Many-body interactions between charged particles in a polymer solution: the protein regime

We study the phase behavior of charged particles in electrolyte solutions wherein non-adsorbing polymers are added to provide an attractive depletion interaction. The polymer has a radius of gyration similar to that of the particle radius, which causes significant many-body effects in the effective polymer mediated interaction between particles. We use a recently developed analytical theory, which gives a closed expression for the full depletion interaction, accounting for all orders of many-body terms in the potential of mean force. We compare with simulations of an explicit polymer model and show that the potential of mean force provides an accurate and computationally efficient description for the charged particle/polymer mixture, over a range of electrolyte concentrations. Furthermore, we demonstrate that the usual pair potential approach is highly inaccurate for these systems. A simple simulation method is used to estimate the limits of stability of the mixture. The pair approximation is shown to predict a much greater region of instability compared with the many-body treatment, due to its overestimation of the polymer depletion effect.