Confinement free energy and chain conformations of homopolymers confined between two repulsive walls.

Lattice Monte Carlo simulations of polymer solutions confined between two parallel plates were performed. The confinement free energy Deltamicro(conf) per chain and the radius of gyrations of the chains parallel and perpendicular to the plates were obtained. When the concentration of the confined solution is above the overlap concentration, Deltamicro(conf) is found to scale with Na/D in a power law, betaDeltamicro(conf) approximately (Na/D)(m), with an exponent m=1.10+/-0.02 for athermal walls where N is the number of monomers in a chain, D is the slit width, and a is the lattice spacing. The presence of a weak attractive polymer/wall interaction epsilon(w) does not change the scaling variable, but the exponent m increases slightly. Extrapolating the results to melt would suggest that the predictions made by de Gennes [C. R. Acad. Sci. Paris II 305, 1181 (1987)] about the confinement free energy cost per chain in polymer melt is correct as far as the scaling variable is concerned, but is incorrect about the exponent m observed. The implication of this result on the predicted force between plates immersed in polymer melt is discussed. The parallel dimensions of the confined chain is expanded when the slit width D is narrow, however, the expansion is reduced at high concentration. It is conceivable that in melt the chain is not expanded when confined in a repulsive slit.