Anomalous size–dependence of interfacial profiles between coexisting phases of polymer mixtures in thin film geometry: A Monte–Carlo simulation

The interfacial profile between coexisting phases of a binary mixture (A,B) in a thin film of thickness D and lateral linear dimensions L depends sensitively on both linear dimensions and on the nature of boundary conditions and statistical ensembles applied. These phenomena generic for systems in confined geometry are demonstrated by Monte–Carlo simulations of the bond fluctuation model of symmetric polymer mixtures, using chains containing NA = NB = N = 32 effective monomers connected by effective bonds with an attractive interaction between monomers of the same type and a repulsive interaction between different types. We use short range potentials at the walls, the right wall favoring A monomers and the left wall B monomers. Periodic boundary conditions are applied in the directions parallel to the walls. Both the canonical and semi-grand-canonical ensemble are studied. We argue that the latter case is appropriate for experiments with a lateral resolution L much less than the actual lateral sample size, in thermal equilibrium. In the canonical ensemble, the interfacial width w increases (from small values which are of the same order as the “intrinsic profile”) like w ∝ √ D, before a crossover to a saturation value wmax (w 2 max ∝ lnL) sets in. In the semi-grand-canonical ensemble, however, one finds the same widths w ∝ √ D as in the canonical ensemble for not too large L, while for large L the interfacial profile is smeared out over a finite fraction of the film thickness (w ∝ D for D → ∞). We discuss the implications of these findings for the interpretation of both simulations and experiments.