Effects of excluded volume and correlated disorder on the shapes of self-avoiding walks

Dr Christian von Ferber (Coventry University, UK)


We apply the field theoretical renormalization group to analyze universal shape properties of long polymer chains modelled as self-avoiding walks in a correlated environment. Many analytical calculations focus on the scaling exponents that govern conformational properties of polymer macromolecules. Here, we consider observables that are related to universal ratios. These are universal in the sense that given a polymer in a good solvent, they are independent of the chemical structure of the macromolecules and the details of the solvent. In particular we focus on ratios characterising the deviation from the spherical shape as well as the relation between the end-end distance and the gyration radius of the polymer. These questions have a long history going back to Kuhn's work on random walks 1934 with the aim to understand the viscosity of polymer solutions. Here, we address the question of the influence of excluded volume and correlated disorder on the shapes acquired by the long flexible macromolecules. This question may be of relevance for the understanding of the behavior of macromolecules in colloidal solutions, near microporous membranes, or even in a biological environment. To this end, we consider a model of polymers in D dimensions in an environment with structural obstacles, characterized by a pair correlation function h(r), that decays with distance r according to a power law: h(r) ~ 1/r^a . We apply the field-theoretical renormalization group approach and expand in both (4-D) and (4-a) to estimate ratios that characterise the end-end distance, the gyration radius and rotationally invariant measures of the deviation from the spherical shape. [V Blavatska, C von Ferber, and Yu. Holovatch; Effects of disorder on the shapes of macromolecules, Condensed Matter Physics (2011)].