Excluded Volume in Polymer Chains

Abstract

A perturbation theory of the excluded volume effect in chain polymers is developed. The theory is applied to the mean square end-to-end distance, 〈L2〉, of a linear chain (second-order perturbation), and to the mean square radius of a linear and a branched chain (first-order perturbation). Flory's approximate theory is found to be in fair agreement with the second-order perturbation theory. Integro-differential equations are developed to discuss the behavior of 〈L2〉/nb2 as n→ ∞, for a chain composed of n segments of length b.