Mode-mode-coupling theory of the dynamics of polymeric liquids

A first principles, statistical mechanical theory of the dynamics of polymer liquids has been developed using the generalized Langevin equation and molecular-scale mode-mode-coupling methods. The essential physics of chain uncrossability and connectivity is contained in a time-dependent dynamical friction matrix, which quantitatively described fluctuating force correlations and many-body caging. For very long chain fluids, the predicted molecular weight dependences of the transport coefficients agree qualitatively with the reptation/tube theory. However, a more general physical interpretation appears to exist, and a natural analogy with critical slowing down is suggested. Polymer shape fluctuation effects are also included in a microscopic fashion, and when dominant generate both a stretched exponential terminal relaxation and a 3.55 exponent for the viscosity-chain-length scaling law. Anomalous segmental and center-of-mass diffusion at early times are also studied.