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On the method of solving the inverse problem of solid-phase reaction kinetics

II. Methods based on generalized descriptions

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Abstract

The second part of this review deals with the methods of inverse kinetic problem (IKP) solving based on generalized descriptions of the process. The application of these methods is considered an alternative (for discrimination) approach to IKP solving. It is shown that the base of this approach is the methodology of complementarity. Different types of generalized descriptions, their merits and their shortcomings are discussed.

Zusammenfassung

Der zweite Teil dieses Rückblickes beschäftigt sich mit Lösungsverfahren für das inverse kinetische Problem (IKP) basierend auf verallgemeinerten Beschreibungen der Prozesse. Eine Anwendung dieser Verfahren wird als alternative Näherung der Lösung des IKP betrachtet. Es wird gezeigt, dass die Grundlage dieser Näherung in der Methodologie der Komplementärität besteht. Verschiedene Arten von verallgemeinerten Beschreibungen, ihre Vorzüge und Mängel werden besprochen.

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References

  1. V. V. Nalimov, T. I. Golikova, Logical Bases of Experimental Design, Metallurgis, Moskva, 1981 (in Russian).

    Google Scholar 

  2. V. V. Nalimov, Yavod. Lab., 44 (1978) 325.

    Google Scholar 

  3. V. V. Nalimov, Zhurn. Vses. Khim. O-va 25 (1980) 3.

    Google Scholar 

  4. V. I. Dimitrov, Simple Kinetics, Nauka, Novosybirsk, 1982 (in Russian)

    Google Scholar 

  5. S. V. Vyazovkin and A. I. Lesnikovich, J. Thermal Anal., 32 (1987) 901.

    Google Scholar 

  6. S. V. Vyazovkin and A. I. Lesnikovich, J. Thermal Anal., 32 (1987) 1145.

    Google Scholar 

  7. Y. Bard, Nonlinear Parameter Estimation, Academic Press, N. Y., e. a., 1974.

    Google Scholar 

  8. J. Šestak and G. Berggren, Thermochim. Acta 3 (1971) 1.

    Google Scholar 

  9. J. Šestak, Themophysical Properties of Solids, Academia Prague, Prague, 1984.

    Google Scholar 

  10. M. E. Brown, D. Dollimore and A. K. Galwey, Reactions in the Solid State, Elsevier, Amsterdam, e. a., 1980.

    Google Scholar 

  11. G. O. Piloyan, I. D. Ryabchikov and O. S. Novikova, Nature 212 (1966) 1229.

    Google Scholar 

  12. J. H. Flynn, J. Thermal Anal., 27 (1983) 95.

    Google Scholar 

  13. K. Heide, Dynamische Termische Analysenmethoden, VEB, Leipzig, 1979.

    Google Scholar 

  14. V. M. Gorbachev, J. Thermal Anal., 18 (1980) 193.

    Google Scholar 

  15. P. S. Nolan and H. E. Lemay, Thermochim. Acta, 6 (1973) 179.

    Google Scholar 

  16. D. T. Y. Chen and K-W. Lai, J. Thermal Anal., 20 (1981) 233.

    Google Scholar 

  17. V. Swaminathan, N. S. Madhavan and D. Radhamony, Thermochim. Acta, 43 (1981) 371.

    Google Scholar 

  18. J. Leyko, M. Maciejewski and R. Szunewich, J. Thermal Anal., 17 (1979) 263.

    Google Scholar 

  19. H. C. Anderson, J. Polym. Sci., Part C 6 (1963) 175.

    Google Scholar 

  20. H. E. Kissinger, J. Res. Nat. Bur. Stand., 57 (1956) 217.

    Google Scholar 

  21. J. Kwarciak, J. Thermal Anal., 30 (1985) 177.

    Google Scholar 

  22. G. Baldassare and V. Amicarelli, J. Thermal Anal., 30 (1985) 339.

    Google Scholar 

  23. S. V. Vyazovkin and A. I. Lesnikovich, J. Thermal Anal., 32 (1987) 249.

    Google Scholar 

  24. J. M. Criado and A. Ortega, J. Thermal Anal., 29 (1984) 1225.

    Google Scholar 

  25. S. V. Vyazovkin and A. I. Lesnikovich, Thermochim. Acta, 122 (1987) 413.

    Google Scholar 

  26. A. I. Lesnikovich, S. V. Vyazovkin and I. S. Romanovsky, J. Thermal Anal., 34 (1988) 85

