Topology and topological effects play a key role in the conformational and dynamic properties of polymer chains in varying situations. Among others, threading in ring polymers emerges as a unique topological phenomenon due to a combinational effect of polymer entanglement and the circular topology of the rings. In this work, the threading statistics of interlocked ring polymers (also called ncatenanes) in melts were investigated by molecular dynamics simulations of the Kremer-Grest model with the aid of a modified algorithm based on primitive path analysis. We mainly studied the threading statistics of ncatenanes with varying n but fixed chain length of the building blocks (i.e., rings), m = 128, of the chain. We found that the relative capability of the middle rings (along the catenane polymer) to be threaded by other chains is smaller, even though slightly, than that of the edging rings. Furthermore, our simulation results reveal that the probability of threading at the chain level, pthchain(n), in ncatenane melts can be well understood by a mean-field theory, i.e., pthchain(n)=1-1-pthchain(n=1)n. As a key finding of this work, we found that the averaged number of threadings per chain scales with n as Nthchain∼nα, with α ≈ 0.7863. This behavior is deeply rooted in the special packing structure of the interlocked ring polymers in a melt, i.e., segregation of territories, which is further attributed to the catenation topology of the chain.
Cheng et al. (Wed,) studied this question.