Analytic liquid-state theory of the interactions between colloids mediated by reversibly adsorbed polymers

We develop an analytic liquid-state theory of the effective interactions induced by reversibly adsorbing polymers, acting between colloids immersed in a polymer melt. This theory is based on the polymer reference interaction site model that has no restrictions with respect to the density of the polymer system and colloid-to-polymer size ratio. By making use of the developed theory, we calculate the potential of the polymer mediated interactions as a function of the colloid radius, strength and range of the adsorption potential, and the polymer density. In addition, we investigate the behavior of the second virial coefficient as a function of the polymer density in both the colloid and nano-particle limits. We found out that the presence of the adsorption interactions significantly changes the polymer mediated forces relative to the case of the pure entropic depletion interactions, showing most pronounced difference in the case of large polymer densities and small colloid-to-polymer size ratios. The significance of the above differences is determined by the relation between the range of the adsorption potential and polymer correlation length.