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Rationale and Myth of Thermoanalytical Kinetic Patterns: How to Model Reaction Mechanisms by the Euclidean and Fractal Geometry and by Logistic Approach

  • Jaroslav ŠestákEmail author
  • Isak Avramov
Chapter
Part of the Hot Topics in Thermal Analysis and Calorimetry book series (HTTC, volume 11)

Abstract

Modeling tradition is reviewed within its historical maturity from Greek Plato to modern Penrose. Metaphors in non-isothermal 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 and can be acquainted with defects. The use of yet atypical fractal geometry is accredited, and associated formal kinetic models based on non-integral power exponents are acknowledged. Mathematical commencement and impact of logistic models are used highlighting the Sesták–Berggren (SB) equation and the impact of logistic approach as a generalized exploit. 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. The chapter contains 117 references.

Keywords

Logistic Curve Truthful Mechanism Heat Inertia Arbitrary Exponent Mathematical Commencement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The present work was also supported by Institutional Research Plan of Institute of Physics ASCR, v.v.i., no. AV0Z1010052 as developed at its Join Research Laboratory with the New Technologies Centre of the University of West Bohemia in Pilzen (the CENTEM project, reg. no. CZ.1.05/2.1.00/03.0088 that is cofunded from the ERDF as a part of the MEYS—Ministry of Education, Youth and Sports OP RDI Program and in the follow-up sustainability stage supported through the CENTEM PLUS LO 1402). The abandoned support by the Grant Agency of ČR for the projected grant ´Thermal inertia and its significance for the analysis of DTA measurements´ (No 17-21840S-2016) is worth mentioning as an example of fatal misunderstanding of current needs of thermal science.

References

  1. 1.
    Russell B (1967) History of western philosophy, Routledge (reedit up to 1995). ISBN 0-415-07854-7.AGoogle Scholar
  2. 2.
    Partington JR (1970) A history of chemistry. Macmillan, LondonGoogle Scholar
  3. 3.
    Habashi F (2000) Zoroaster and the theory of four elements. Bull Hist Chem 25:109–116Google Scholar
  4. 4.
    Ball P (2004) The elements: a very short introduction. OUP Oxford, p 33. ISBN 9780191578250Google Scholar
  5. 5.
    Šesták J (2004) Heat, thermal analysis and society. Nucleus, Hradec KrálovéGoogle Scholar
  6. 6.
    Šesták J (2005) Science of heat and thermophysical studies: a generalized approach to thermal analysis. Elsevier, AmsterdamGoogle Scholar
  7. 7.
    Šesták J (2008) Some model classification of geometrical bodies and their development in historical applications. In: Wittwer A, Knut E, Pliska V, Folker G (eds) Chapter in book: Approaching scientific knowledge, Collegieum Helveticum, Zurich, pp 87–91Google Scholar
  8. 8.
    Penrose R (1994) Shadow of the mind: approach to the missing science of consciousness. Oxford University Press, OxfordGoogle Scholar
  9. 9.
    Kepler J (1611) Strena seu de nive sexangula (The six-cornered snowflake). ISBN 978-1-58988-053-5Google Scholar
  10. 10.
    Hales TC (2006) Historical overview of the Kepler conjecture. Discr Comput Geom 36:5–20CrossRefGoogle Scholar
  11. 11.
    Bravais A (1846) Analyse mathématique sur les probabilités des erreurs de situation d’un point. Acad R Sci Inst Fr 9:255–332Google Scholar
  12. 12.
    Bravais A (1866) Études cristallographiques. ParisGoogle Scholar
  13. 13.
    Penrose R (2004) The road to reality: a complete guide to the laws of the Universe. Vintage, LondonGoogle Scholar
  14. 14.
    Šesták J, Zámečník J (2007) Can clustering of liquid water be of assistance for better understanding of biological germplasm exposed to cryopreservation. J Thermal Anal Calor 8:411–419Google Scholar
  15. 15.
    Chvoj Z, Šesták J, Tříska A (eds) (1991) Kinetic phase diagrams: nonequilibrium phase transitions. Elsevier, AmsterdamGoogle Scholar
  16. 16.
