Density functional theory and Monte Carlo simulation of mixtures of hard sphere chains confined in a slit

Abstract

A density functional theory (DFT) is presented for polymer mixtures confined between two planar walls. Polymer molecules are treated as tangentially jointed hard sphere chains. The Helmholtz free energy functional consists of an ideal gas part and an excess contribution. The latter is constructed based on coarse graining approximation. A weighting function is adopted for local densities appearing in the expressions. For simplicity, a Heaviside function is used in this work. To calculate the density profiles of chain beads, a direct iterative algorithm combined with a relaxation factor is used. Simulations of a single chain moving in an effective field are needed. A new simulation method is developed in this work. Mixtures of the chains with 4, 8 and 32 beads are studied, covering a wide range of densities. Results are compared with corresponding computer simulations.