Gaussian field model of fluids with an application to polymeric fluids

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Abstract
This paper extends the Gaussian model of Li and Kardar [Phys. Rev. Lett. 67, 3275 (1991)]. When applied self-consistently to density fluctuations of a hard-sphere fluid, it is shown that the model gives the Percus-Yevick theory. With the addition of an attractive tail potential, the mean spherical approximation is obtained. Unlike the random-phase approximation, this appraoch determines the normal modes of the model consistent with the presence of an excluding manifold. The resulting fluid response in the presence of such an object is derived. For a D=1 manifold, the self-consistent approach is a theory of polymeric fluids. Here, with an averaging approximation, the reference-interaction-site-model (RISM) equation in the thread limit is obtained. For polymer blends, the analysis yields a seemingly exact formula for a demixing critical temperature. It scales linearly with polymer mass, as in Flory’s theory, but with an effective χ parameter smaller than that in Flory’s theory. The analysis sheds light on an erroneous prediction of different scaling made by others applying the RISM theory.