Computer simulation study of the structure and dynamics of ring polymers

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Abstract
We study the equilibrium structure and dynamics of unconcatenated, unknotted polymer rings in the melt. In agreement with earlier studies we find that rings in the melt are more compact than linear chains. In addition, we show that the “correlation hole” in the equilibrium correlation functions is deeper and wider for rings than for linear chains. This suggests that there is less interpenetration in the melt of rings compared to the melt of linear chains. We also find that rings diffuse faster than linear chains. For smaller rings this result agrees with the earlier work of Müller, Wittmer, and Cates [Phys. Rev. E 53, 5063 (1996)]. The main result of this study is that faster ring diffusion persists up to ring size at least ten times greater than the entanglement crossover of linear chains. Furthermore, we show that, for all ring sizes studied, the dependence of the single-chain relaxation time on ring size is weaker than for linear chains. Finally, we find that both faster diffusion and faster relaxation can be rationalized by the smaller size of rings: The dependence of self-diffusion coefficient and relaxation time on radius of gyration of rings and linear chains is remarkably similar.