Analytical Functions for Molecular Weight and Branching Distributions in Star-, Comb-, and Random-Branched Polymers

Long-chain branching has a significant effect on various polymer properties. One of the determining molecular parameters is the bivariate distribution of molecular weight and branching density. This work presents analytical distribution functions for three types of branched polymers: random, comb, and star. The primary chains are assumed to have a Schulz−Zimm distribution. It is shown that the distribution shape strongly depends on the type of branching with polydispersity in the order of star < comb < random.