Statistical Thermodynamic Theory of Heat-Induced Gelation of Aqueous Methylated Polyrotaxane Solutions

Chemically modified polyrotaxanes by methylation are water-soluble and show high-temperature gelation in water. To elucidate the molecular mechanism, we developed a theoretical model incorporating the following contributions: hydration-dehydration of cyclic molecules, formation of one-dimensional aggregates composed of a various number of cyclic molecules along the polymer chain, and formation of junction structures by associating between the aggregates. We numerically calculated the sol-gel transition line, the average aggregate length, the average junction multiplicity, the heat capacity change of the solution, the hydration ratio of cyclic molecules, and the translational entropy of cyclic molecules along the chain. We compared our results with the previously reported experimental data, and we discussed the molecular mechanism of the high-temperature gelation and the formation of the junction structures based on the sliding feature of cyclic molecules.