Journal of Thermal Analysis and Calorimetry

, Volume 110, Issue 1, pp 5–16 | Cite as

Rationale and fallacy of thermoanalytical kinetic patterns

How we model subject matter
  • J. Šesták


Modeling tradition is reviewed within its historical maturity from Plato do Penrose. Metaphors in nonisothermal kinetics achieved a wide application mostly employing models derived by means of undemanding isothermal descriptions. Geometrical basis of such modeling is revised and discussed in terms of symmetrical and asymmetrical (pentagonal) schemes. The properties of interface (reaction separating line) are found decisive in all cases of heterogeneous kinetics. Application of fractal geometry is accredited, and associated formal kinetic models based on nonintegral power exponents are acknowledged. Typical erroneous beliefs are dealt with showing common kinetic misinterpretation of measured data and associated mathematical manipulability of kinetic equations. The correction of a measured DTA peak is mentioned assuming the effects of heat inertia and temperature gradients.


Nonisothermal kinetics Reaction mechanism Geometrical modeling Fractals Evaluation Misinterpretation DTA Heat inertia 



The results were developed within the CENTEM project, reg. no. CZ.1.05/2.1.00/03.0088 that is co-funded from the ERDF within the OP RDI program of the Ministry of Education, Youth and Sports. I feel also indebted to my scientific friends, coworkers, and uppermost kineticists: late Joseph H. Flynn (Bethesda), Jerry Czarnecki (Fullerton), Klaus Heide (Jena), Pavel Holba (Prague), Nobuyoshi Koga (Hiroshima), Jiří Málek (Pardubice), Eugéne Segal (Bucharest), Peter Šimon (Bratislava), Donald R. Uhlmann (Tucson) and Živan Živkovič (Serbian Bor).


  1. 1.
    Šesták J. Philosophy of non-isothermal kinetics. J Therm Anal. 1979;16:520–603.Google Scholar
  2. 2.
    Šesták J. Mystery of derivatives in the nonisothermal rate equation. Thermochim Acta. 1985;83:391–4.CrossRefGoogle Scholar
  3. 3.
    Šesták J. Nonisothermal kinetics: art, debate or applied science. J Therm Anal. 1988;33:1263–7.CrossRefGoogle Scholar
  4. 4.
    Šesták J. Plenary lectures: nonisothermal kinetics. In: Wiedemann HG, editors. The proceedings: thermal analysis, conference 3rd ICTA in Davos, Birghausser, Basel; 1972. p. 3–9.Google Scholar
  5. 5.
    Šesták J. Rationale and fiction of thermochemical kinetics. In: Vitez I, editor. The proceedings: the 34th conference of North American Thermal Analysis Society, Bowling Green; 2006. p. 68–9.Google Scholar
  6. 6.
    Šestak J. Citation records and some forgotten anniversaries in thermal analysis. J Therm Anal Calorim. 2011 (in press). doi: 10.1007/s10973-011-1625-3.
  7. 7.
    Šatava V. Utilization of thermographic methods for studying reaction kinetics. Silikáty (Prague). 1961;1:68–72. (in Czech).Google Scholar
  8. 8.
    Proks I. Influence of pace of temperature increase on the quantities important for the evaluation of DTA curves. Silikaty (Prague). 1961;1:114–21 (in Czech).Google Scholar
  9. 9.
    Šesták J. Temperature effects influencing kinetic data accuracy obtained by thermographic measurements under constant heating. Silikaty (Prague). 1963;7:125–31 (in Czech).Google Scholar
  10. 10.
    Garn PD. Thermoanalytical methods of investigation. New York: Academic; 1965.Google Scholar
  11. 11.
    Flynn JH, Wall LA. General treatment of the thermogravimetry of polymers. J Res Nat Bur Stand. 1966;70A:487.CrossRefGoogle Scholar
  12. 12.
    Šesták J. Review of kinetic data evaluation from nonisothermal and isothermal data. Silikáty (Prague). 1967;11:153–90 (in Czech).Google Scholar
  13. 13.
