Molecular Dynamics Simulations of Ring Shapes on a Ring Fraction in Ring-Linear Polymer Blends

Threading of a linear chain through a ring has been known to have a strong effect on slowing the dynamics of the ring. To enhance the toughness of soft materials using ring-linear polymer blends, it is important to understand the effects of parameters such as the average of the squared radius of gyration (Rg2) of the rings, the number of linear chains penetrating a ring (nP), and the nP dependence of the shape indexes on the ring fraction fring. Using the Kremer-Grest model for flexible chains, we simulated rings of length Nring = 70 and 140 for 0.2 ≤ fring ≤ 0.97. The exponent α for the relation Rg2» fring-α was 0.06 and 0.09 for Nring = 70 and 140, respectively. The increase in α for the increasing Nring was similar to the experimental results for polystyrene reported in the study by Iwamoto et al. (Macromolecules 2018, 51, 1539-1548 and 6836-6847). Rg2»of the rings increases as fring decreases. This increase in the size of the rings results in an increase in the average number of linear chains nP»that penetrate the rings. nP»was also observed to increase with the increasing Nring. In particular, for fring = 0.2 and Nring = 140, multiple linear chains penetrated the ring. We also confirmed that the Kremer-Grest model with the bending potentials proposed by Everaers et al. to map this model to polystyrene shows good agreement with the exponent α found experimentally by Iwamoto et al.