Polymer-Mode-Coupling Theory of Finite-Size-Fluctuation Effects in Entangled Solutions, Melts, and Gels. 1. General Formulation and Predictions

The transport coefficients of dense polymeric fluids are approximately calculated from the microscopic intermolecular forces. The following finite molecular weight effects are discussed within the polymer-mode-coupling theory (PMC) and compared to the corresponding reptation/tube ideas: constraint release mechanism, spatial inhomogeneity of the entanglement constraints, and tracer polymer shape fluctuations. The entanglement corrections to the single polymer Rouse dynamics are shown to depend on molecular weight via the ratio N/Ne, where the entanglement degree of polymerization, Ne, can be measured from the plateau shear modulus. Two microscopically defined nonuniversal parameters, an entanglement strength 1/α, and a length scale ratio, δ = ξρ/b, where ξρ and b are the density screening and entanglement length, respectively, are shown to determine the reduction of the entanglement effects relative to the reptation-like asymptotes of PMC theory. Large finite size effects are predicted for reduced degrees...