Evaluation of diffusion and dethreading in blends of ring and linear polymers

Blends of linear and ring polymers can have slower dynamics and higher viscosities than the pure individual components. This is due to the threading of ring polymers by linear polymers, which introduces topological constraints that hinder chain diffusion. We simulate blends of linear and ring polymers for long time scales to study the relaxation of these topological constraints. We find that the diffusion time of a ring polymer scales like N_L^3.4N_R² in ring-linear blends. Here N_L and N_R represent the length of the linear polymer and ring polymer, respectively. In contrast, the diffusion time of a ring in a pure ring melt scales like N_R^2.8. The scaling of ring diffusion in a blend can be understood by considering the relaxation of thread constraints on the ring. Ring-linear threadings are characterized using the Gauss linking integral, which provides a quantitative measure of the degree of entanglement and can be evaluated quickly allowing for analysis of threading dynamics.