</p><p>Whether data has been smoothed and the method, if any, used is seldom easy to ascertain.</p><p>Very smooth traces with little noise may indicate either excellent instrumentation or heavy</p><p>smoothing. Various types of numerical filters are available. Savitsky-Golay [10]</p><p>smoothing involves a least-squares convolution method and weighting factors are given</p><p>[10] for from 5 to 25-point polynomials. Where it is important not to lose points from the</p><p>ends of the data sets, a modification developed by Gorry [11] can be used. Ebert et al.</p><p>[12] have published a spline smoothing program in Basic. Marchand and Marmet [13]</p><p>have described a binomial filter and Bussian and Hardle [14] a robust filter. The</p><p>application of some of these smoothing routines to a noisy DSC trace is illustrated in</p><p>Figure C1.</p><p>Numerical differentiation</p><p>A DSC or DTA curve is already an example of a differential measurement and so such</p><p>curves are not usually differentiated further. If an integral measurement such as a TG</p><p>curve has been recorded, then a DTG curve can be obtained by numerical differentiation.</p><p>The usual method is that of Savitsky and Golay [10]. Data points must be at equally</p><p>spaced time intervals. As an example of a 9-point convolution acting on point with</p><p>a normalising constant [10] of 60:</p><p>Peak integration</p><p>Peak area determination (see Figure C2) is usually done by numerical integration using</p><p>either Simpson's rule or the trapezoidal rule. For a large number of closely spaced points,</p><p>the trapezoidal rule is adequate and simpler. As an example, the cumulative area</p><p>calculated by the trapezoidal rule is:</p><p>243</p><p>244</p><p>References</p><p>W.W. Wendlandt, Thermochim. Acta, 5 (1973) 225.</p><p>B. Wunderlich, Int. Lab., October 1982, 32.</p><p>R.F. Speyer, Thermal Analysis of Materials, Marcel Dekker,</p><p>New York, 1994, Ch. 4.</p><p>L. Reich and S.H. Patel, Amer. Lab., 19(9) (1987) 23.</p><p>L. Reich and S.S. Stivala, Thermochim. Acta, 138 (1989) 177.</p><p>L. Reich, Thermochim. Acta, 143 (1989) 311; 164 (1990) 1,7; 173 (1990) 253.</p><p>L. Reich, Thermochim. Acta, 180 (1991) 303; 185 (1991) 205; 195 (1992) 221;</p><p>200(1992)349.</p><p>L. Reich and S.H. Patel, Thermochim. Acta, 222 (1993) 85; 246 (1994) 107.</p><p>L. Reich, Thermochim. Acta, 231 (1994) 177; 273 (1996) 113.</p><p>A. Savitsky and M.J.E. Golay, Anal. Chem., 36 (1964) 628.</p><p>P.A. Gorry, Anal. Chem., 62 (1990) 570.</p><p>K. Ebert, H. Ederer and T.L. Isenhour, Computer Applications in Chemistry,</p><p>VCH Verlag, Weinheim, 1989.</p><p>Marchand and Marmet, Rev. Sci. Instr., 54 (1984) 1034.</p><p>B-M. Bussian and W. Hardle, J. Appl. Spectrosc., 38 (1984) 309.</p><p>1.</p><p>2.</p><p>3.</p><p>4.</p><p>5.</p><p>6.</p><p>7.</p><p>8.</p><p>9.</p><p>13.</p><p>14.</p><p>10.</p><p>11.</p><p>12.</p><p>APPENDIX D: INTRODUCTORY EXPERIMENTS IN THERMAL ANALYSIS</p><p>A selection of introductory experiments is given below. What can be done will obviously be</p><p>determined by the apparatus available, and constant reference should be made to the manuals</p><p>supplied with the instruments. Modern computerized instruments will usually operate</p><p>interactively, providing some of the directions given in the procedures below. Access to</p><p>simultaneous techniques and/or evolved gas analysis will add to the possibilities suggested</p><p>below and provide a great deal more information.</p><p>D.1 DIFFERENTIAL SCANNING CALORIMETRY (DSC)</p><p>A1) Calibration: Calibrate a DSC with respect to temperature and heat flow. Check on the</p><p>reproducibility. Compare the results obtained on different instruments, if possible. Carefully</p><p>compare the calibration procedures given in the respective manuals for power-compensated</p><p>and heat-flux instruments.</p><p>A2) Dehydration: Determine the temperatures and enthalpy changes for the dehydration</p><p>stages of Carry out similar measurements on some other hydrates, e.g.</p><p>(formate) or (oxalate) and see how the</p><p>enthalpy of dehydration per mole of varies from salt to salt. Check the reproducibility</p><p>of the enthalpy measurements and examine the influence of baseline choice on the values</p><p>obtained.</p><p>A3) Decompositions: Study the decompositions of some metal carboxylates, e.g.,</p><p>or after first having dehydrated them (see 2). Try to carry</p><p>out an isothermal DSC run at a suitable temperature. Use the data obtained in programmed</p><p>temperature experiments at different heating rates to estimate kinetic parameters using some</p><p>of the procedures described in Chapter 10.</p><p>A4) Phase transitions: Determine the temperatures and enthalpy changes of phase transitions</p><p>in salts such as or Study the reversibility of these changes</p><p>on cooling and comment on the use of these transition temperatures as temperature standards</p><p>for instrument calibration. Use a hot-stage microscope (HSM) for visual detection of the</p><p>phase changes.</p><p>A5) Glass transition: Determine the glass-transition temperatures of several polymers.</p><p>A6) Polymer crystallinity: Polyethylene (PE) is a semicrystalline thermoplastic. From a DSC</p><p>curve, determine the temperature range over which melting occurs as well as the enthalpy of</p><p>melting. The percentage crystallinity is calculated by comparing the measured value with that</p><p>for 100% crystalline material</p><p>245</p><p>246</p><p>A7) Polymer stability: compare the degradation in nitrogen of a suitable polymer with its</p><p>oxidation in air or oxygen.</p><p>Examine the temperature regions before degradation starts to determine the glass-transition</p><p>temperatures (see 5) and the occurrence of crystallization and/or melting.</p><p>A8) Curing of an epoxy resin: Do a DSC run on an epoxy glue mixture. Determine the</p><p>enthalpy change of the exothermic curing process. Rescan the product and determine the</p><p>glass-transition temperature of the polymer.</p><p>A9) Specific heat capacity: Determine the specific heat capacity of an inert substance, such</p><p>as relative to that of aluminium metal at 25°C). Comment on the</p><p>variation of the specific heat capacity with temperature.</p><p>A10) Purity determination: Compare the melting endotherm of pure indium with that for</p><p>benzoic acid and estimate the purity of the benzoic acid.</p><p>D.2 THERMOGRAVIMETRY (TG)</p><p>B1) Temperature calibration: Use magnetic standards of known Curie point, to calibrate the</p><p>temperature of the furnace.</p><p>B2) Dehydration: Determine the temperatures and mass losses accompanying the dehydration</p><p>stages of Compare your results with those from the DSC experiment A2 and</p><p>draw up a full description of the dehydration process.</p><p>B3) Decompositions: The studies carried out in the DSC experiment A3 can be</p><p>complemented by determining the mass-losses accompanying the thermal events detected.</p><p>Kinetics may be determined from non-isothermal experiments at different heating rates, or</p><p>from a series of experiments at different isothermal temperatures.</p><p>B4) Percentage filler in a polymer: Decompose a sample of an expoxy putty in nitrogen. The</p><p>residue is the filler.</p><p>B5) Analysis of coal or of a rubber: (a) Heat a sample in nitrogen until no further mass-loss</p><p>occurs. This gives the proportion of volatile material. (b) Change the purge gas to oxygen</p><p>while holding the sample at the high end of the temperature range. The mass-loss corresponds</p><p>to the proportion of carbon residue. (c) The mass of the residue in oxygen corresponds to the</p><p>inorganic ash.</p><p>APPENDIX E: EXAMPLES OF EXAMINATION QUESTIONS</p><p>1. Answer TWO of the following :</p><p>(a) Describe the problems of and the techniques used for temperature</p><p>calibration of thermal analysis instruments.</p><p>(b) Discuss the problems</p><p>of obtaining kinetic parameters from a single</p><p>thermal analysis experiment.</p><p>(c) Estimates of the purity of a material which melts may be made from</p><p>analysis of a DSC melting endotherm. Describe the procedure.</p><p>2. Answer TWO of the following :</p><p>(a) All thermal analysis instruments have features in common. Discuss</p><p>these common features and the way in which the individual techniques</p><p>differ from the generalized instrument.</p><p>(b) Describe, with examples, the various types of curves obtained from</p><p>thermogravimetric (TG) experiments, and discuss their interpretation.</p><p>(c) Make a detailed comparison of the techniques of differential thermal</p><p>analysis (DTA) and differential scanning calorimetry (DSC) and</p><p>discuss the relative advantages and disadvantages of the techniques.</p><p>3. Write a report to the Managing Director of your company, which produces</p><p>organic polymers, advising him of the advantages (and disadvantages) of</p><p>introducing thermal analysis techniques into the research and quality-</p><p>control laboratories.</p><p>4. Discuss the use of thermomechanical analysis (TMA) and dynamic mechanical</p><p>analysis (DMA) in studying the physical properties of polymers.</p><p>247</p><p>248</p><p>(a) Explain what is meant by a 'transducer' and describe the transducers</p><p>used in the main thermal analysis techniques.</p><p>(b) Discuss the information obtainable by applying thermal analysis</p><p>techniques to the study of solid polymers.</p><p>(a) Discuss the possibilities of obtaining kinetic information from</p><p>two thermal analysis experiments.</p><p>(b) Describe the uses of hot-stage microscopy (HSM) and evolved gas</p><p>analysis (EGA) in extending the information obtainable from</p><p>differential scanning calorimetry (DSC) or differential thermal</p><p>analysis (DTA).</p><p>Answer TWO of the following sections :</p><p>(a) Discuss the use of a wide range of thermal analysis techniques</p><p>in the study of the properties of polymers.</p><p>(b) Describe the techniques of evolved gas analysis (EGA) and their</p><p>use in combination with other thermal analysis techniques.</p><p>(c) Outline the approach used to estimate the purity of organic</p><p>compounds using differential scanning calorimetry (DSC).</p><p>Write a concise report (use your imagination) advising a polymer</p><p>chemist on the possibility and advantages of using the techniques of</p><p>thermal analysis in his or her research.</p><p>5.</p><p>6.</p><p>7.</p><p>8.</p><p>249</p><p>9. Discuss TWO of the following topics :</p><p>(a) Combinations of thermal analysis techniques with themselves and</p><p>with evolved gas analysis and other complementary techniques.</p><p>(b) The principles, interpretation of results, and applications of</p><p>differential scanning calorimetry.