Journal of thermal analysis

, Volume 35, Issue 7, pp 2169–2188 | Cite as

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

I. Methods based on discrimination
  • S. V. Vyazovkin
  • A. I. Lesnikovich
Article

Abstract

This review deals with the choice of a method of solving the inverse kinetic problem (IKP) which would provide the most definite description of the process under conditions of ambiguity. Two fundamentally different methodologies are possible for the IKP solution: one is based on the principle of unambiguous description (discrimination), while the other relies upon the complementarity principle (generalized descriptions). Specific IKP solution methods have been classified, the methodological differences being taken into account. In the first part of this review, general and special limitations in discrimination of formal models have been analysed.

Keywords

Polymer Physical Chemistry Inorganic Chemistry Inverse Problem Formal Model 

Zusammenfassung

Diese Übersicht handelt von der Auswahl einer Methode zur Lösung des inversen kinetischen Problémes (IKP), welches die präziseste Beschreibung des Vorganges auch unter nichteindeutigen Bedingungen liefern kann. Zur Lösung des IKP Problemes sind zwei grundlegend verschiedene Methoden möglich: die erste beruht auf dem Prinzip der eindeutigen Beschreibung (Unterscheidbarkeit), während die zweite auf dem Komplementärprinzip (generalisierte Beschreibung) aufbaut. Die konkreten IKP Lösungsverfahren wurden auf der Grundlage ihrer methodischen Unterschiede klassifiziert. Im ersten Teil dieses Überblicks wurden allgemeine und spezielle Beschränkungen bei der Unterscheidung formaler Modelle untersucht.

Резюме

Обзор посвящен пробл еме выбора метода реш ения обратной кинетическ ой задачи, позволяющего в услов иях неоднозначности получить наиболее определенн ые описания процесса. Отмечается, что возмо жны две принципиальн о различные методологии решения обратной задачи: методология, о снованная на принцип е однозначного описан ия (дискриминация), и методология, основан ная на принципе допол нительности (обобщенные описания). С учетом различия методологи ческих принципов про ведена классификация конкр етных методов решени я обратной кинетическ ой задачи. В первой час ти обзора проанализированы об щие и специфические ограничения метода д искриминации.

