Theory of segmental relaxation and shear elasticity in polymer nanocomposites

We recently studied dynamic elasticity in melt polymer nanocomposites (PNCs) using naïve mode coupling theory with structural inputs obtained from PRISM theory (J. Chem. Phys. 153, 114901 (2020)). The glassy shear modulus can be either softened or reinforced by nanoparticle (NP) addition, and connections with the interfacial cohesive energy, a specific measure of free volume, and entropic depletion attractions were established. The same PNC model is now adopted to formulate a theory for the activated segmental relaxation time based on a generalization of the microscopic Elastically Collective Nonlinear Langevin Equation (ECNLE) approach to mixtures that self-consistently captures cooperative activated motion of segments and nanoparticles. A rich dynamical behavior is predicted as a function of particle-segment size ratio, interfacial attraction strength, and NP loading, with both plasticization and anti-plasticization possible. The complexity reflects changes of PNC microstructure with increasing polymer-NP attraction from NP contact clustering, to steric stabilization via adsorbed polymer layers, to polymer-mediated bridging. The key physics relates to the competition between the total PNC density fluctuation amplitude (free volume) and interfacial physical bonding.