    Murgulescu JG, Segal E. Reviewing kinetic data evaluations by thermal analysis. St Cerc Chim Tom (Bucharest). 1967;15:261 (in Romanian).Google Scholar
  14. 14.
    Šesták J. Thermophysical properties of solids: their measurements and theoretical thermal analysis. Amsterdam: Elsevier; 1984 and Teoretičeskij termičeskij analyz. Mir, Moscow; 1987 (in Russian).Google Scholar
  15. 15.
    Chvoj Z, Šesták J, Tříska A, editors. Kinetic phase diagrams: nonequilibrium phase transitions. Amsterdam: Elsevier; 1991.Google Scholar
  16. 16.
    Šesták J, editor. Reaction kinetics by thermal analysis. Special issue of Thermochim Acta, vol. 203. Amsterdam: Elsevier; 1992.Google Scholar
  17. 17.
    Šesták J, Sorai M, editors. Transition phenomena in condensed matter. Special issue of Thermochim Acta, vol. 266. Amsterdam: Elsevier; 1995.Google Scholar
  18. 18.
    Šesták J. Heat, thermal analysis and society. Nucleus, Hradec Králové; 2004.Google Scholar
  19. 19.
    Šesták J. Science of heat, thermophysical studies a generalized approach to thermal analysis. Amsterdam: Elsevier; 2005.Google Scholar
  20. 20.
    Šesták J. Some model classification of geometrical bodies and their development in historical applications. In: Wittwer A, Knut E, Pliska V, Folker G, editors. Approaching scientific knowledge. Zurich: Collegieum Helveticum; 2008. p. 87–91.Google Scholar
  21. 21.
    Penrose R. Shadow of the mind: approach to the missing science of consciousness. Oxford: Oxford University Press; 1994.Google Scholar
  22. 22.
    Penrose R. The road to reality: a complete guide to the laws of the Universe. London: Vintage; 2004.Google Scholar
  23. 23.
    Šesták J, Zámečník J. Can clustering of liquid water be of assistance for better understanding of biological germplasm exposed to cryopreservation. J Therm Anal Calorim. 2007;8:411–9.Google Scholar
  24. 24.
    Barrow JD. The origin of the universe. Orion, London 1994, impossibility limits of science and science of limits. New York: Vintage; 1999.Google Scholar
  25. 25.
    Šesták J, Chvoj Z. Irreversible thermodynamics and true thermal dynamics in view of generalized solid-state reaction kinetics. Thermochim Acta. 2002;388:427–31.CrossRefGoogle Scholar
  26. 26.
    Jacobs PWM, Tompkins FC. Classification and theory of solid reactions. In: Garner WE, editor. Chemistry of the solid state. London: Butterworth; 1955. p. 184–212.Google Scholar
  27. 27.
    Young DA. Decomposition of solids. In: Tompkins FC, editor. Solid and surface kinetics. Oxford: Pergamon; 1966. p. 43–144.Google Scholar
  28. 28.
    Johnson WA, Mehl RF. Reaction kinetics in processes of nucleation and growth. Trans Am Inst Min Metal Petro Eng. 1939;135:416; reprinted in Metall Mater Trans A. 2010;41A:2713–75.Google Scholar
  29. 29.
    Hulbert HF. Models for solid-state reactions in powdered compacts: a review. J Br Ceram Soc. 1969;6:11–20.Google Scholar
  30. 30.
    Brown ME, Dollimore D, Galway AK. Reactions in the solid-state. In: Bamford CH, Tipper CFH, editors. Comprehensive chemical kinetics, vol. 22. Amsterdam: Elsevier; 1980.Google Scholar
  31. 31.
    Galwey AK, Brown ME. Thermal decomposition of ionic solids. Amsterdam: Elsevier; 1999.Google Scholar
  32. 32.
    Málek J, Criado JM, Šesták J, Militký J. The boundary conditions for kinetic models. Thermochim Acta. 1989;153:429–32.CrossRefGoogle Scholar
  33. 33.
    Málek J, Mitsuhashi T, Criado JM. Kinetic analysis of solid-state processes. J Mater Res. 2001;16:1862–71.CrossRefGoogle Scholar
  34. 34.
