Control of the threading ratio of rings in a polypseudorotaxane: A computer simulation study

As a conceptually new class of polymers, mechanically interlocked polymers (MIPs) have been attracting much attention during last decades due to their uniqueness in property profiles and promising industrial applications. The unique properties of MIPs are essentially rooted in special modes of motion of its basic constituents, e. g., physical properties of polyrotaxanes (PRs) or polyrotaxane (PR) derivatives mainly stem from sliding motion of rings along the linear axle in a PR. Control of the threading ratio of rings in a PR is a key to regulate the sliding behavior of the rings and thus the property profiles of PRs or PR derivatives. Usually, poly-pseudorotaxane (PPR), a supramolecular complex composed of a linear polymer threaded by a number of rings, acts as a precursor of a PR, which can be formed in experiments by simply end-capping of the PPR. Thus, controlling the threading ratio of a PPR is determinant for regulation of the threading ratio of a PR formed from it. In this work, by using molecular dynamics simulation of the Kremer-Grest model, we systematically investigate dependence of the threading ratio of rings (e.g., mean value of the threading ratios and fluctuation feature of the normalized number of threaded rings) in PPRs obtained on those key relevant factors, including molecular interactions between the linear polymer (its backbone and chain ends) and the rings, chain length and stiffness of the linear polymer, ring concentration, temperature. It is concluded that the threading ratio of rings in PPR over a wide range can be effectively controlled by tuning the above-mentioned molecular parameters. Finally, we propose a theoretical understanding of main simulation results based on the two-state model.