BIVARIATE DISTRIBUTION OF CHAIN-LENGTH AND COMPOSITION IN MULTICOMPONENT POLYMERIZATION

The theory of Markovian processes is used to investigate the bivariate distribution of chain length and composition in free-radical polymeri zation consisting of N types of monomer. By following the matrix calcu lation procedure, it is straightforward to determine the full composit ion distribution of polymers with a given chain length numerically, wi th the help of computer softwares capable of conducting symbolic calcu lations. For long polymer chains, the instantaneous composition distri bution is approximated by a Gaussian distribution and the variance is inversely proportional to the chain length. These features are the sam e as those for copolymers (N = 2), which is conveniently represented b y the Stockmayer bivariate distribution. Simpler numerical methods to determine the variance of the composition distribution are proposed. T he Gaussian approximation of the composition distribution is a practic al method to theoretically calculate the bivariate distribution formed in multicomponent polymerizations. (C) 1998 Published by Elsevier Sci ence Ltd. All rights reserved.