Dynamics of polymer solutions and melts. Reptation predictions and scaling of relaxation times

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Abstract
The bond fluctuation model on the simple cubic lattice is studied by Monte Carlo simulations on a multitransputer array, for polymer volume fractions φ in the range 0.025≤φ≤0.500 and chain lengths N in the range 20≤N≤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 (τ∼N 1+2ν, ν being the exponent describing the radius R of the chains, R∼N ν ) to reptation, τ∼N 3. Since the excluded volume screening length is found to be smaller than the tube diameter by a factor of about 3, the rescaled times Wτ/N 1+2ν decrease first as a function of the scaled chain length Ñ∼Nφ1/(3ν−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.