    Šesták J (1984) Thermophysical Properties of Solids: their measurements and theoretical thermal analysis. Elsevier, Amsterdam; and (1987) Teoretičeskij termičeskij analys. Mir, Moscow (in Russian)Google Scholar
  17. 17.
    Barrow JD (1994) The origin of the Universe. Orion, LondonGoogle Scholar
  18. 18.
    Barrow JD (1999) Impossibility: limits of science and science of limits. Vintage, New YorkGoogle Scholar
  19. 19.
    Šesták J, Holba P (2013) Heat inertia and temperature gradient in the treatment of DTA peaks: existing on every occasion of real measurements but until now omitted. J Therm Anal Calorim 113:1633–1643CrossRefGoogle Scholar
  20. 20.
    Barghathi H, Vojta T (2014) Phase transitions on random lattices: how random is topological disorder? Phys Rev Lett 113:120602; and Okabe A, Boots B, Sugihara K, Chiu S (2000) Spatial tessellations: concepts and applications of Voronoi and delaunay diagrams. Wiley, ChichesterGoogle Scholar
  21. 21.
    Giazitzidis P, Avramov I, Argyrakis P (2015) Variation of the critical percolation threshold with the method of system preparation. Eur Phys J B 88:331CrossRefGoogle Scholar
  22. 22.
    Šesták J (1979) Philosophy of non-isothermal kinetics J Thermal Anal 16:503–520; and (1988) Nonisothermal kinetics: art, debate or applied science. J Thermal Anal 33:1263–1267Google Scholar
  23. 23.
    Jacobs PWM, Tompkins FC (1955) Classification and theory of solid reactions. In: Garner WE (ed) Chemistry of the solid state. Butterworth, LondonGoogle Scholar
  24. 24.
    Young DA (1966) Decomposition of solids. In: Tompkins FC (ed) Solid and surface kinetics. Pergamon, OxfordGoogle Scholar
  25. 25.
    Šesták J (1979) Thermodynamic basis for the theoretical description and correct interpretation of thermoanalytical experiments. Thermochim Acta 28:197–227CrossRefGoogle Scholar
  26. 26.
    Kopelman R (1988) Fractal reaction kinetics. Science 241:620–625CrossRefGoogle Scholar
  27. 27.
    Kopelman R, Parus SJ (1986) Fractals in reaction kinetics. In: Schaefer DW, Mandelbrot BB (eds) Fractal aspects of materials. Material Res. Soc. BostonGoogle Scholar
  28. 28.
    Avnir D (1989) Fractal approach to heterogeneous chemistry. Wiley, New York; and Schröde M (1991) Fractals, chaos and power laws. Freeman, New YorkGoogle Scholar
  29. 29.
    Šesták J (2002) The role of order and disorder in thermal science (I) and Universe, matter and society (II), J Mining Metal 38:1–6; and 2003; 39:1–7Google Scholar
  30. 30.
    Šesták J, Chvoj Z (2002) Irreversible thermodynamics and true thermal dynamics in view of generalized solid-state reaction kinetics. Thermochim Acta 388:427–431CrossRefGoogle Scholar
  31. 31.
    Šesták J (2012) Rationale and fallacy of thermoanalytical kinetic patterns: how we model subject matter. J Thermal Anal Calor 110:5–16CrossRefGoogle Scholar
  32. 32.
    Šimon P, Zmeškal O, Šesták J (2013) Fractals in solid-state processes. In: Šesták J, Šimon P (eds) Chapter 12 in book Thermal analysis of micro-, nano- and non-crystalline materials. Springer, Berlin, pp 257–290. ISBN 978-90-481-3149-5Google Scholar
  33. 33.
    Šesták J (2006) Plenary lectures: rationale and fiction of thermochemical kinetics. In: Vitez I (ed) The proceedings of the 34th conference of North American thermal analysis society. Bowling Green, pp 68–69; and Šesták J (1972) Plenary lectures: nonisothermal kinetics. In: Wiedemann HG (ed) The Proceedings of the thermal analysis conference 3rd ICTA in Davos, Birghausser, Basel, pp 3–9Google Scholar
  34. 34.
