Line contribution to the critical Casimir force between a homogeneous and a chemically stepped surface

TL;DR

This paper investigates how chemical steps on surfaces influence the critical Casimir force in binary liquid mixtures, using simulations and theory to quantify their universal contribution and validate force decomposition in striped geometries.

Contribution

It provides the first detailed analysis of the universal scaling function for the critical Casimir force contribution from individual chemical steps.

Findings

Universal scaling function for chemical step contribution determined

Force decomposition into homogeneous parts and steps validated

Results applicable to arbitrarily shaped, wide stripes

Abstract

Recent experimental realizations of the critical Casimir effect have been implemented by monitoring colloidal particles immersed in a binary liquid mixture near demixing and exposed to a chemically structured substrate. In particular, critical Casimir forces have been measured for surfaces consisting of stripes with periodically alternating adsorption preferences, forming chemical steps between them. Motivated by these experiments, we analyze the contribution of such chemical steps to the critical Casimir force for the film geometry and within the Ising universality class. By means of Monte Carlo simulations, mean-field theory, and finite-size scaling analysis we determine the universal scaling function associated with the contribution to the critical Casimir force due to individual, isolated chemical steps facing a surface with homogeneous adsorption preference or with Dirichlet boundary condition. In line with previous findings, these results allow one to compute the critical Casimir force for the film geometry and in the presence of arbitrarily shaped, but wide stripes. In this latter limit the force decomposes into a sum of the contributions due to the two homogeneous parts of the surface and due to the chemical steps between the stripes. We assess this decomposition by comparing the resulting sum with actual simulation data for the critical Casimir force in the presence of a chemically striped substrate.