Nanoscale Structural\nHeterogeneity in Inter- and Intrachain\nEntangled Polymer Networks Probed Using the Random Barrier Model

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