Nanoscale Structural Heterogeneity in Inter- and Intrachain Entangled Polymer Networks Probed Using the Random Barrier Model

The previously reported Brownian yet non-Gaussian diffusion of small-molecule probes in solvent-swollen poly(methyl methacrylate) films composed of inter- and intrachain entangled networks is further examined to gain in-depth insight into chain-conformation-dependent structural heterogeneity in polymer networks. The characteristic length scale obtained from the non-Gaussian tails of van Hove distributions is shown to spread as the square root of the lag time regardless of the film and its swelling degree, which indicates that anomalous long-distance probe hopping in both networks is primarily driven by the heterogeneity of the network structure. The random barrier model is used to examine the probability distribution of retention time between consecutive hopping events as a function of threshold displacement, and an appropriately chosen threshold displacement identifies the length scale of the region wherein probe motion can be Brownian within structurally heterogeneous entangled networks. The average energy of barriers with structural origins in local regions with excessive chain density has an insignificant network dependence; however, the barrier density in the intrachain entangled network exceeds that in the interchain one because of the greater structural heterogeneity of the former, limiting the size of the region of Brownian motion.