Conformation of branched polymers

Abstract

We study the conformation of randomly branched, monodispersed polymers both in dilute and concentrated solutions in their reaction bath. We first extend the Zimm-Stockmayer mean field theory to such properties as elasticity and concentration correlations. We then take this mean field theory as a basis for a Flory approach. In a dilute solution, we recover previous results by Isaacson and Lubensky in a good solvent. In a theta solvent, the critical dimension above which the mean field approach is valid is 6. The exponent for the molecular weight dependence of the radius of gyration, R ∼ Nν, is ν = 7/4 ( d + 1), where d is the dimension of space. In a melt the polymer chains overlap very weakly, leading to an exponent ν = 1/d. In all these regimes, we give scaling laws for the local properties of the chain, and we study the cross-over to linear chain behaviour when the branching fraction is reduced