Structure, scattering patterns and phase behavior of polymer nanocomposites with nonspherical fillers

Polymer nanocomposites made with carbon nanotubes, clay platelets, laponite disks and other novel nonspherical fillers have been the focus of many recent experiments. However, the effects of nanoparticle shape on statistical structure, polymer-mediated effective interactions, scattering patterns, and phase diagrams are not well understood. We extend and apply the polymer reference interaction site model liquid state theory to study the equilibrium properties of pseudo one-, two- and three-dimensional particles (rod, disk, cube) of modest steric anisotropy and fixed space-filling volume in a dense adsorbing homopolymer melt up to relatively high volume fractions. The second virial coefficient, nanoparticle potential-of-mean force, osmotic compressibilities, and isotropic spinodal demixing boundaries have been determined. The entropic depletion attraction between nanoparticles is dominant for weakly adsorbing polymer, while strongly adsorbing chains induce a bridging attraction. Intermediate interfacial cohesion results in the formation of a steric stabilizing adsorbed polymer layer around each nanoparticle, which can partially damp inter-filler collective order on various length scales and increase order on an averaged length scale. The details of depletion, stabilization, or bridging behavior are shape-dependent and often, but not always, trends are monotonic with increasing filler dimensionality. Distinctive nanoparticle shape-dependent low angle features are predicted for the collective polymer structure factor associated with competing macrophase fluctuations and microphase-like ordering. The influence of nonzero mixture compressibility on the scattering profiles is established.