Polymer-Mode-Coupling Theory of Finite-Size-Fluctuation Effects in Entangled Solutions, Melts and Gels. I. 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 non-universal 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\le10^3. Effective power law variations for intermediate N/N_e of the viscosity, eta\sim N^x, and the diffusion constant, D\sim N^{-y}, can be explained with exponents significantly exceeding the asymptotic, reptation-like values, x\ge 3 and y\ge2, respectively. Extensions of the theory to treat tracer dielectric relaxation, and polymer transport in gels and other amorphous systems, are also presented.Comment: Latex, figures and styles files included; Macromolecules, in press (1997

Polymer-Mode-Coupling Theory of Finite-Size-Fluctuation Effects in Entangled Solutions, Melts and Gels. II. Comparison with Experiment

The predictions of the polymer mode coupling theory for the finite size corrections to the transport coefficients of entangled polymeric systems are tested in comparisons with various experimental data. It is found that quantitative descriptions of the viscosities, eta, dielectric relaxation time, tau_e, and diffusion coefficients, D, of polymer melts can be achieved with two microscopic structural fit parameters whose values are in the range expected from independent theoretical or experimental information. An explanation for the (apparent) power law behaviors of eta, taue, and D in (chemically distinct) melts for intermediate molecular weights as arising from finite size corrections, mainly the self-consistent constraint release mechanism, is given. The variation of tracer dielectric relaxation times from Rouse to reptation-like behavior upon changes of the matrix molecular weight is analyzed. Self and tracer diffusion constants of entangled polymer solutions can be explained by the theory as well, if one further parameter of the theory is adjusted. The anomalous scaling of the tracer diffusion coefficients in semidilute and concentrated polystyrene solutions, D\sim N^{-2.5}, is predicted to arise due to the spatial correlations of the entanglement constraints, termed ``constraint porosity''. Extensions of the theory to polymer tracer diffusion through polyvinylmethylether and polyacrylamide gels provide an explanation of the observation of anomalously high molecular weight scaling exponents in a range where the size of the tracer, R_g, already considerably exceeds the gel pore size, xi_g.Comment: Latex, figures and styles files included; Macromolecules, in press (1997