    Šesták J, Málek J. Diagnostic limits of phenomenological models of heterogeneous reactions and thermoanalytical kinetics. Solid State Ion. 1993;63/65:254–9.Google Scholar
  35. 35.
    Vyazovkin S, Wight CA. Kinetic concepts of thermally stimulated reactions in solids: a view from a historical perspective. Int Rev Phys Chem. 2000;19:45–60.CrossRefGoogle Scholar
  36. 36.
    Mamleev V, Bourbigot S, LeBras M, Duquesne S, Šesták J. Modeling of nonisothermal kinetic mechanism in thermogravimetry. Phys Chem Chem Phys. 2000;2:4708–16.CrossRefGoogle Scholar
  37. 37.
    Koga N, Šesták J. TA kinetics and physical-geometry of the nonisothermal crystallization. Bull Soc Espaňa Cer Vidro. 1992;31:185–9.Google Scholar
  38. 38.
    Koga N. Physico-geometric kinetics of solid-state reactions as exemplified by thermal dehydration. J Therm Anal. 1997;49:45–56.CrossRefGoogle Scholar
  39. 39.
    Koga N, Tanaka H. A physico-geometric approach to the kinetics of solid-state reactions. Thermochim Acta. 2002;388:41–61.CrossRefGoogle Scholar
  40. 40.
    Khawam A, Flanagan DR. Solid-state kinetic models: basics and mathematical fundamentals. J Phys Chem B. 2006;110:17315–28.CrossRefGoogle Scholar
  41. 41.
    Kimura T, Koga N. Thermal dehydration of monohydrocalcite: overall kinetics and physico-geometrical mechanisms. J Phys Chem A. 2011;115:10491–501.CrossRefGoogle Scholar
  42. 42.
    Koga N, Šesták J, Šimon P. Some fundamental and historical aspects of phenomenological kinetics. In: Šesták J, Šimon P, editors. Thermal analysis of micro-, nano- and non-crystalline materials, Chap. 1. New York: Springer; 2012 (in press). ISBN 978-90-481-3149-5.Google Scholar
  43. 43.
    Smith CS. Microstructure and geometry. Trans Am Soc Metals. 1953;45:533–75.Google Scholar
  44. 44.
    Smith CS. Some elementary principles of polycrystalline microstructure. Metal Rev. 1964;9:1–17.CrossRefGoogle Scholar
  45. 45.
    Pfeifer O. Macromolecules and colloidal aggregates—fractal dimension as concealed symmetry of irregular structures. Chimia. 1985;39:120.Google Scholar
  46. 46.
    Avnir D, Farin D, Pfeifer P. Molecular fractal surfaces. Nature. 1984;308:261–3.CrossRefGoogle Scholar
  47. 47.
    Avnir D. Fractal approach to heterogeneous chemistry. New York: Wiley; 1989.Google Scholar
  48. 48.
    Kopelman R. Fractal reaction kinetics. Science. 1988;241:620–5.CrossRefGoogle Scholar
  49. 49.
    Schröde M. Fractals, chaos and power laws. New York: Freeman; 1991.Google Scholar
  50. 50.
    Šesták J. The role of order and disorder in thermal and material sciences part 1: heat and society. J Mining Metal. 2002;38:1–22.CrossRefGoogle Scholar
  51. 51.
    Šesták J. The role of order and disorder in thermal and material sciences part 2: scientific world and new insights. J Mining Metal. 2003;39:1–7.Google Scholar
  52. 52.
    Glicksman E. Free dendritic growth. Mater Sci Eng. 1984;65:45–54.CrossRefGoogle Scholar
  53. 53.
    Lipton J, Glicksman ME, Kurz W. Dendritic growth into undercooled alloy melts. Mater Sci Eng. 1984;65:57–64.CrossRefGoogle Scholar
  54. 54.
    Roduner E, Cronin L. Nanoscopic materials: size-dependent phenomena. Cambridge: RSC-publ; 2006 & 2007. IBSN 978-1-84755-763-6.Google Scholar
  55. 55.
