Predicting cyclodextrin assembly on end-functionalized polyethylene glycol for designing polypseudorotaxane hydrogels

Cyclodextrin (CD) and polyethylene-glycol (PEG) based polypseudorotaxanes (PRX) are the building blocks of high-performance soft materials, such as slide-ring gels and 3D-printable networks. For these materials, the final mechanical properties depend on the linear density of CD along the PEG backbone. End-functionalization of PEG, which varies the free energy barrier for CD assembly, is an effective approach for controlling PRX microstructures. Experimentally exploring the vast design space of the end moieties, however, is challenging. We apply a multiscale approach to predict the assembly of alpha-cyclodextrin (αCD) on end-functionalized PEG axles. Combining all-atom molecular dynamics simulations and two-dimensional (2D) umbrella sampling, we compute the free energy landscape of the host-guest interaction between αCD and the small molecule used for PEG functionalization. By comparison with experimental binding constants, we show that our simulations and sampling method capture the thermodynamics of αCD assembly across the functional moieties. Using the free energy landscapes, we estimate the rate constants for association and dissociation between αCD and PEG, as well as the diffusion of αCD along the PEG backbone. A kinetic Monte Carlo (kMC) model is then applied to predict the formation of PRX structures and intra-chain dispersion of αCD along the PEG backbone. We expect our multiscale to help design novel PRX-based materials.