Depletion forces beyond the diluted limit

The determination of the effective interactions in many-body systems still possesses a tremendous challenge in Condensed Matter Physics. The problem mainly resides in the fact that, on the one hand, there is not a unique route to obtain the effective forces between the ”observable” constituents and, on the other hand, one typically considers that the diluted limit of those components always corresponds to the effective forces at all particle concentrations. In the particular case of colloidal dispersions, it is very important to have experimental, theoretical, and computational tools that allow us to determine, accurately and without using significant approximations, the effective interactions between colloids. In this contribution, we report on a detailed study of depletion potentials in colloidal mixtures at finite concentration, namely, binary and ternary mixtures of disks (in two dimensions or 2D) and spheres (in three dimensions or 3D). To this end, the depletion forces between the large colloidal species are determined through a recently developed scheme based on the so-called contraction of the description, which has been extended and built at the level of the bare forces, i.e., we basically consider that all particles interact through the bare potentials and the net force acting on a given particle is determined by the second’s Newton law. This scheme can be easily adapted to Molecular Dynamics simulations. To verify the physical consistency of the formalism, we explicitly show that in the diluted limit of large particles, the resulting depletion potential reproduces correctly the AO-Vrij limit. As further proof of the accuracy of the results, a comparison of the structure of the large colloids in the whole mixture with the one that results using exclusively the depletion potential is carried out. In 3D, the results are explicitly compared with the potential of mean force and those obtained with the integral equations formalism. We also report a new colloidal stability mechanism based on the use of two different species of depletant agents at low and equal concentrations. Although we highlight the fact that the depletion potential depends on the concentration of the large species, we show that this dependence can be eliminated when the colloidal dispersion is open to a reservoir of small particles, i.e., when the chemical potential of small particles is fixed. Finally, we report the effects of polydispersity on the depletion interaction between large colloids.