Twiston vs. random fluctuation as the source of the rapid motion of polyethylene in the inclusion complex with perhydrotriphenylene

Recently molecular dynamics simulations were performed for polyethylene in the inclusion complex with perhydrotriphenylene. The system contained ninety molecules of perhydrotriphenylene, arranged in six stacks of fifteen molecules each, and one molecule of n-tetracontane, C₄₀H₈₂. The internal CH₂-CH₂ bonds in n-tetracontane have a very strong preference for the trans state. Nevertheless, the chain exhibits a high degree of internal flexibility. This motion produces a characteristic pattern in δ|ψ N + i ψi| vs. N, where ψ_i describes the instantaneous angle of a C-H bond vector at carbon atom i about the axis defined by the channel, and δ denotes the fluctuation. The pattern expected for δ|ψ N + i ψi| vs. N is derived for the case where the rapid internal motion is produced by a twiston. It is compared with the results from the simulation and from the expectation for the case where the rapid motion arises from uncorrelated internal fluctuations within the trans state at each CH₂-CH₂ bond.