    Šesták J (ed) (1992) Reaction kinetics by thermal analysis. Special issue of Thermochim Acta, vol 203, Elsevier, AmsterdamGoogle Scholar
  35. 35.
    Šesták J, Sorai M (eds) (1995) Transition phenomena in condensed matter. Special issue of Thermochim Acta, vol 266. Elsevier AmsterdamGoogle Scholar
  36. 36.
    Šesták J, Mareš JJ, Hubík P (eds) (2011) Glassy, amorphous and nano-crystalline materials: thermal physics, analysis, structure and properties, vol 8. Springer, Berlin, Heidelberg. ISBN 978-90-481-2881-5Google Scholar
  37. 37.
    Kožíšek Z, Demo P, Sveshnikov A (2013) Kinetics of crystal nucleation in closed systems; and nucleation on strongly curved surfaces, In: Šesták J, Šimon P (eds) Chapters 9 and 19 in book Thermal analysis of micro-, nano- and non-crystalline materials: transformation, crystallization, kinetics and thermodynamics, vol 9. Springer, Berlin, Heidelberg, pp 190–208 and 419–428. ISBN 978-90-481-3149-5Google Scholar
  38. 38.
    Glicksman E (1984) Dendritic growth. Mater Sci Eng 65:45–55; and Lipton J, Glicksman ME, Kurz W (1984) Dendritic growth into undercooled alloy melts. Mater Sci Eng 65:57–63Google Scholar
  39. 39.
    Smith CS (1953) Microstructure and geometry. Trans Am Soc Metals 45:533–575; and (1964) Some elementary principles of polycrystalline microstructure. Metal Rev 9:1–17Google Scholar
  40. 40.
    Avnir D, Farin D, Pfeifer P (1984) Molecular fractal surfaces. Nature 308:261–263; and Bonde A, Havlin S (1991) Fractals and disordered systems. Springer, BerlinGoogle Scholar
  41. 41.
    Hulbert HF (1969) Models for solid-state reactions in powdered compacts: a review. J Br Ceram Soc 6:11–20; and Khawam A, Flanagan DR (2006) Solid-state kinetic models: basics and mathematical fundamentals J Phys Chem B 110:17315–17328Google Scholar
  42. 42.
    Illeková E, Šesták J (2013) Crystallization kinetics of metallic micro-, nano- and non-crystalline alloys. In: Šesták J, Šimon P (eds) Chapter 13 in book: Thermal analysis of micro-, nano- and non-crystalline materials, pp 257–290. Springer, Berlin. ISBN 978-90-481-3149-5Google Scholar
  43. 43.
    Málek J, Criado JM, Šesták J, Militký J (1989) The boundary conditions for kinetic models. Thermochim Acta 153:429–432; and Málek J, Mitsuhashi T, Criado JM (2001) Kinetic analysis of solid-state processes. J Mater Res 16:1862–1871Google Scholar
  44. 44.
    Koga N, Šesták J, Šimon P (2013) Some fundamental and historical aspects of phenomenological kinetics in solid-state studied by thermal analysis. In: Šesták J, Šimon P (eds) Chapter 1 in book: Thermal analysis of micro-, nano- and non-crystalline materials. Springer, Berlin, pp 1–45. ISBN 978-90-481-3149-5Google Scholar
  45. 45.
    Šesták J (2005) Modeling of reaction mechanism: use of Euclidian and fractal geometry. In: Chapter 10 in his book: Science of heat and thermophysical studies: a generalized approach to thermal analysis. Elsevier, Amsterdam, pp 276–314Google Scholar
  46. 46.
    Mandelbrot BB (2003) Gaussian self-similarity, fractals and 1/f noise. Springer, New York; and Falcone K (2002) Fractal geometry. Wiley, ChichesterGoogle Scholar
  47. 47.
    Hiller R (ed) (1993) Application of fractional calculus in physics. World Sci, River Edge, NJ; and Milledr KS, Ross B (2000) Introduction to the fractional calculus and fractional differential equations. Wiley, New YorkGoogle Scholar
  48. 48.