</p><p>(c) The use of thermal analysis in obtaining kinetic parameters for</p><p>solid-state reactions.</p><p>(d) The use of thermomechanical analysis and of dynamic mechanical</p><p>analysis in the characterisation of polymers.</p><p>10. EITHER</p><p>Discuss the possibility of determining the kinetics of a reaction from</p><p>a single programmed-temperature experiment. Describe the simplifications</p><p>that occur when experimentation is extended to at least a second</p><p>programmed-temperature run or an isothermal run.</p><p>OR</p><p>It is claimed that absolute purities of certain solid substances may be</p><p>determined using differential scanning calorimetry (DSC). Outline the</p><p>approach and discuss this claim with particular reference to the</p><p>underlined words.</p><p>11. Thermal analysis may be defined as the measurement of changes in</p><p>properties of materials as a function of temperature. Describe the</p><p>main properties which have been used and the information which can be</p><p>obtained from such studies.</p><p>250</p><p>12. Compare the principles, practical limitations and the quantitative</p><p>information obtainable from differential thermal analysis (DTA) and</p><p>differential scanning calorimetry (DSC).</p><p>Answer TWO of the following :</p><p>(a) Discuss the similarities and differences between thermomechanical</p><p>analysis (TMA) and dynamic mechanical analysis (DMA).</p><p>(b) Give a definition of "thermal analysis" and discuss this definition</p><p>in terms of the materials studied, the types of changes taking</p><p>place in these materials and the properties of these materials used</p><p>to study these changes.</p><p>(c) Describe the techniques used for the analysis of gases evolved</p><p>during thermal analysis experiments and compare the advantages and</p><p>disadvantages of these techniques.</p><p>14. Attempt TWO of the following :</p><p>(a) Describe in detail the differences between differential scanning</p><p>calorimetry (DSC) and differential thermal analysis (DTA).</p><p>(b) Describe the principles, apparatus and applications of dynamic</p><p>mechanical analysis (DMA).</p><p>(c) Discuss the possibility of obtaining kinetic information from</p><p>conventional (i.e. non-isothermal) thermogravimetry (TG).</p><p>(d) Describe a method for determining the purity of an organic compound</p><p>using differential scanning calorimetry (DSC).</p><p>(e) Discuss the possibilities and problems of combining thermal analysis</p><p>techniques and include discussion of evolved gas analysis.</p><p>13.</p><p>251</p><p>EXPLANATION OF THE SYMBOLS USED IN THE TEXT</p><p>= area; amplitude of vibration; Arrhenius pre-exponential factor; component of</p><p>binary mixture</p><p>= calibration factor (heat capacity); bulk modulus; sample thickness; component</p><p>of binary mixture; amplitude of modulation</p><p>= heat capacity; calibration constant; Curie constant</p><p>= thermal diffusivity; amplitude of kinetically hindered response</p><p>= Young’s modulus; emanating power; Arrhenius activation energy</p><p>= storage modulus</p><p>= loss modulus</p><p>= force; fraction melted</p><p>= averaged function</p><p>= shear modulus, Gibbs energy</p><p>= enthalpy; magnetic field strength</p><p>= instrument constant; heat transfer coefficient</p><p>= crysoscopic constant</p><p>= length</p><p>= magnetization; molar mass</p><p>= period of oscillation</p><p>= heat</p><p>= as constant; thermal resistance</p><p>= entropy; area</p><p>= temperature</p><p>= volume; voltage; attenuation</p><p>= general abcissa</p><p>= general ordinate</p><p>= constant; partial area; activity</p><p>= constant</p><p>= specific heat capacity; constant</p><p>= diameter; thickness</p><p>A</p><p>B</p><p>C</p><p>D</p><p>E</p><p>E’</p><p>E’‘</p><p>F</p><p>F ( )</p><p>G</p><p>H</p><p>K</p><p>L</p><p>M</p><p>P</p><p>Q</p><p>R</p><p>S</p><p>T</p><p>V</p><p>X</p><p>Y</p><p>a</p><p>b</p><p>c</p><p>d</p><p>252</p><p>= angle; Weiss constant</p><p>= function of temperature</p><p>= thermal conductivity</p><p>= chemical potential; micro</p><p>= ultrasonic velocity</p><p>= Poisson’s ratio</p><p>= resonance frequency</p><p>= density</p><p>= stress; ionic conductivity</p><p>= volume magnetic susceptibility</p><p>= angular frequency</p><p>= calibrant; completion</p><p>= Curie point</p><p>= eutectic; extrapolated</p><p>= furnace; fusion; final</p><p>= fusion</p><p>= glass transition</p><p>= initial</p><p>= melting</p><p>= general number</p><p>= initial or at 0 K or at 0°C; melting</p><p>= onstant pressure; peak; programme</p><p>= peak-to-peak</p><p>= reference</p><p>= measured reference</p><p>= sample</p><p>= measured sample</p><p>= time or temperature in Celsius</p><p>= refers to solvent</p><p>= refers to solute</p><p>= half-step</p><p>= standard</p><p>= molar quantity</p><p>= impurity</p><p>Subscripts</p><p>Superscripts</p><p>c</p><p>C</p><p>e</p><p>f</p><p>fus</p><p>g</p><p>i</p><p>m</p><p>n</p><p>o</p><p>p</p><p>p-p</p><p>r</p><p>rm</p><p>s</p><p>sm</p><p>t</p><p>1</p><p>2</p><p>½</p><p>o</p><p>*</p><p>–</p><p>253</p><p>= exponential base</p><p>= frequency</p><p>= conversion function; general function</p><p>= fusion</p><p>= conversion function</p><p>= gas</p><p>= conversion function</p><p>= baseline displacement; height; relative amplitude of vibration</p><p>= rate coefficient</p><p>liquid</p><p>= mass; constant exponent in rate equation</p><p>= apparent order of reaction; number of moles</p><p>= pressure; constant exponent in rate equation</p><p>= temperature integral defined in Chapter 10</p><p>= heat</p><p>= thermocouple resistance</p><p>= partial area; mass magnetic susceptibility</p><p>= solid</p><p>= time; temperature in Celsius</p><p>= weighting factor</p><p>= mole fraction; dimension;</p><p>= mole fraction of solvent</p><p>= mole fraction of solute</p><p>= mole fraction of impurity</p><p>= dimension</p><p>= dimension; charge</p><p>= change or finite difference; damping</p><p>= coefficient of linear expansion; fractional reaction; constant for thermocouple</p><p>= heating rate; constant for thermocouple</p><p>= constant for thermocouple; phase angle</p><p>= strain; dielectric constant</p><p>= undetermined premelting</p><p>= viscosity coefficient</p><p>e</p><p>f</p><p>f( )</p><p>fus</p><p>g( )</p><p>(g)</p><p>h( )</p><p>h</p><p>k</p><p>m</p><p>n</p><p>p</p><p>p(x)</p><p>q</p><p>r</p><p>s</p><p>(s)</p><p>t</p><p>x</p><p>=</p><p>w</p><p>y</p><p>z</p><p>(x = E/RT)</p><p>(= E/RT )</p><p>INDEX</p><p>absorbent tubes 147</p><p>ac (see alternating current) 9</p><p>acceleratory models 186</p><p>acoustic emission 164-166,170</p><p>acoustic transducer 164</p><p>activation energy (E) 110,181,200,204</p><p>activity 217</p><p>algorithms 209,241,242</p><p>alloys 110,112</p><p>alternating current thermoelectrical</p><p>analysis (ac-TEA) 9</p><p>American Society for Testing and</p><p>Materials (ASTM) 215</p><p>ammonium perchlorate 176,207</p><p>analysis 2</p><p>Analytical Chemistry 229,236</p><p>anisotropic materials 106</p><p>annealing 164</p><p>antiferromagnetism 43</p><p>aqueous solutions 127</p><p>archeaology 94,95</p><p>area (see peak area)</p><p>Arrhenius equation 181,191</p><p>Arrhenius parameters (E and A)</p><p>181,182,191,195,200-204,209</p><p>Arrhenius plot 181</p><p>atmosphere control 2,24</p><p>atomic force microscopy (AFM)</p><p>91,99,230</p><p>atmosphere self-generating 24</p><p>Austin-Rickett equation 193</p><p>autocatalysis 186</p><p>automation 40,42,88</p><p>average signal 62</p><p>Avrami-Erofeev equation</p><p>186,195,201,202,205</p><p>C</p><p>Cahn balance 21</p><p>calcium carbonate 183,207</p><p>calcium oxalate monohydrate 146</p><p>calcium sulfate dihydrate (gypsum)</p><p>47,97</p><p>calcium sulfate hemihydrate (Plaster of</p><p>Paris) 97</p><p>calibration 36-</p><p>40,67,102,106,142,215,245</p><p>calibration chemical 37,39</p><p>calibration factors, DSC/DTA 67,68</p><p>calibration, fusible link 36</p><p>calibration, heat capacity 72</p><p>calibration mass 36</p><p>calibration materials (see also</p><p>reference materials and calibrants)</p><p>40,69</p><p>calibration, temperature (see also</p><p>temperature calibration) 36</p><p>calorimetry 1</p><p>capillary inlet 142</p><p>carbon black 126</p><p>carbon tetrachloride</p><p>(tetrachloromethane) 82</p><p>catalytic reactions 94,152</p><p>cement 162</p><p>ceramics 112</p><p>certified reference materials (see</p><p>CRM)</p><p>cesium perchlorate 170</p><p>characteristics of measured curves</p><p>4,37,41,65,66</p><p>255</p><p>B</p><p>balance (see thermobalance)</p><p>baseline 65,66,241</p><p>baseline construction 66,67</p><p>Boersma DTA (see also heat flux</p><p>DSC) 57</p><p>brake linings 110,111</p><p>buoyancy effects 24,241</p><p>butter 87</p><p>A</p><p>(see fractional reaction) 183</p><p>curves 183,185,200-</p><p>204,208</p><p>curves 183,185,189,208</p><p>256</p><p>chemical potential 217</p><p>chemiluminescence 95</p><p>choosing thermal analysis equipment</p><p>238</p><p>clamping (see also DMA) 124</p><p>clays 112,169</p><p>coal 48,50,98,246</p><p>coatings 124</p><p>cobalt tartrate 143</p><p>coefficient of linear expansion</p><p>106,110,119</p><p>cold stage 92</p><p>combination of techniques (see also</p><p>simultaneous measurements) 129</p><p>combustion 16</p><p>compensation effect (kinetic)</p><p>193,196,204</p><p>competitive reactions 205,206</p><p>complementary techniques</p><p>131,181,189</p><p>complex reactions 205</p><p>concurrent measurements 129</p><p>concurrent reactions 205,207</p><p>consecutive reactions 206</p><p>constant acceleration 191</p><p>consumed gas analysis 152</p><p>contracting geometry models 187,200-</p><p>204</p><p>controlled rate thermal analysis</p><p>(CRTA) (see also SCTA) 29</p><p>controlled transformation rate thermal</p><p>analysis</p><p>conversion functions (see</p><p>also kinetic triplet) 185-190,193</p><p>coordination compounds 95,110,111</p><p>copper oxide reduction 152,153</p><p>copper sulfate pentahydrate</p><p>34,46,47,80,81,147,176</p><p>correlation coefficient 194,195</p><p>corrosion 50,51</p><p>coupled techniques (see simultaneous</p><p>techniques)</p><p>covalent crystals 13,14</p><p>creep 92,107</p><p>CRM (certified reference materials)</p><p>69,70</p><p>CRTA (see controlled rate thermal</p><p>analysis)</p><p>crucibles (see sample containers)</p><p>crystal defects</p><p>15,16,94,112,157,164,175,183</p><p>crystal imperfections (see crystal</p><p>defects)</p><p>crystalline solids 13</p><p>crystallization 83,97,107,136,159,245</p><p>Curie constant 43</p><p>Curie temperature (Curie point) 36,43</p><p>Curie temperature calibration 38,246</p><p>Curie-Weiss law 43</p><p>curing 62,83,85,174,246</p><p>curve characteristic points</p><p>4,37,41,65,66</p><p>D</p><p>-</p><p>D</p><p>temperature curves</p><p>185,189,200-204</p><p>-time curves 185,189,190</p><p>damping 121-124</p><p>databases 242</p><p>data