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References

  1. 1.
    P. Eykhoff, System Identification Parameter and State Estimation, Wiley, N.Y. e.a., 1974.Google Scholar
  2. 2.
    A. N. Tikhonov and V. Ya. Arsenin, The Methods of Solving of Uncorrect Problems, Nauka, Moskva, 1984 (in Russian).Google Scholar
  3. 3.
    V. G. Gorsky, Kinetic Experiments Design, Nauka, Noskva, 1984 (in Russian).Google Scholar
  4. 4.
    S. I. Spivak and V. G. Gorsky, Dokl. AN SSSR, 257 (1981) 412.Google Scholar
  5. 5.
    S. I. Spivak and V. G. Gorsky, Khim. Fizika, 1 (1982) 237.Google Scholar
  6. 6.
    M. V. Klibanov, S. I. Spivak, V. I. Timoshenko and M. G. Slinko, Dokl. AN SSSR, 208 (1973) 1387.Google Scholar
  7. 7.
    S. V. Vyazovkin and A. I. Lesnikovich, Thermochim. Acta, 122 (1987) 413.CrossRefGoogle Scholar
  8. 8.
    S. V. Vyazovkin and A. I. Lesnikovich, J. Thermal Anal., 32 (1987) 901.Google Scholar
  9. 9.
    H. J. Borchart and F. Daniels, J. Am. Chem. Soc., 79 (1957) 41.CrossRefGoogle Scholar
  10. 10.
    J. Šesták and G. Berggren, Thermochim. Acta, 3 (1971) 1.CrossRefGoogle Scholar
  11. 11.
    V. A. Logvinenko, Thermal Analysis of Coordination Compounds and Clatrates, Nauka, Novosybirsk, 1982 (in Russian).Google Scholar
  12. 12.
    W. W. Wendlandt, Thermal Methods of Analysis, Wiley, N.Y., 1974.Google Scholar
  13. 13.
    J. Šesták, Thermophysical Properties of Solids, Academia Prague, Prague, 1984.Google Scholar
  14. 14.
    M. E. Brown, D. Dollimore and A. K. Galwey, Reactions in the Solid State, Elsevier, Amsterdam e.a., 1980.Google Scholar
  15. 15.
    K. Heide, Dynamische Termische Analysenmethoden, VEB, Leipzig, 1979.Google Scholar
  16. 16.
    J. H. Flynn, J. Thermal Anal., 27 (1983) 95.Google Scholar
  17. 17.
    N. L. Johnson and F. C. Leone, Statistics and Experimental Design in Engineering and the Physical Sciences, Vol. 1, Wiley, N.Y. e.a., 1977.Google Scholar
  18. 18.
    E. F. Brin, O. N. Karpukhin and V. M. Goldenberg, Khim. Fizika, 5 (1986) 938.Google Scholar
  19. 19.
    L. Hernan, J. Morales, A. Ortega and J. L. Tirado, J. Thermal Anal., 29 (1984) 479.Google Scholar
  20. 20.
    S. V. Vyazovkin and A. I. Lesnikovich, J. Thermal Anal., 30 (1985) 831.Google Scholar
  21. 21.
    N. A. Chernova, I. V. Arkhangelskii and L. N. Komissarova, J. Thermal Anal., 13 (1978) 315.Google Scholar
  22. 22.
    N. J. Carr and A. K. Galwey, Thermochim. Acta, 79 (1984) 323.CrossRefGoogle Scholar
  23. 23.
    J. Zsakó, J. Phys. Chem., 72 (1968) 2406.CrossRefGoogle Scholar
  24. 24.
    T. P. Prasad, Thermochim. Acta, 65 (1983) 147.CrossRefGoogle Scholar
  25. 25.
    S. Vatsala and O. Parameswaran, J. Thermal Anal., 31 (1986) 883.Google Scholar
  26. 26.
    L. Reich and S. S. Stivala, Thermochim. Acta, 73 (1984) 165.CrossRefGoogle Scholar
  27. 27.
    C. Santiago, A. R. Araiz, L. Lorente, J. M. Arrieta and M. A. Martinez, J. Thermal Anal., 31 (1986) 343.Google Scholar
  28. 28.
    M. M. Barbooti and D. A. Al-Sammerrai, Thermochim. Acta, 98 (1986) 119.CrossRefGoogle Scholar
  29. 29.
