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/N-e, where the entanglement degree of polymerization, N-e, can be measured from the plateau shear modulus. Two microscopically defined nonuniversal parameters, an entanglement strength 1/alpha, and a length scale ratio, delta = xi(rho)/b, where xi(rho) 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 of polymerization up to N/N-e less than or equal to 10(3). Effective power law variations for intermediate N/N-e of the viscosity, eta similar to N-x, and the diffusion constant, D similar to N-gamma, can be explained with exponents significantly exceeding the asymptotic values, x greater than or equal to 3 and y greater than or equal to 2, respectively. Extensions of the theory to treat tracer dielectric relaxation, and polymer transport in gels and other amorphous systems, are also presented.