Turkish Journal of Physics

A Microscopic Model for Diffusion of a Polymer Chain in the Entangled Regime




In the entangled regime the reptation concept [1,2] is the most successful in describing the dynamical behavior of a single chain. Using scaling concepts some quantities such as translational diffussion coefficient for the polymer center of mass D_{tr}, and renewal time {\tau} [3] have been calculated in the reptation model. This model is used for representing the low-frequency motions of a polymer molecule in a fluid of entangled chains, neglecting rapid relaxation processes that are attributed to local conformal transitions of backbone. Helfand and collabrators have studied the kinetics of conformational transitions in chain molecules, and they find that single-bond rotations followed by the compensating rearrangement of neigboring units are predominantly responsible for local motions [4]. Such models have also been considered by Erman and co-workers [5]. The purpose of this study to understand reptation at a microscopic level. We consedir rapid relaxation processes, that are singlet- or double -bond rotations; motion along the contour of the chain is due to displacments caused by rearangements of the neighboring units. We recover the usual scaling behavior of the diffusion coefficients and relaxation times with the chain mass. Moreover, the effective activation energy that is found from the local jump model for translational motion of the chain center of mass compares favorably with experiment and is independent of the molecular weight for large enough chains [6]. We are also able to account for the apparent temperature of this "activation energy".

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