Numerically Exact Approach to Ultra-Small Particles in Near-Critical Mixtures

Abstract

The critical Casimir forces between solute particles in a solvent can arise from the medium fluctuations. The properties of ultra-small particles immersed in a binary liquid mixture close to its consolute point Tc are studied using the exact statistical-mechanical derivation based on the two-dimensional Ising model. Each solute particle is represented by a local magnetic field acting on an individual spin. The ensemble average for the distance between particles placed on the torus is determined as a temperature-dependent function. It has been shown how the presence of other particles modifies the separation distance for a pair of particles with the same or opposing preferential adsorption.