Structures of Two-dimensional Ring Polymer Solutions using Bond Fluctuation Model

This study attempts to reveal structures of two-dimensional ring polymer solutions in various polymer concentrations ranging from dilute to concentrated regime. Polymer sizes, single molecule structure factors, bond correlation functions and monomer density distribution functions from center of mass are given in order to clarify the polymer structures. Our study shows that a ring in dilute solution maintain pseudo-circular structure with self-avoiding walk (SAW) statistics, and it seems to be composed of two connecting SAW linear chains. In semidilute solutions, ring polymers are not entangled with each other and adopt collapsed configurations. Such assumption of collapsed structures in the semidilute regime gives an overlap concentration of ${\varphi}^*{\sim}N^{-1/2}$ where N is degree of polymerization. By normalizing the polymer concentration by these overlap concentration, we find universal behaviors of polymer sizes and structure factors regardless of N.