DYNAMICS OF POLYMER-SOLUTIONS AND MELTS - REPTATION PREDICTIONS AND SCALING OF RELAXATION-TIMES

The bond fluctuation model on the simple cubic lattice is studied by Monte Carlo simulations on a multitransputer array, for polymer volume fractions-phi in the range 0.025 less-than-or-equal-to phi less-than-or-equal-to 0.500 and chain lengths N in the range 20 less-than-or-equal-to N less-than-or-equal-to 200. Extensive data are presented on the dynamics of monomer displacements, center-of-gravity displacements, and relaxation times. This study is complementary to previous work, in which the crossover scaling properties of the chain linear dimensions, structure factor, and self-diffusion constant were tested for the same athermal model. The simulation technique takes both excluded volume interactions and entanglement constraints into account, but ignores hydrodynamic forces. Our results describe the crossover from Rouse behavior of swollen chains (tau approximately N1 + 2v, v being the exponent describing the radius R of the chains, R approximately N(v)) to reptation, tau approximately N3. Since the excluded volume screening length is found to be smaller than the tube diameter by a factor of about 3, the rescaled times W-tau/N1 + 2v decrease first as a function of the scaled chain length approximately N approximately N-phi-1/(3v - 1), before they increase due to the onset of reptation. Additional evidence for reptative behavior is found by identifying the several successive crossovers in the time-dependent displacements predicted by de Gennes.