Bivariate Distribution and Related Analytical Solutions for Batch Step‐Growth Polymerization of AB2‐Type Monomer

Abstract

AbstractBased on the analytical solution for the bivariate distribution N(n,k) of the degree of polymerization n and the number of dendritic units k, it is shown that the batch step‐growth polymerization of AB2‐type monomer leads to form random hyperbranched architecture, irrespective of the magnitude of reactivity ratio r that represents the reactivity of the second B group. The bivariate distribution function enables one to obtain various useful analytic relationships for the hyperbranched architecture. The degree of branching at large n limit, DBn → ∞, is an important property to represent the branched polymer system, rather than the average DB of the whole reaction mixture. For the case with r = 1, the value of DBn → ∞ is always 0.5, and is unchanged at any stage of batch polymerization. On the other hand, DBn → ∞ changes with the progress of polymerization for r ≠ 1, but the change is not very significant for the high conversion region. The degree of branching at large k limit, DBk → ∞, is always larger than DBn → ∞, but the relationship DBk → ∞ = DBn → ∞ holds at 100% conversion.