Molecular weight distribution of living radical polymers - 1. Fundamental distribution

The molecular weight distribution formed in an ideal living radical polymerization is considered theoretically. It was found that the hypergeometric function that combines the most probable and the Poisson distribution represents a fundamental distribution of the living radical polymers. The number- and weight-average molecular weights are derived for this fundamental distribution, together with those for polymerizations in a batch and in a continuous stirred tank reactor. These average molecular weight functions are obtained based on the arithmetic calculations without deriving the distribution functions. The effect of the monomer transfer reactions on the formed MWD is also considered. The present study clarifies the relationship between the reaction mechanism and the formed molecular weight distribution as well as the fundamental characteristics of living radical polymers.