    Fleschinger MF, Zaslavsky GM, Klaufter J (1993) Strange kinetics. Nature 363:31–33CrossRefGoogle Scholar
  49. 49.
    Mareš JJ, Šesták J, Hubík P (2013) Transport constitutive relations, quantum diffusion and periodic reactions. In: Šesták J, Mareš J, Hubík P (eds) Chapter 14 in book Glassy, amorphous and nano-crystalline materials: thermal physics, analysis, structure and properties, pp 227–245. Springer, Berlin. ISBN 978-90-481-2881-5Google Scholar
  50. 50.
    Stávek J, Šesták Šípek M, Šesták J (2002) Application of the principle of least action to some self-organized chemical reactions. Thermochim Acta 388:440CrossRefGoogle Scholar
  51. 51.
    Mareš JJ, Stávek J, Šesták J (2004) Quantum aspects of self-organized periodic chemical reaction. J. Chem Phys 121:1499–1503CrossRefGoogle Scholar
  52. 52.
    Galwey AK (2004) Is the science of thermal analysis kinetics based on solid foundations? A literature appraisal. Thermochim Acta 413:139–183CrossRefGoogle Scholar
  53. 53.
    Galwey AK (2006) What theoretical and/or chemical significance is to be attached to the magnitude of an activation energy determined for a solid-state decomposition? J Therm Anal Calor 86:267–286CrossRefGoogle Scholar
  54. 54.
    Šesták J (2015) The quandary aspects of non-isothermal kinetics beyond the ICTAC kinetic committee recommendations. Thermochim Acta 611:26–35CrossRefGoogle Scholar
  55. 55.
    Ozao R, Ochiai M (1993) Fractal nature and thermal analysis of powders. J Thermal Anal: 1331Google Scholar
  56. 56.
    Serra R, Nomen R, Sempere J (1998) Non-Parametric kinetics: a new method for kinetic study. J Thermal Anal Calor 52:933CrossRefGoogle Scholar
  57. 57.
    Šimon P (2005) Single-step kinetic approximation employing non-Arrhenius T-functions. J Thermal Anal Calor 79:703; and (2007) Single-step approximation: attributes, strong and weak sides. J Therm Anal Calorim 88:709–715Google Scholar
  58. 58.
    Vyazovkin S (2006) Model-free kinetics: staying free of multiplying entities without necessity. J Thermal Anal Calor 83:45CrossRefGoogle Scholar
  59. 59.
    Šimon P, Dubaj T, Cibulková Z (2015) Equivalence of the Arrhenius and non-Arrhenian temperature functions in the temperature range of measurements. J Therm Anal Calorim, 120: 231–238; and T. Dubaj, Z. Cibulková, P. Šimon (2015) An incremental isoconversional method for kinetic analysis based on the orthogonal distance regression. J Comput Chem 36: 392–398Google Scholar
  60. 60.
    Holba P., Šesták J. Sedmidubsky D (2013) Heat transfer and phase transition at DTA experiments. In: Šesták J, Šimon P (eds) Chapter 5 in book: Thermal analysis of micro-, nano- and non-crystalline materials. Springer, Berlin, pp 99–134. ISBN 978-90-481-3149-5Google Scholar
  61. 61.
    Holba P, Šesták J (2015) Heat inertia and its role in thermal analysis. J Thermal Anal Calor 121:303–307CrossRefGoogle Scholar
  62. 62.
    Šesták J (2015) Kinetic phase diagrams as a consequence of radical changing temperature or particle size. J Thermal Anal Calor, 120:129–137; and Šesták J (2016) Measuring “hotness”: should the sensor’s readings for rapid temperature changes be named “tempericity”? J Thermal Anal Calor 125:991–999Google Scholar
  63. 63.
    Höhne GWH (2003) Calorimetry on small systems—a thermodynamic contribution. Thermochim Acta 403:25–36CrossRefGoogle Scholar
  64. 64.
    Perepezko JH, Glendenning TW, Wang J-Q (2015) Nanocalorimnetry measurements of metastable states. Thermochim Acta 603:24–28CrossRefGoogle Scholar
  65. 65.