presentation 37</p><p>data processing 241-244</p><p>dc conductance 172</p><p>deceleratory models 187</p><p>decomposition (see also thermal</p><p>decomposition)</p><p>15,46,76,139,164,184,245,246</p><p>deconvolution 205</p><p>decrepitation 92</p><p>defects (see crystal defects)</p><p>definitions 1,2,6-10</p><p>degradation 16,83,95,151,246</p><p>dehydration 76,164,245,246</p><p>dehydroxylation 169</p><p>dentures 120</p><p>depression of the melting point 215</p><p>derivative kinetic methods (see kinetic</p><p>methods, derivative)</p><p>derivative thermogravimetry (see</p><p>DTG)</p><p>257</p><p>Derivatograph 130,131</p><p>desorption 46,139</p><p>df (see dynamic force) 7</p><p>diamagnetism 43</p><p>diamonds 97</p><p>dielectric analysis 172-175</p><p>dielectric constant 173</p><p>dielectric thermal analysis (DETA)</p><p>9,172-175</p><p>differential methods (see also</p><p>derivative methods) 2</p><p>differential scanning calorimetry (see</p><p>DSC)</p><p>differential thermal analysis (see DTA)</p><p>diffusion 163,206</p><p>diffusion models 187</p><p>dilatometry 106</p><p>discriminatory kinetic methods (see</p><p>kinetic methods)</p><p>Doyle’s approximation for the</p><p>temperature integral 192,200</p><p>DMA (see dynamic mechanical</p><p>analysis)</p><p>DSC 6,55-90,172,173</p><p>DSC calibration 67-72</p><p>DSC-FTIR 151</p><p>DSC, heat flux 56,57,60</p><p>DSC, interpretation 76,77</p><p>DSC, modulated temperature (see also</p><p>modulated temperature DSC) 61</p><p>DSC, power compensated 57,60</p><p>DSC, purity determination using 215-</p><p>227</p><p>DSC-XRD 130,135,136</p><p>DTA 2,6,55-90</p><p>DTA, Boersma 57</p><p>DTA, calorimetric 57</p><p>DTA, classical 55,60</p><p>DTA, interpretation 76,77</p><p>DTG (derivative thermogravimetry)</p><p>21,44</p><p>dynamic force thermomechanometric</p><p>analysis (df-TMA) 7,105</p><p>dynamic force thermomechanometry</p><p>(df-TM) 7,105</p><p>E</p><p>EGA (evolved gas analysis)</p><p>10,76,130,139</p><p>EGD (evolved gas detection)</p><p>10,76,139</p><p>elastomers (see also rubbers)</p><p>72,124,127</p><p>emanating power 160</p><p>emanation thermal analysis (ETA)</p><p>10,157-164</p><p>endotherm 55,215</p><p>endothermic processes 55</p><p>enthalpy 67</p><p>enthalpy of fusion (melting)</p><p>70,71,80,215,216,222</p><p>enthalpy of sublimation 85</p><p>enthalpy of vaporization 85,87</p><p>environmental aspects 152</p><p>epoxy resins 85</p><p>ETA (see emanation thermal analysis)</p><p>eutectic 78,217</p><p>eutectic formation 16</p><p>eutectic phase diagram 78, 219</p><p>evolved gas analysis (see EGA)</p><p>evolved gas collection 147</p><p>evolved gas detection (see EGD)</p><p>examination questions 247-250</p><p>exotherm 55</p><p>exothermic processes 55</p><p>expansion coefficient (see coefficient</p><p>of linear expansion)</p><p>experiments 245,246</p><p>explosion 16</p><p>explosives 72,97</p><p>exponential law 186</p><p>dynamic mechanical analysis (DMA)</p><p>105,120,121</p><p>dynamic mechanical thermal analysis</p><p>(DMTA) (see dynamic mechanical</p><p>analysis, DMA)</p><p>dynamic rate TG 34</p><p>dynamic thermomechanical analysis</p><p>(DTMA) (see dynamic mechanical</p><p>analysis (DMA))</p><p>258</p><p>H</p><p>hazardous products 152,164</p><p>heat 1</p><p>heat capacity 59,69,73,83,220,241,246</p><p>heat capacity, calibration (see</p><p>calibration, heat capacity)</p><p>heat-flux DSC (see DSC, heat flux)</p><p>heat-flux DTA (see DTA, heat flux)</p><p>heating rate, 55,183,200,203</p><p>heat transfer 182,185</p><p>heterogeneous reactions 181,182</p><p>hexachloroethane 170</p><p>high pressure 3</p><p>high resolution (Hi-Res) TG 34</p><p>history of thermal analysis 1,4</p><p>homogeneous reactions 181</p><p>Hooke’s law 115,117</p><p>hot stage 92</p><p>hot-stage microscopy (see</p><p>thermomicroscopy)</p><p>hygrometer 148</p><p>extent of reaction (see fractional</p><p>reaction 183</p><p>extrapolated onset temperature 83</p><p>F</p><p>fats 87</p><p>ferroelectric materials 176</p><p>ferromagnetism 38,43</p><p>fibres 120,125,171</p><p>films 102,124</p><p>“fingerprint” comparison 80,166</p><p>first-order kinetics 188</p><p>flow rates 25</p><p>Flynn and Wall kinetic method 198</p><p>foaming 92</p><p>foods 87,127</p><p>Fourier transform 61</p><p>Fourier transform infrared</p><p>spectroscopy (see FTIR)</p><p>fractional reaction 183</p><p>fraction melted (F) 218</p><p>frequency factor (A) 181,202,203</p><p>Friedman kinetic method 197</p><p>FTIR (Fourier transform infrared</p><p>spectroscopy) 139,143-146</p><p>FTIR microscope 97</p><p>furnace 22,23,29</p><p>fusible-link temperature calibration 36</p><p>fusion (see melting)</p><p>G</p><p>garbage 152</p><p>gas cell for FTIR 144,145</p><p>gas chromatography (GC) 139,144</p><p>gas density detectors 140</p><p>gas detectors 147,148</p><p>gases, inert 157</p><p>gases, thermal conductivity 141</p><p>gas release in ETA 160</p><p>gas sampling valve 144</p><p>geometrical models 187</p><p>Ginstling-Brounshtein equation 187</p><p>glass transition 13,62,67,68,83,97,</p><p>119,120.127,164,175,245</p><p>I</p><p>ICTAC (see International</p><p>Confederation for Thermal Analysis)</p><p>ICTAC-NIST magnetic standards 40</p><p>ICTAC reference materials</p><p>36,40,69,71,165</p><p>impact resistance 124</p><p>imperfections (see crystal defects)</p><p>indium 67,216</p><p>induction period 194</p><p>inert gases (see gases,inert)</p><p>influence of temperature on reaction</p><p>rate 191</p><p>infrared detector 144,147</p><p>glass transition temperature</p><p>13,83,164,175,241,245</p><p>glasses 13,106,178</p><p>grain size 161</p><p>Gram-Schmidt plot 144,146</p><p>graphite 97</p><p>growth of nuclei 97,170,184,195</p><p>gypsum 47,97</p><p>259</p><p>infrared heating 23</p><p>infrared pyrometers 23</p><p>infrared spectroscopy (see also FTIR)</p><p>instrument, choosing 238</p><p>instrument specifications 4,5</p><p>integral kinetic methods 210</p><p>International Confederation for</p><p>Thermal Analysis and Calorimetry</p><p>(ICTAC)(see www.ictac.org) 1,4,229</p><p>interpretation of results</p><p>3,44,45,76,77,143,165</p><p>inverse kinetic problem (IKP) 193</p><p>ion implantation 158,159</p><p>ionic crystals 13,14</p><p>ionization detectors 140</p><p>iron(II) carbonate (siderite) 50</p><p>irreversible processes 62,63</p><p>isoconversional kinetic methods (see</p><p>kinetic methods, isoconversional)</p><p>isokinetic effect 204</p><p>isothermal conditions 183,205,209</p><p>isothermal kinetic analysis 194</p><p>isothermal yield-time curves 183</p><p>L</p><p>laser dilatometer 108,109</p><p>lasers 23</p><p>Leco-TGA 42</p><p>less-common techniques 157-178</p><p>linear variable differential transformer</p><p>(LVDT) 107,108,121,166,174</p><p>liquid crystals 85,86,97,106</p><p>liquids 65,107,124,175</p><p>literature of thermal analysis 231-237</p><p>literature, books 231-234</p><p>literature, computer courses 234</p><p>literature, conference proceedings</p><p>235,236</p><p>literature, history 237</p><p>literature, journals 236</p><p>literature, manufacturers 237</p><p>literature, videos 234</p><p>loss tangent (see phase angle)</p><p>low temperature 57,81,87</p><p>LVDT (see linear variable differential</p><p>transformer)</p><p>J</p><p>jet separator 142</p><p>JMAEK equation (see Avrami-Erofeev</p><p>equation)</p><p>Journal of Thermal Analysis and</p><p>Calorimetry 229,236</p><p>K</p><p>kaolins (see clays) 169</p><p>katharometers 140</p><p>kinetic analysis 181-214,241</p><p>kinetic behaviour prediction of</p><p>181, 206</p><p>kinetic compensation effect (KCE)</p><p>(see compensation effect)</p><p>kinetic method, Flynn and Wall 198</p><p>kinetic method, Friedman 197</p><p>kinetic method, Kissinger 198,205</p><p>kinetic method, Serra, Nomen and</p><p>Sempere (non-parametric method) 199</p><p>kinetic method, Ozawa 198,199</p><p>kinetic methods, classification 195</p><p>kinetic methods, drivative 195</p><p>kinetic methods, discriminatory 195</p><p>kinetic methods, integral 195</p><p>kinetic methods, isoconversional 195</p><p>kinetic methods, non-discriminatory</p><p>195</p><p>kinetic methods, second derivative 198</p><p>kinetic model 181</p><p>kinetic parameters (see also kinetic</p><p>triplet) 181,195,200</p><p>kinetic parameters and shapes of TA</p><p>curves 200-204</p><p>kinetic results, publication 209</p><p>kinetic standards 206,207</p><p>kinetic test data 207,208</p><p>kinetic triplet 197,209</p><p>Kissinger kinetic method 198,205</p><p>Knudsen cell 49</p><p>M</p><p>magnesium hydroxide (brucite) 169</p><p>260</p><p>magnetic field 43</p><p>magnetic standard temperature</p><p>calibration (see temperature</p><p>calibration) 36-40,246</p><p>magnetic susceptibility 43,49</p><p>magnetic susceptibility, mass 43</p><p>magnetic susceptibility, volume 43</p><p>magnetic transitions 43</p><p>manufacturers 238,239</p><p>margarine 87</p><p>mass and weight 19</p><p>mass calibration 36</p><p>mass spectrometry (MS) 139,141,151</p><p>mass transfer 185</p><p>mechanism of reaction 181</p><p>melting 14,76,119,164,215,219</p><p>metals 13,14,162</p><p>Mettler-Toledo Thermomicroscopy-</p><p>DSC 96</p><p>Mettler-Toledo Thermomicroscopy-</p><p>TG 97</p><p>Mettler-Toledo TMA/SDTA 134</p><p>mf (see modulated force) 7</p><p>Micro Thermal Analysis 91,99-</p><p>102,229</p><p>micro thermomechanical analysis 102</p><p>microwave heating 23</p><p>microwave thermal analysis (MWTA)</p><p>177,178</p><p>minerals 48</p><p>modulated force thermomechanometric</p><p>analysis (mf-TMA) 7,105</p><p>modulated force thermomechanometry</p><p>(mf-TM) 7,105,120</p><p>modulated temperature DSC</p><p>(MTDSC) 61,191,229</p><p>modulated temperature</p><p>thermogravimetry 35</p><p>modulated temperature</p><p>thermomechanical analysis (MTMA)</p><p>118</p><p>modulation 62,63</p><p>modulation amplitude 61</p><p>modulation frequency 61</p><p>modulus, complex 121</p><p>N</p><p>neoprene rubber 119</p><p>neutron irradiation 158</p><p>Netzsch TG-DTA 130,132</p><p>Newton’s law of cooling 60</p><p>Newton’s law of viscous flow 115-117</p><p>nickel oxide reduction 161,162</p><p>NIK (see non-isothermal kinetics)</p><p>NMR 225</p><p>noise 25,62,165</p><p>noise abatement 124</p><p>nomenclature 2,3,6-10,35,237</p><p>non-crystalline solids 13</p><p>non-discriminatory kinetic methods</p><p>(see kinetic methods, isoconversional)</p><p>non-isothermal conditions</p><p>non-isothermal kinetics (NIK)</p><p>182,195,209</p><p>non-isothermal kinetics, history 182</p><p>non-linear regression 205,210</p><p>non-parametric kinetic method (see</p><p>kinetic methods) 199</p><p>non-reversing signal 62,63</p><p>nucleation 16,170,182,184,195</p><p>nuclei 16</p><p>nucleus growth 16,182</p><p>numerical differentiation 241,242</p><p>numerical integration 241,242</p><p>numerical smoothing 243</p><p>Nyquist theorem 165</p><p>O</p><p>oil shales 171,176</p><p>optical encoder 121</p><p>optoelectronic transducer 108,109</p><p>order