Skip to main content
SpringerLink
Log in

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

  • Chapter
  • First Online:
Thermal Physics and Thermal Analysis

Part of the book series: Hot Topics in Thermal Analysis and Calorimetry ((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.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Russell B (1967) History of western philosophy, Routledge (reedit up to 1995). ISBN 0-415-07854-7.A

    Google Scholar 

  2. Partington JR (1970) A history of chemistry. Macmillan, London

    Google Scholar 

  3. Habashi F (2000) Zoroaster and the theory of four elements. Bull Hist Chem 25:109–116

    CAS  Google Scholar 

  4. Ball P (2004) The elements: a very short introduction. OUP Oxford, p 33. ISBN 9780191578250

    Google Scholar 

  5. Šesták J (2004) Heat, thermal analysis and society. Nucleus, Hradec Králové

    Google Scholar 

  6. Šesták J (2005) Science of heat and thermophysical studies: a generalized approach to thermal analysis. Elsevier, Amsterdam

    Google Scholar 

  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 87–91

    Google Scholar 

  8. Penrose R (1994) Shadow of the mind: approach to the missing science of consciousness. Oxford University Press, Oxford

    Google Scholar 

  9. Kepler J (1611) Strena seu de nive sexangula (The six-cornered snowflake). ISBN 978-1-58988-053-5

    Google Scholar 

  10. Hales TC (2006) Historical overview of the Kepler conjecture. Discr Comput Geom 36:5–20

    Article  Google Scholar 

  11. Bravais A (1846) Analyse mathématique sur les probabilités des erreurs de situation d’un point. Acad R Sci Inst Fr 9:255–332

    Google Scholar 

  12. Bravais A (1866) Études cristallographiques. Paris

    Google Scholar 

  13. Penrose R (2004) The road to reality: a complete guide to the laws of the Universe. Vintage, London

    Google Scholar 

  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 8:411–419

    Google Scholar 

  15. Chvoj Z, Šesták J, Tříska A (eds) (1991) Kinetic phase diagrams: nonequilibrium phase transitions. Elsevier, Amsterdam

    Google Scholar 

  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. Barrow JD (1994) The origin of the Universe. Orion, London

    Google Scholar 

  18. Barrow JD (1999) Impossibility: limits of science and science of limits. Vintage, New York

    Google Scholar 

  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 113:1633–1643

    Article  Google Scholar 

  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, Chichester

    Google Scholar 

  21. Giazitzidis P, Avramov I, Argyrakis P (2015) Variation of the critical percolation threshold with the method of system preparation. Eur Phys J B 88:331

    Article  Google Scholar 

  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 33:1263–1267

    Google Scholar 

  23. Jacobs PWM, Tompkins FC (1955) Classification and theory of solid reactions. In: Garner WE (ed) Chemistry of the solid state. Butterworth, London

    Google Scholar 

  24. Young DA (1966) Decomposition of solids. In: Tompkins FC (ed) Solid and surface kinetics. Pergamon, Oxford

    Google Scholar 

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

    Article  Google Scholar 

  26. Kopelman R (1988) Fractal reaction kinetics. Science 241:620–625

    Article  Google Scholar 

  27. Kopelman R, Parus SJ (1986) Fractals in reaction kinetics. In: Schaefer DW, Mandelbrot BB (eds) Fractal aspects of materials. Material Res. Soc. Boston

    Google Scholar 

  28. Avnir D (1989) Fractal approach to heterogeneous chemistry. Wiley, New York; and Schröde M (1991) Fractals, chaos and power laws. Freeman, New York

    Google Scholar 

  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; 39:1–7

    Google Scholar 

  30. Šesták J, Chvoj Z (2002) Irreversible thermodynamics and true thermal dynamics in view of generalized solid-state reaction kinetics. Thermochim Acta 388:427–431

    Article  Google Scholar 

  31. Šesták J (2012) Rationale and fallacy of thermoanalytical kinetic patterns: how we model subject matter. J Thermal Anal Calor 110:5–16

    Article  Google Scholar 

  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 978-90-481-3149-5

    Google Scholar 

  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 3–9

    Google Scholar 

  34. Šesták J (ed) (1992) Reaction kinetics by thermal analysis. Special issue of Thermochim Acta, vol 203, Elsevier, Amsterdam

    Google Scholar 

  35. Šesták J, Sorai M (eds) (1995) Transition phenomena in condensed matter. Special issue of Thermochim Acta, vol 266. Elsevier Amsterdam

    Google Scholar 

  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 978-90-481-2881-5

    Google Scholar 

  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 978-90-481-3149-5

    Google Scholar 

  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 65:57–63

    Google Scholar 

  39. Smith CS (1953) Microstructure and geometry. Trans Am Soc Metals 45:533–575; and (1964) Some elementary principles of polycrystalline microstructure. Metal Rev 9:1–17

