A model for effective interactions in binary colloidal systems of soft particles

TL;DR

This paper introduces an analytical theory for effective interactions in binary soft particle systems, enabling simplified calculations and reproducing key phenomena like attraction and repulsion effects.

Contribution

The authors develop a new analytical framework translating many-particle Hamiltonians into Gaussian integrals, simplifying the analysis of effective interactions in complex binary systems.

Findings

Reproduces effective attraction in Gaussian particle mixtures

Analyzes interactions in Yukawa particle systems

Demonstrates attraction-through-repulsion and repulsion-through-attraction effects

Abstract

While the density functional theory with integral equations techniques are very efficient tools in numerical analysis of complex fluids, an analytical insight into the phenomenon of effective interactions is still limited. In this paper we propose a theory of binary systems which results in a relatively simple analytical expression combining arbitrary microscopic potentials into the effective interaction. The derivation is based on translating many particle Hamiltonian including particle-depletant and depletant-depletant interactions into the occupation field language. Such transformation turns the partition function into multiple Gaussian integrals, regardless of what microscopic potentials are chosen. In result, we calculate the effective Hamiltonian and discuss when our formula is a dominant contribution to the effective interactions. Our theory allows us to analytically reproduce several important characteristics of systems under scrutiny. In particular, we analyze the effective attraction as a demixing factor in the binary systems of Gaussian particles, effective interactions in the binary mixtures of Yukawa particles and the system of particles consisting of both repulsive core and attractive/repulsive Yukawa interaction tail, for which we reproduce the 'attraction-through-repulsion' and 'repulsion-through-attraction' effects.