    L. Reich and S. S. Stivala, Thermochim. Acta, 62 (1983) 129.CrossRefGoogle Scholar
  30. 30.
    J. G. Carrera and M. Eddleston, Thermochim. Acta, 70 (1983) 237.CrossRefGoogle Scholar
  31. 31.
    L. Hernan, J. Morales, A. Ortega and J. L. Tirado, J. Thermal Anal., 29 (1984) 491.Google Scholar
  32. 32.
    C. Barriga, J. Morales and J. L. Tirado, J. Mater. Sci., 21 (1986) 947.CrossRefGoogle Scholar
  33. 33.
    V. Šatava, Thermochim. Acta, 2 (1971) 423.CrossRefGoogle Scholar
  34. 34.
    S. Boy and K. Bohme, Thermochim. Acta, 20 (1977) 195.CrossRefGoogle Scholar
  35. 35.
    A. W. Coats and J. P. Redfern, Nature, 201 (1964) 68.Google Scholar
  36. 36.
    R. M. Rojas, M. L. de Paz and E. Vila, J. Thermal Anal., 30 (1985) 83.Google Scholar
  37. 37.
    J. Maslowska, J. Thermal Anal., 29 (1984) 895.Google Scholar
  38. 38.
    K. S. Kunihisa and H. Ogawa, J. Thermal Anal., 30 (1985) 49.Google Scholar
  39. 39.
    “Mettler TA 3000”, Operating Instruction, p. 320.Google Scholar
  40. 40.
    R. Dallenbach and P. Tissot, J. Thermal Anal., 20 (1981) 409.Google Scholar
  41. 41.
    D. Munteanu and S. Turcu, J. Thermal Anal., 20 (1981) 281.Google Scholar
  42. 42.
    A. Cronowski and Z. Wojtczak, J. Thermal Anal., 26 (1983) 233.Google Scholar
  43. 43.
    M. I. O. Urbie, A. R. Salvador and A. I. Gulias, Thermochim. Acta, 94 (1985) 323.CrossRefGoogle Scholar
  44. 44.
    E. Eugenia and E. Segal, Thermochim. Acta, 105 (1986) 247.CrossRefGoogle Scholar
  45. 45.
    H. Tanaka and H. Fujimaru, J. Thermal Anal., 24 (1982) 207.Google Scholar
  46. 46.
    H. Tanaka and M. Tokumitsu, J. Thermal Anal., 29 (1984) 87.Google Scholar
  47. 47.
    H. Tanaka, Thermochim. Acta, 52 (1982) 1.CrossRefGoogle Scholar
  48. 48.
    J. M. Criado, M. Gonzales, A. Ortega and C. Real, J. Thermal Anal., 29 (1984) 243.Google Scholar
  49. 49.
    J. Šesták, J. Thermal Anal., 30 (1985) 1223.Google Scholar
  50. 50.
    A. E. Venger, Yu. E. Fraiman and F. B. Yurevich, J. Thermal Anal., 27 (1983) 325.Google Scholar
  51. 51.
    E. S. Freeman and B. Carroll, J. Phys. Chem., 62 (1958) 394.CrossRefGoogle Scholar
  52. 52.
    J. M. Criado, D. Dollimore and G. R. Heal, Thermochim. Acta, 54 (1982) 159.CrossRefGoogle Scholar
  53. 53.
    Y. P. Khanna and E. M. Pearce, J. Thermal Anal., 26 (1983) 107.Google Scholar
  54. 54.
    A. Jerez, J. Thermal Anal., 26 (1983) 315.Google Scholar
  55. 55.
    D. T. Y. Chen and K.-W. Lai, J. Thermal Anal., 20 (1981) 233.Google Scholar
  56. 56.
    O. F. Shlensky, J. Thermal Anal., 20 (1981) 519.Google Scholar
  57. 57.
    D. Fatu and E. Segal, J. Thermal Anal., 24 (1982) 311.Google Scholar
  58. 58.
    L. Elegant, P. Tomi, G. Augier, J. P. Nicolas and B. Pecqueux, J. Thermal Anal., 31 (1986) 1351.Google Scholar
  59. 59.
    H. E. Kissinger, J. Res. Nat. Bur. Stand., 57 (1956) 217.Google Scholar
  60. 60.
    G. Widmann, J. Thermal Anal., 25 (1982) 45.Google Scholar
  61. 61.
    L. Reich and S. S. Stivala, Thermochim. Acta, 52 (1982) 337.CrossRefGoogle Scholar
  62. 62.
    J. E. House, Jr., Thermochim. Acta, 57 (1982) 47.CrossRefGoogle Scholar
