Scaling properties of the entropy of polymer solutions

Publisher Website
Google Scholar
Abstract
Direct renormalisation group equations are derived and solved for the entropy S(cp, L, (P(x)), ov) of a polymer solution with specified polydispersity cp(x) identical to cp(1/L)P(x/L). A two-parameter description of the universal scaling function S is developed which characterises the scaling behaviour of the entropy for all temperatures T>or= theta , 'the Flory temperature', and all concentrations cp. Explicit representations are constructed parametrically for all values of the 'overlap' ov approximately uL2dp to O( epsilon 2) in the epsilon expansion. Dilute solution expressions are reproduced, the limit ov>>1 of semi-dilute physics is discussed and a simple phenomenological model is proposed.