The physics of a ring polymeric melt: from structure to dynamics

Abstract

A ring polymer is one of the novel topological classes in polymer physics. Unlike linear and branched polymers, its two ends are connected to each other, thus two intrinsic constraints, non-knotting and non-concatenation inhere in the ring polymer. Due to very constraints, a ring in a melt adapts a compact globular structure with high fractal dimension. Interestingly, the structure of a ring in a melt resembles chromosomes in eukaryotic nuclei during interphase. Although a chromatin fiber is a polymer with open ends, its structure in a nucleus seems to be not tangled to each other. Therefore, to understand the nature of the chromosome packing, it is instructive to study the physics of a ring in a melt in terms of polymer physics. In this thesis, we first present a theory and molecular dynamics simulation results for the ring polymer melt structure in a bulk phase. Unlike a linear polymer, it is found that the Flory exponent of a ring varies from 1/2 to 1/3 as degree of polymerization increases. Especially for the long rings, it turns out that compact and segregated structures are favored due to the topological constraints. A theoretical study of Flory-type free energy minimization by con- sidering the topological constraints as an effective excluded volume supports the numerical results. We also study structural properties of a ring polymeric melt confined in a film in comparison to a linear counterpart using molecular dynamics simulations. Local structure orderings of ring and linear polymers in the vicinity of the surface are similar to each other because the length scale of surface-monomer excluded volume interaction is smaller than the size of an ideal blob of the ring. In a long length scale, while the Silberberg hypothesis can be used to provide a physical origin of confined linear polymer results, it no longer holds for a ring polymer case. We also present different structural properties of ring and linear polymers in a melt, including the size of polymers, an adsorbed amount, and the coordination number of a polymer, Our observation reveals that a confined ring in a melt adapts highly segregated conformation due to a topological excluded volume repulsion. In addition to the structural studies, we investigate an origin of the slow dynamics of ring polymer melts. Diffusion of long ring polymers in a melt is shown to be much slower than the reorganization of their internal structures. While direct evidence for entanglements has not been observed in the log ring polymers unlike linear polymer melts, threading between the rings is suspected to be the main reason for slowing down of ring polymer diffusion. It is, however, difficult to define the threading configuration between two rings because the rings have no chain end. In this thesis, evidence for threading dynamics of ring polymers is presented by using molecular dynamics simulation and applying a novel analysis method. The simulation results are analyzed in terms of the statistics of persistence and exchange times that have proved useful in studying heterogeneous dynamics of glassy systems. It is found that the threading time of ring polymer melts increases more rapidly with the degree of polymerization than that of linear polymer melts. This indicates that threaded ring polymers cannot diffuse until an unthreading event occurs, which results in the slowing down of ring polymer diffusion. These studies for structures and dynamics of the ring polymer melts provide not only a new perspective to understand the unsolved problem in biological system, but a possibility to utilize new materials with novel viscoelastic prop- erties.