Polymer-mediated spatial organization of nanoparticles in dense melts: Transferability and an effective one-component...

We study two problems in the framework of the integral equation theory of polymer-mediated spatial organization of nanoparticles in dense melts motivated by multiscale simulation and many body physics issues. How nonspherical nanoparticle shape modifies polymer-induced interactions under dilute nanoparticle conditions is investigated over a range of primary particle sizes and interfacial cohesion strengths. Nonuniversal consequences of nonspherical shape are found for the pair-correlation function on local scales and some qualitative differences on larger scales due primarily to intraparticle connectivity constraints. For a large enough nanoparticle site diameter, the potentials of mean force (PMF) for all shapes studied (sphere, rod, disk, compact tetrahedral cluster) exhibit linear scaling with the size ratio of nanoparticle to polymer monomer site diameter and quite good "transferability." The ability of a simple effective one-component approach, based on the dilute nanoparticle PMF as an effective pair-decomposable potential, to describe interparticle structure at nonzero volume fractions is also studied. Although not generally quantitatively accurate due to neglect of many body correlation effects, especially at high nanoparticle loadings and near contact separations, the simple approach captures rather well many aspects of the real space structure. The errors incurred depend systematically on whether interfacial cohesion strength results in contact aggregation, steric stabilization, or bridging. For the filler collective static structure factor, many body effects are weakest for local cage scale correlations and grow significantly at smaller wavevectors under depletion or bridging conditions.