    Google Scholar 

  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, Berlin

    Google Scholar 

  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 110:17315–17328

    Google Scholar 

  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 978-90-481-3149-5

    Google Scholar 

  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 16:1862–1871

    Google Scholar 

  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 978-90-481-3149-5

    Google Scholar 

  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 276–314

    Google Scholar 

  46. Mandelbrot BB (2003) Gaussian self-similarity, fractals and 1/f noise. Springer, New York; and Falcone K (2002) Fractal geometry. Wiley, Chichester

    Google Scholar 

  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 York

    Google Scholar 

  48. Fleschinger MF, Zaslavsky GM, Klaufter J (1993) Strange kinetics. Nature 363:31–33

    Article  Google Scholar 

  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 978-90-481-2881-5

    Google Scholar 

  50. Stávek J, Šesták Šípek M, Šesták J (2002) Application of the principle of least action to some self-organized chemical reactions. Thermochim Acta 388:440

    Article  Google Scholar 

  51. Mareš JJ, Stávek J, Šesták J (2004) Quantum aspects of self-organized periodic chemical reaction. J. Chem Phys 121:1499–1503

    Article  Google Scholar 

  52. Galwey AK (2004) Is the science of thermal analysis kinetics based on solid foundations? A literature appraisal. Thermochim Acta 413:139–183

    Article  CAS  Google Scholar 

  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 86:267–286

    Article  CAS  Google Scholar 

  54. Šesták J (2015) The quandary aspects of non-isothermal kinetics beyond the ICTAC kinetic committee recommendations. Thermochim Acta 611:26–35

    Article  Google Scholar 

  55. Ozao R, Ochiai M (1993) Fractal nature and thermal analysis of powders. J Thermal Anal: 1331

    Google Scholar 

  56. Serra R, Nomen R, Sempere J (1998) Non-Parametric kinetics: a new method for kinetic study. J Thermal Anal Calor 52:933

    Article  CAS  Google Scholar 

  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 88:709–715

    Google Scholar 

  58. Vyazovkin S (2006) Model-free kinetics: staying free of multiplying entities without necessity. J Thermal Anal Calor 83:45

    Article  CAS  Google Scholar 

  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: 392–398

    Google Scholar 

  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 978-90-481-3149-5

    Google Scholar 

  61. Holba P, Šesták J (2015) Heat inertia and its role in thermal analysis. J Thermal Anal Calor 121:303–307

    Article  CAS  Google Scholar 

  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 125:991–999

    Google Scholar 

  63. Höhne GWH (2003) Calorimetry on small systems—a thermodynamic contribution. Thermochim Acta 403:25–36

    Article  Google Scholar 

  64. Perepezko JH, Glendenning TW, Wang J-Q (2015) Nanocalorimnetry measurements of metastable states. Thermochim Acta 603:24–28

    Article  CAS  Google Scholar 

  65. Barnard AS (2010) Modeling of nanoparticles: approaches to morphology and evolution—a review. Rep Prog Phys 73:6502–6554

    Article  Google Scholar 

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

    CAS  Google Scholar 

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

    Article  Google Scholar 

  68. Avramov I (2008) Diffusion coefficient of foreign particles in glass-forming melts. J Non-Cryst Sol 354(14):1537–1540

    Article  CAS  Google Scholar 

  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 358:1486–1490

    Article  CAS  Google Scholar 

  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. Avramov I, Šesták J (2014) Generalized kinetics of overall phase transition explicit to crystallization. J Therm Anal Calorim 118:1715–1720

    Article  CAS  Google Scholar 

  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. Broadbent SR, Hammersley JM (1957) Percolation processes. Math Proc Cambridge Philos Soc 53:629–641

    Article  CAS  Google Scholar 

  74. Avramov I (2009) Rigid–floppy percolation threshold. J Phys Condens Matter 21:215402

    Article  CAS  Google Scholar 

  75. Qiwu C, Lawson GJ (1982) Study on models of single population: an expanse of the logistic and exponential equations. J Theoret Biol 98:645–659

    Article  Google Scholar 

  76. Avramov I (2007) Kinetics of distribution of infections in network. Phys A 379:615

    Article  Google Scholar 

  77. Verhulst PF (1844) Recherches mathématiques sur la loi d’accroisement de la population. Mem Acad R Brux 18:1

    Google Scholar 

  78. Pearl R (1924) Studies in human biology. Williams & Wilkins, Baltimore

    Google Scholar 

  79. Berkson J (1944) Application of the logistic function to bio-assay. J Amer Stat Soc 39:357–365

    CAS  Google Scholar 

  80. Galton F (1875) Statistics by inter-comparison, with remarks on the law of frequency of errors. Phil Mag 49:33–46

    Google Scholar 

  81. Yule GU (1925) The growth of population and the factors which control it. J Roy Stat Soc 88:1–62

    Article  Google Scholar 

  82. Andersen EB (1977) Sufficient statistics and latent trait models. Psychometrika 42:69–81

    Article  Google Scholar 

  83. Latour B, Woolgar S (1979) The societal construction of scientific facts. Beverly Hills Sage Publ., London

    Google Scholar 

  84. Sakanoue S (2013) Ecological modeling 261/262:93–97

    Google Scholar 

  85. Ferretti NK, Rahman A (1988) Study of coupled logistic map and its applications in chemical physics. Chem Phys 119:275–288