    Barnard AS (2010) Modeling of nanoparticles: approaches to morphology and evolution—a review. Rep Prog Phys 73:6502–6554CrossRefGoogle Scholar
  66. 66.
    Pfeifer O (1985) Macromolecules and colloidal aggregates—fractal dimension as concealed symmetry of irregular structures. Chimia 39:120Google Scholar
  67. 67.
    Alexander S, Orbach R (1982) Density of states on fractals—fractons. J Phys Lett 43:L625CrossRefGoogle Scholar
  68. 68.
    Avramov I (2008) Diffusion coefficient of foreign particles in glass-forming melts. J Non-Cryst Sol 354(14):1537–1540CrossRefGoogle Scholar
  69. 69.
    Karamanov A, Avramov I, Arrizza L, Pascova R, Gutzow I (2012) Variation of Avrami parameter during non-isothermal surface crystallization of glass powders with different sizes. J Non-Cryst Sol 358:1486–1490CrossRefGoogle Scholar
  70. 70.
    Avramova K, Karamanov A, Avramov I (2015) Variations in non-isothermal surface crystallization kinetics due to minor composition changes, J Non-Cryst Sol 428:49–53; and Thieme K, Avramov I, Rüssel C (2016) The mechanism of deceleration of nucleation and crystal growth by the small addition of transitive metals. Sci Rep doi: 10.1038/srep25451
  71. 71.
    Avramov I, Šesták J (2014) Generalized kinetics of overall phase transition explicit to crystallization. J Therm Anal Calorim 118:1715–1720CrossRefGoogle Scholar
  72. 72.
    Šesták J (2016) Outline of hyperfree energy, equilibrium background and heat inertia opening new frontiers of thermal analysis. J Thermal Anal Calor doi: 10.1007/s10973-016-5880-1
  73. 73.
    Broadbent SR, Hammersley JM (1957) Percolation processes. Math Proc Cambridge Philos Soc 53:629–641CrossRefGoogle Scholar
  74. 74.
    Avramov I (2009) Rigid–floppy percolation threshold. J Phys Condens Matter 21:215402CrossRefGoogle Scholar
  75. 75.
    Qiwu C, Lawson GJ (1982) Study on models of single population: an expanse of the logistic and exponential equations. J Theoret Biol 98:645–659CrossRefGoogle Scholar
  76. 76.
    Avramov I (2007) Kinetics of distribution of infections in network. Phys A 379:615CrossRefGoogle Scholar
  77. 77.
    Verhulst PF (1844) Recherches mathématiques sur la loi d’accroisement de la population. Mem Acad R Brux 18:1Google Scholar
  78. 78.
    Pearl R (1924) Studies in human biology. Williams & Wilkins, BaltimoreGoogle Scholar
  79. 79.
    Berkson J (1944) Application of the logistic function to bio-assay. J Amer Stat Soc 39:357–365Google Scholar
  80. 80.
    Galton F (1875) Statistics by inter-comparison, with remarks on the law of frequency of errors. Phil Mag 49:33–46Google Scholar
  81. 81.
    Yule GU (1925) The growth of population and the factors which control it. J Roy Stat Soc 88:1–62CrossRefGoogle Scholar
  82. 82.
    Andersen EB (1977) Sufficient statistics and latent trait models. Psychometrika 42:69–81CrossRefGoogle Scholar
  83. 83.
    Latour B, Woolgar S (1979) The societal construction of scientific facts. Beverly Hills Sage Publ., LondonGoogle Scholar
  84. 84.
    Sakanoue S (2013) Ecological modeling 261/262:93–97Google Scholar
  85. 85.
    Ferretti NK, Rahman A (1988) Study of coupled logistic map and its applications in chemical physics. Chem Phys 119:275–288CrossRefGoogle Scholar
  86. 86.
    Finkelshtein D, Kondratiev Y, Kozitsky Y, Kutoviy O (2015) The statistical dynamics of a spatial logistic model and the related kinetic equation. Math Models Methods Appl Sci 25:343–370CrossRefGoogle Scholar
  87. 87.
    Ng WL (1975) Thermal decomposition in the solid state. Aust J Chem 28:1169–1178CrossRefGoogle Scholar
  88. 88.
