Mode-coupling theory of entangled polymer fluids

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Abstract
A microscopic mode-coupling theory of entangled linear chain polymer melts and solutions has been developed. Coupled generalized Langevin equations of motion for the segments of a tagged polymer are derived and two new fluctuating cage forces emerge associated with intermolecular excluded volume and chain connectivity. In the long chain limit the theory analytically predicts the emergence of a plateau shear modulus, anomalous diffusion and relaxation, self-similiar viscoelastic repsonse, and molecular weight and polymer density dependent renormalization of transport coefficients. These predictions are in general accord with experiments. Crossover from bare Rouse dynamics to entangled behavior, and the significant corrections due to finite chain lengths, are both addressed. Analogies with critical slowing down and the ideal dynamical glass transition, and connections with the phenomenological reptation/tube approach, are discussed.