Nanoparticles in solutions of adsorbing polymers: pair interactions, percolation, and phase behavior.

We study the polymer adsorption characteristics, pair-interaction potentials, and phase and percolation behavior in nanoparticle-polymer mixtures. We propose a "saturable" adsorption model to capture the effect of the finite surface saturation capacity for adsorption, and use polymer self-consistent field theory in combination with a McMillan-Mayer framework [McMillan, W. G., Jr.; Mayer, J. E. J. Chem. Phys. 1945, 13, 276] to compute the pair-interaction potentials. Our results demonstrate novel size effects that distinguish the adsorption characteristics of nanoparticles from that of larger particles. Specifically, we predict that the nanoparticle regime is characterized by a significant adsorbance of polymers, albeit distributed predominantly in the form of tails. We also demonstrate that an interplay between the surface saturation, polymer-to-particle size ratios, and the polymer concentrations governs the overall effective interactions between nanoparticles in the presence of an adsorbing polymer. We use simple, mean-field models to relate these characteristics to the phase and percolation behavior in such systems. Our results show that the percolation thresholds for smaller particles are significantly smaller (and, overall, correspond only to a few volume percent) compared to that of the larger particles. Further, with a decrease in the size of the particles, we also predict a considerable increase in the miscibility of the polymer-particle mixtures. Our results are qualitatively in accord with many experimental observations in the nanoparticle regime.