Density functional theory of polymers: A Curtin-Ashcroft type weighted density approximation

A density functional theory is presented that combines an exact expression for the ideal gas free energy functional with a weighted density approximation for the excess free energy functional. The weighting function required in the theory is obtained from the Curtin-Ashcroft recipe, with a bulk fluid direct correlation function from the polymer reference interaction site model integral equation theory. The theory is in quantitative agreement with computer simulations for the density profiles of freely jointed tangent sphere hard chains at a hard wall, about as accurate as the Curtin-Ashcroft theory is for hard spheres at a hard wall. For a more realistic fused-sphere chain model with fixed bond angles and bond lengths, the theory is in excellent agreement with simulations at low and intermediate densities but overestimates the magnitude of layering at high densities for short chains. The theory becomes more accurate as the chain length is increased.