Mode-coupling theory of macromolecular liquids

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. Modecoupling 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.