of reaction models 188,200,202</p><p>modulus, loss 121</p><p>modulus, shear 121</p><p>modulus, storage 121</p><p>modulus, tensile 121</p><p>modulus, Young's 116,120,124</p><p>moisture analyzer 148</p><p>molecular crystals 13</p><p>mole fraction 218</p><p>261</p><p>P</p><p>paper 127</p><p>parallel measurements 129</p><p>peak area 55,67, 220,221,241,242,244</p><p>peak resolution 241</p><p>peak shape 220</p><p>peak temperature 65,66</p><p>perfect crystal 13</p><p>perfect solid 13</p><p>Perkin-Elmer DSC Robotic system 88</p><p>Perkin-Elmer magnetic standards 40</p><p>Perkin-Elmer TG-FTIR 145,146</p><p>PET, MTDSC 63</p><p>pharmaceuticals 92,97,102</p><p>phase angle 121</p><p>phase diagrams 78,80</p><p>phase transitions 14,245</p><p>photothermal reactions 176</p><p>piezoelectric transducers 166</p><p>Plaster of Paris 97</p><p>plastic waste 83,84</p><p>platinum resistance thermometers</p><p>28,58</p><p>PMMA 177</p><p>polarizing filters 92</p><p>polybutadiene/PVC blend 101</p><p>polyethylene 84,119,125,245</p><p>polymers 48,81,82-84,95,101,102,</p><p>117a,118,120,125,127,151,169,171,175</p><p>polymer crystallinity 245</p><p>polymer filler 246</p><p>polymorphism 97</p><p>polystyrene 151</p><p>potassium chlorate 170</p><p>potassium nitrate 97,98,161,162,170</p><p>potassium perchlorate 169,170</p><p>potassium sulfate 169,170</p><p>Q</p><p>quartz crystal balance 20</p><p>quasi-isothermal methods 30</p><p>R</p><p>radiation damage 164</p><p>radioactive substances 157,159</p><p>radionuclides 157</p><p>radon 157,159</p><p>rate coefficient 186-188</p><p>rate constant (see rate coefficient)</p><p>rate controlled thermal analysis (see</p><p>controlled rate thermal analysis,</p><p>CRTA)</p><p>rate equations 182,185-188</p><p>rate equations table 186-188</p><p>rate jump 30,33</p><p>reactant-product interface 185</p><p>reaction geometry 185</p><p>reaction interface 185</p><p>reaction mechanism 185</p><p>powders 161</p><p>power compensated DSC (see DSC,</p><p>power compensated)</p><p>power law 186</p><p>prediction of kinetic behaviour 206</p><p>pre-exponential factor (see also</p><p>frequency factor) 181,200,203</p><p>pre-melting 220-222</p><p>presentation of results 37,143,144,146</p><p>programmed temperature experiments</p><p>(see non-isothermal conditions)</p><p>propellants 72</p><p>Prout-Tompkins equation 186</p><p>proximate analysis of coal 48</p><p>publication of kinetic results 209</p><p>pulsed gas thermal analysis 139,152</p><p>pulse generator 167</p><p>purge gas 24,65</p><p>purity 76,81,215-227,241,246</p><p>PVC 175,176</p><p>pyrites 48,50,143</p><p>pyrometers 23</p><p>pyrotechnics 75,96</p><p>oscillating DSC (see modulated</p><p>temperature DSC)</p><p>oxidation 16,46,83,84,95,162</p><p>oxidation of graphite 97</p><p>oxides 112</p><p>oxyluminescence 95</p><p>Ozawa kinetic method 198,199</p><p>262</p><p>reaction order (RO) models</p><p>188,200,202,205,210</p><p>reactive gases 24</p><p>recrystallisation (see crystallization)</p><p>recycling 83</p><p>reduced time 194,205</p><p>reference materials (see also</p><p>calibration materials) 40,55,69</p><p>reference materials certified (see</p><p>CRM)</p><p>reference materials ICTAC (see</p><p>ICTAC reference materials)</p><p>repeatability 130</p><p>reproducibility 130,166,185</p><p>residuals 194</p><p>resistance thermometers 28</p><p>resonance frequency 120</p><p>reversible decompositions 182,191</p><p>reversible processes 76,191,205</p><p>reversing signal 62</p><p>robotic systems (see automation)</p><p>rubbers (see also elastomers)</p><p>119,126,246</p><p>scanning tunnelling microscopy (STM)</p><p>91,99</p><p>SCTA (see sample controlled thermal</p><p>analysis)</p><p>secondary reactions 144</p><p>second-order kinetics 188</p><p>self-cooling 182,206</p><p>self-generated atmosphere 24</p><p>self-heating 182,206</p><p>Serra, Nomen and Sempere kinetic</p><p>method (non-parametric) 199</p><p>Sesták-Berggren equation 193</p><p>Setaram TG-DSC/DTA 130,132,133</p><p>sf (see static force)</p><p>shelf-lives 206</p><p>Shimadzu TMA-50 instrument 114</p><p>siderite 50</p><p>sigmoid models 186</p><p>signal-to-noise (see noise)</p><p>Simpson’s rule for integration 242</p><p>simulated kinetic data 208</p><p>simultaneous measurements 129,172</p><p>simultaneous TG-DSC 130</p><p>simultaneous TG-DTA 130</p><p>simultaneous TG-FTIR 139</p><p>simultaneous TG-MS 139</p><p>simultaneous TL-DSC 94</p><p>simultaneous TM-DTA</p><p>simultaneous thermal analysis 129,172</p><p>simultaneous thermomicroscopy -</p><p>DSC/DTA 95,96,225</p><p>simultaneous thermomicroscopy - TG</p><p>96-98</p><p>simultaneous thermomicroscopy -</p><p>XRD 97</p><p>simultaneous thermoptometry - DSC</p><p>sintering 14,110,112,161</p><p>smoothing of data 241,242</p><p>sodium bicarbonate 151</p><p>sodium nitrite 176</p><p>sodium perchlorate 170</p><p>soils 152</p><p>solid-gas reactions 152,162</p><p>solid-liquid reactions 162</p><p>solid-solid reactions 163</p><p>S</p><p>sample 2,13,26</p><p>sample containers (see sample pans)</p><p>sample controlled thermal analysis</p><p>(SCTA) (see also controlled rate</p><p>thermal analysis, CRTA) 29-35</p><p>sample mass 26</p><p>sample pans 64</p><p>sample preparation 64,65,157</p><p>sample press 64</p><p>sampling 64</p><p>sapphire discs 72</p><p>sapphire sample pans 92</p><p>Savitsky-Golay numerical methods</p><p>242,243</p><p>SBR 126</p><p>scanning electron microscopy (SEM)</p><p>98</p><p>scanning thermal microscope (see</p><p>Micro Thermal Analysis) 147</p><p>263</p><p>T</p><p>TA Instruments DMA 2980 121,123</p><p>TA Instruments Micro TA 99-102</p><p>TA Instruments DEA 2970 175</p><p>(see phase angle)</p><p>techniques, primary 6</p><p>techniques, special derived 7-10</p><p>temperature 1,6</p><p>temperature calibration</p><p>102,114,115,246</p><p>temperature control 28,29</p><p>temperature difference 6</p><p>temperature influence on reaction rate</p><p>191,192</p><p>temperature integral (p(x)) 192</p><p>temperature jump 30,32,191</p><p>temperature measurement 26</p><p>temperature onset 65</p><p>temperature peak 65</p><p>temperature programme 2,3,29</p><p>(see glass-transition temperature)</p><p>TG (see thermogravimetry)</p><p>TG-DTA 37, 130</p><p>TG-FTIR 139,148,151</p><p>TG-MS 139,148-152</p><p>TGA (see thermogravimetric analysis)</p><p>thermal analysis 1,2,229,230</p><p>thermal analysis definition 2,6-10</p><p>thermal analysis examination questions</p><p>247-250</p><p>thermal analysis experiments 245,246</p><p>thermal analysis literature 231-237</p><p>thermal conductivity 72,74,75</p><p>thermal conductivity detector</p><p>(katharometer) 140</p><p>thermal conductivity of gases 141</p><p>thermal decomposition 15</p><p>thermal diffusivity 72</p><p>thermal events 4,15</p><p>thermal lag 216,220,221</p><p>thermal resistance 59,216</p><p>thermally stimulated current analysis</p><p>(TSCA) 9</p><p>thermally stimulated current</p><p>measurement (TSCM) 9</p><p>thermally stimulated discharge current</p><p>measurement (TSDC) 172</p><p>thermally stimulated emanation</p><p>measurement (ETA) 10</p><p>thermally stimulated exchanged gas</p><p>detection (EGD) 6</p><p>thermally stimulated exchanged gas</p><p>measurement (EGA) 6</p><p>thermoacoustimetric analysis (TAA) 6</p><p>thermoacoustimetry 6,164-171</p><p>thermobalance 19,20</p><p>thermobalance sensitivity 19</p><p>Thermochimica Acta 229,236</p><p>thermocouples 26-28</p><p>solid solutions 16,78,97,215,225</p><p>solid state 13</p><p>solid-state reactions 160,182</p><p>specific heat capacity (see heat</p><p>capacity)</p><p>spinel formation 163</p><p>spreadsheets 242</p><p>standard conditions (thermodynamic)</p><p>217</p><p>standard materials 40,206</p><p>static electricity 25</p><p>static force thermomechanometric</p><p>analysis (sf-TMA) 7,105,112</p><p>static force thermomechanometry (sf-</p><p>TM) 7,105,112</p><p>statistical criteria 194</p><p>step method for purity determination</p><p>224,225</p><p>stepwise isothermal analysis 30,191</p><p>stethoscope 164,165</p><p>stress, compression 116</p><p>stress, shear 116</p><p>stress-strain relationships 115,117</p><p>stress, tensile 115</p><p>strontium oxalate 148,149</p><p>sublimation 14,85,159,215</p><p>sucrose 127</p><p>symbols used in the text 251,252</p><p>synthesis methods of kinetic analysis</p><p>195</p><p>264</p><p>thermocouples composition 27,28</p><p>thermodiffractometric analysis 10</p><p>thermodiffractometry 10</p><p>thermodilatometric analysis 7,105</p><p>thermodilatometry (TD) 7,105-</p><p>107,163</p><p>thermodynamics 1</p><p>thermoelectrical analysis (TEA) 6,172</p><p>thermoelectrometry 6,9,157,172</p><p>thermogram (misuse) 4</p><p>thermogravimetric analysis (TGA) (see</p><p>also thermogravimetry) 6</p><p>thermogravimetry (TG) 6,19-54</p><p>thermogravimetry data 44</p><p>thermoluminescence analysis 8,91</p><p>thermoluminescence measurement</p><p>8,91,94,95,98,99</p><p>thermomagnetic analysis 6</p><p>thermomagnetometry (TM) 6,43,48-51</p><p>thermomanometric analysis 6</p><p>thermomanometry 6</p><p>thermomechanical analysis (see also</p><p>TMA) 105,112-114</p><p>thermomechanometry 6,105</p><p>thermometry 1,6</p><p>thermomicroscopic analysis 8,91</p><p>thermomicroscopy 8,48,91-93,170</p><p>thermomicroscopy-DSC or DTA 95</p><p>thermomicroscopy, history 91</p><p>thermomolecular flow 24</p><p>thermophotometric analysis 8</p><p>thermophotometry 8,91-93</p><p>thermo-optical analysis (TOA) (see</p><p>also thermoptometry) 6,91</p><p>thermoptometric analysis 6,91</p><p>thermoptometry 6,8,91</p><p>thermorefractometry 91</p><p>thermosonimetric analysis (TSA) 9</p><p>thermosonimetry (TS) 9,157,164-171</p><p>thermosonimetry - DTA 165,170</p><p>thermosonimetry - dilatometry 165,170</p><p>thermospectrophotometric analysis</p><p>8,91</p><p>thermospectrophotometry 8,91</p><p>thermovoltaic detection (TVD) 172</p><p>third-order reaction 188</p><p>TM (see thermomagnetometry)</p><p>TMA (see thermomechanical analysis)</p><p>TMA probes 114</p><p>transducer 4,107-109,164-167</p><p>trapezoidal rule for integration 242</p><p>TS (see thermosonimetry)</p><p>Z</p><p>zero-order reaction 188</p><p>Y</p><p>Young's modulus (see modulus,</p><p>Young's)</p><p>X</p><p>X-ray diffraction (XRD) 135,136,178</p><p>W</p><p>water 87</p><p>waxes 87</p><p>websites 239</p><p>Weiss constant 43</p><p>V</p><p>vaporization 85,87</p><p>vibration dissipation 124</p><p>video camera 92,98</p><p>viscoelasticity 116</p><p>viscosity coefficient 116</p><p>vulcanization 127</p><p>U</p><p>uniqueness of kinetic parameters</p><p>195,196</p><p>></p><p>/ColorImageDict ></p><p>/JPEG2000ColorACSImageDict ></p><p>/JPEG2000ColorImageDict ></p><p>/AntiAliasGrayImages false</p><p>/DownsampleGrayImages true</p><p>/GrayImageDownsampleType /Bicubic</p><p>/GrayImageResolution 150</p><p>/GrayImageDepth 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[</p><p>0.00000</p><p>0.00000</p><p>0.00000</p><p>0.00000</p><p>]</p><p>/PDFXOutputIntentProfile (None)</p><p>/PDFXOutputCondition ()</p><p>/PDFXRegistryName (http://www.color.org?)