Scaling theory of polydispersity, an infinite chain, and the Flory-Huggins approximation

Abstract

We develop a scaling theory of polydispersity in an equilibrium ensemble of polymers. The theory predicts the existence of an ‘‘infinite’’ chain. The radius of gyration exponent for ‘‘finite’’ chains in the ‘‘semidilute’’ regime is (43/76>0.5 in two dimensions. Thus, this exponent cannot be (1/2 in general. We also show that the Flory-Huggins approximation is qualitatively incorrect.