A note on the Flory-Huggins and self-consistent field theories of polymersA. J. Masters
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 in final form 28 February 2007; published April 2007
published online 29 March 2007
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.
61.25.Hq - Macromolecular and polymer solutions; polymer melts; swelling.
82.60.Fa - Heat capacities and heats of phase transitions.
© Europhysics Letters Association 2007