Abstract
For the first time the possibility of the description of the products of non-random irreversible polycondensation by the theory of branching processes is rigorously substantiated. The formalism of this theory is shown to be efficient in finding any statistical characteristics not only of finite molecules but those of a polymer network as well. Exact equations are derived and their simplified forms are presented for networks being formed in the vicinity of the gel-point. Errors arising under the application of an approximation based on the traditional statistical approach are evaluated proceeding from the analysis of the numerical solutions of these equations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Reference
Kinetics of Aggregation and Gelation, F. Family and D. P. Landau, eds. (Elsevier Science Publishers, Amsterdam, 1984).
M. H. Ernst, in Nonequilibrium Phenomena. I. Boltzmann Equation, J. L. Lebowitz and E. W. Montroll, eds. (Elsevier Science Publishers, Amsterdam, 1983), chap. 3.
R. M. Ziff, in Kinetics of Aggregation and Gelation, F. Family and D. P. Landau, eds. (Elsevier Science Publishers, Amsterdam, 1984), pp. 191-199.
M. H. Ernst, in Fundamental Problems in Statistical Mechanics, Vol. 6, E. G. D. Cohen, ed. (Elsevier Science Publishers, Amsterdam, 1985), pp. 329-364.
M. Ernst, in Fractals in Physics, L. Pietronero and E. Tossati, eds. (Elsevier Science Publishers, Amsterdam, 1986), chap. 6.
S. I. Kuchanov, Methods of Kinetic Calculation in Polymer Chemistry (Khimia, Moscow, 1978).
S. I. Kuchanov, Adv. Polym. Sci. 152:157(2000).
M. Gordon and G. R. Scantlebury, Trans. Faraday Society 60:604(1964).
G. Dobson and M. Gordon, J. Chem. Phys. 41:2389(1964).
K. Dusek, Discuss. Faraday Chem. Soc. 57:101(1974).
P. Luby, J. Chem. Phys. 78:1083(1974).
D. P. Kochetov, Vysokomol. Soedin. Ser. B 26:756(1984).
S. I. Kuchanov, (to be published).
S. I. Kuchanov, in Abstracts of Papers Presented on IUPAC Symposium on Macromolecular Chemistry, Tashkent, USSR, 1978, Vol. 3 (Nauka, Moscow, 1978), p. 50.
S. I. Kuchanov, Dok. Akad. Nauk SSSR 249:899(1979).
S. I. Kuchanov and E. S. Povolotskaya, Vysokomol. Soedin. Ser. A 24:2190(1982).
H. Galina, Europhys. Lett. 3:1155(1987).
H. Galina and A. Szustalewicz, Macromolecules 22:3124(1989).
H. Galina, Makromol. Chem., Macromol. Symposia 40:45(1990).
J. Mikes and K. Dusek, Macromolecules 15:93(1982).
S. I. Kuchanov and A. G. Kholostyakov, J. Polym. Sci. Ser. A 37:2145(1999).
C. Sarmoria and D. R. Miller, Macromolecules 24:1833(1991).
D. R. Miller and C. Sarmoria, Polym. Eng. Sci. 38:535(1998).
O. E. Philippova, Polymer Science Ser. C 42(2):208(2000).
Responsive Gels 1, 2. Adv. Polym. Sci., Vols. 109-110 (1993).
Polymer Gels and Networks, Y. Osada and A. R. Khokhlov, eds. (Marcel Dekker, New York, Basel, 2002).
M. Gordon and M. Judd, Nature 234:96(1971).
Numerical Solution of Integral Equations, L. M. Delves and J. Walsh, eds. (Clarendon Press, Oxford, 1974).
Numerical Recipes, http://www.nr.com.
T. E. Harris, Theory of Branching Process (Springer, Berlin, 1963).
A. T. Bharucha-Reid, Elements of the Theory of Markov Processes and Their Applications (McGraw-Hill, N.-Y., Toronto, London, 1960).
R. Courant and D. Hilbert, Methods of Mathematical Physics (Interscience Publishers, N.-Y., London, 1953).
F. Leyvraz and H. R. Tschudi, J. Phys. Ser. A 14:3389(1981).
F. Leyvraz and H. R. Tschudi, J. Phys. Ser. A 15:1951(1982).
M. Ziff, E. M. Hendricks, and M. H. Ernst, Phys. Rev. Lett. 49:593(1982).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kuchanov, S.I., Zharnikov, T.V. Stochastic Branching Process for Description of Non-Random Irreversible Polycondensation. Journal of Statistical Physics 111, 1273–1298 (2003). https://doi.org/10.1023/A:1023008401138
Issue Date:
DOI: https://doi.org/10.1023/A:1023008401138