    Zhang Z, Li JC, Jiang Q. Modeling for size-dependent and dimension-dependent melting of nanocrystals. J Phys D. 2000;33:2653–6.CrossRefGoogle Scholar
  56. 56.
    Guisbiers G, Buchaillot L. Universal size/shape-dependent law for characteristic temperatures. Phys Lett A. 2009;374:305–8.CrossRefGoogle Scholar
  57. 57.
    Barnard AS. Modelling of nanoparticles: approaches to morphology and evolution—a review. Rep Prog Phys. 2010;73:6502–54.CrossRefGoogle Scholar
  58. 58.
    Elliot RS. Eutectic solidification processing: crystalline and glassy alloys. London: Butterworth; 1989.Google Scholar
  59. 59.
    Alexander S, Orbach R. Density of states on fractals—fractons. J Phys Lett. 1982;43:L625.CrossRefGoogle Scholar
  60. 60.
    Bonde A, Havlin S. Fractals and disordered systems. Berlin: Springer; 1991.CrossRefGoogle Scholar
  61. 61.
    Peitgen HO, Jurgen H, Saupe D. Chaos and fractals: new frontiers of science. New York: Springer; 1992.Google Scholar
  62. 62.
    Mandelbrot BB. Gaussian self-similarity, fractals, globallity and 1/f noise. New York: Springer; 2002.Google Scholar
  63. 63.
    Falcone K. Fractal geometry. Chichester: Wiley; 2003.CrossRefGoogle Scholar
  64. 64.
    Prout EG, Tompkins FC. The thermal decomposition of potassium permanganate. Trans Faraday Soc. 1944;40:488–98.CrossRefGoogle Scholar
  65. 65.
    Ng WL. Thermal decomposition in the solid state. Aust J Chem. 1975;28:1169–78.CrossRefGoogle Scholar
  66. 66.
    Šesták J, Berggren G. Study of the kinetics of the mechanism of solid-state reactions at increasing temperature. Thermochim Acta. 1971;3:1–13.CrossRefGoogle Scholar
  67. 67.
    Málek J, Criado JM. Is the Šesták–Berggren equation a general expression of kinetic models? Thermochim Acta. 1991;175:305–9.CrossRefGoogle Scholar
  68. 68.
    Šimon P. Forty years of Šesták–Berggren equation. Thermochim Acta. 2011. doi: 10.1016/j.tca.2011.03.030.
  69. 69.
    Heal GR. Explanation of the Šestak–Berggren equation. Unpublished communication; 2011.Google Scholar
  70. 70.
    Yerofeev BV. Reaction rate of processes involving solids with different specific surfaces. In: The proceedings: 4th international symposium reactivity of solids. Amsterdam: Elsevier; 1961. p. 273–82.Google Scholar
  71. 71.
    Málek J. Crystallization kinetics by thermal analysis. J Therm Anal Calorim. 1999;56:763–9.CrossRefGoogle Scholar
  72. 72.
    Málek J. Kinetic analysis of crystallization processes in amorphous materials. Thermochim Acta. 2000;355:239–53.CrossRefGoogle Scholar
  73. 73.
    Šesták J, Kratochvil. Rational approach to thermodynamic processes and constitutive equations in kinetics. J Therm Anal. 1973;5:193–201.CrossRefGoogle Scholar
  74. 74.
    Šesták J. Thermodynamic basis for the theoretical description and correct interpretation of thermoanalytical experiments. Thermochim Acta. 1979;28:197–227.CrossRefGoogle Scholar
  75. 75.
    Holba P, Šesták J. Kinetics with regard to the equilibrium of processes studied by non-isothermal techniques. Zeit physik Chem NF. 1972;80:1–20.CrossRefGoogle Scholar
  76. 76.
    Šesták J. Key lecture: integration of nucleation-growth equation when considering non-isothermal regime and shared phase separation. In: Dolimore D, editor, The 2nd ESTAC (Europ. symp. on thermal analysis) in proc. thermal analysis, Heyden, London; 1981. p. 115–20.Google Scholar
  77. 77.
    Hiller R, editor. Application of fractional calculus in physics. River Edge: World Science; 2000.Google Scholar
  78. 78.
