Disentangling the effects of many-body forces on depletion interactions.

Abstract

When considering effective interactions in a many-body or thermodynamic system, it is important to recognize that the inherent character of the effective forces between two bodies already incorporates many-body effects that appear unified in a nontrivial way. Working backward to disentangle these effects into the contributions of pairs, triplets, or larger groups is generally complicated and seldom accomplished. However, this could offer essential insights into the structural architecture and self-assembly of complex systems, such as soft materials. In this contribution, we tackle this problem by employing a simulation-based method, here termed contraction of the bare forces (CBF), which, on the one hand, permits a precise evaluation of the effective interactions between colloids [de los Santos-López et al., J. Chem. Phys. 157, 074903 (2022)0021-960610.1063/5.0099919] and, on the other hand, makes it possible to quantify the many-body contributions to these effective interactions. The CBF approach is applied to calculate the depletion forces in asymmetric binary mixtures of hard spheres; the approach is sufficiently sensitive to quantify the effects of higher-order terms on the depletion forces between large particles. To assess the accuracy of our approach, we first explore and confirm the long-established prediction founded on purely geometric considerations, which states that for the particle size ratio, q, smaller than q<q_{3}=0.1547, the depletion interaction between large colloids does not depend on the concentration of large particles, provided that the chemical potential of the smaller particles is kept constant. 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 values of q=0.45 and 0.60. We directly compare our results for the depletion forces with those obtained from the integral equation framework for effective interactions. Through the use of a naive approximation formulated at the level of the bridge functions, this comparison has further enabled us to identify higher-order contributions to the depletion forces between large colloids, thereby improving and sharpening the underlying theoretical approximations. More importantly, in this work, we explicitly disentangle the many-body components of the depletion forces and assess how significantly they affect the contact attraction strength as a function of both the size ratio and the concentration of the large colloids.