Models of Directed Self-Avoiding Walks and Statistics of Rigid Polymer Molecules

Abstract

Many physical properties of polymer systems are determined by the conformational properties of macromolecules, i.e., the set of their possible conformations and their conformational mobility. The progress achieved in the description of the statistics of the conformations of linear polymer chains is largely due to the fact that the conformational properties of polymer chains as a whole depend very little on the characteristic features of their chemical structure, i.e., they reflect certain general, fundamental properties of polymers. In addition, the fact that the number N of links in a polymer chain is large makes it possible to pass, when necessary, to the asymptotic limit (N → ∞). The simplest model that makes it possible to take into account the conformational properties of long linear molecules is the model of an ideal (phantom) flexible polymer chain consisting of freely-jointed immaterial links 1–3. Even though this model is extreme idealized it is extremely helpful for understanding many features of polymer systems. Furthermore, according to Flory theorem, the model of ideal (phantom) flexible polymer chain describes the properties of real polymer chains in dilute solutions in θ-solvents and polymer melts, where the interaction of the units of one chain is compensated by their interaction with the environment chains 1, 2 .