Elastic properties of polycatenane chains and ribbons

Single-chain elasticity is of fundamental importance in polymer physics, as it underlies many of the unique properties of polymer systems. Recently, there has been interest in characterizing the elastic properties of catenanes, molecular architectures composed of linked molecular rings. To date most studies have focused on the force-extension behavior of polycatenane and catenane dimers. In this study, we employ Monte Carlo computer simulations to investigate the elastic properties of a collection of catenane chains. In addition to polycatenane, we also examine the properties of catenane ribbons constructed by connecting two or three polycatenane chains together with a variable number of side-link rings. After first characterizing the behavior of free polycatenane chains and catenane ribbons, we examine their mechanical response to both an elongational force and a torque applied to the end rings of the chain. We find that the stretching induced by the force is counterbalanced by increasing the torque, which tends to twist the chains and in so doing reduce the extension length. At low torque, the twist angle of the end rings of the chain varies linearly with torque, and the associated torsional spring constant, characterizing the resistance of the chain to twist with the applied torque, tends to increase with stretching force. Relative to polycatenane, ribbons tend to be more elongated at low force and less elongated at strong force. In addition, increasing the ribbon width dramatically increases the torsional stiffness of the chain. Finally, decreasing the degree of side-linking in ribbons tends to decrease slightly the extension length at moderate force and to increase the torsional stiffness for sufficiently large gaps.