Interfacial profiles between coexisting phases in thin films: Cahn Hilliard treatment versus capillary waves

TL;DR

This paper investigates how confinement in thin films affects the structure of interfaces between two phases, combining theoretical models and simulations to show that film thickness influences interfacial width and structure.

Contribution

It extends the Cahn-Hilliard and capillary wave theories to confined geometries and compares analytical results with Monte Carlo simulations for polymer mixtures.

Findings

Interfacial width scales linearly with film thickness in very thin films.

Interfacial width scales with the square root of film thickness in thicker films.

Theoretical predictions are confirmed by Monte Carlo simulations.

Abstract

We consider an interface between two demixed A and B phases, confined in a thin film between two antisymmetric walls, one of which prefers A and the other B. Above the wetting transition, the interface is stabilized in the center of the film. Based on a suitable extension of the Cahn-Hilliard gradient-square theory in combination with the capillary wave theory, we argue that the confinement influences the interfacial structure in two ways: It squeezes the intrinsic structure and cuts off the capillary wave spectrum. As a result, the interfacial width is proportional to the film thickness D in very thin films, and proportional to the square root of D in thicker films. These effects are then discussed in detail for the special case of an interface between demixed homopolymer phases. The width of the intrinsic profile is calculated analytically as a function of film thickness in the Cahn-Hilliard approximation (weak segregation limit) and in the Helfand theory (strong segregation limit), and numerically in the self-consistent field approximation. The results are confirmed by Monte Carlo simulations of a lattice model for a polymer mixture.