Multi-ring configurations and penetration of linear chains into rings on bonded ring systems and polycatenanes in linear chain matrices

Ring-linear blends composed of complexes bearing multiple rings are promising candidates for soft devices, and understanding the penetration of linear chains into rings is essential for enhancing their mechanical properties. Coarse-grained molecular dynamics simulations of ring-linear blends composed of bonded rings or polycatenanes bearing two or three rings were performed for revealing the conformations in blends. To investigate the relationship between the conformations of ring polymers and penetration of linear chains, we considered linear-rich systems with f_ring = 0.05 and 0.1, where f_ring is the fraction of ring complex. The number of linear chains penetrating rings (n_P) was estimated from the Gauss linking number for all the pairs of ring polymers and linear chains. Dependence of penetration on the ring size was determined from the probability distributions of n_P. Average n_P (n_P) of the systems with polycatenanes was slightly higher than those of the systems with bonded rings. For f_ring = 0.1, n_P of the single ring was 3.41 when number of beads per a ring was N_ring = 160. n_P of the bonded two-ring system and poly-[2]-catenane with N_ring = 80 was 2.60 and 2.87, respectively, while n_P of the bonded three-ring system and poly-[3]-catenane with N_ring = 80 was 3.63 and 3.87, respectively, which were slightly higher than that of the single ring with N_ring = 160. Since the ring complexes had multiple chains penetrating even for low N_ring, mechanical properties of the crosslinked ring-linear blend were expected to be controlled by the ring complexes instead of the single ring.