Dynamical Theory of Segmental Relaxation and Emergent Elasticity in Supercooled Polymer Melts

We generalize the force-level Elastically Collective Nonlinear Langevin Equation theory of supercooled molecular liquid dynamics to polymer melts based on mapping chains to disconnected and noninterpenetrating Kuhn-sized spheres. This allows first-principles, no adjustable parameter calculations to be performed for the temperature-dependent mean segmental relaxation time of chemically diverse van der Waals polymers over a wide range of molecular weights. Despite the simplicity of the mapping, the theory does a good job of a priori predicting the glass transition temperature (T_g), the dynamic fragility, and full temperature dependence of the α-relaxation time for some high molecular weight polymers and the chain length dependence of T_g as the consequence of the molecular weight dependence of backbone stiffness. The minimalist model does not capture the unusually low and high fragilities of certain long chain polymers which are not typical of van der Waals molecular liquids. This seems likely due to the simple coarse graining adopted which ignores longer range chain connectivity and nonuniversal factors on the sub-Kuhn length scale. Elasticity, not of an entropic single chain origin, emerges in deeply supercooled polymer liquids due to transient segmental localization and is studied at the microscopic stress-tensor level. Calculations of the frequency-dependent dynamic storage modulus close to T_g appear to be qualitatively consistent with recent measurements.