Statistical mechanical theory of structure and miscibility of polymer nanocomposites: Effects of density, filler shape, and chemical heterogeneity

Motivated by increasing interest in various types of nanoparticles or fillers added to polymers to enhance the material properties, the Polymer Reference Site Interaction Model (PRISM) theory is applied to study the structure and miscibility of polymer nanocomposites (PNCs). Spherical fillers are studied in homopolymers of varying density and interfacial interaction strengths, with specific favorable comparisons to experimental scattering results. Also discussed briefly are copolymers composed of two types of monomer which interact differently with the filler. The polymer induced depletion attraction is dominant and causes phase separation if interfacial attractions are weak. Complete miscibility can be achieved at moderate interfacial attraction strengths, due to a sterically stabilizing bound polymer layer. The bound layer remains with a strong interfacial attraction, but phase separation is induced by polymer bridging between nanoparticles. For copolymers, the bridging attraction is strongly affected by chemistry and monomer spatial arrangement (random versus alternating). The effect of nanoparticle dimensionality is explored by comparing rod, disk, and cube shaped fillers. Nanoparticle interactions on several length scales are relevant in the depletion regime. The bound polymer layer present in the miscible and bridging regimes damps out order on these length scales in favor of increased order on an averaged filler length scale. The effect of nanoparticle chemical heterogeneity was briefly explored by investigation of fillers composed of two tangentially connected spheres with different polymer interfacial attraction strengths or with an added inter-nanoparticle site-site attraction. Such heterogeneous diatomic fillers exhibited additional structural features and particle clustering compared to analogous homogeneous nanoparticles. Motivated by recent experimental interest in carbon nanotubes, thin rod particles were further investigated. Adding a strong rod-rod attraction relevant to nanotubes predictably leads to a strongly attractive potential of mean force at contact, especially when there is little bound polymer. In the stabilized and bridging regimes, miscibility can persist until a stronger rod-rod attraction if it is of shorter spatial range than the polymer-rod interfacial attraction. An initial investigation of these attractive rods in a random copolymer revealed that replacing the homopolymer with copolymer can significantly reduce miscibility.