Theory of effective interactions and dispersion of soft nanoparticles in polymer melts

Integral equation theory is employed to investigate the consequences of nanoparticle softness (surface fluctuations) and corrugation (discrete roughness) on the equilibrium behavior of polymer-particle mixtures in the dilute filler limit. Monomer-particle pair correlations exhibit qualitatively different features relative to hard spheres which depend on both roughness and softness. Under athermal nonadsorbing polymer conditions, depletion effects on the interparticle potential-of-mean-force (PMF) are qualitatively modified by surface corrugation and/or fluctuations. As particle softness increases, monomer-scale PMF oscillations are destroyed, and the strongest attraction occurs at a particle separation and attraction depth that depends sensitively on surface fluctuation amplitude, as does the dependence on monomer-nanoparticle size asymmetry ratio (R). For corrugated particles, the most attractive nanoparticle separation does not occur at contact, and is far weaker and less sensitive to R than for hard spheres. Second virial coefficient calculations are performed to estimate how particle softness/roughness modifies miscibility in chemically matched blends. How surface corrugation and softness modifies bridging and sterically stabilized states has also been studied..