Kinetics of polymer crystallization - I. Discrete and continuum models
- 8 April 1988
- journal article
- Published by The Royal Society in Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- Vol. 416 (1851) , 443-461
- https://doi.org/10.1098/rspa.1988.0043
Abstract
The kinetics of growth of lamellar crystals by chain folding of polymer molecules are described by Markov rate processes whose states are representations of the edge of a lamella. The dynamic reversibility of these processes allows their equilibrium distributions to be found and these describe states of steady crystal growth. For a hexagonal crystal structure the equilibrium distribution is the Gibbs distribution for a constrained, one-dimensional Ising antiferromagnet. For a square crystal structure it is a constrained exponential distribution. These distributions provide a description of the roughness of the edge of a growing crystal and expressions for the growth rate. The continuum limit of these models is shown to coincide with the model of Frank and of Bennett et al . ( J. statist. Phys . 24, 419 (1981)). Frank’s approximate equations (Frank, F. C. J. Cryst. Growth 22, 233 (1974)) are also examined.Keywords
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