Mapping of atomistic simulation data for the dynamics of entangled polymers onto the tube model: Calculation of the segmental survival probability function for mono- and bi- disperse melts and comparison with modern tube models

Abstract

Topological constraints, arising from chain and chain uncrossability, are of primary importance for the high molecular weight polymeric liquids which are typically employed in practical polymer processing. However, it is tremendously difficult to consider these topological interactions in a rigorous fashion due to the huge number of degrees of freedom associated with polymer configurations. The problem was considerably simplified by the notion of a confining tube, introduced for the very first time by Edwards and de Gennes, [1] through which a chain can execute a reptation-like motion, as small-length scale fluctuations, irrelevant to the large-scale rheological properties of the polymer, may be neglected. A few years later, Doi and Edwards [2] (DE) developed a more elaborate version of the reptation theory which, since then, has attracted considerable attention and development.