Density functional theory of simple polymers in a slit pore. II. The role of compressibility and field type

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Abstract
Simple tangent, hard site chains near a hard wall are modeled with a density functional (DF) theory that uses the direct correlation function, c(r), as its “input.” Two aspects of this DF theory are focused upon: (1) the consequences of variations in c(r) ’s detailed form; and (2) the correct way to introduce c(r) into the DF formalism. The most important aspect of c(r) is found to be its integrated value, ĉ(0). Indeed, it appears that, for fixed ĉ(0), all reasonable guesses of the detailed shape of c(r) result in surprisingly similar density distributions, ρ(r). Of course, the more accurate the c(r), the better the ρ(r). As long as the length scale introduced by c(r) is roughly the hard site diameter and as long as the solution remains liquid-like, the ρ(r) is found to be in good agreement with simulation results. The c(r) is used in DF theory to calculate the medium-induced potential, U M (r), from the density distribution, ρ(r). The form of U M (r) can be chosen to be one of a number of different forms. It is found that the forms for U M (r) which yield the most accurate results for the wall problem are also those which were suggested as accurate in previous, related studies.