</p><p>/PDFXTrapped /False</p><p>/SyntheticBoldness 1.000000</p><p>/Description</p><p>/ENU</p><p>>></p><p>>> setdistillerparams</p><p>> setpagedevice</p><p>The sensitivity of a thermobalance and the maximum load which it can accept, without</p><p>damage, are related. Typical values are maximum loads of 1 g and sensitivities of the order of</p><p>19</p><p>20</p><p>Electrobalances suitable for simultaneous DTA-TG are available. The electrical signals for</p><p>simultaneous measurements are usually taken off the balance beam near the fulcrum so as to</p><p>minimize disturbance of the balance mechanism. Simultaneous measurements are described</p><p>in Chapter 7.</p><p>The use of quartz crystal microbalances has also been suggested [5-10]. Sensitivities of the</p><p>order of 0.1 ng have been reported [4], but stability and operating temperature range are limited.</p><p>3.3 Heating the Sample</p><p>In conventional thermobalances, there are three main variations in the position of the sample</p><p>relative to the furnace as shown in Figure 3.3. The sample may be suspended from the balance</p><p>beam and hang down into a furnace or controlled-temperature environment. The suspension</p><p>system needs protection by baffles or cooling to prevent rising hot gas from affecting the</p><p>balance mechanism. Alternatively, the sample may be placed upon a rigid vertical support</p><p>above the balance beam and the furnace suitably modified for this position. Heat convection</p><p>is then less of a problem, but the mass of the sample support required is a disadvantage. The</p><p>third major configuration is when the sample support is a horizontal extension of the balance</p><p>beam and the furnace is also arranged horizontally. Problems of condensation of evolved</p><p>volatiles on the sample supports are decreased, but thermal expansion of the beam material has</p><p>to be minimized.</p><p>Software usually provides for electrical taring and for scale expansion to give an output of</p><p>mass loss as a percentage of the original sample mass. The output may be differentiated</p><p>numerically, with respect to time or temperature, to give a derivative thermogravimetric (DTG)</p><p>curve.</p><p>21</p><p>The furnace is normally an electrical resistive heater and may also, as shown in Figure 3.3,</p><p>be within the balance housing, part of the housing, or external to the housing. The internal</p><p>arrangement is suitable for small furnaces and both heating and cooling rates can be high,</p><p>allowing a rapid turnaround time during use of the instrument.</p><p>The furnace should (i) be non-inductively wound, (ii) be capable of reaching 100 to 200°C</p><p>above the maximum desired working temperature, (iii) have a uniform hot-zone of reasonable</p><p>length, (iv) reach the required starting temperature as quickly as possible, (i.e. have a low heat</p><p>capacity), (v) not affect the balance mechanism through radiation or convection. Transfer of</p><p>22</p><p>heat to the balance mechanism should be minimized by inclusion of radiation shields and</p><p>convection baffles. The materials used for construction of the resistance elements are governed</p><p>by both the temperature range that is to be used and the nature of the gaseous environment in</p><p>the furnace. Beyond the maximum limits of rhodium (about 1800°C), molybdenum (2200°C)</p><p>or tungsten (2800°C) elements may be used, but only in non-oxidizing atmospheres. The</p><p>working life of a resistive furnace is limited and can be increased by limiting the time of</p><p>operation at high temperatures to the minimum possible for the information required.</p><p>Manufacturers market a variety of furnaces and modular control systems to combine with</p><p>their balance [3], e.g. a Nichrome or Kanthal based furnace in conjunction with fused silica</p><p>refractories for operation up to 1000°C, and a platinum/rhodium or based furnace</p><p>combined with alumina refractories for operation to 1500-1700°C. Protective circuits to</p><p>prevent thermal runaway in the event of thermocouple failure are also a necessity.</p><p>The magnetic field generated by the resistive heating must be considered when working with</p><p>magnetic samples [3]. To minimize the magnetic field, it is common to wind the furnace in a</p><p>bifilar fashion by having the direction of flow for the electrical current opposite in each half</p><p>of the winding.</p><p>Steinheil [11] described a vacuum microbalance system, for use at high temperatures (1600</p><p>to 2400°C) which incorporated induction heating by a high-frequency electromagnetic field,</p><p>but did not allow weighing during actual heating because of the electromagnetic forces acting</p><p>on the sample.</p><p>Furnaces containing electrical resistive heaters rely mainly on heating of the sample by</p><p>conduction, through solid or gas, with inevitable large temperature gradients, especially when</p><p>dealing with samples of low thermal conductivity such as polymers and inorganic glasses.</p><p>Heating by radiation becomes significant only at high temperatures in such furnaces, but</p><p>alternative heating systems using either infrared or microwave radiation have been considered.</p><p>For infrared heating [3,12,13] the light from several halogen lamps is focused onto the</p><p>sample by means of elliptic or parabolic reflectors. Heat transfer is virtually instantaneous,</p><p>provided that the path between lamp and sample, which includes the balance container, is</p><p>transparent to the radiation. Temperatures of over 1400°C may be achieved at heating rates of</p><p>up to 1000°C/min and control within If infrared-absorbing gases are evolved from</p><p>the sample during heating, the heat flux reaching the sample will change, particularly if these</p><p>gases condense on the surfaces of the balance container which are in the radiation pathway.</p><p>Karmazin et al. [14,15] have suggested the use of microwaves to generate heat uniformly</p><p>within the sample. Such a process would have the immediate advantage of allowing for use of</p><p>larger and more representative samples than are often used in thermal analysis. Temperature</p><p>measurement and power control both present problems in using microwaves. A thermocouple</p><p>may be positioned in the waveguide if its orientation is such that it collects no energy itself</p><p>from the microwaves, and its size is small compared to the guide so that reflected waves are</p><p>negligible. The thermocouple is then used [14] for power control via a microcomputer system.</p><p>The use of lasers for heating and infrared pyrometers for remote temperature measurement</p><p>in the in situ thermal analysis of bulk materials has also been suggested [16].</p><p>23</p><p>3.4 The Atmosphere</p><p>24</p><p>Thermobalances are normally housed in glass or metal systems [17], to allow for operation at</p><p>pressures ranging from high vacuum (about to high pressure (about 70 bar), of inert,</p><p>oxidizing, reducing or corrosive gases [18]. Microbalances are affected by a variety of</p><p>disturbances [1,3,4,17]. One correction which may have to be made is for buoyancy arising</p><p>from lack of symmetry in the weighing system. If the asymmetry can be measured in terms of</p><p>a volume V, the mass of displaced gas (assuming ideal gas behaviour) is m = pM V/RT (where</p><p>p is the pressure and M the molar mass). The buoyancy thus depends not only on the</p><p>asymmetry V, but also on the pressure, temperature and nature of the gas. Attempts may be</p><p>made to reduce V to zero, or a correction may be calculated, or an empirical correction may be</p><p>applied by heating an inert sample under similar conditions to those to be used in the study of</p><p>the sample of interest [4]. Gallagher [3] has pointed out that the masses of of air,</p><p>hydrogen and carbon dioxide, at room temperature and pressure, are about 120 g, 9 g and</p><p>196 g, respectively. Very accurate work requires allowance for these differences. Generally,</p><p>during the evolution of volatile products the buoyancy effects will change.</p><p>At low pressures to 270 Pa), a particular problem is thermomolecular flow [1] which</p><p>results when there is a temperature gradient along the sample holder and support. This gradient</p><p>causes 'streaming' of molecules in the direction hot cold, i.e. up the suspension as a rule, giving</p><p>spurious mass changes. Thermomolecular flow may be minimized: (i) by working outside the</p><p>pressure range by adding inert gas, or (ii) by careful furnace design and sample placement,</p><p>including use of a symmetrical balance design with twin furnaces, or (iii) by determination of</p><p>corrections required,</p><p>using an inert sample, as is done for buoyancy corrections.</p><p>The sample may be heated in a small container with a restricted opening. Decomposition</p><p>then occurs in a self-generated atmosphere [19] of gaseous decomposition products. The</p><p>inhibiting or catalytic effects ofthese products on the decomposition can then be studied. Garn</p><p>and co-workers [20,21 ] have described the design and use of furnaces for carrying out reactions</p><p>in controlled atmospheres of ligand. Such systems are essential for studying the</p><p>thermodynamic reversibility of dissociations of coordination compounds.</p><p>At atmospheric pressure, the atmosphere can be static or flowing. A flowing atmosphere</p><p>has the advantages that it: (i) decreases condensation of reaction products on cooler parts of</p><p>the weighing mechanism, (ii) flushes out corrosive products, (iii) decreases secondary</p><p>reactions, and (iv) acts as a coolant for the balance mechanism. The balance mechanism</p><p>should, however, not be disturbed by the gas flow. It is possible for the balance mechanism to</p><p>be protected by an inert gas atmosphere, while a corrosive gas or vapour is passed over the</p><p>sample (e.g. vapour for dehydration studies).</p><p>The choice of purge gas is determined not only by its reactivity, or lack of reactivity, towards</p><p>the sample, but also by cost, availability, purity, density, and thermal conductivity. It may be</p><p>necessary to decrease the amount of residual oxygen in a nominally “inert” gas stream. Passage</p><p>over heated titanium turnings or powder is effective. The density of a purge gas can be used</p><p>25</p><p>to minimize back-streaming [3]. If the balance is above the furnace and sample, then denser</p><p>argon is preferable to helium, but the reverse holds for the opposite configuration of balance</p><p>and furnace [22]. The high thermal conductivity of a purge gas such as helium can significantly</p><p>affect heat transfer compared to gases such as argon or nitrogen.