How Do α-Cyclodextrins Self-Organize on a Polymer Chain?

Abstract

The relative conformation of the mobile cyclic molecules of a polyrotaxane has been analyzed quantitatively by means of both molecular dynamics and Monte Carlo simulations. Here, the polyrotaxane is formed by several α-cyclodextrins (α-CDs) threaded onto a poly(ethylene glycol) (PEG) chain. The dimerization free energies for three possible spatial arrangements of two consecutive α-CDs, viz., head to head (HH), head to tail (HT), and tail to tail (TT), were determined. The computed dimerization free energies were then introduced into the theoretical framework of a lattice model to predict the percentage of HH and TT motifs in all possible arrangements, employing Monte Carlo simulations. Our results show that this percentage fluctuates when the number of CDs is less than eight and rapidly tends toward 73% when the latter is greater than eight. This theoretical estimate, which is dominated by the dimerization free energy, agrees well with experiments. Deconvolution of the free-energy profiles indicates that ...