Abstract
We determine the statistical properties of block copolymers in solution. These complexes are assumed to have the topological structure of connected graphs with “nonnested” loops and cycles. The generating function method is used to determine the number of topologically different complexes containing a given number of block copolymers. It is shown that at sufficiently high concentration the system undergoes a transition to a gel phase. Furthermore, the average number of polymers per complex is calculated. Finally, the relative increase in viscosity is found under the assumption that the complexes can be treated as porous spheres.
Similar content being viewed by others
References
B. J. Geurts and R. van Damme,J. Stat. Phys. 57:1069 (1989).
F. W. Wiegel and A. S. Perelson,J. Stat. Phys. 29:813 (1982).
F. W. Wiegel, B. J. Geurts, and B. Goldstein,J. Phys. A: Math. Gen. 20:5205 (1987).
J. Spouge,J. Stat. Phys. 43:143 (1986).
K. Visscher and P. F. Mijnlieff, In preparation (1989).
P. Harary and F. Palmer,Graphical Enumeration (Academic Press, 1973).
M. Abramowitz and I. A. Stegun,Handbook of Mathematical Functions (Dover, New York, 1964).
A. C. Hearn,REDUCE User's Manual (Rand, 1983).
B. U. Felderhof,Physica 80A:172 (1975).
P. G. de Gennes,Scaling Concepts in Polymer Physics (Cornell University Press, 1979).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
van Damme, R., Geurts, B.J. Complexes of block copolymers in solution: A graph-theoretical approach. J Stat Phys 57, 1099–1122 (1989). https://doi.org/10.1007/BF01020050
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01020050