</p><p>Measurement and/or control of the flow rate of the purge gas selected can be done using</p><p>various devices, including floats and tubes, or soap-film bubble towers, or more expensive mass</p><p>flow controllers [3]. Valves for programmed switching of gas streams, e.g. to change from an</p><p>inert to an oxidizing atmosphere, as in the proximate analysis of coal, are also available.</p><p>The balance mechanism may need to be protected from reactive gases (incoming reactants</p><p>or volatile products) by passing an independent stream of inert purge gas through the balance</p><p>chamber.</p><p>Reactive gas streams can be prepared by incorporating volatile liquid or solid species into</p><p>the purge gas by passing the gas stream through the liquid, or over the solid, at the appropriate</p><p>temperature and rate.</p><p>Many decompositions are reversible if a supply of the gaseous products of reaction is</p><p>maintained. Such studies thus require careful control of the surrounding atmosphere and</p><p>should include runs at reduced pressures. Reducing the pressure, though, worsens the heat</p><p>exchange, causing problems in temperature measurement.</p><p>The noise level of TG traces at pressures above about 20 kPa usually increases as the</p><p>temperature increases, on account of thermal convection [1,23,24]. The use of dense carrier</p><p>gases at high pressures in hot zones with large temperature gradients gives the most noise.</p><p>Variations in the flow rate of the gas do not affect the noise level much, but may shift the</p><p>weighing zero. Noise levels also increase as the radius of the hangdown tube increases.</p><p>Thermal convection, and hence noise, can be reduced by altering the gas density gradient by</p><p>introducing a low density gas, such as helium, above the hot region. Alternatively, and more</p><p>practically, baffles can be introduced in the hangdown tube. A series of close-fitting</p><p>convoluted baffles was found to be most successful [25]. Even with the baffles it was found</p><p>that changes in ambient temperature caused non-turbulent gas movements in the hangdown tube</p><p>and hence apparent changes of mass. Sample containers should be of low mass and of inert</p><p>material (e.g. platinum containers may catalyze some reactions). Samples should generally be</p><p>thinly spread to allow for ready removal of evolved gases. Results should be checked for</p><p>sample-holder geometry effects.</p><p>Build up of electrostatic charge on glass housings is another source of spurious mass effects.</p><p>Methods proposed for dealing with this problem include use of weak radioactive sources for</p><p>ionization of the balance atmosphere, coating of glassware with a sputtered metal film or other</p><p>metal shielding, and the use of various commercial sprays or solutions. Wiping the outside of</p><p>the glassware with ethanol is reasonably effective.</p><p>26</p><p>3.5 The Sample</p><p>Although solid samples may be nominally of the same chemical composition, there may be</p><p>considerable differences in their behaviour on heating. These differences arise from structural</p><p>differences in the solid, such as the defect content, the porosity and the surface properties,</p><p>which are dependent on the way in which the sample is prepared and treated after preparation.</p><p>For example, very different behaviour will generally be observed for single crystals compared</p><p>to finely ground powders of the same compound [26]. In addition to the influence of defects</p><p>on reactivity [27], the thermal properties of powders differ markedly from those of the bulk</p><p>material.</p><p>As the amount of sample used increases, several problems may arise. The temperature of</p><p>the sample becomes non-uniform through slow heat transfer and through either self-heating or</p><p>self-cooling as reaction occurs. Exchange of gas with the surrounding atmosphere is also</p><p>decreased. These factors may lead to irreproducibility. Even when the sample material is</p><p>inhomogeneous and hence a larger sample becomes desirable (e.g. coal and mineral samples),</p><p>the sample mass should be kept to a minimum and replicates examined for reproducibility if</p><p>necessary. Small sample masses also protect the apparatus in the event of explosion or</p><p>deflagration. The sample should be powdered where possible and spread thinly and uniformly</p><p>in the container [26].</p><p>3.6 Temperature Measurement</p><p>The sample temperature, will usually lag behind the furnace temperature, and cannot</p><p>be measured very readily without interfering with the weighing process. The lag, may</p><p>be as much as 30°C, depending upon the operating conditions. The lag is marked when</p><p>operating in vacuum or in fast-flowing atmospheres and with high heating rates. Temperature</p><p>measurement is usually by thermocouples (see section 3.6.1.) and it is advisable to have</p><p>separate thermocouples for measurement of and for furnace regulation. (Platinum resistance</p><p>thermometers are used in some controllers).</p><p>The commonly used thermocouple types [28] are identified by letter designations originally</p><p>assigned by the Instrument Society of America (ISA) and adopted as an American Standard in</p><p>ANSI C96.1-1964. The upper temperature limits for use are dependent upon the diameter of</p><p>the wire used. Values given in brackets (°C) refer to 24 gauge (0.51 mm) wire in conventional</p><p>closed-end protecting tubes [28]. The reference junction of the thermocouple must be held at</p><p>a fixed and defined temperature. Traditionally this was 0°C, established by an ice bath. Modern</p><p>instruments use an isothermal block maintained at a temperature slightly above typical room</p><p>temperatures and the software uses appropriately adjusted temperature versus voltage curves</p><p>used to convert the signal into temperature.</p><p>3.6.1 Thermocouples</p><p>27</p><p>Factors such as stability, sensitivity (V/C), and cost determine the choice of thermocouple.</p><p>Stability can be improved, at the expense of increased response time, by enclosing the</p><p>thermocouple in a inert sheath. The response time and lifetime of the thermocouple are</p><p>strongly influenced by the diameter of the wire. Larger diameters add to the mechanical</p><p>strength and lifetime, but also decrease the sensitivity and increase the response time [3]. The</p><p>long term stability of a thermocouple depends upon its composition being maintained. At high</p><p>temperatures, diffusion</p><p>and/or vaporization can make the two metals or alloys more similar and</p><p>thus decrease the sensitivity.</p><p>Type B - Platinum-30 percent rhodium (+) versus platinum-6 percent rhodium (-) (1700°C).</p><p>Recommended for continuous use in oxidizing or inert atmospheres and short term use in</p><p>vacuum. They should not be used in reducing atmospheres, nor those containing metallic or</p><p>nonmetallic vapors, unless suitably protected.</p><p>Type E - Nickel-10 percent chromium (+) versus constantan (-) (430°C). Type E thermocouples</p><p>develop the highest emf per degree of all the commonly used types and are often used primarily</p><p>because of this feature. Recommended for use in oxidizing or inert atmospheres. In reducing</p><p>atmospheres, alternately oxidizing and reducing atmospheres, marginally oxidizing</p><p>atmospheres, and in vacuum they are subject to the same limitations as Type K thermocouples.</p><p>They are suitable for subzero temperature measurements since they are not subject to corrosion</p><p>in atmospheres with high moisture content.</p><p>Type J - Iron (+) versus constantan (-) (370°C). These are suitable for use in vacuum and in</p><p>oxidizing, reducing, or inert atmospheres, but the rate of oxidation of the iron thermoelement</p><p>is rapid above 540°C and the use of heavy-gauge wires is recommended when long life is</p><p>required at the higher temperatures. Bare thermocouples should not be used in sulfurous</p><p>atmospheres above 540°C. Possible rusting and embrittlement of the iron wire makes its use</p><p>less desirable than Type T for low temperature measurements.</p><p>Type K - Nickel-10 percent chromium (+) versus Nickel-5 percent (aluminium, silicon) (-)</p><p>(870°C). (NOTE: Silicon, or aluminium and silicon, may be present in combination with other</p><p>elements.). Recommended for continuous use in oxidizing or inert atmospheres. Suitable for</p><p>temperature measurements as low as -250°C. May be used in hydrogen or cracked ammonia</p><p>atmospheres, but should not be used in: atmospheres that are reducing or alternately oxidizing</p><p>and reducing unless suitably protected with protection tubes; sulfurous atmospheres unless</p><p>properly protected; and vacuum except for short time periods (vaporization of chromium from</p><p>the positive element will alter calibration).</p><p>Type R - Platinum-13 percent rhodium (+) versus platinum (-) (1480°C).</p><p>Type S - Platinum-10 percent rhodium (+) versus platinum (-) (1480°C).</p><p>28</p><p>Types R and S thermocouples are recommended for continuous use in oxidizing or inert</p><p>atmospheres. They should not be used in reducing atmospheres, nor those containing metallic</p><p>or nonmetallic vapors, unless suitably protected. They may be used in a vacuum for short</p><p>periods of time, but greater stability will be obtained by using Type B thermocouples for such</p><p>applications. Continued use of Types R and S thermocouples at high temperatures causes</p><p>excessive grain growth which can result in mechanical failure of the platinum element.</p><p>Calibration changes also are caused by diffusion of rhodium from the alloy wire into the</p><p>platinum, or by volatilization of rhodium from the alloy.</p><p>Type T - Copper (+) versus constantan (-) (200°C). They are resistant to corrosion in moist</p><p>atmospheres and are suitable for subzero temperature measurements. They can be used in a</p><p>vacuum and in oxidizing, reducing, or inert atmospheres.</p><p>3.6.2 Resistance Thermometers</p><p>The electrical resistances of metallic conductors increase with rising temperature [29].</p><p>Temperature coefficients for different metals are not very different. Platinum wire of high</p><p>purity and small diameter (25 to 650 m), annealed so that it is strain-free and protected against</p><p>contamination, is commonly used for temperature measurement in the range 120 to 1300°C,</p><p>although evaporation causes the zero to drift above about 980°C.</p><p>The relationship [29] for the temperature, t (°C), is:</p><p>where is the observed resistance in ohms at t°C, is the resistance at 0°C and and are</p><p>constants for the particular resistance element determined by calibration.