Journal of Thermal Analysis and Calorimetry

, Volume 127, Issue 1, pp 1131–1133 | Cite as

On the eliminating attempts toward Šesták–Berggren equation

  • Jiří Militký
  • Jaroslav Šesták


Some recent commentaries doubt the originality of Šesták–Berggren equation even though it received until today almost eight hundred citation responses. The worth of SB equation is examined in terms of general logistic equation showing its divergent philosophical strategy from dissimilar orthodox geometrical modeling in kinetics. The use of appended terms ‘truncated’ and ‘extended’ is questioned.


Šesták–Berggren equation Logistics Kinetics Truncated Extended 



The results were developed within the CENTEM project, reg. no. CZ.1.05/2.1.00/03.0088, that is co-funded by the ERDF as 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) by financial aid of above MEYS under the “National Sustainability Program I.”


  1. 1.
    Verhulst PF. Recherches mathématiques sur la loi d’accroisement de la population. Mem. Acad. R. Bruxelles. 1844;18:1–10.Google Scholar
  2. 2.
    Peleg M, Corradini MG, Normand MD. The logistic Verhulst model for sigmoidal microbial growth curves revisited. Food Res. Int. 2007;40:808–18.CrossRefGoogle Scholar
  3. 3.
    Avramov I. Kinetics of distribution of infections in network. Phys. A. 2007;379:615.CrossRefGoogle Scholar
  4. 4.
    Avramov I, Šesták J. Generalized kinetics of overall phase transition explicit to crystallization. J. Therm. Anal. Calorim. 2014;118:1715–20.CrossRefGoogle Scholar
  5. 5.
    Militký J, Šesták J. Evaluation and interpretation of nonisothermal kinetic models. Thermochim. Acta. 1992;203:31–7.CrossRefGoogle Scholar
  6. 6.
    J. Šesták, Modeling of Reaction Mechanism: Use of Euclidian and Fractal Geometry, Chapter 10 in His Book: Science of Heat and Thermophysical Studies: a Generalized Approach to Thermal Analysis (Elsevier, Amsterdam 2005), pp. 276–314Google Scholar
  7. 7.
    M. Meloun, J. Militký, Nonlinear Regression Models, Chapter 8 in their book: Statistical Data Analysis: a practical guide (Woodhead, Cambridge, 2011), pp. 667–768Google Scholar
  8. 8.
    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
  9. 9.
    Šesták J. Šesták–Berggren equation: now questioned but formerly celebrated—what is right. J. Therm. Anal. Calorim. 2016. doi: 10.1007/s10973-015-4998-x.Google Scholar
  10. 10.
    Burnham AK. Response to statements by Professor Šesták concerning logistic equations in kinetics. J. Thermal. Anal. Calorim. 2016. doi: 10.1007/s10973-015-5216-6.
  11. 11.
    Vyazovkin S. The truncated Šesták–Berggren equation is still the Šesták–Berggren equation, just truncated. J. Thermal. Anal. Calorim. 2016. doi: 10.1007/s10973-015-5215-7.
  12. 12.
    Xu Q, Zhang H, Li H, Zhao S, Wan L, Yan Y. Pyrolysis kinetics mechanism analysis of sawdust by Šesták–Berggren function. Energy Sour. Part A. 2013;35:936–44.CrossRefGoogle Scholar
  13. 13.
    Munteanu G, Segal E. Šesták–Berggren function in temperature –programmed reduction. J. Therm. Anal. Calorim. 2010;101:89–95.CrossRefGoogle Scholar
  14. 14.
    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
  15. 15.
    Šimon P. Forty years of the Šesták–Berggren equation. Thermochim. Acta. 2011;520:156–7.CrossRefGoogle Scholar
  16. 16.
    N.G. Heal, An explanation of the Šesták–Berggren equation. Submitted to Thernochim. Acta (2000) but rejected for publicationGoogle Scholar
  17. 17.
    Akulov NS. Basics of Chemical Dynamics. Moscow: Moscow State University; 1940. p. 56 (in Russian).Google Scholar
  18. 18.
    Prodan AE. Heterogeneous Chemical Reactions. (Minsk, Nauka i Technika 1965), p. 22 (in Russian)Google Scholar
  19. 19.
    Akulov NS. On the genesis of chemical reactions. Comp. Rend. Acad. Sci. URSS. 1940;28:135–8 (in Russian).Google Scholar
  20. 20.
    Kolmogorov A. Statistical theory for the recrystallization of metals. Akad. Nauk SSSR. Izv. Ser. Matem. 1937;1:355 (in Russian).Google Scholar
  21. 21.
    Gorbachev VM. Aspects of Šesták’s generalized equation applied to thermal analysis kinetic. Zh. Fiz. Khim. USSR. 1977;51:1100 (in Russian).Google Scholar
  22. 22.
    Gavrichev KS, Holba P. International conference on thermal analysis and calorimetry in Russia 2013 and hot topic discussion. J. Therm. Anal. Calorim. 2015;119:1453–8.CrossRefGoogle Scholar
  23. 23.
    Arshad MA, Maaroufi A. Relationship between Johnson–Mehl–Avrami and Šesták–Berggren models in the kinetics of crystallization in amorphous materials. J. Non Cryst. Solids. 2015;413:53–8.CrossRefGoogle Scholar
  24. 24.
    Šesták J, Fiala J, Gavrichev SK. Evaluation of the professional worth of scientific papers, their citation responding and the publication authority of Journal of Thermal Analysis and Calorimetry (presented at RCTAC, St Petersburg, September 2016). J. Therm. Anal. Calorim (submitted).Google Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2016

Authors and Affiliations

  1. 1.Technical University in LiberecLiberecCzech Republic
  2. 2.University of West BohemiaPlzeňCzech Republic

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