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

TL;DR

This paper develops a polymer-mode-coupling theory to predict finite-size effects on transport properties of entangled polymer solutions, melts, and gels, highlighting the influence of molecular weight and entanglement parameters.

Contribution

It introduces a microscopic, parameter-dependent framework for understanding finite-size effects in polymer dynamics, extending previous models to include inhomogeneity and shape fluctuations.

Findings

Finite size effects are significant up to N/N_e ≤ 10^3.

Viscosity scales as N^x with x ≥ 3, exceeding asymptotic predictions.

Diffusion constant scales as N^{-y} with y ≥ 2, showing stronger size dependence.

Abstract

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.