Skip to main content
Log in

Rationale and fallacy of thermoanalytical kinetic patterns

How we model subject matter

  • Published:
Journal of Thermal Analysis and Calorimetry Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1

Similar content being viewed by others

References

  1. Šesták J. Philosophy of non-isothermal kinetics. J Therm Anal. 1979;16:520–603.

    Google Scholar 

  2. Šesták J. Mystery of derivatives in the nonisothermal rate equation. Thermochim Acta. 1985;83:391–4.

    Article  Google Scholar 

  3. Šesták J. Nonisothermal kinetics: art, debate or applied science. J Therm Anal. 1988;33:1263–7.

    Article  Google Scholar 

  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.

  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.

  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. Šatava V. Utilization of thermographic methods for studying reaction kinetics. Silikáty (Prague). 1961;1:68–72. (in Czech).

    Google Scholar 

  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. 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. Garn PD. Thermoanalytical methods of investigation. New York: Academic; 1965.

    Google Scholar 

  11. Flynn JH, Wall LA. General treatment of the thermogravimetry of polymers. J Res Nat Bur Stand. 1966;70A:487.

    Article  Google Scholar 

  12. Šesták J. Review of kinetic data evaluation from nonisothermal and isothermal data. Silikáty (Prague). 1967;11:153–90 (in Czech).

    Google Scholar 

  13. Murgulescu JG, Segal E. Reviewing kinetic data evaluations by thermal analysis. St Cerc Chim Tom (Bucharest). 1967;15:261 (in Romanian).

    CAS  Google Scholar 

  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).

  15. Chvoj Z, Šesták J, Tříska A, editors. Kinetic phase diagrams: nonequilibrium phase transitions. Amsterdam: Elsevier; 1991.

    Google Scholar 

  16. Šesták J, editor. Reaction kinetics by thermal analysis. Special issue of Thermochim Acta, vol. 203. Amsterdam: Elsevier; 1992.

    Google Scholar 

  17. Šesták J, Sorai M, editors. Transition phenomena in condensed matter. Special issue of Thermochim Acta, vol. 266. Amsterdam: Elsevier; 1995.

    Google Scholar 

  18. Šesták J. Heat, thermal analysis and society. Nucleus, Hradec Králové; 2004.

  19. Šesták J. Science of heat, thermophysical studies a generalized approach to thermal analysis. Amsterdam: Elsevier; 2005.

    Google Scholar 

  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. Penrose R. Shadow of the mind: approach to the missing science of consciousness. Oxford: Oxford University Press; 1994.

    Google Scholar 

  22. Penrose R. The road to reality: a complete guide to the laws of the Universe. London: Vintage; 2004.

    Google Scholar 

  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. 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. Šesták J, Chvoj Z. Irreversible thermodynamics and true thermal dynamics in view of generalized solid-state reaction kinetics. Thermochim Acta. 2002;388:427–31.

    Article  Google Scholar 

  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. Young DA. Decomposition of solids. In: Tompkins FC, editor. Solid and surface kinetics. Oxford: Pergamon; 1966. p. 43–144.

    Google Scholar 

  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. Hulbert HF. Models for solid-state reactions in powdered compacts: a review. J Br Ceram Soc. 1969;6:11–20.

    CAS  Google Scholar 

  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. Galwey AK, Brown ME. Thermal decomposition of ionic solids. Amsterdam: Elsevier; 1999.

    Google Scholar 

  32. Málek J, Criado JM, Šesták J, Militký J. The boundary conditions for kinetic models. Thermochim Acta. 1989;153:429–32.

    Article  Google Scholar 

  33. Málek J, Mitsuhashi T, Criado JM. Kinetic analysis of solid-state processes. J Mater Res. 2001;16:1862–71.

    Article  Google Scholar 

  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. 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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  37. Koga N, Šesták J. TA kinetics and physical-geometry of the nonisothermal crystallization. Bull Soc Espaňa Cer Vidro. 1992;31:185–9.

    CAS  Google Scholar 

  38. Koga N. Physico-geometric kinetics of solid-state reactions as exemplified by thermal dehydration. J Therm Anal. 1997;49:45–56.

    Article  CAS  Google Scholar 

  39. Koga N, Tanaka H. A physico-geometric approach to the kinetics of solid-state reactions. Thermochim Acta. 2002;388:41–61.

    Article  CAS  Google Scholar 

  40. Khawam A, Flanagan DR. Solid-state kinetic models: basics and mathematical fundamentals. J Phys Chem B. 2006;110:17315–28.

