Diffusion in nanoporous phases: size dependence and levitation effect.

Self-diffusivity, D, of diffusants in widely differing mediums such as liquids (e.g., solution), porous solids (e.g., guests in zeolites), or ions in polar solvents exhibit strong size dependence. We discuss the nature of the size dependence observed in these systems. Altogether, different theoretical approaches have been proposed to understand the nature of size dependence of D not only across these widely differing systems but even in just one medium or class of systems such as, for example, ions in polar solvents. But molecular dynamics investigations in the past decade have shown that the size dependence of self-diffusion in guest-porous solids could have origins in the mutual cancellation of forces that occurs when the size of the diffusant is comparable to the size of the void. The effect leading to the maximum in D is known as the levitation effect (LE). Such a cancellation is a consequence of symmetry. This effect exists in all porous solids irrespective of the geometrical and topological details of the pore network provided by the solid. Recent studies show that the levitation effect and size-dependent diffusivity maximum exists for uncharged solutes in solvents. One of the consequences of this is the breakdown in the Stokes-Einstein relationship over a certain range of solute-solvent size ratio. Experimental measurements of ionic conductivity over the past hundred years have found the existence of a size-dependent diffusivity maximum leading to violation of the Walden's rule for ions in polar solvents. Molecular dynamics simulations and experimental data suggest that even this maximum has its origin in LE. Simulation studies of impurity atom diffusion in close-packed solids as well as ions in superionic and other solids suggest the existence of a size-dependent diffusivity maximum in these materials as well. The levitation effect is a universal effect leading to a maximum in diffusivity of a diffusant in a variety of condensed matter phases. The only condition for its existence appears to be the presence of van der Waals or electrostatic interactions.