Casimir-like forces at the percolation transition

TL;DR

This paper demonstrates that near the percolation transition, colloidal particles experience long-range attractive forces analogous to critical Casimir forces, which can be tuned by controlling solvent clustering.

Contribution

It introduces a theoretical and numerical framework showing long-range forces emerge near percolation, akin to critical Casimir forces, linking percolation phenomena with colloidal interactions.

Findings

Effective potential becomes attractive and long-ranged near percolation

Divergence of interaction range is captured by a polydisperse Asakura-Oosawa model

Solvent clustering controls colloidal interaction strength

Abstract

Percolation and critical phenomena show common features such as scaling and universality. Colloidal particles, immersed in a solvent close to criticality, experience long-range effective forces, named critical Casimir forces. %These originate from the confinement of the solvent critical fluctuations between the colloids. Building on the analogy between critical phenomena and percolation, we explore the possibility of observing long-range forces near a percolation threshold. To this aim we numerically evaluate the effective potential between two colloidal particles dispersed in a chemical sol and we show that it becomes attractive and long-ranged on approaching the sol percolation transition. We develop a theoretical description based on a polydisperse Asakura-Oosawa model which captures the divergence of the interaction range, allowing us to interpret such effect in terms of depletion interactions in a structured solvent. Our results provide the geometric analogue of the critical Casimir force, suggesting a novel way for tuning colloidal interactions by controlling the clustering properties of the solvent.