Relating dynamic free volume to cooperative relaxation in a glass-forming polymer composite

There are a variety of complementary descriptions of the temperature dependence of the structural relaxation time τ in glass-forming materials, which we interpret positively as suggesting an underlying unified description. We examine the inter-relation between the string model, an outgrowth of the Adam and Gibbs approach that emphasizes collective particle exchange motion, and the localization model, which emphasizes the volume explored by particles in their caged states, a kind of dynamic "free volume." Each model of liquid dynamics is described by a limited set of parameters that must be interrelated if both descriptions simultaneously describe the relaxation behavior. We pursue the consequences of this idea by performing coarse-grained molecular simulations of polymer melts with additives of variable size and interaction strength with the polymer matrix, thereby significantly altering the relaxation of the composite material. Both the string and localization models describe our relaxation time data well, and a comparison of the model parameters allows us to relate the local caging scale ⟨u²⟩ (the Debye-Waller parameter) to the entropy of activation for molecular rearrangements in the string model, thereby developing a bridge between these seemingly disparate approaches to liquid dynamics.