    Article  CAS  Google Scholar 

  41. Kimura T, Koga N. Thermal dehydration of monohydrocalcite: overall kinetics and physico-geometrical mechanisms. J Phys Chem A. 2011;115:10491–501.

    Article  CAS  Google Scholar 

  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.

  43. Smith CS. Microstructure and geometry. Trans Am Soc Metals. 1953;45:533–75.

    CAS  Google Scholar 

  44. Smith CS. Some elementary principles of polycrystalline microstructure. Metal Rev. 1964;9:1–17.

    Article  CAS  Google Scholar 

  45. Pfeifer O. Macromolecules and colloidal aggregates—fractal dimension as concealed symmetry of irregular structures. Chimia. 1985;39:120.

    CAS  Google Scholar 

  46. Avnir D, Farin D, Pfeifer P. Molecular fractal surfaces. Nature. 1984;308:261–3.

    Article  CAS  Google Scholar 

  47. Avnir D. Fractal approach to heterogeneous chemistry. New York: Wiley; 1989.

    Google Scholar 

  48. Kopelman R. Fractal reaction kinetics. Science. 1988;241:620–5.

    Article  Google Scholar 

  49. Schröde M. Fractals, chaos and power laws. New York: Freeman; 1991.

    Google Scholar 

  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.

    Article  Google Scholar 

  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. Glicksman E. Free dendritic growth. Mater Sci Eng. 1984;65:45–54.

    Article  CAS  Google Scholar 

  53. Lipton J, Glicksman ME, Kurz W. Dendritic growth into undercooled alloy melts. Mater Sci Eng. 1984;65:57–64.

    Article  CAS  Google Scholar 

  54. Roduner E, Cronin L. Nanoscopic materials: size-dependent phenomena. Cambridge: RSC-publ; 2006 & 2007. IBSN 978-1-84755-763-6.

  55. Zhang Z, Li JC, Jiang Q. Modeling for size-dependent and dimension-dependent melting of nanocrystals. J Phys D. 2000;33:2653–6.

    Article  CAS  Google Scholar 

  56. Guisbiers G, Buchaillot L. Universal size/shape-dependent law for characteristic temperatures. Phys Lett A. 2009;374:305–8.

    Article  CAS  Google Scholar 

  57. Barnard AS. Modelling of nanoparticles: approaches to morphology and evolution—a review. Rep Prog Phys. 2010;73:6502–54.

    Article  Google Scholar 

  58. Elliot RS. Eutectic solidification processing: crystalline and glassy alloys. London: Butterworth; 1989.

    Google Scholar 

  59. Alexander S, Orbach R. Density of states on fractals—fractons. J Phys Lett. 1982;43:L625.

    Article  Google Scholar 

  60. Bonde A, Havlin S. Fractals and disordered systems. Berlin: Springer; 1991.

    Book  Google Scholar 

  61. Peitgen HO, Jurgen H, Saupe D. Chaos and fractals: new frontiers of science. New York: Springer; 1992.

    Google Scholar 

  62. Mandelbrot BB. Gaussian self-similarity, fractals, globallity and 1/f noise. New York: Springer; 2002.

    Google Scholar 

  63. Falcone K. Fractal geometry. Chichester: Wiley; 2003.

    Book  Google Scholar 

  64. Prout EG, Tompkins FC. The thermal decomposition of potassium permanganate. Trans Faraday Soc. 1944;40:488–98.

    Article  CAS  Google Scholar 

  65. Ng WL. Thermal decomposition in the solid state. Aust J Chem. 1975;28:1169–78.

    Article  CAS  Google Scholar 

  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.

    Article  Google Scholar 

  67. Málek J, Criado JM. Is the Šesták–Berggren equation a general expression of kinetic models? Thermochim Acta. 1991;175:305–9.

    Article  Google Scholar 

  68. Šimon P. Forty years of Šesták–Berggren equation. Thermochim Acta. 2011. doi:10.1016/j.tca.2011.03.030.

  69. Heal GR. Explanation of the Šestak–Berggren equation. Unpublished communication; 2011.

  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.

  71. Málek J. Crystallization kinetics by thermal analysis. J Therm Anal Calorim. 1999;56:763–9.

    Article  Google Scholar 

  72. Málek J. Kinetic analysis of crystallization processes in amorphous materials. Thermochim Acta. 2000;355:239–53.

    Article  Google Scholar 

  73. Šesták J, Kratochvil. Rational approach to thermodynamic processes and constitutive equations in kinetics. J Therm Anal. 1973;5:193–201.

