Effects of long-chain branching on distribution of degree of polymerization

The method of generating functions is used to calculate the number fraction of molecules having any specified degree of polymerization and number of long branches for polymers produced under conditions in which the probabilities of chain propagation and of branching on a monomer unit incorporated in the polymer are both constant; termination by combination is assumed absent. Expressions are given for the moments of degree of polymerization and the first two moments of branch number. It is shown that all moments of degree of polymerization are finite, for this model. An asymptotic expression for the number distribution at very high degrees of polymerization is obtained. The way in which the average number of branches per monomer unit varies with degree of polymerization is studied.