Critical Casimir forces and adsorption profiles in the presence of a chemically structured substrate

TL;DR

This study investigates the universal critical Casimir forces and adsorption profiles in a binary liquid mixture confined between chemically structured surfaces, using Monte Carlo simulations to analyze the effects of lateral inhomogeneity.

Contribution

It introduces a detailed analysis of the critical Casimir force in systems with chemically patterned substrates, extending understanding of boundary condition effects on critical phenomena.

Findings

Universal scaling function of the Casimir force depends linearly on aspect ratio for small values.

Critical Casimir force reduces to mean of homogeneous ++ and +- boundary conditions in the zero aspect ratio limit.

Order-parameter profiles at criticality match theoretical predictions and aid experimental comparisons.

Abstract

Motivated by recent experiments with confined binary liquid mixtures near demixing, we study the universal critical properties of a system, which belongs to the Ising universality class, in the film geometry. We employ periodic boundary conditions in the two lateral directions and fixed boundary conditions on the two confining surfaces, such that one of them has a spatially homogeneous adsorption preference while the other one exhibits a laterally alternating adsorption preference, resembling locally a single chemical step. By means of Monte Carlo simulations of an improved Hamiltonian, so that the leading scaling corrections are suppressed, numerical integration, and finite-size scaling analysis we determine the critical Casimir force and its universal scaling function for various values of the aspect ratio of the film. In the limit of a vanishing aspect ratio the critical Casimir force of this system reduces to the mean value of the critical Casimir force for laterally homogeneous ++ and +- boundary conditions, corresponding to the surface spins on the two surfaces being fixed to equal and opposite values, respectively. We show that the universal scaling function of the critical Casimir force for small but finite aspect ratios displays a linear dependence on the aspect ratio which is solely due to the presence of the lateral inhomogeneity. We also analyze the order-parameter profiles at criticality and their universal scaling function which allows us to probe theoretical predictions and to compare with experimental data.