    Milledr KS, Ross B. Introduction to the fractional calculus and fractional differential equations. New York: Wiley; 1993.Google Scholar
  79. 79.
    Fleschinger MF, Zaslavsky GM, Klaufter J. Strange kinetics. Nature. 1993;363:31–3.CrossRefGoogle Scholar
  80. 80.
    Galwey AK, Brown ME. Application of the Arrhenius equation to solid-state kinetics: can this be justified? Thermochim Acta. 2002;386:91–8.CrossRefGoogle Scholar
  81. 81.
    Galwey AK. Eradicating erroneous Arrhenius arithmetic. Thermochim Acta. 2003;399:1–29.CrossRefGoogle Scholar
  82. 82.
    Galwey AK. Theory of solid-state thermal decomposition: scientific stagnation or chemical catastrophe? An alternative approach apprised and advocated. Unpublished communication; 2011.Google Scholar
  83. 83.
    L’vov BV. Thermal decomposition of solids and melts: a new thermochemical approach to the mechanism, kinetics and methodology. Berlin: Springer; 2007.Google Scholar
  84. 84.
    Kissinger HE. Reaction kinetics in differential thermal analysis. Anal Chem. 1957;29:1702–6.CrossRefGoogle Scholar
  85. 85.
    Šesták J. On the applicability of π(x)-function to the determination of reaction kinetics under nonisothermal conditions. Thermochim Acta. 1971;3:150–4.CrossRefGoogle Scholar
  86. 86.
    Henderson DW. Experimental analysis of nonisothermal transformations involving nucleation and growth. J Therm Anal. 1979;15:325–31.CrossRefGoogle Scholar
  87. 87.
    Kemeny J, Šesták J. Comparison of crystallization kinetic theories derived by isothermal and nonisothermal methods. Thermochim Acta. 1987;110:113–9.CrossRefGoogle Scholar
  88. 88.
    Broido A, Williams AF. Use of asymptotic analysis of the large activation energy limit to compare various graphical methods of treating TG data. Thermochim Acta. 1970;6:245–53.CrossRefGoogle Scholar
  89. 89.
    Moynihan CT. Correlation between the width of the glass-transition region and the temperature dependence of glass viscosity. J Am Ceram Soc. 1993;76:1081–8.CrossRefGoogle Scholar
  90. 90.
    Šesták J. Applicability of DTA to study of crystallization kinetics of glasses. Phys Chem Glass. 1974;15:137–40.Google Scholar
  91. 91.
    Christian JW. Theory of transformations in metals and alloys. Oxford: Pergamon; 1975.Google Scholar
  92. 92.
    Málek J, Šesták J, Rouquerol F, Rouquerol J, Criado JM, Ortega A. Possibilities of two non-isothermal procedures (temperature-and/or rate-controlled) for kinetic studies. J Therm Anal. 1992;38:71–87.CrossRefGoogle Scholar
  93. 93.
    Criado JM, Gotor FJ, Ortega A, Real C. New method of CRTA-application to discrimination of the kinetic models of solid-state reactions. Thermochim Acta. 1992;199:235–8.CrossRefGoogle Scholar
  94. 94.
    Koga N, Tanak H, Criado JM. Kinetic analysis of inorganic solid-state reactions by CRTA. Netsu Sokutei (Jap J Therml Anal). 2000;27:128–40.Google Scholar
  95. 95.
    Koga N. A review of the emutual dependence of Arrhenius parameters evaluated by the thermoanalytical study of solid-state reactions: the kinetic compensation effect. Thermochim Acta. 1994;244:1–10.CrossRefGoogle Scholar
  96. 96.
    Koga N. Kinetic analysis of thermoanalytical data by extrapolating to infinite temperature. Thermochim Acta. 1995;258:145–9.CrossRefGoogle Scholar
  97. 97.
    Šesták J, Mareš JJ, Krištofik J, Hubík P. True physical meaning of the so called kinetic compensation effect. Glastech Ber Glass Sci Technol. 2000;73(C1):104–8.Google Scholar
  98. 98.