    Article  Google Scholar 

  74. Šesták J. Thermodynamic basis for the theoretical description and correct interpretation of thermoanalytical experiments. Thermochim Acta. 1979;28:197–227.

    Article  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

  77. Hiller R, editor. Application of fractional calculus in physics. River Edge: World Science; 2000.

    Google Scholar 

  78. Milledr KS, Ross B. Introduction to the fractional calculus and fractional differential equations. New York: Wiley; 1993.

    Google Scholar 

  79. Fleschinger MF, Zaslavsky GM, Klaufter J. Strange kinetics. Nature. 1993;363:31–3.

    Article  Google Scholar 

  80. Galwey AK, Brown ME. Application of the Arrhenius equation to solid-state kinetics: can this be justified? Thermochim Acta. 2002;386:91–8.

    Article  CAS  Google Scholar 

  81. Galwey AK. Eradicating erroneous Arrhenius arithmetic. Thermochim Acta. 2003;399:1–29.

    Article  CAS  Google Scholar 

  82. Galwey AK. Theory of solid-state thermal decomposition: scientific stagnation or chemical catastrophe? An alternative approach apprised and advocated. Unpublished communication; 2011.

  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. Kissinger HE. Reaction kinetics in differential thermal analysis. Anal Chem. 1957;29:1702–6.

    Article  CAS  Google Scholar 

  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.

    Article  Google Scholar 

  86. Henderson DW. Experimental analysis of nonisothermal transformations involving nucleation and growth. J Therm Anal. 1979;15:325–31.

    Article  CAS  Google Scholar 

  87. Kemeny J, Šesták J. Comparison of crystallization kinetic theories derived by isothermal and nonisothermal methods. Thermochim Acta. 1987;110:113–9.

    Article  CAS  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  90. Šesták J. Applicability of DTA to study of crystallization kinetics of glasses. Phys Chem Glass. 1974;15:137–40.

    Google Scholar 

  91. Christian JW. Theory of transformations in metals and alloys. Oxford: Pergamon; 1975.

    Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  96. Koga N. Kinetic analysis of thermoanalytical data by extrapolating to infinite temperature. Thermochim Acta. 1995;258:145–9.

    Article  CAS  Google Scholar 

  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. 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.

    Article  CAS  Google Scholar 

  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.

  100. Málek J, Zmrhalová Z, Barták J, Honcová P. A novel method to study crystallization of glasses. Thermochim Acta. 2010;511:67–73.

    Article  Google Scholar 

  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.

  102. Dubaj T, Cibulková Z, Šimon P. Justification of the use of non-Arrhenian temperature functions, prepared for publication 2012.

  103. Šimon P. Single-step kinetics approximation employing non-Arrhenius temperature functions. J Therm Anal Calorim. 2005;79:703.

    Article  Google Scholar 

  104. Šimon P. The single-step approximation: attributes, strong and weak sides. J Therm Anal Calorim. 2007;88:709–15.

    Article  Google Scholar 

  105. Serra R, Nomen R, Sempere J. Non-parametric kinetics: a new method for kinetic study. J Therm Anal Calorim. 1998;52:933.

    Article  CAS  Google Scholar 

  106. Vyazovkin S. Model-free kinetics: staying free of multiplying entities without necessity. J Therm Anal Calorim. 2006;83:45.

    Article  CAS  Google Scholar 

  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. 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. 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. 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.

    Article  CAS  Google Scholar 

  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.

  112. Höhne GWH, Hemminger W, Flammersheim HJ. Differential scanning calorimetry. Dordrecht: Springer; 2003.

    Google Scholar 

  113. Brown ME, Gallagher PK, editors. Handbook of thermal analysis and calorimetry. Amsterdam: Elsevier; 2008.

    Google Scholar 

  114. Gabbott G, editor. Principles and application of thermal analysis. Oxford: Blackwell; 2008.

    Google Scholar 

  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 

Download references

Acknowledgements

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).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. Šesták.

Additional information

Devoted to the 90th birth anniversary (July 2012) of Vladimir Šatava (Prague) and also written on the occasion of passing away (October 2011 at the age 85) of Ivo Proks (Bratislava) both the foremost pioneers in the fields of thermodynamics and thermal analysis, to whom this paper is dedicated.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Šesták, J. Rationale and fallacy of thermoanalytical kinetic patterns. J Therm Anal Calorim 110, 5–16 (2012). https://doi.org/10.1007/s10973-011-2089-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10973-011-2089-1

Keywords

Navigation