Sliding dynamics of ring on a fixed rod-like block copolymer in rotaxane: Molecular dynamics simulations vs Lifson-Jackson formula

Rotaxane is a mechanically interlocked molecule in which ring chains are threaded onto a linear axial polymer chain, and a typical feature of rotaxane is that the ring chains can slide along the axial chain. In this study, molecular dynamics simulations and Lifson-Jackson formula are performed to examine the sliding dynamics of ring chain threaded on a fixed rod-like AB block copolymer consisting of A and B blocks in which the A-block composed of N-A monomers is attractive to the ring chain, while the B-block with N-B monomers is repelled from the ring chain. From a series of studies on ring sliding along the AB block copolymer with the repeat unit of A(NA )B(NB), we find that the sliding dynamics of ring relies strongly on the block length of (N-A + N-B), the volume fraction f(a )of A-block as well as the block-ring interaction epsilon. First, the sliding diffusion coefficient D of ring decreases sharply by several orders magnitude with an increase in block length or block-ring interaction strength. Next, the sliding dynamics has a strongly non-monotonic dependence on fa, and the slowest diffusion motion occurs for ring threaded onto the symmetric block copolymer with f(a) = 0.5. From the view of free energy potential, both the width of free energy potential well and the height of free energy potential barrier govern the sliding diffusion behavior of ring chain. According to potential of mean force (PMF) of ring sliding along the fixed rod-like block copolymer, we find that our results are good agreement with the theoretical analysis using the Lifson-Jackson formula. Our investigation can provide a simple as well as practical model to study the diffusion of particle in a periodic medium, which is one of the interesting problems in many different fields of sciences, such as physics, chemistry and biology.

Automated summary

This study investigates the sliding dynamics of a ring chain on a fixed block copolymer using molecular dynamics simulations and the Lifson-Jackson formula. The study reveals that the sliding dynamics strongly depend on the block length, A-block volume fraction, and block-ring interaction strength. The width and height of the free energy potential well and barrier determine the sliding diffusion behavior. The findings are in good agreement with theoretical analysis and offer insights into diffusion in periodic media.