Coarse graining the dynamics of nano-confined solutes: the case of ions in clays

We investigate the possibility of describing by a continuous solvent model the dynamics of solutes confined down to the molecular scale. We derive a generalised Langevin equation (GLE) for the generic motion of a solute in an external potential using the Mori–Zwanzig formalism. We then compute the corresponding memory function from molecular simulations, in the case of cesium ions confined in the interlayer porosity of montmorillonite clays, with a very low water content (only six solvent molecules per ion). Previous attempts to describe the dynamics of cesium in this system by a simple Langevin equation were unsuccessful. The purpose of this work is not to carry out GLE simulations using the memory function from molecular simulations, but rather to analyse the separation of time scales between the confined ions and solvent. We show that such a separation is not achieved and discuss the relative contribution of the ion–surface, ion–solvent and ion–ion interactions to the dynamics. On the picosecond time scale, the ion oscillates in a surface-and-solvent cage, which relaxes on much longer time scales extending to several nanoseconds. The resulting overall dynamics resembles that of glasses or diffusion inside a solid by site-to-site hopping.