Relations Between Dynamic Localization and Solute Diffusion in Polymers

Various public health concerns can arise from the unintended leaching of additives and impurities from polymeric medical devices or food packaging, which is directly related to each solute's diffusivity D. Both experimental and simulation methods can be used to quantify D, but slow diffusion at physiologic temperature in glassy polymers can render these approaches impractical. Here, we investigate a simulation approach with the potential to more rapidly calculate D. Specifically, we examine links between dynamic localization, characterized by the Debye-Waller factor, ⟨u²⟩, and D in a variety of polymer/solute systems using atomistic molecular dynamics (MD) simulations. Using short, high-temperature MD simulations to estimate D at physiologic temperature, we find that the relation ln D ∝ 1/⟨u²⟩ quantitatively predicts D for small solutes and produces an upper-bound estimate of D for larger solutes. Upper-bound estimates are useful in certain contexts, and we compare our results with another approach for determining upper bounds, the Piringer model, to show where each method may be useful. Then, we examine a modified relation where the Debye-Waller factor is rescaled by the mode coupling temperature T_c, which can produce better estimates of D if T_c is carefully chosen. Last, we compare our approach with several other models that relate temperature or localized dynamics with diffusivity. Although each of these approaches can be used to model D across wide temperature ranges using one or more adjustable parameters, none of them are truly predictive in glassy polymers. Further developments are needed to predict the optimal values of the adjustable parameters a priori.