A multiscale approach to ion diffusion in clays: building a two-state diffusion-reaction scheme from microscopic dynamics.

The mobility of particles is generally lowered by the presence of a confining medium, both because of geometrical effects, and because of the interactions with the confining surfaces, especially when the latter are charged. The water/mineral interface plays a central role in the dynamics of ions. The ionic mobility in clays is often understood as an interplay between the diffusion of mobile ions and their possible trapping at the mineral surfaces. We describe how to build a two-state diffusion-reaction scheme from the microscopic dynamics of ions, controlled by their interaction with a mineral surface. The starting point is an atomic description of the clay interlayer using molecular simulations. These provide a complete description of the ionic dynamics on short time and length scales. Using the results of these simulations, we then build a robust mesoscopic (Fokker-Planck) description. In turn, this mesoscopic description is used to determine the mobility of the ions in the interlayer. These results can then be cast into a diffusion-reaction scheme, introducing in particular the fraction of mobile ions, or equivalently the distribution coefficient Kd. This coefficient is of great importance in characterizing electrokinetic phenomena in porous materials.