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

TL;DR

This study uses Monte-Carlo simulations to explore how the interfacial profiles between coexisting phases in thin polymer films depend on system size, boundary conditions, and statistical ensembles, revealing anomalous size-dependent behaviors.

Contribution

It demonstrates the size and boundary condition dependence of interfacial widths in confined polymer mixtures using Monte-Carlo simulations, highlighting differences between canonical and semi-grand-canonical ensembles.

Findings

Interfacial width scales as sqrt{D} in both ensembles for small L.

In the canonical ensemble, width saturates at w_max proportional to sqrt{ln L}.

In the semi-grand-canonical ensemble, width can scale linearly with D for large L.

Abstract

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. Both the canonical and semi-grand-canonical ensemble are studied. In the canonical ensemble, the interfacial width w increases (from small values which are of the same order as the intrinsic profile) like sqrt{D}, before a crossover to a saturation value w_max (w_max^2 proportional to ln L) sets in. In the semi-grand-canonical ensemble, however, one finds the same widths (w proportional to sqrt{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 proportional to D for D -> infinity). We discuss the implications of these findings for the interpretation of both simulations and experiments.