Mode-coupling theory of macromolecular liquids

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Abstract
A mode-coupling theory of entangled polymer liquids has been developed and extensively applied to dense melts of long chains. The theory predicts the emergence of a plateau shear modulus due to dynamical correlations induced by chain connectivity and excluded volume interactions. Mode-coupling predictions for the dependence of transport coefficients on degree of polymerization agree with the phenomenological reptation/tube theory. Anomalous early and intermediate time diffusion also occurs due to power-law decay of the fluctuating force memory functions. The mode-coupling renormalizations are found to depend sensitively on spatial and polymer fractal dimensions in analogy with dynamic critical phenomena. An alternative, self-consistent approximation for the memory functions results in the prediction of a nonreptation viscosity scaling law for chains, and an ideal "entanglement-induced" glass transition at very large molecular weights.