Critical Casimir interaction between colloidal Janus-type particles in two spatial dimensions

TL;DR

This paper provides an exact analytical study of the critical Casimir interactions between Janus-type colloidal particles in two dimensions, revealing how surface inhomogeneities influence forces near criticality.

Contribution

It introduces a conformal invariance-based formalism to exactly compute universal profiles and interactions of Janus particles in 2D critical binary mixtures, including asymptotic expressions and comparisons with simulations.

Findings

Exact expressions for order parameter and stress tensor profiles.

Asymptotic formulas for particle interactions at various distances.

Agreement with simulation data for Janus particle interactions.

Abstract

We study colloidal particles with chemically inhomogeneous surfaces suspended in a critical binary liquid mixture. The inhomogeneous particle surface is composed of patches with alternating adsorption preferences for the two components of the binary solvent. By describing the binary liquid mixture \emph{at} its consolute point in terms of the critical Ising model we exploit its conformal invariance in two spatial dimension. This allows us to determine exactly the universal profiles of the order parameter, the energy density, and the stress tensor as well as some of their correlation functions around a single particle for various shapes and configurations of the surface patches. The formalism encompasses several interesting configurations, including Janus particles of circular and needle shapes with dipolar symmetry and a circular particle with quadrupolar symmetry. From these single-particle properties we construct the so-called small particle operator expansion (SPOE), which enables us to obtain asymptotically exact expressions for the position- and orientation-dependent critical Casimir interactions of the particles with distant objects, such as another particle or the confining walls of a half plane, strip, or wedge, with various boundary conditions for the order parameter. In several cases we compare the interactions at large distances with the ones at close distance (but still large on the molecular scale). We also compare our analytical results for two Janus particles with recent simulation data.