Threading-unthreading equilibrium in solution of molecular nanotubes and linear flexible polymer chains.

Using the Flory-Huggins lattice model, we investigate the threading-unthreading equilibrium in a solution of linear flexible polymer chains and molecular nanotubes formed by covalently bonding the ringlike molecules, such as cyclodextrins (CDs). It is found that the threading-unthreading equilibrium depends on the temperature and the molar concentrations of the ringlike molecules and polymer chain segments but is independent of the polymer chain length, which agrees with the experimental observations. By fitting the experimental data of alpha-CD and poly(ethylene glycol) (PEG), the inclusion energy between alpha-CD and PEG, which includes the conformation energy loss of PEG resulted from the inclusion, is calculated to be approximately -20.45 kJ/mol per PEG unit.