  63. 63.
    L. Reich and S. S. Stivala, Thermochim. Acta, 58 (1982) 383.CrossRefGoogle Scholar
  64. 64.
    L. Reich and S. S. Stivala, Thermochim. Acta, 66 (1983) 383.CrossRefGoogle Scholar
  65. 65.
    L. Reich and S. S. Stivala, Thermochim. Acta, 94 (1985) 413.CrossRefGoogle Scholar
  66. 66.
    G. N. Natu, S. B. Kulkarui and P. S. Dhar, J. Thermal Anal., 23 (1982) 101.Google Scholar
  67. 67.
    K. Boguslawska and A. Cygansky, J. Thermal Anal., 24 (1982) 15.Google Scholar
  68. 68.
    N. Cutillas, J. Galvez, G. Garcia and G. Lopez, J. Thermal Anal., 24 (1982) 67.Google Scholar
  69. 69.
    J. Chako and G. Parameswaran, J. Thermal Anal., 29 (1984) 3.Google Scholar
  70. 70.
    J. E. House, Jr. and G. L. Jeyaraj, J. Thermal Anal., 29 (1984) 41.Google Scholar
  71. 71.
    M. Frenclach in: Combustion Chemistry, Ed. W. Gardiner, Jr. Sprioger-Verlag, N.Y., 1984.Google Scholar
  72. 72.
    D. M. Himmelblau, Process Analysis by Statistical Methods, Wiley, N.Y., 1970.Google Scholar
  73. 73.
    I. V. Arkhangel'skii, L. N. Komissarova and N. A. Chernova, J. Thermal Anal., 18 (1980) 347.Google Scholar
  74. 74.
    E. Z. Demidenko, Linear and Nonlinear Regression, Finansy i Statistika, Moskva, 1981 (in Russian).Google Scholar
  75. 75.
    R. Altofer, Thermochim. Acta, 24 (1978) 17.CrossRefGoogle Scholar
  76. 76.
    R. Rock, Thermochim. Acta, 24 (1978) 182.CrossRefGoogle Scholar
  77. 77.
    Z. Smieszek, Z. S. Kolenda, J. Norwisz and N. Hajduk, J. Thermal Anal., 25 (1982) 377.Google Scholar
  78. 78.
    W. W. Wendlandt, Anal. Chem., 54 (1982) 97.Google Scholar
  79. 79.
    N. Eisenreich and A. Pfeil, Thermochim. Acta, 61 (1983) 13.CrossRefGoogle Scholar
  80. 80.
    R. P. L. Absil, J. B. Butt and J. S. Dranoff, J. Catal., 87 (1984) 530.CrossRefGoogle Scholar
  81. 81.
    C. Rozycki, J. Thermal Anal., 29 (1984) 959.Google Scholar
  82. 82.
    S. V. Vyazovkin and A. I. Lesnikovich, 8th ICTA '85, Bratislava, Thermochim. Acta, 92 (1985) 161.Google Scholar
  83. 83.
    J. Militky, 8th ICTA '85, Bratislava, Thermochim. Acta, 92 (1985) 77.Google Scholar
  84. 84.
    J. Křiž and J. Šesták, Thermochim. Acta, 110 (1987) 87.CrossRefGoogle Scholar
  85. 85.
    S. V. Vyazovkin and A. I. Lesnikovich, J. Thermal Anal., 31 (1986) 319.Google Scholar
  86. 86.
    M. O'Neil, I. G. Sinclar and F. J. Smith, Comput. J., 12 (1969) 52.Google Scholar
  87. 87.
    D. R. Powell and J. R. Macdonald, Comput. J., 15 (1972) 148.Google Scholar
  88. 88.
    J. A. Irvin and T. I. Quickindem, J. Chem. Educ., 60 (1983) 711.Google Scholar
  89. 89.
    Robustness in Statistics. Ed. R. L. Launer, G. N. Wilkinson, Academic Press, N.Y., e.a., 1979.Google Scholar
  90. 90.
    J. W. Tukey, Exploration Data Analysis. Addison-Wesley Publ. Co. Inc., Reading, Massachussets, 1977.Google Scholar
  91. 91.
    R. N. Whitten, W. I. Stuart and J. H. Levy, Thermochim. Acta, 57 (1982) 235.CrossRefGoogle Scholar
  92. 92.
    J. R. Harrison, J. Thermal Anal., 31 (1986) 875.Google Scholar
  93. 93.
    J. Font, J. Muntasell and J. Navarro, Thermochim. Acta, 99 (1986) 11.CrossRefGoogle Scholar
