Statistical mechanical theory of equilibrium structure and miscibility of polymer nanocomposites: effects of polymer chemical heterogeneity and architecture, and nanoparticle surface corrugation and softness

Motivated by the persistent interest in different nanoparticles added to various polymer matrices, the Polymer Reference Interaction Site Model (PRISM) theory is extended and applied to study the thermodynamics, statistical structure, and miscibility of diverse polymer nanocomposites (PNCs). Under chemistry-matched conditions and in the absence of interfacial attractions between a spherically smooth nanoparticle and the matrix fluid, the polymer-induced depletion attraction is dominant and induces entropic phase separation. The depletion attraction can be potentially reduced by modifying the nanoparticle surface topography as recently observed in experiments. Two types of surface-modified nanoparticles have been considered in this thesis – (1) spheres with ordered roughness on the surface and (2) soft polymeric nanoparticles with surface fluctuations and fuzziness. Monte Carlo integration and other computational techniques have been developed to compute the effective interactions between such particles. The morphologically diverse particles introduce additional length scales, making the physics non-monotonic, subtle, and rich. The common advantage with using either of the particles is reduced contact aggregation and enhanced miscibility. Optimal surface corrugation and/or particle softness allow monomer penetration resulting in favourable (entropic) mixing. However, high enough degree of corrugation/softness can also result in destabilization by excluding the polymer from its interior. Another route of developing new nanocomposites is by tuning the polymer-particle interfacial chemistry. Prior work has established three states of spatial organization, namely depletion, steric stabilization and bridging, depending upon the effective interfacial attraction strengths. Introducing polymer chemical heterogeneity via the use of AB copolymers offers additional control over the equilibrium structure. Specifically, two types of copolymers are considered – (1) random copolymers (RCP) of disordered sequence and (2) ordered, alternating multiblock copolymers (MBCP). Quantum chemical calculations are combined with the polymer liquid state theory to predict structure and miscibility. The chain connectivity, monomer sequence, copolymer composition and differential wettability results in unique frustration in the system leading to novel states of organization of the polymer around the nanoparticles. In the context of strongly attractive nanoscopic fullerenes, this results in improved miscibility relative to the corresponding homopolymers. For some of the systems studied, maximum dispersion is predicted at an intermediate copolymer composition due to packing correlations and differential wetting effects with favourable comparison to experiments