Nonuniversal Coupling of Cage Scale Hopping and Collective Elastic Distortion as the Origin of Dynamic Fragility Diversity in Glass-Forming Polymer Liquids

Abstract

We formulate a theoretical mechanism for the physical origin of the massive dynamic fragility range observed in long chain glass-forming polymer melts within the context of the force-level elastically collective nonlinear Langevin equation theory of coupled local–nonlocal activated segmental relaxation. The hypothesis involves how the cage scale barrier hopping process on the three Kuhn segment length scale is quantitatively coupled to the longer range collective elastic distortion required to sterically allow large-amplitude events to occur. The key nonuniversal aspect is proposed to be an effective microscopic jump distance, a dynamical quantity associated with the activation barrier, which is influenced by nanometer-scale conformational transition physics and monomer chemistry. By introducing a single numerical factor that breaks the universality of the jump distance in our mapping of polymers to liquids of disconnected Kuhn-sized hard spheres, one can account rather well, and simultaneously, for the v...