Chain-length distribution in a model of equilibrium polymerization

Abstract

Using renormalization-group techniques, I derive a general scaling form of the chain-length distribution for the equilibrium-polymerization model of des Cloizeaux [J. Phys. (Paris) 36, 281 (1975)]. The result allows more freedom than was assumed in some previous work. This disproves arguments suggesting that in semidilute polymer solutions there exists a phase related to some anomaly of the zero-component field theory. The scaling function of the chain-length distribution is calculated to first order in ε. It varies with the overlap of the chains and, in general, differs somewhat from a Schultz distribution. No anomaly related to the semidilute limit is found. Some rather nontrivial aspects of the result are well understood in terms of de Gennes ‘‘blob’’ concept.