Assembling the self-depletion interaction puzzle

Why do hard spheres tend to stay together even though they experience strong repulsive forces upon contact? This intriguing phenomenon is widely recognized and has been precisely measured in the study of liquids. Here, we examine it within the framework of the integral equations theory of depletion forces, which offers a unique perspective. This approach provides new insights into the self-depletion effects among identical particles. We examine the phenomenon in monodisperse systems to clarify, from this viewpoint, why hard spheres tend to self-assemble into structured fluids. In binary mixtures, we examine how altering the concentration of one particle type affects the depletion interactions among these particles while also accounting for effects that go beyond the mediating influence of the other particle species. The main result of this contribution is that, by reformulating the theoretical framework around the notion of self-depletion, we develop an approach that represents any mixture of p components, at arbitrary concentrations, as an equivalent mixture of p + 1 components in which the additional component, composed of the particles under consideration, is present at a very low concentration. In this way, the general task of determining depletion potentials is reduced to the much simpler problem of computing the potential of mean force.