  94. 94.
    M. Arnold, G. E. Veress, J. Paulik and F. Paulik, J. Thermal Anal., 17 (1979) 507.Google Scholar
  95. 95.
    J. Blažejowski, Thermochim. Acta, 76 (1984) 359.CrossRefGoogle Scholar
  96. 96.
    V. I. Dimitrov, Simple Kinetics, Nauka, Novosybirsk, 1982 (in Russian).Google Scholar
  97. 97.
    V. V. Nalimov and T. I. Golikova, Logical Bases of Experimental Design, Metallurgia, Moskva, 1981 (in Russian).Google Scholar
  98. 98.
    N. D. Topor, L. I. Tolokonnikova and B. M. Kadenatsi, J. Thermal Anal., 20 (1981) 169.Google Scholar
  99. 99.
    V. M. Gorbachev, J. Thermal Anal., 23 (1982) 161.Google Scholar
  100. 100.
    B. M. Nirsha, A. A. Fakeev and G. R. Allakhverdov, Zh. Neorg. Khim., 24 (1979) 298.Google Scholar
  101. 101.
    V. M. Gorbachev, E. A. Kolosovskaya and B. S. Chudinov, J. Thermal Anal., 26 (1983) 151.Google Scholar
  102. 102.
    V. Yu. Zakharov and I. A. Shchuchkin, J. Thermal Anal., 31 (1986) 805.Google Scholar
  103. 103.
    T. B. Tang, Thermochim. Acta, 57 (1982) 93.CrossRefGoogle Scholar
  104. 104.
    J. E. House, Jr. and J. D. House, Thermochim. Acta, 61 (1983) 277.CrossRefGoogle Scholar
  105. 105.
    J. E. House, Jr. and D. K. Tcheng, Thermochim. Acta, 64 (1983) 195.CrossRefGoogle Scholar
  106. 106.
    M. Yu. Sinev, B. M. Maevskaya, E. P. Babaeva and Yu. N. Simulin in: “Trudy 8 Vses. konf. po term. anal.”, Kuibyshev, 1982, p. 26.Google Scholar
  107. 107.
    V. M. Gorbachev, V. M. Durasov and E. Ya. Gimelsheyn, J. Thermal Anal., 23 (1982) 167.Google Scholar
  108. 108.
    J. Zsakó, J. Horák and Cs. Várhelyi, J. Thermal Anal., 20 (1981) 435.Google Scholar
  109. 109.
    Yu. H. Shevchenko, V. A. Logvinenko, N. I. Yashchina and E. A. Pisarev, J. Thermal Anal., 30 (1985) 365.Google Scholar
  110. 110.
    T. B. Tang and M. M. Chaudhri, J. Thermal Anal., 18 (1980) 247.Google Scholar
  111. 111.
    D. Blečič, Ž. D. Živkovic and M. Martinovič, Thermochim. Acta, 60 (1983) 61.CrossRefGoogle Scholar
  112. 112.
    J. H. Flynn, Thermochim. Acta, 92 (1985) 153.CrossRefGoogle Scholar
  113. 113.
    D. A. Deshpade, K. R. Ghormare, N. D. Deshpade and A. V. Tankhiwale, Thermochim. Acta, 66 (1983) 255.CrossRefGoogle Scholar
  114. 114.
    A. I. Lesnikovich and S. V. Levchik, J. Thermal Anal., 30 (1985) 677.Google Scholar
  115. 115.
    D. 'Blečič and Ž. D. Živkovic, Thermochim. Acta, 60 (1983) 69.Google Scholar
  116. 116.
    J. Ribas, A. Escuer, M. Serra and R. Vicente, Thermochim. Acta, 102 (1986) 125.CrossRefGoogle Scholar
  117. 117.
    S. V. Levchik, G. F. Levchik and A. I. Lesnikovich, 8th ICTA '85, Bratislava, Thermochim. Acta, 92 (1985) 157.Google Scholar
  118. 118.
    A. I. Lesnikovich and S. V. Levchik, J. Thermal Anal., 27 (1983) 89.Google Scholar
  119. 119.
    J. Calvez, J. Palazon, G. Lopez and G. Garcia, J. Thermal Anal., 29 (1984) 465.Google Scholar
  120. 120.
    M. Lalia-Kantouri and G. E. Manoussakis, J. Thermal Anal., 29 (1984) 1151.Google Scholar
  121. 121.
    J. P. Elder and V. B. Reddy, J. Thermal Anal., 31 (1986) 395.Google Scholar
  122. 122.
