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

Abstract

Motivated by recent experiments with confined binary liquid mixtures near demixing, westudy the universal critical properties of a system, which belongs to the Ising universalityclass, in the film geometry. We employ periodic boundary conditions in the twolateral directions and fixed boundary conditions on the two confining surfaces, suchthat one of them has a spatially homogeneous adsorption preference while theother one exhibits a laterally alternating adsorption preference, resembling locallya single chemical step. By means of Monte Carlo simulations of an improvedHamiltonian, so that the leading scaling corrections are suppressed, numericalintegration and finite-size scaling analysis we determine the critical Casimir force andits 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 systemreduces 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 toequal and opposite values, respectively. We show that the universal scaling function of thecritical Casimir force for small but finite aspect ratios displays a linear dependence on theaspect ratio which is solely due to the presence of the lateral inhomogeneity. We alsoanalyse the order-parameter profiles at criticality and their universal scaling function,which allows us to probe theoretical predictions and to compare with experimentaldata.