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Kinetics of reversible polymerization

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Abstract

This paper extends the kinetic theory of irreversible polymerization (Smoluchowski's equation) by including fragmentation effects in such a way, that the most probable (equilibrium) size distribution from the classical polymerization theories is contained in our theory as the stationary distribution. The time-dependent cluster size distributionc k (a(t)) in Flory's polymerization modelsRA f andA f RB g , expressed in terms of the extent of reactionα, has the same canonical form as in equilibrium, and the time dependence ofα(t) is determined from a macroscopic rate equation. We show that a gelation transition may or may not occur, depending on the value of the fragmentation strength, and, in case a phase transition takes place, we give Flory- and Stockmayer-type postgel distributions.

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References

  1. P. J. Flory,Principles of Polymer Chemistry (Cornell University Press, Ithaca, New York, 1953).

    Google Scholar 

  2. W. H. Stockmayer,J. Chem. Phys. 11:45 (1943).

    Google Scholar 

  3. R. L. Drake,Topics in Current Aerosol Research, Vol. 3, Hidy and Brock, eds. (Pergamon Press, New York, 1972), Part 2.

    Google Scholar 

  4. R. M. Ziff,J. Stat. Phys. 23:241 (1980).

    Google Scholar 

  5. P. J. Flory,Principles of Polymer Chemistry (Cornell University Press, Ithaca, New York, 1953), Section III.2.

    Google Scholar 

  6. T. A. Witten and L. M. Sander,Phys. Rev. Lett. 47:1400 (1981).

    Google Scholar 

  7. P. Meakin,Phys. Rev. A 27:604 (1983).

    Google Scholar 

  8. M. Muthukumar,Phys. Rev. Lett. 50:839 (1983).

    Google Scholar 

  9. L. M. Sander, inProceedings of the International Topical Conference on the Kinetics of Aggregation and Gelation, University of Georgia, 1984, F. Family and D. P. Landau, eds. (North-Holland, Amsterdam, 1984).

    Google Scholar 

  10. P. Meakin,Phys. Rev. Lett. 51:1119 (1983).

    Google Scholar 

  11. M. Kolb, R. Botet, and R. Jullien,Phys. Rev. Lett. 51:1123 (1983); R. Botet, R. Jullien, and M. Kolb,J. Phys. A: Math. Gen. 17:L75 (1984); R. Botet, R. Jullien, and M. Kolb,J. Phys. Lett. 45:L211 (1984).

    Google Scholar 

  12. See many papers inProceedings of the International Topical Conference on the Kinetics of Aggregation and Gelation, University of Georgia, 1984, F. Family and D. P. Landau, eds. (North-Holland, Amsterdam, 1984).

    Google Scholar 

  13. J. L. Spouge,Macromolecules 16:5, 831 (1983).

    Google Scholar 

  14. P. G. J. van Dongen and M. H. Ernst,J. Phys. A Math. Gen. 17:2281 (1984).

    Google Scholar 

  15. E. M. Hendriks and M. H. Ernst,J. Coll. Interf. Sci. 97:176 (1984).

    Google Scholar 

  16. B. A. Trubnikov,Dokl. Sov. Phys. 16:124 (1971).

    Google Scholar 

  17. P. G. J. van Dongen and M. H. Ernst,J. Phys. A: Math. Gen. 16:L327 (1983).

    Google Scholar 

  18. J. L. Spouge,Macromolecules 16:121 (1983).

    Google Scholar 

  19. Z. A. Melzak,Trans. Am. Math. Soc. 85:547 (1957).

    Google Scholar 

  20. J. L. Spouge,Math. Proc. Cambridge Philos. Soc. 96:351 (1984).

    Google Scholar 

  21. P. J. Blatz and A. V. Tobolsky,J. Phys. Chem. 49:77 (1945).

    Google Scholar 

  22. M. Aizenmann and T. A. Bak,Commun. Math. Phys. 65:203 (1979).

    Google Scholar 

  23. M. H. Ernst,Studies in Statistical Mechanics, Vol. X, Montroll and Lebowitz, Eds. (North-Holland, Amsterdam, 1983), Chap. 3.

    Google Scholar 

  24. J. D. Barrow,J. Phys. A: Math. Gen. 14:729 (1981).

    Google Scholar 

  25. R. C. Srivastava,J. Atmosph. Sci. 39:1317 (1982).

    Google Scholar 

  26. C. DeLisi and A. Perelson,J. Theor. Biol. 62:159 (1976); A. Perelson and C. DeLisi,Math. Biosciences 48:71 (1980).

    Google Scholar 

  27. R. J. Cohen and G. B. Benedek,J. Phys. Chem. 86:3696 (1982).

    Google Scholar 

  28. J. Spouge,J. Stat. Phys. 31:363 (1983).

    Google Scholar 

  29. S. Glasstone, K. J. Laider, and H. Eyring,The Theory of Rate Processes (McGraw-Hill, New York, 1941), pp. 7 and 8.

    Google Scholar 

  30. D. Stauffer, A. Coniglio, and M. Adam,Advances in Polymer Science, Vol. 44, K. Dusek, ed. (Springer Verlag, Berlin, 1982).

    Google Scholar 

  31. R. M. Ziff, M. H. Ernst, and E. M. Hendriks,J. Phys. A: Math. Gen. 16:2293 (1983).

    Google Scholar 

  32. R. M. Ziff and G. Stell,J. Chem. Phys. 73:3492 (1980).

    Google Scholar 

  33. M. Falk and R. E. Thomas,Can. J. Chem. 52:3285 (1974).

    Google Scholar 

  34. R. W. Samsel and A. S. Perelson,Biophys. J. 37:493 (1982).

    Google Scholar 

  35. F. W. Wiegel and A. S. Perelson,J. Stat. Phys. 29:813 (1982).

    Google Scholar 

  36. A. S. Perelson, inProceedings of the International Topical Conference on the Kinetics of Aggregation and Gelation, University of Georgia, 1984, F. Family and D. P. Landau, Eds. (North-Holland, Amsterdam, 1984).

    Google Scholar 

  37. P. G. J. van Dongen and M. H. Ernst, inProceedings of the International Topical Conference on the Kinetics of Aggregation and Gelation, University of Georgia, 1984, F. Family and D. P. Landau, eds. (North-Holland, Amsterdam, 1984).

    Google Scholar 

  38. R. M. Ziff, E. M. Hendriks, and M. H. Ernst,Phys. Rev. Lett. 49:593 (1982);J. Stat. Phys. 31:519 (1983).

    Google Scholar 

  39. F. Leyvraz and H. R. Tschudi,J. Phys. A: Math. Gen. 15:1951 (1982).

    Google Scholar 

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Authors and Affiliations

  1. Institute for Theoretical Physics, State University, P.O. Box 80.006, 3508, TA Utrecht, The Netherlands

    P. G. J. van Dongen & M. H. Ernst

Authors
  1. P. G. J. van Dongen
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  2. M. H. Ernst
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Inspec numbers: 0550, 6460, 8235, 6475.

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van Dongen, P.G.J., Ernst, M.H. Kinetics of reversible polymerization. J Stat Phys 37, 301–324 (1984). https://doi.org/10.1007/BF01011836

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  • DOI: https://doi.org/10.1007/BF01011836

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