Abstract
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 Kuhnsized
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 (Tg), the dynamic fragility, and full
temperature dependence of the α-relaxation time for some high molecular weight
polymers and the chain length dependence of Tg 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