Mesoscopic theory of the viscoelasticity of polymers

We have advanced our previous static theory of polymer entanglement involving an extended Cahn-Hilliard functional, to include time-dependent dynamics. We go beyond the Gaussian approximation, to the one-loop level, to compute the frequency dependent storage and loss moduli of the system. The four parameters in our theory are obtained by fitting to available experimental data on polystyrene melts of various chain lengths. This provides a physical representation of the parameters in terms of the chain length of the system. It is shown that the parameters chosen describe the crossover from an unentangled to an entangled state. The crossover is characterized by a dramatic increase in a time scale appearing in the theory, analogous to critical slowing down in phase transition theory. This result should stimulate more detailed experiments in this regime to test this concept.