    Article  Google Scholar 

  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 25:343–370

    Article  Google Scholar 

  87. Ng WL (1975) Thermal decomposition in the solid state. Aust J Chem 28:1169–1178

    Article  CAS  Google Scholar 

  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 12:3481–3488

    Article  Google Scholar 

  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 108:19432–19441

    Article  CAS  Google Scholar 

  90. Cao R, Naya S, Artiaga R, Garcia A, Varela A (2004) Logistic approach to polymer degradation in dynamic TGA. Poly Degrad Stab 85:667–674

    Article  CAS  Google Scholar 

  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 20:158–163

    Article  CAS  Google Scholar 

  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 87:223–227

    Article  CAS  Google Scholar 

  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 118:1253–1268

    Article  CAS  Google Scholar 

  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. Prout EG, Tompkins FC (1944) The thermal decomposition of potassium permanganate. Trans Faraday Soc 40:488–498

    Article  CAS  Google Scholar 

  96. Šimon P (2011) Forty years of the Šesták-Berggren equation. Thermochim Acta 520:156–157

    Article  Google Scholar 

  97. Šesták J, Berggren G (1971) Study of the kinetics of the mechanism of solid-state reactions at increasing temperature. Thermochim Acta 3:1–13

    Article  Google Scholar 

  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 127:1131–1133

    Google Scholar 

  99. Nolan PS, LeMay HE (1973) Evaluation of the non-isothermal rate equation proposed by Sestak and Berggren by computer methods. Thermochim Acta 16:179–186

    Article  Google Scholar 

  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. Málek J, Criado JM (1991) Is the Šesták-Berggren equation a general expression of kinetic models? Thermochim Acta 175:305–309

    Article  Google Scholar 

  102. Burnham AK (2000) Application of the Šesták-Berggren equation to organic and inorganic materials of practical interest. J Therm Anal Calor 60:895–908

    Article  CAS  Google Scholar 

  103. Munteanu G, Segal E (2010) Sestak–Berggren function in temperature—programmed reduction. J Therm Anal Calorim 101:89–95

    Google Scholar 

  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 413:53–58

    Article  CAS  Google Scholar 

  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 273–282

    Google Scholar 

  106. Atkinson HV (1988) Theories of normal grain growth in pure single phase systems. Acta Metall 36:469–491

    Article  CAS  Google Scholar 

  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 63/65:254–259

    Google Scholar 

  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 355:239–253

    Google Scholar 

  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 110:12456–12462

    Article  CAS  Google Scholar 

  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 1986

    Google Scholar 

  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 355:155–163

    Article  CAS  Google Scholar 

  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 520:1–19

    Article  CAS  Google Scholar 

  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 590:1–23

    Article  CAS  Google Scholar 

  114. Vyazovkin S (2015) Isoconversional kinetics of thermally stimulated processes. Springer, Berlin, Heidelberg. ISBN 10: 3319141740

    Google Scholar 

  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 40:486–449

    Google Scholar 

  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. 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 

Download references

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.

Author information

Authors and Affiliations

  1. New Technologies Research Centre (NTC-ZČU), University of West Bohemia, Universitní 8, 30114, Pilsen, Czech Republic

    Jaroslav Šesták

  2. Institute of Physical Chemistry, Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria

    Isak Avramov

Authors
  1. Jaroslav Šesták
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Isak Avramov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jaroslav Šesták .

Editor information

Editors and Affiliations

  1. New Technologies (NTC-ZČU) Research Centre of the Westbohemian Region, University of West Bohemia, Plzeň, Czech Republic

    Jaroslav Šesták

  2. Division of Solid-State Physics, Czech Academy of Sciences, Institute of Physics, Praha , Czech Republic

    Pavel Hubík

  3. Division of Solid-State Physics, Czech Academy of Sciences, Institute of Physics, Praha, Czech Republic

    Jiří J. Mareš

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Šesták, J., Avramov, I. (2017). Rationale and Myth of Thermoanalytical Kinetic Patterns: How to Model Reaction Mechanisms by the Euclidean and Fractal Geometry and by Logistic Approach. In: Šesták, J., Hubík, P., Mareš, J. (eds) Thermal Physics and Thermal Analysis. Hot Topics in Thermal Analysis and Calorimetry, vol 11. Springer, Cham. https://doi.org/10.1007/978-3-319-45899-1_14

Download citation

Publish with us

Policies and ethics

Search

Navigation