</p><p>3.7 Temperature Control</p><p>Controlling the temperature of the sample is the most difficult and critical aspect of</p><p>thermogravimetry [3]. The three fundamental aspects are: (i) heat transfer to (and from) the</p><p>sample; (ii) determination of the actual sample temperature, and (iii) feedback and control of</p><p>the furnace temperature. Adjustment of the temperature of the sample's surroundings is the</p><p>main means of controlling the temperature of the sample.</p><p>Cooling the sample in a controlled manner is generally more difficult than the heating</p><p>process. The purge gas has a natural cooling effect and this effect may be increased by passing</p><p>the gas through a refrigerant. The desired amount of cooling is obtained by balancing the</p><p>cooling effect of the flowing atmosphere against the energy input from the furnace heater.</p><p>Precise control of the sample's temperature requires that the furnace, controller, sensor, and</p><p>system geometry be carefully matched and optimized [3]. A furnace system must respond</p><p>rapidly to control commands but not be susceptible to unstable oscillations.</p><p>Because any direct contact between the temperature sensor and the sample will interfere with</p><p>the measurement of the sample mass, the true temperature of the sample is seldom measurable.</p><p>Indirect measurements of temperature, such as by optical means, measure the temperature of</p><p>only that portion of the sample or its holder on which the optics are focused [3].</p><p>Separate sensors are thus usually used for control of the furnace and for measurement of the</p><p>sample temperature. The latter thermocouple is positioned as close to the sample as possible</p><p>without interfering with the weighing process. The larger the size of the uniformly heated zone</p><p>of the furnace, the less critical is the placement of the thermocouple. Thermal expansion of both</p><p>the sample suspension system and the thermocouple can cause contact problems as the system</p><p>is heated.</p><p>Furnace control is based on comparison of the temperature of the furnace thermocouple with</p><p>a set time-temperature programme. Power to the furnace is supplied so as to maintain the</p><p>difference between the thermocouple reading and the control setting at a minimum. The offset</p><p>between the furnace temperature and the true sample temperature has to be determined by a</p><p>suitable calibration procedure (see below).</p><p>The most common temperature programme is a linear heating or cooling ramp. Isothermal</p><p>programmes are used to measure changes in mass as a function of time and are often used in</p><p>kinetic studies (see Chapter 10). More complex temperature programmes may contain</p><p>combinations of linear and isothermal segments. Other possibilities include programmes to</p><p>produce a constant rate of change of mass with time or temperature, or to separate complex</p><p>changes in mass with the highest possible resolution. Modulated temperature techniques</p><p>developed recently, particularly for differential scanning calorimetry, DSC (see Chapter 4),</p><p>superimpose another function, e.g., a sine wave, on an underlying linear heating ramp [30-32].</p><p>These types of programme and their advantages are discussed further below.</p><p>Proportional integral derivative (PID) control [3], rather than simple “on - off” switching of</p><p>power to the furnace in response to the difference between the thermocouple reading and the</p><p>control setting, is generally used to produce too satisfactory programmed temperature or</p><p>heating/cooling rates for measurement of the processes under investigation. Departures from</p><p>heating or cooling progammes may be related to inappropriate PID values, or simple inability</p><p>of the furnace to keep up with programmed rate.</p><p>29</p><p>3.8 Sample Controlled Thermal Analysis (SCTA)</p><p>(or Controlled Rate Thermal Analysis, CRT A)</p><p>In “conventional” thermal analysis, the temperature programme is chosen by the experimenter</p><p>and proceeds irrespective of any changes undergone by the sample. A group of methods has</p><p>been developed in which the response of the sample to the initial heating programme is used</p><p>as feedback to the control system to influence the continuation of the temperature programme</p><p>in some way. The simplest method is to set a rate of mass loss and use the difference between</p><p>the set value and the observed rate of mass loss as the input signal to the furnace controller.</p><p>The historical development of these methods has been reviewed by Reading [33].</p><p>30</p><p>In the early 1960s Rouquerol [34] and Paulik and Paulik [35] independently developed</p><p>methods for holding the rate of reaction at a constant value by using the measured mass loss</p><p>or pressure of evolved gas as feedback to the furnace temperature controller. The temperature-</p><p>time profiles that result are important in understanding what has occurred [36]. Often they</p><p>correspond to almost isothermal conditions during much of the reaction, so the techniques have</p><p>also been called quasi-isothermal [37], for example the study by Paulik and Paulik of the</p><p>decomposition of calcium carbonate [37]. The principle of the CRTA approach is compared</p><p>with conventional thermal analysis in Figures 3.4 and 3.5 [38].</p><p>Closely-related techniques [39], particularly useful in obtaining kinetic information (see</p><p>Chapter 10), are those involving either a temperature jump (Figure 3.6) or a rate jump (Figure</p><p>3.7). In stepwise isothermal analysis [40] upper and lower limits are set for the reaction rate</p><p>and when the rate falls below the minimum set value, typically 0.08% of the maximum rate of</p><p>loss at a normal linear heating rate, the temperature is increased (at a generally fast linear rate)</p><p>until the reaction rate exceeds the maximum set value. The temperature is then held constant</p><p>until the reaction rate again falls below the minimum.</p><p>31</p><p>32</p><p>33</p><p>34</p><p>A method developed fairly recently by TA Instruments, known as high resolution, Hi-Res TG</p><p>[41] or dynamic rate TG [42], produces a marked decrease in the heating rate when the system</p><p>crosses the upper threshold set for the rate. The changes in heating or cooling rates are</p><p>controlled by adjustment of the values of two numerical parameters, referred to as resolution</p><p>and sensitivity. An example of the output from Hi-res TG using is shown</p><p>in Figure 3.8.</p><p>The problems of consistent and acceptable nomenclature for the variety of techniques</p><p>described above have been reviewed by Reading [33]. The term sample controlled thermal</p><p>analysis (SCTA) for all methods where the transformation undergone by the sample in some</p><p>way influences the course of the temperature programme it experiences, has now been</p><p>proposed.</p><p>Use of SCTA methods can provide a more uniform reaction environment than usually exists</p><p>in conventional TA. Pressure and temperature gradients within the sample can be a problem,</p><p>particularly for rapid, strongly endothermic decompositions. These gradients can be minimized</p><p>by using small sample masses and setting slow decomposition rates, if adequate sensitivity is</p><p>available. Isothermal experiments suffer particularly in comparison with SCTA [43] because</p><p>often the reaction rate can be too rapid at the beginning of the experiment and far too slow near</p><p>the end for the reaction to be complete in a realistic time. In linear rising temperature</p><p>experiments, the rate goes through a maximum near the midpoint of a reaction step. Lowering</p><p>the heating rate to decrease this maximum rate gives unduly long experiments. In SCTA,</p><p>provided that the temperature gradients at the rate chosen are acceptable, obtaining undistorted</p><p>results will take the minimum time possible. Barnes et al. [44] have compared SCTA methods</p><p>and supported the claims of enhanced resolution over conventional TG.</p><p>Because SCTA usually provides better control of the sample environment, it is often used as</p><p>a method of preparing porous or finely divided solids by thermal decomposition [45], especially</p><p>for use in catalysis [46]. The results of SCTA are also sometimes preferred for measuring</p><p>kinetic parameters (see Chapter 10).</p><p>For maximum resolution of multi-stage reactions the dynamic rate method may be suitable.</p><p>Reading has pointed out [33] that the slowest heating rate should be applied during the</p><p>transition from one stage to another, in contrast to the usual method where the heating rate</p><p>decreases during a reaction and then increases during the passage from one stage to another.</p><p>The required algorithm takes the rate of change of temperature into account (Figure 3.6).</p><p>Reading [33] has speculated on future developments and has suggested algorithms that look</p><p>at the shapes of curves of reaction rate against time rather than simply at peak heights. The aim</p><p>is always to avoid long times being spent on large peaks because of a threshold value set too</p><p>low, or small peaks being missed because of a threshold value set too high.</p><p>The use of modulated temperature programmes in TG, similar to those described in Chapter</p><p>4 for differential scanning calorimetry, is another interesting recent development [32].</p><p>35</p><p>36</p><p>3.9 Calibration</p><p>The precision (reproducibility) of a measurement of a quantity depends upon factors such as</p><p>the instrumentation, the homogeneity of the sample, and experimental techniques. Good</p><p>precision is required for determination of the true value of the quantity (accuracy), but</p><p>systematic errors may produce constant offsets in the experimental measurements, rather than</p><p>the random fluctuations that determine precision. To detect and eliminate these systematic</p><p>errors, calibration is required. For TG, both mass and temperature calibrations are required.</p><p>3.9.1. Mass Calibration [3]</p><p>Calibration masses in a wide range of sizes and several classes of accuracy may be obtained</p><p>from the national standards organizations or commercial suppliers. Class M standards are used</p><p>by standards organizations for certification of other classes of mass pieces. A 100 mg Class</p><p>S mass has a tolerance of mg or 250 ppm, while a Class S-1 mass has a tolerance of</p><p>twice that. Changes in buoyancy resulting from changing temperature usually have to be</p><p>determined from blank runs under essentially identical conditions. Gallagher [3] warns that,</p><p>at very high temperatures (above about 1300°C for platinum) vaporization of metal from the</p><p>sample suspension system may give an unexpected mass loss.