Dimensions of catenated ring polymers in dilute solution studied by Monte-Carlo simulation.

Abstract

Interaction between two simple ring chains catenated in a molecule was estimated by a Metropolis Monte Carlo simulation, and the result was compared with a model. We employed catenated ring chains in this study; they were composed of two simple ring chains, and the topology was kept as . The temperature dependence of the distance between two ring chains in a molecule was discussed using Flory's scaling exponent, ν, in R g ∝ N ν , where R g is the radius of gyration of a simple ring chain catenated in a molecule. In the simulation, the topology of the component rings and their links were kept because chain crossing was prohibited. The excluded volume of chains was screened by the attractive force between polymer segments, and the strength of the attractive force depends on temperature, T. At the θ temperature for trivial ring polymers, where the condition ν = 1/2 holds, their trajectories can be described statistically as a closed-random walk, i.e., a closed-phantom chain model. The temperature at which interaction between trivial ring polymers, i.e., inter-molecular interaction, is repulsive; trivial ring polymer molecules show the excluded volume generated with keeping their own topology, 01. A catenated molecule is composed of two simple rings, and so forth a component ring can be affected by the existence of the counterpart rings. Under that temperature, the mean-square distance between two rings in a catenated molecule, ⟨L 2⟩, was obtained and compared with that of the simple model composed of two circles in three-dimensions, where interaction between circles is set as zero. It has been found that the simulated ⟨L 2⟩ values were constantly larger than those of the model owing to the excluded volume of rings in a molecule.