    F. Cornea, L. Ivan, I. Pescaru and E. Segal, Thermochim. Acta, 105 (1986) 239.CrossRefGoogle Scholar
  123. 123.
    A. R. Salvador, E. G. Calvo and A. I. Gulias, Thermochim. Acta, 73 (1984) 101.CrossRefGoogle Scholar
  124. 124.
    V. V. Fedorov, Theory of Optimal Experiment, Nauka, Moskva, 1971 (in Russian).Google Scholar
  125. 125.
    M. I. O. Urbie, A. R. Salvador and A. I. Gulias, Thermochim. Acta, 94 (1985) 333.CrossRefGoogle Scholar
  126. 126.
    I. Bozhov and T. Jubrailov, Godishn. Vish. Chim.-Tekhnol. Int, Sofia, 25 (1978–79) 223.Google Scholar
  127. 127.
    V. A. Fedorov, I. D. Isaev, D. M. Gorelik and S. M. Bereshev, Koord. Khim., 8 (1982) 386.Google Scholar
  128. 128.
    V. I. Belevantsev and V. I. Malkova, in: Direct and Inverse Problems of Chemical Thermodynamics, Nauka, Novosybirsk, 1987, p. 13. (in Russian).Google Scholar
  129. 129.
    V. A. Vatutin, T. M. Televinova and V. P. Chistyakov, Probability Methods in Physical Investigations, Nauka, Moskva, 1985 (in Russian).Google Scholar
  130. 130.
    Mathematical Theory of Experimental Design: Ed. S. M. Ermakov, Nauka, Moskva, 1983 (in Russian).Google Scholar
  131. 131.
    A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov and A. G. Yagola, Regularizing Algorithms and Prior Information, Nauka, Moskva, 1983 (in Russian).Google Scholar
  132. 132.
    T. B. Tang, Thermochim. Acta, 58 (1982) 373.CrossRefGoogle Scholar
  133. 133.
    J. M. Criado and A. Ortega, J. Thermal Anal., 29 (1984) 1225.Google Scholar
  134. 134.
    B. Delmon, Introduction à la Cinétique Heterogène, Editions Technip, Paris, 1969.Google Scholar
  135. 135.
    M. E. Brown and G. M. Swallowe, Thermochim. Acta, 49 (1981) 333.CrossRefGoogle Scholar
  136. 136.
    A. Ya. Neiman, A. G. Shapovalov and I. P. Zapasskaya, Zhurn. Fiz. Khim., 60 (1986) 314.Google Scholar
  137. 137.
    H. S. Ray and N. Kundu, Thermochim. Acta, 101 (1986) 107.CrossRefGoogle Scholar
  138. 138.
    M. J. Hernandez, M. A. Ulibari and J. Cornejo, J. Thermal Anal., 31 (1986) 633.Google Scholar
  139. 139.
    T. Gondova, P. Kralik and P. Domansky, J. Thermal Anal., 32 (1987) 237.Google Scholar
  140. 140.
    N. Z. Lyakhov, Izv. SO AN SSSR, Ser. Khim. Nauki, 2 (1985) 3.Google Scholar
  141. 141.
    E. A. Prodan, Inorganic Topochemistry, Nauka i Teknika, Minsk, 1986 (in Russian).Google Scholar
  142. 142.
    J. Pysiak, in: Heterogeneous Chemical Reactions, Nauka i Tekhnika, Minsk, 1970, p. 71 (in Russian).Google Scholar
  143. 143.
    L. Brillouin, Scientific Uncertainty and Information, Academic Press, N.Y. & London, 1964.Google Scholar
  144. 144.
    V. V. Nalimov, Theory of Experiment, Nauka, Moskva, 1971 (in Russian).Google Scholar
  145. 145.
    N. Bohr, Erkenntnis, 6 (1937) 293.Google Scholar

Copyright information

© Wiley Heyden Ltd, Chichester and Akadémiai Kiadó, Budapest 1989

Authors and Affiliations

  • S. V. Vyazovkin
    • 1
  • A. I. Lesnikovich
    • 1
  1. 1.Institute of Physico-Chemical ProblemsByelorussian State UniversityMinskU.S.S.R.

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