</p><p>3.9.2. Temperature Calibration</p><p>For TG measurements to be meaningful, careful calibration of temperature at the sample</p><p>position is essential. An ingenious method of temperature calibration [47] for small furnaces,</p><p>makes use of the Curie points of a range of metals and alloys. On heating a ferromagnetic</p><p>material, it loses its ferromagnetism at a characteristic temperature known as the Curie point,</p><p>If a magnet is positioned below the furnace containing the suspended sample of</p><p>ferromagnetic material, as shown in Figure 3.9(a), the total downward force on the sample, at</p><p>temperatures below the Curie point, is the sum of the sample weight and the magnetic force.</p><p>At the Curie point the magnetic force is reduced to zero and an apparent mass-loss is observed,</p><p>Figure 3.9(b). By using several ferromagnetic materials, a multi-point temperature calibration</p><p>may be obtained (Figure 3.9(c)). The calibration is an example of the use of</p><p>thermomagnetometry (TM) (see further below). The extrapolated end point of the magnetic</p><p>effect is equated to The derivative (DTM) curve, which is more sensitive, may also be</p><p>used [3]. The Standardization Committee of ICTAC has certified five materials and marketed</p><p>them through NIST (USA) [48].</p><p>An alternative method, known as the “fusible link” method [49,50] uses inert mass-pieces</p><p>that are suspended from the balance in place of the sample by links of thin fusible wire. When</p><p>the temperature is raised through the melting point, the link melts and drops from its support,</p><p>causing a momentary detectable disturbance in the mass signal.</p><p>Whichever of the above methods is used, the final stage of calibration is to correlate the</p><p>known transition temperatures with the “apparent” temperatures measured using the</p><p>instrument’s temperature sensor in its normal operating position.</p><p>37</p><p>Even with careful temperature calibration, may still not be accurately known,</p><p>because</p><p>slow heat transfer may cause self-heating or self-cooling from strongly exothermic or</p><p>endothermic processes in relatively large samples.</p><p>Early attempts to use the mass losses associated with some thermal decomposition reactions</p><p>for temperature calibration were unsuccessful because of the slow rates of most of such</p><p>reactions. Brown et al. [51] have proposed some peroxo coordination compounds, which</p><p>undergo explosive decomposition over a very narrow temperature range, as possible</p><p>temperature standards. The temperatures of onset of decomposition can be determined by the</p><p>sharp exotherms in their DTA or DSC curves. These DTA or DSC instruments would have</p><p>been calibrated in the normal way using the melting points of appropriate pure metal standards.</p><p>The DSC and TG curves of the glycine (gly) complex are shown,</p><p>as an example, in Figure 3.10 [51].</p><p>Simultaneous TG-DTA instruments can be calibrated by measuring temperatures directly in</p><p>the DTA system [52-54]. A suitable pair of pure metals, whose melting points should bracket</p><p>the magnetic transition, are placed in the sample pan alongside the magnetic material. The</p><p>measured melting points are used to construct a correction curve for the observed Curie</p><p>temperatures, [3] Some of the magnetic materials used as temperature standards in TG are</p><p>listed in Table 3.1 [3]. In a series of simultaneous TG-DTA experiments [52-54], nickel gave</p><p>the best result, but its standard deviation of 5.4°C is not good enough for a reference standard.</p><p>A certification programme is in progress [3] to use cobalt- and nickel-based alloys to provide</p><p>a series of standards in the temperature range of 160 to 1130°C.</p><p>3.10 Presentation of TG Data</p><p>Results from TG experiments can be presented in a variety of graphical ways (see Figure 3.11)</p><p>[3,55]. Mass or mass percent is usually plotted as the ordinate (Y-axis) and temperature or</p><p>time as the the abscissa (X-axis). Mass percent has the advantage that results from different</p><p>experiments can be compared on normalized sets of axes. When time is used as the abscissa,</p><p>a second curve of temperature versus time needs to be plotted to indicate the temperature</p><p>programme used.</p><p>38</p><p>39</p><p>40</p><p>Derivative plots showing the rate of mass change as a function of time or temperature</p><p>(derivative thermogravimetry, DTG) are useful in attempting to resolve overlapping processes</p><p>and for some methods of kinetic analysis (see Chapter 11). DTG curves are also readily</p><p>comparable with other derivative measurements such as DTA, DSC, or EGA. Derivative plots</p><p>usually show increased noise, so some form of smoothing may be needed (see Appendix).</p><p>3.11 Automation of TG</p><p>Thermal analysis equipment does not generally lend itself to full automation in the sense of</p><p>analysis of sample after sample without operator intervention [56]. Thermogravimetry is</p><p>frequently used for routine quality control types of analyses and there is thus a demand for</p><p>equipment which can run multiple samples, either simultaneously or sequentially. If there is</p><p>some means of changing the sample automatically, the required heating/cooling programme and</p><p>the switching of carrier gas is readily implemented on modern instruments. A multi-specimen</p><p>'carousel' thermobalance has been designed by Ferguson et al. [57] (see Figure 3.7.), which</p><p>allows twenty specimens, mounted on arms radiating from a central shaft, to be weighed</p><p>sequentially. There is obviously a limit to the sorts of treatment which the samples can receive</p><p>between weighings, but they can all be exposed to a similar environment.</p><p>41</p><p>42</p><p>The LECO Model TGA-500, operates in a similar fashion [3]. It can operate one or two</p><p>furnace systems simultaneously and have as many as 19 specimens per furnace. TA</p><p>Instruments also use a carousel of identical sample holders to supply the samples, but each</p><p>sample is run individually, in sequence, under any set of programmed experimental conditions.</p><p>When a sample is placed in a magnetic field, it may experience either attractive or repulsive</p><p>forces. Attractive forces arise from three types of property of the sample: antiferromagnetism,</p><p>paramagnetism and ferromagnetism (with ferromagnetism causing the strongest interaction).</p><p>The diamagnetic properties of a sample, arising from the orbital motion of electrons, and hence</p><p>present in all samples, but sometimes swamped by the other magnetic properties, give rise to</p><p>weak repulsive forces. Antiferromagnetism occurs in only a few transition-metal compounds.</p><p>The volume magnetic susceptibility of a sample is defined as where M is the</p><p>magnetization and H is the magnetic field strength. The mass magnetic susceptibility, s, then</p><p>where is the density of the sample. Materials in which is positive are called</p><p>paramagnetic, and those for which is negative are called diamagnetic.</p><p>Different types of magnetic behaviour can be distinguished by their temperature dependence.</p><p>For paramagnetic samples, the magnetic susceptibility decreases with absolute temperature</p><p>according to the Curie-Weiss law: where C is the Curie constant and is the</p><p>Weiss constant. The susceptibility of diamagnetic materials does not change much with</p><p>temperature, while ferromagnetic materials have high susceptibilities at temperatures below</p><p>what is known as the Curie point. Above their Curie points, ferromagnetic materials become</p><p>paramagnetic and these magnetic transitions are used for temperature calibration of TG systems</p><p>(see Section 3.8.2.).</p><p>Gallagher and Warne have provided recent reviews of thermomagnetometry in general</p><p>[58,59]and its applications to minerals [60] and inorganic materials [61].</p><p>The strength of the magnetic field used for TM [3] depends on the purpose of the</p><p>measurement. When determining magnetic transition temperatures, a strong field may not</p><p>be necessary or even desirable, provided that the apparent mass change is detectable. However,</p><p>when attempting to detect the formation of magnetic intermediates or final products during the</p><p>course of a reaction, the sensitivity of detection increases with the strength of the magnetic</p><p>field gradient at the sample position. This strength depends on the strength of the magnet as</p><p>well as its position relative to the sample. A large furnace may cause problems in bringing the</p><p>magnet close enough to the sample, and increasing the strength of the magnetic field may affect</p><p>the accuracy of the balance mechanism.</p><p>43</p><p>3.12 Thermomagnetometry (TM)</p><p>3.12.1. Introduction</p><p>3.12.2. Apparatus</p><p>Both the apparatus used, and the techniques and precautions required for thermomagnetometry</p><p>are basically those required for thermogravimetry (TG), with the addition of means of</p><p>producing a strong magnetic field around the sample. The apparent mass of the</p><p>sample is then the sum of the actual sample mass and the magnetic force. Allowance obviously</p><p>has to be made for the effect of the field on the sample container, which should thus have a low</p><p>magnetic susceptibility e.g. quartz. The magnetic field may be applied periodically so that</p><p>measurements of actual mass (TG) and apparent mass (TM) can be compared. Interference of</p><p>Actual TG curves obtained may be classified into various types [62] as illustrated in Figure</p><p>3.13. Possible interpretations of the curves shown in Figure 3.13 are as follows:</p><p>Type (i) curves: The sample undergoes no decomposition with loss of volatile products over</p><p>the temperature range shown. No information is obtained, however, on whether solid phase</p><p>transitions, melting, polymerisation or other reactions involving no volatile products have</p><p>occurred. Use of some of the other techniques (Table 1.2) is necessary to eliminate these</p><p>possibilities. Assuming that these possibilities are eliminated, the sample would then be known</p><p>to be stable over the temperature range considered. This could be good news if a heat resistant</p><p>material was being sought, or bad news if potential explosives were being tested!</p><p>Type (ii) curves: The rapid initial mass-loss observed is characteristic of desorption or drying.</p><p>It could also arise, when working at reduced pressures,</p>