    Google Scholar 

  27. S. V. Vyazovkin, I. S. Romanovsky and A. I. Lesnikovich, J. Thermal Anal., 34 (1988) 239.

    Google Scholar 

  28. V. Jesenak, 8-th ICTA'85, Bratislava Rmochim. Acta 92 (1985) 39.

    Google Scholar 

  29. S. V. Vyazovkin and A. I. Lesnikovich, Thermochim. Acta 128 (1988) 69.

    Google Scholar 

  30. R. Bar-Gadda, Thermochim. Acta 34 (1979) 161

    Google Scholar 

  31. A. A. Fotiev and V. V. Mochalov, Zh. Neorgan. Khim., 13 (1968) 3147.

    Google Scholar 

  32. L. K. Avramov, Thermochim. Acta., 54 (1982) 337.

    Google Scholar 

  33. M. Lasocka, J. Thermal Anal., 16 (1979) 197.

    Google Scholar 

  34. S. Zeman and E. Zemanova, J. Thermal Anal., 20 (1981) 331.

    Google Scholar 

  35. J. Colmenero, J. M. Barandiaran and J. M. Criado, Thermochim. Acta, 35 (1982) 367.

    Google Scholar 

  36. A. Marotta and A. Buri, J. Thermal Anal., 16 (1979) 449.

    Google Scholar 

  37. A. Marotta, A. Buri and S. Saiello, J. Thermal Anal., 23 (1982) 239.

    Google Scholar 

  38. J. M. Criado, J. Thermal Anal., 19 (1981) 221.

    Google Scholar 

  39. J. M. Criado and A. Ortega, J. Thermal Anal., 29 (1984) 1075.

    Google Scholar 

  40. J. Morales, L. Hernan, L. V. Flores and A. Ortega, J. Thermal Anal., 24 (1982) 23.

    Google Scholar 

  41. M. Lalia-Kantouri, G. A. Katsoulos and F. D. Vakoulis, J. Thermal Anal., 31 (1986) 447.

    Google Scholar 

  42. H. L. Friedman, J. Polym. Aci., Part C, 6 (1963) 183.

    Google Scholar 

  43. T. Ozawa, Bull. Chem. Soc. Japan, 38 (1965) 1881.

    Google Scholar 

  44. J. H. Flynn and L. A. Wall, Polym. Lett., 4 (1966) 323.

    Google Scholar 

  45. T. B. Tang and M. M. Chaudhri, J. Thermal Anal., 18 (1980) 247.

    Google Scholar 

  46. C. Popescu and E. Segal, Thermochim. Acta, 63 (1983) 381.

    Google Scholar 

  47. J. C. M. Torfs, L. Deij, A. J. Dorrepaal and J. C. Heijens, Anal. Chem., 56 (1984) 2863.

    Google Scholar 

  48. A. Irabien, C. Santiago and A. Araiz, J. Thermal Anal., 29 (1984) 1131.

    Google Scholar 

  49. J. A. Augis and J. E. Bennet, J. Thermal Anal., 13 (1978) 283.

    Google Scholar 

  50. G. Blumental, Z. Chem., 22 (1982) 49.

    Google Scholar 

  51. J. P. Elder and V. B. Reddy, J. Thermal Anal., 31 (1986) 395.

    Google Scholar 

  52. G. M. Reddy, V. K. Mohan, B. K. M. Murali and A. K. Chatterjee, Thermochim. Acta, 43 (1981) 61

    Google Scholar 

  53. P. K. Gallagher and M. E. Gross, J. Thermal Anal., 31 (1986) 1231.

    Google Scholar 

  54. A. A. Van Dooren and B. M. Muller, Thermochim. Acta, 65 (1983) 257.

    Google Scholar 

  55. E. Louis and G. Garcia-Cordovilla, J. Thermal Anal., 29 (1984) 1139.

    Google Scholar 

  56. N. P. Bansal, R. H. Doremus, A. J. Bruce and C. T. Moynihan. J. Amer. Ceram. Soc., 66 (1983) 233.

    Google Scholar 

  57. C. Bouster, C. Comel, P. Vermande and J. Veron, J. Thermal Anal., 20 (1981) 115.

    Google Scholar 

  58. Y. P. Khanna and E. M. Pearce, J. Thermal Anal., 26 (1983) 107.

    Google Scholar 

  59. W. W. Wendlandt, Thermal Methods of Analysis, Wiley, N. Y., 1974.

    Google Scholar 

  60. V. A. Logvinenko, Thermal Analysis of Coordination Compounds and Clatrates, Nauka, Novosybirsk, 1982 (in Russian).

    Google Scholar 

  61. N. J. Carr and A. K. Galwey, Thermochim. Acta, 79 (1984) 323.

    Google Scholar 

  62. J. D. Cooney, M. Day and D. M. Wiles, J. Appl. Polym. Sci., 26 (1983) 2887.

    Google Scholar 

  63. A. Ballisteri, G. Montando and C. Puglisi, J. Thermal Anal., 29 (1984) 237.

    Google Scholar 

  64. N. Fatemi, R. Whitehead, D. Pirce and D. Dollimore, Thermochim. Acta, 104 (1986) 93.

    Google Scholar 

