Microscopic Theory of Concentration Scaling in Entangled Polymer Solutions and Melts

The microscopic polymer mode coupling theory of entangled solution and melt dynamics is combined with equilibrium integral equation methods and a theory for the Rouse/entangled crossover to make predictions for the concentration and statistical segment length dependences of transport properties. Both Θ and good solvents are treated, and analytic scaling laws are derived for the crossover chain lengths, plateau modulus, diffusion constant, terminal relaxation time, and shear viscosity. The physical origin of the concentration and segment length scaling behavior is a direct connection between dynamics and equilibrium conformational and intermolecular correlations. The predictions appear to be consistent with most, but not all, of the existing data in solutions and melts. Comparisons with phenomenological reptation and entanglement scaling ideas, and a nonreptation correlated cluster dynamics approach, are made. Similarities and differences between the various theories are identified.