Kinetic Analysis Using Multivariate Non-linear Regression. I. Basic concepts

  • J. Opfermann


In principle, the kinetic analysis of thermal effects has limitations when based on a single measurement. Using a simulated example and the dehydration of Ca(OH)2 , it will be shown that, through the simultaneous application of non-linear regression to several measurements run at different heating rates (multivariate non-linear regression), the difficult problem of determining the probable reaction type can be reliably solved.

Ca(OH)2 multiple-step kinetics multivariate non-linear regression 


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  1. 1.
    H. Mauser, Formale Kinetik, Bertelsmann Universitätsverlag.Google Scholar
  2. 2.
    H. J. Flammersheim, N. Eckardt and J. Opfermann, Thermochim. Acta, 229 (1993) 281.CrossRefGoogle Scholar
  3. 3.
    J. Málek, J. Šesták, F. Rouquerol, J. Rouquerol, J. Criado and A. Ortega, J. Thermal Anal., 38 (1992) 71.CrossRefGoogle Scholar
  4. 4.
    M. Maciejewski, J. Thermal Anal., 38 (1992) 51.CrossRefGoogle Scholar
  5. 5.
    J. Opfermann, G. Wilke, W. Ludwig, S. Hagen, M. Gebhardt and E. Kaisersberger in Thermische Analyseverfahren in Industrie und Forschung, VI. Herbstschule, Meisdorf 14.18. Nov. 1988, Friedrich-Schiller-Universität 1991, ISBN 3-86007-018-5.Google Scholar
  6. 6.
    M. E. Brown, Introduction to Thermal Analysis, Techniques and Applications, Chapman and Hall, London, New York 1989.Google Scholar
  7. 7.
    M. E. Brown, D. Dollimore and A. K. Galwey in Comprehensive Chemical Kinetics, Vol. 22, Reactions in Solid State, ed. C. H. Bamford and C. F. Tipper, Amsterdam 1980, p. 57.Google Scholar
  8. 8.
    A. I. Lesnikovich and S. V. Levchik, J. Thermal Anal., 27 (1983) 85.CrossRefGoogle Scholar
  9. 9.
    A. I. Lesnikovich, S. V. Levchik and V. S. Guslev, Thermochim. Acta, 77 (1984) 357.CrossRefGoogle Scholar
  10. 10.
    S. Bourbigot, R. Delobel, M. Le Bras and D. Normand, J. Chim. Phys., 90 (1993) 1909.Google Scholar
  11. 11.
    E. Kaisersberger and J. Opfermann, Thermochim. Acta, 187 (1991) 151.CrossRefGoogle Scholar
  12. 12.
    E. Kaisersberger and J. Opfermann, Laborpraxis, 4 (1992) 360.Google Scholar
  13. 13.
    J. Opfermann, Proceedings of ESTAC 6, Grado / Italy, p. 219.Google Scholar
  14. 14.
    J. Opfermann, F. Giblin, J. Mayer and E. Kaisersberger: American Laboratory, Febr. 1995, 34.Google Scholar
  15. 15.
    G. Pokol, S. Gál and E. Pungor, Anal. Chim. Acta, 175 (1985) 289.CrossRefGoogle Scholar
  16. 16.
    J. P. Elder, Thermochim. Acta, 95 (1985) 41.CrossRefGoogle Scholar
  17. 17.
    J. M. Criado and A. Ortega, J. Thermal Anal., 29 (1984) 1075.CrossRefGoogle Scholar
  18. 18.
    M. E. Brown, J. Thermal Anal., 49 (1997) 17.CrossRefGoogle Scholar
  19. 19.
    J. M. Criado, A. Ortega and F. Gotor, Thermochim. Acta, 157 (1990) 171.CrossRefGoogle Scholar
  20. 20.
    J. Madarász, G. Pokol and S. Gál, Proceedings of ESTAC 6, Grado / Italy, p. 180.Google Scholar
  21. 21.
    T. Ozawa, Bull. Chem. Soc. Japan, 38 (1965) 1881.CrossRefGoogle Scholar
  22. 22.
    J. Flynn and L. A. Wall, Polym. Lett., 4 (1966) 232.CrossRefGoogle Scholar
  23. 23.
    J. Opfermann and E. Kaisersberger, Thermochim. Acta, 11 (1992) 167.CrossRefGoogle Scholar
  24. 24.
    J. Šesták, Thermophysical Properties of Solids, Academia, Prag 1984.Google Scholar
  25. 25.
    S. D. Christian and E. R. Tucker, Internat. Laboratory, March 1984, p. 10.Google Scholar
  26. 26.
    H. J. Flammersheim, private communication.Google Scholar
  27. 27.
    G. Engeln-Müllges and F. Reuter, Formelsammlung zur Numerischen Mathematik, Bibliographisches Institut & F. A. Brockhaus AG, Mannheim 1991, ISBN 3-411-15003-3.Google Scholar
  28. 28.
    J. Opfermann, Rechentechnik/Datenverarbeitung 22.3 (1985) 26.Google Scholar
  29. 29.
    J. Opfermann, Manual of the Program NETZSCH Thermokinetics, Version 1998.Google Scholar
  30. 30.
    D. Rasch, G. Herrendörfer, J. Bock and K. Busch, Verfahrensbibliothek — Versuchsplanung und Auswertung, VEB Deutscher Verlag Landwirtschaftsverlag Berlin, Berlin 1981, p. 1105.Google Scholar
  31. 31.
    H.-W. Jank and A. Meister, Kulturpflanze, 30 (1982) 30.CrossRefGoogle Scholar
  32. 32.
    J. Opfermann, J. Therm. Anal. Cal., in preparation.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • J. Opfermann
    • 1
  1. 1.NETZSCH-Gerätebau GmbHSelb

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