Quantifying many-body contributions to depletion forces

Abstract

Effective interactions inherently encompass many-body effects that appear unified. Analyzing these in reverse, that is, separating them into contributions from pairs, triples, or larger groups, is typically intricate and seldom pursued. However, this could offer essential insights into the structural architecture of complex systems, such as soft materials. This contribution tackles this issue employing a new simulation-based approach to accurately determine effective interactions. The approach is sufficiently sensitive to assess the effects of higher-order terms in the depletion potentials between large particles. Previous research has primarily focused on the role of small particles, and this work expands on these findings. However, understanding the contributions of large particles on the effective forces, particularly beyond the dilute limit, remains challenging and is not yet fully grasped, leading us to primarily focus on exploring this topic. Within the range of particle concentrations examined here, while maintaining a constant chemical potential for smaller particles, we have observed that the concentration of larger particles has no impact on the entropic potential between large colloids, as long as the size ratio remains below $q=0.15$. This confirms a long-established prediction founded on purely geometric considerations, which we have confirmed by means of direct observation. In contrast, for mixtures with less size asymmetry, such effects become considerably influential. Specifically, we have conducted an in-depth examination of scenarios with size asymmetries of $q=0.45$ and $0.60$. Our results for the depletion forces were directly compared with those obtained from the integral equation theory, which has also enabled us to improve and refine the approaches involved.