  65. A. Marotta, A. Buri and F. Branda, J. Thermal Anal., 21 (1981) 227.

    Google Scholar 

  66. N. D. Topor, L. I. Tolokonnikova and B. M. Kadenatsi, J. Thermal Anal., 22 (1981) 221.

    Google Scholar 

  67. T. Kemény and J. Šestak, Közp. Fiz. Kut Intéz. Prepr., 1985, N115, 26pp.

  68. M. Reading, F. Dollimore, J. Rouquerol and F. Rouquerol, J. Thermal Anal., 29 (1984) 775.

    Google Scholar 

  69. S. Basan and D. Guven, Thermochim. Acta, 106 (1986) 169.

    Google Scholar 

  70. J. D. Cooney, M. Day and D. M. Wiles, J. Appl. Polym. Sci., 29 (1984) 911.

    Google Scholar 

  71. A. I. Lesnikovich and S. V. Levchik, J. Thermal Anal., 30 (1985) 677.

    Google Scholar 

  72. J. Pysiak and B. Sabalski, J. Thermal Anal., 17 (1979) 287.

    Google Scholar 

  73. S. V. Vyazovkin and A. I. Lesnikovich, Thermochim. Acta, 128 (1988) 297.

    Google Scholar 

  74. L. Hernan, J. Morales, A. Ortega and J. L. Tirado, J. Thermal Anal., 29 (1984) 491.

    Google Scholar 

  75. J. P. Elder, J. Thermal Anal., 29 (1984) 1327.

    Google Scholar 

  76. H. S. O. Chan and J. R. Lusty, J. Thermal Anal., 30 (1985) 25.

    Google Scholar 

  77. J. P. Elder, Thermochim. Acta, 95 (1985) 41.

    Google Scholar 

  78. P. K. Gallagher, J. Thermal Anal., 25 (1982) 7.

    Google Scholar 

  79. T. Ozawa, J. Thermal Anal., 7 (1975) 601.

    Google Scholar 

  80. A. G. Merzhanov, V. V. Barzykin, A. S. Shteinberg and V. T. Gontkovskaya, Thermochim. Acta, 21 (1977) 301.

    Google Scholar 

  81. A. G. Merzhanov, V. G. Abramov and L. T. Abramova, Zh. Fiz. Khim., 41 (1967) 179.

    Google Scholar 

  82. J. Meindl, I. V. Arkhangelskii and N. A. Chernova, J. Thermal Anal., 20 (1981) 39.

    Google Scholar 

  83. V. A. Bir, Kinetika i kataliz, 28 (1987) 550.

    Google Scholar 

  84. E. Urbanovici and E. Segal, Thermochim. Acta, 94 (1985) 399.

    Google Scholar 

  85. E. Urbanovici and E. Segal, Thermochim. Acta, 98 (1986) 385.

    Google Scholar 

  86. D. R. Dowdy, J. Thermal Anal., 32 (1987) 137.

    Google Scholar 

  87. Y. Masuda, Y. Ito, R. Ito and K. Iwata, Thermochim. Acta, 99 (1986) 205.

    Google Scholar 

  88. A. Romero and E. Garcia, Thermochim. Acta, 104 (1986) 71.

    Google Scholar 

  89. N. I. Vaganova, V. I. Rozenband and V. V. Barzykin in: Mater.8 Vses. Simp. po Goreniyu i Vzryvu, Tashkent, 1986. Chernogolovka, 1986, P. 108.

    Google Scholar 

  90. M. R. Kenan, Thermochim. Acta, 98 (1986) 263.

    Google Scholar 

  91. C. D. Doyle, Nature, 207 (1965) 290.

    Google Scholar 

  92. L. Reich and S. S. Stivala, Thermochim. Acta, 61 (1983) 361.

    Google Scholar 

  93. D. Fatu and E. Segal, Thermochim. Acta, 61 (1983) 215.

    Google Scholar 

  94. T. Ozawa, J. Thermal Anal., 9 (1976) 369.

    Google Scholar 

  95. T. Ozawa, Thermochim. Acta, 100 (1986) 109.

    Google Scholar 

  96. T. Ozawa, J. Thermal Anal., 31 (1986) 547.

    Google Scholar 

  97. A. I. Lesnikovich and S. V. Levchik, J. Thermal Anal., 27 (1983) 89.

    Google Scholar 

  98. A. I. Lesnikovich, S. V. Levchik and G. F. Levchik, J. Appl. Polym. Sci., 31 (1986) 1943.

    Google Scholar 

  99. M. Iwao, S. Yasuko and M. Mikiko, Gakugaku Zasshi (J. Pharm. Soc. Jap.), 104 (1984) 280.

    Google Scholar 

  100. S. V. Vyazovkin, A. I. Lesnikovich and I. S. Romanovsky, J. Thermal Anal., 34 (1988) 609.

    Google Scholar 

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Vyazovkin, S.V., Lesnikovich, A.I. On the method of solving the inverse problem of solid-phase reaction kinetics. Journal of Thermal Analysis 36, 599–615 (1990). https://doi.org/10.1007/BF01914513

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