Phenomenological theory of the dynamics of polymer melts. II. Viscoelastic properties
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A phenomenological theory of the nonmechanical and viscoelastic properties of polymer melts is developed. Consistent with computer simulation results [A. Kolinski, J. Skolnick, and R. Yaris, J. Chem. Phys. 86, 1567, 7164, 7174 (1987)], that fail to find evidence for reptation as the dominant mechanism of long distance motion in a melt, we assume that the long-time behavior of a chain is that of a Rouse-like chain having a number of slow moving points, each with a friction constant proportional to the degree of polymerization n. Coupled with the assumption of rubber like behavior at short times made previously by Doi and Edwards [J. Chem. Soc., Faraday Trans. 2 74, 1802 (1978)], the theory predicts that over a broad molecular weight range the shear viscosity scales with n as approximately the 3.4 power of the molecular weight, and that ~n³ in the infinite molecular weight limit. Furthermore, the theory rationalizes the origin of the different crossover molecular weights for the shear viscosity and the self-diffusion coefficient, D. It also accounts for the origin of the intermediate time coupling of the center-of-mass motion into the internal coordinates and for the time dependence of the single bead positional autocorrelation functions seen in previous simulations. Proceeding by analogy to Graessley [J. Poly. Sci. Poly. Phys. Ed. 18, 27 (1980)], in the large molecular weight limit, phenomenological expressions for D and are derived and comparison is made with experiment.