    ShaBian Lin-WeiDu, Yu-XiGao JianHuang, Gou Bao-Di, XiuhongLi YiLiu, Zhang Tian-Lan, Wang Kui (2012) Crystallization in aggregates of calcium phosphate nanocrystals: A logistic model for kinetics of fractal structure development. Cryst Growth Des 12:3481–3488CrossRefGoogle Scholar
  89. 89.
    Burnham AK, Weese RK, Weeks BL (2004) Distributed activation energy model of thermodynamically inhibited nucleation and growth reactions and its logistic application to the b–d phase transition. J Phys Chem B 108:19432–19441CrossRefGoogle Scholar
  90. 90.
    Cao R, Naya S, Artiaga R, Garcia A, Varela A (2004) Logistic approach to polymer degradation in dynamic TGA. Poly Degrad Stab 85:667–674CrossRefGoogle Scholar
  91. 91.
    Naya S, Cao R, Lopez de Ullibarri I, Artiaga R, Barbadillo F, Garcia A (2006) Logistic mixture versus Arrhenius for kinetic study of material degradation by dynamic thermogravimetric analysis. J Chemom 20:158–163CrossRefGoogle Scholar
  92. 92.
    Barbadillo F, Fuentes A, Naya S, Cao R, Mier JL, Artiaga R (2007) Evaluating the logistic mixture model on real and simulated TG curves. J Therm Anal Calorim 87:223–227CrossRefGoogle Scholar
  93. 93.
    Tarrio-Saavedra J, Lopez-Beceiro J, Naya S, Francisco-Fernandez M, Artiaga R (2014) Simulation study for generalized logistic function in thermal data modeling. J Therm Anal Calorim 118:1253–1268CrossRefGoogle Scholar
  94. 94.
    Akulov NS (1940) On the genesis of chemical reactions, Comp Rend Acad Sci URSS 28:135–138 (in Russian); and (1940) Comp Rend Acad Sci USSR 27:135–138 (English translation); and (1940) book: Basics of chemical dynamics. By Moscow State University; Moscow (in Russian)Google Scholar
  95. 95.
    Prout EG, Tompkins FC (1944) The thermal decomposition of potassium permanganate. Trans Faraday Soc 40:488–498CrossRefGoogle Scholar
  96. 96.
    Šimon P (2011) Forty years of the Šesták-Berggren equation. Thermochim Acta 520:156–157CrossRefGoogle Scholar
  97. 97.
    Šesták J, Berggren G (1971) Study of the kinetics of the mechanism of solid-state reactions at increasing temperature. Thermochim Acta 3:1–13CrossRefGoogle Scholar
  98. 98.
    Šesták J (2017) The Šesták-Berggren equation: now questioned but formerly celebrated—what is right? J Therm Anal Calorim 127:1117–1123; and Militký J, Šesták J (2017) On the eliminating attempts toward Sestak-Berggren equation. J Therm Anal Calorim 127:1131–1133Google Scholar
  99. 99.
    Nolan PS, LeMay HE (1973) Evaluation of the non-isothermal rate equation proposed by Sestak and Berggren by computer methods. Thermochim Acta 16:179–186CrossRefGoogle Scholar
  100. 100.
    Gorbachev VM (1980) Some aspects of Sesták’s generalized kinetic equation in thermal analysis. J Therm Anal 18:193–197; and in Zh Fiz Khim USSR 51(1977) 1100 (in Russian)Google Scholar
  101. 101.
    Málek J, Criado JM (1991) Is the Šesták-Berggren equation a general expression of kinetic models? Thermochim Acta 175:305–309CrossRefGoogle Scholar
  102. 102.
    Burnham AK (2000) Application of the Šesták-Berggren equation to organic and inorganic materials of practical interest. J Therm Anal Calor 60:895–908CrossRefGoogle Scholar
  103. 103.
    Munteanu G, Segal E (2010) Sestak–Berggren function in temperature—programmed reduction. J Therm Anal Calorim 101:89–95Google Scholar
  104. 104.
