Dynamics of Dense Polymer Systems Dynamic Monte Carlo Simulation Results and Analytic Theory
Dynamic Monte Carlo simulations of long chains confined to cubic and tetrahedral systems as a function of both volume fraction and chain length were employed to investigate the dynamics of entangled polymer melts. It is shown for a range of chain lengths there is a crossover from a much weaker degree of polymerization (n) dependence of the self-diffusion coefficient to a much stronger one, consistent with D ∼ n −2. Similarly, systems have been identified having a terminal relaxation time that varies as n3.4. Since such scaling with molecular weight signals the onset of highly constrained dynamics, an analysis of the character of chain contour motion was performed. No evidence whatsoever was found for the existence of a well defined tube required by the reptation model. Lateral motions of the chain contour are remarkably large, and the motion appears to be essentially isotropic in the local coordinates. Results from this simulation indicate that the motion of a polymer chain is essentially Rouse-like, albeit, slowed down. Motivated by the simulation results, an analytic theory for the self-diffusion coefficient and the viscoelastic properties have been derived which is in qualitative agreement with both experimental data and the simulations.
KeywordsDynamic Entanglement Diamond Lattice Friction Constant Entangle Polymer Rouse Model
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