Anisotropy dependent Relaxation of Topologically-modified polymers

Abstract

This thesis is an investigation of relaxation dynamics of topologically modified polymers. We work with modified ring polymer systems whose importance have been shown in pre vious work where these topologies are able to explain the spatiotemporal organization of the chromosome inside the E.Coli bacterial cell. The effect of these polymer topologies on the emergent properties and dynamics of the chromosomes is yet unknown. In order to understand that, one first needs to understand the dynamical properties of the individual topologically modified polymers and how cross-links affect these properties. This demands a more robust and systematic study of the dynamics of these complex systems. Herein, we will also present the shortcomings of the End-to-End vectors method to study the relaxation time of the polymers because of the ambiguity that arises while choosing vectors in more complicated topologies. Then I will present two global methods to study the dynamics. Importantly, these global methods - the correlation in fluctuations of radius of gyration and time autocorrelation of eigenvectors of gyration tensor - does not depend on the intricate structural/topological details of the polymer topology. And hence, provides us a mechanism to study any form of complex topology by overcoming the problems with end-to-end vector method. Later in the thesis we also explain the properties of the relaxation dynamics for different ratios of Dumbbell architecture (two loops formed by adding a crosslink between two monomers of ring polymer) and Arc1 2 architectures (three loops formed via adding two additional cross links in ring polymer) by correlating it with the Anisotropy or the aspheric ity of the polymer. This also lead us to a scaling relation between the relaxation time and Anisotropy of the polymer.