    Arshad MA, Maaroufi A (2015) Relationship between Johnson-Mehl-Avrami and Šesták-Berggren models in the kinetics of crystallization in amorphous materials. J Non-Cryst Sol 413:53–58CrossRefGoogle Scholar
  105. 105.
    Kolmogorov A (1961) Reaction rate of processes involving solids with different specific surfaces. In: The proceedings of the 4th international symposium reactivity of solids. Elsevier, Amsterdam, pp 273–282Google Scholar
  106. 106.
    Atkinson HV (1988) Theories of normal grain growth in pure single phase systems. Acta Metall 36:469–491CrossRefGoogle Scholar
  107. 107.
    Šesták J (1991) Diagnostic limits of phenomenological kinetic models when introducing an accommodation function. J Therm Anal 36:1997; and Šesták J, Málek J (1993) Diagnostic limits of phenomenological models of heterogeneous reactions and thermoanalytical kinetics. Solid State Ionics 63/65:254–259Google Scholar
  108. 108.
    Málek J (1999) Crystallization kinetics by thermal analysis. J Thermal Anal Calor 56:763–769; and (2000) Kinetic analysis of crystallization processes in amorphous materials. Thermochim Acta 355:239–253Google Scholar
  109. 109.
    Perez_Maqueda LA, Criado JM, Sanchez-Jimenez PE (2006) Combined kinetic analysis of solid-state reactions: a powerful tool for simultaneous determination of kinetic parameters and the kinetic models without previous assumptions on the reaction mechanism. J Phys Chem A 110:12456–12462CrossRefGoogle Scholar
  110. 110.
    Flynn JH, Brown M, Šesták J (1987) Report on the workshop: current problems of kinetic data reliability evaluated by thermal analysis. Thermochim Acta 110:101–112. A segment of the Special issue “Thermal analysis highlights” edited by V. Balek and J. Šesták, Elsevier, Amsterdam 1986Google Scholar
  111. 111.
    Vyazovkin S (2000) Computational aspects of kinetic analysis.: part C. The ICTAC Kinetics Project- the light at the end of the tunnel? Thermochim Acta 355:155–163CrossRefGoogle Scholar
  112. 112.
    Vyazovkin S, Burnham AK, Criado JN, Perez-Maqueda LA, Popescu C, Sbirrazzuoli N (2011) ICTAC kinetics committee recommendations for performing kinetic computations on thermal analysis data. Thermochim Acta 520:1–19CrossRefGoogle Scholar
  113. 113.
    Vyazovkin S, Chrissafis K, DiLorenzo ML, Koga N, Pijolat M, Roduit MB, Sbirrazzuoli N, Suñol JJ (2014) ICTAC Kinetics Committee recommendations for collecting experimental thermal analysis data for kinetic computations. Thermochim Acta 590:1–23CrossRefGoogle Scholar
  114. 114.
    Vyazovkin S (2015) Isoconversional kinetics of thermally stimulated processes. Springer, Berlin, Heidelberg. ISBN 10: 3319141740Google Scholar
  115. 115.
    Šesták J (2014) Is the original Kissinger equation obsolete today—not obsolete the entire non-isothermal kinetics? J Thermal Anal Calorim 117:1173–1177; and Holba P, Šesták J (2014) Imperfections of Kissinger evaluation method and crystallization kinetics. Glass Phys Chem 40:486–449Google Scholar
  116. 116.
    Muravyev NV, Koga N, Meerova DB, Pivkinaa AN (2017)  Kinetic analysis of overlapping multistep thermal decomposition comprising exothermic and endothermic processes: thermolysis of amonium dinitramide. Phys Chem Chem Phys doi: 10.1039/c6cp08218a  
  117. 117.
    Yerofeev BV (1961) Reaction rate of processes involving solids with different specific surfaces. In: The proceedings: 4th international symposium reactivity of solids. Elsevier, Amsterdam, pp 273–282 Google Scholar

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Authors and Affiliations

  1. 1.New Technologies Research Centre (NTC-ZČU)University of West BohemiaPilsenCzech Republic
  2. 2.Institute of Physical ChemistryBulgarian Academy of SciencesSofiaBulgaria

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