Polymer-mode-coupling theory of the slow dynamics of entangled macromolecular fluids

Abstract

A microscopic statistical dynamical theory of the slow dynamics of entangled macromolecular fluids has been formulated at the level of effective generalized Langevin equations- of-motion of a tagged polymer. A novel macromolecular version of mode-coupling theory is employed to approximately capture the cooperative motions of entangled polymers induced by the long range, self-similiar interchain correlations. Polymer integral equation methods are used to determine the required equilibrium structural input. Entanglements arise due to time and space correlations of the excluded volume forces exerted by the surrounding matrix on a tagged macromolecule. A spatially resolved description of entanglement constraint amplitudes relates the fluctuating forces to fluid structure. Constraint relaxation proceeds via three parallel processes: probe center-of-mass translation and shape fluctuations, and collective matrix relaxation. Asymptotic scaling law predictions for the molecular weight and concentration dependences of transport coefficients and relaxation times of chain polymer solutions and melts are in qualitative agreement with the phenomenological reptation theory. Predictions for finite frequency properties such as anomalous diffusion, and shear stress and dielectric relaxation, are derived. Enhanced, power law dissipation for properties controlled by conformational relaxation is predicted, with the corresponding frequency scaling exponents in good agreement with experiments but differing from reptation behavior. For experimentally accessible chain lengths strong finite size corrections for the transport coefficients arise due to entanglement constraint porosity and constraint release. Successful quantitative applications to many experimental data sets suggest the theory provides a unified microscopic understanding of the non-asymptotic scaling laws observed for the viscosity, dielectric relaxation time, and solution self and tracer diffusion constants. Generalization to fractal macromolecular architectures allows semi-quantitative treatment of ring and spherical microgel melts, and tracer diffusion in gels. A theory for the influence of concentration fluctuations in entangled polymer blends and diblock copolymers has also been developed. Self-diffusion in blends is quantitatively suppressed due to dynamical constraints associated with domain formation. Much stronger suppression of diffusion and chain relaxation is predicted near and well below the order-disorder transition of diblock copolymer melts due to microdomain formation. New dynamical scaling laws are predicted, and quantitative agreement of the theory with recent measurements on polyolefin diblocks is demonstrated. Limitations of the theory, open problems, and possible future directions are discussed.