Modeling the solid-like behavior of entangled polymer nanocomposites at low frequency regimes

A theory for the linear viscoelastic behavior of entangled polymeric liquids reinforced with non-aggregated colloidal nanoparticles is presented. Composites with low filler concentration and strong polymer-particle interaction are considered. A fraction of entangled chains is assumed to be reversibly adsorbed on the surface of fillers, due to the affinity between the polymer molecules in the matrix and dispersed filler particles. The relaxation of the system is analyzed by the combination of stress relaxation functions for free and adsorbed polymer chains. It is demonstrated that the emergence of solid-like behavior at low frequency regimes, is due to the significant slow down in relaxation of adsorbed chains. Fitting the model predictions with relevant experimental data indicates that while the effect of constraint release should be considered to obtain a reasonable estimation of neat polymer behavior, the linear combination of stress relaxation functions of free and adsorbed chains (i.e., no thermal constraint release) leads to a better agreement with experimental data of filled systems.