A model of relaxation in supercooled polymer melts

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Abstract
We present a dynamical mean-field model for molecular motions in a supercooled polymer melt. A macromolecule is represented by a harmonic chain undergoing Brownian motion whose bead mobilities fluctuate between zero and a finite value. These fluctuations mimic the dynamic obstacles formed by the chain segments surrounding a given segment, whose effects become more pronounced as T decreases. The rate of these mobility fluctuations is determined self-consistently by equating it to the asymptotic long-time relaxation rate of the shortest-wavelength Rouse mode. The resulting fluctuating rate vanishes as c, the equilibrium fraction of mobile beads, approaches a threshold value c * . As c→c * , relaxation times become arbitrarily large, permitting the modeling of fluids as T approaches T g . Calculations of autocorrelation functions of Rouse mode coordinates and of segmental mean-squared displacements are presented and compared to results from recent simulations of melts at low temperatures. The deviations from the Rouse model observed in the simulations are features of this theory.