A closed-form, free-energy functional for a binary polymer mixture

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Abstract
A new, closed-form, free-energy functional is derived for a binary polymer mixture. When the free-energy functional is expanded in series form around the mean concentration, the leading term in the expansion is the usual Flory–Huggins free energy. The Fourier transform of the coefficients of this expansion are approximate vertex functions Γ̄(n). A useful and tractable form for Γ̄(n) is obtained for all n which only depends on the magnitudes of the n wave vectors. It is shown that Γ̄(2) is exact and Γ̄(3) and Γ̄(4) reduce to the correct limiting values in the small and large wave vector limits.

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