A note on the Flory-Huggins and self-consistent field theories of polymers

School of Chemical Engineering and Analytical Science, University of Manchester - P.O. Box 88, Sackville Street, Manchester M60 1QD, UK

Received: 20 February 2007
Accepted: 28 February 2007

Abstract

We consider the relationship between the Flory-Huggins theory of polymer solutions and self-consistent field theory (SCFT). We show that for uniform solutions, the external field in SCFT is related to the excess chemical potential of a polymer chain and that this is approximated by multiplying the number of segments in the chain by the excess chemical potential of a single segment in a fluid of segments. If the excess chemical potential of the segment is taken to be that of a lattice gas in the Bragg-Williams approximation, one regains the Flory-Huggins expression for the Helmholtz energy. In this approach the Flory-Huggins term commonly ascribed to the entropy of mixing of the solvent, arises directly from the chosen form of the segment excess chemical potential. As for SCFT, a result of this work is the clarification of the nature of the mean-field potential and whether solvent entropic effects have or have not already been taken into account.