Effect of chain-penetration on ring shape for mixtures of rings and linear polymers

Coarse-grained molecular dynamics simulations of Kremer–Grest-type bead-spring models were performed on mixtures of ring and linear polymers to investigate the effects of chain-penetration on polymer ring shape. We found that the number of linear chains penetrating through a ring increased with ring size, while penetration was inhibited for smaller rings composed of less than 80 beads. From the eigenvalue analyses of the gyration tensor of each ring, the ring shape was characterized by asphericity and prolateness. The number of chains penetrating through a ring (nP) was determined from the Gauss linking numbers of all ring and linear chain pairs. The radius of gyration of the rings were dependent on the nP value, suggesting that the linear chains expanded the ring upon penetration. The obtained results provide important insights in ring-linear blends for theoretical research as well as simulations and experiments especially for rheological measurements.