    Galwey AK, Mortimer M. Compensation effects and compensation defects in kinetic and mechanistic interpretations of heterogeneous chemical reactions. Int J Chem Kinet. 2006;38:464–73.CrossRefGoogle Scholar
  99. 99.
    Šesták J, Strnad Z. Simulation of DTA crystallization peak on basis of nucleation-growth curves determined by optical microscopy. In: Gotz J, editor, The proceedings: XI inter. congress on glass, DT CVTS, Vol. II, Prague; 1977. p. 249–61.Google Scholar
  100. 100.
    Málek J, Zmrhalová Z, Barták J, Honcová P. A novel method to study crystallization of glasses. Thermochim Acta. 2010;511:67–73.CrossRefGoogle Scholar
  101. 101.
    Málek, J, Shánělová J. Crystallization kinetics in amorphous materials studied by means of calorimetry, microscopy and dilatometry. In: Šesták J, Šimon P, editors. Thermal analysis of micro-, nano- and non-crystalline materials, Chap. 14. New York: Springer; 2012 (in press). ISBN 978-90-481-3149-5.Google Scholar
  102. 102.
    Dubaj T, Cibulková Z, Šimon P. Justification of the use of non-Arrhenian temperature functions, prepared for publication 2012.Google Scholar
  103. 103.
    Šimon P. Single-step kinetics approximation employing non-Arrhenius temperature functions. J Therm Anal Calorim. 2005;79:703.CrossRefGoogle Scholar
  104. 104.
    Šimon P. The single-step approximation: attributes, strong and weak sides. J Therm Anal Calorim. 2007;88:709–15.CrossRefGoogle Scholar
  105. 105.
    Serra R, Nomen R, Sempere J. Non-parametric kinetics: a new method for kinetic study. J Therm Anal Calorim. 1998;52:933.CrossRefGoogle Scholar
  106. 106.
    Vyazovkin S. Model-free kinetics: staying free of multiplying entities without necessity. J Therm Anal Calorim. 2006;83:45.CrossRefGoogle Scholar
  107. 107.
    Šesták J, Holba P. Theory of thermoanalytical methods based on the indication of enthalpy changes. Silikáty (Prague). 1976;29:83–8. (in Czech).Google Scholar
  108. 108.
    Šesták J, Holba P, Lombardi G. Quantitative evaluation of thermal effects: theoretical basis of DTA/DSC. Annali di Chimica (Roma). 1977;67:73–9.Google Scholar
  109. 109.
    Nevřiva M, Holba P, Šesták J. Utilization of DTA for the determination of transformation heats. Silikaty (Prague). 1976;29:33–8. (in Czech).Google Scholar
  110. 110.
    Holba P, Nevřiva M, Šesták J. Analysis of DTA curve and related calculation of kinetic data using computer technique. Thermochim Acta. 1978;23:223–31.CrossRefGoogle Scholar
  111. 111.
    Holba P, Šesták J, Sedmidubsky D. Heat transfer and phase transition at DTA experiments. In: Šesták J, Šimon P, editors. Thermal analysis of micro-, nano- and non-crystalline materials, Chap. 4. New York: Springer; 2012 (in press). ISBN 978-90-481-3149-5.Google Scholar
  112. 112.
    Höhne GWH, Hemminger W, Flammersheim HJ. Differential scanning calorimetry. Dordrecht: Springer; 2003.Google Scholar
  113. 113.
    Brown ME, Gallagher PK, editors. Handbook of thermal analysis and calorimetry. Amsterdam: Elsevier; 2008.Google Scholar
  114. 114.
    Gabbott G, editor. Principles and application of thermal analysis. Oxford: Blackwell; 2008.Google Scholar
  115. 115.
    Boerio-Goates J, Callen JE. Differential thermal methods. In: Rossiter BW, Beatzold RC, editors. Determination of thermodynamic properties. New York: Wiley; 1992. p. 621–718.Google Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2011

Authors and Affiliations

  1. 1.New Technology—Research Centre in the Westbohemian RegionWest Bohemian UniversityPilsenCzech Republic

Personalised recommendations