Diffusion in Nanoporous Phases:  Size Dependence and Levitation Effect

Abstract

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.

Fickian yet non-Gaussian behaviour: A dominant role of the intermittent dynamics

“…In our present system there is no domain formation and the intermittency is the effect of attractive solute-solvent interaction. While undergoing random walk, the solute explores the transient solvent cage 4,11 . As the solute is small when it passes through the neck of the cage it feels uneven attraction from the different solvent particles and spends longer time near a particular solvent, which can be envisaged as a sticky point and leads to the intermittency in the solute dynamics.…”

“…Diffusion of smaller particles in a crowded medium is ubiquitous in nature and has huge industrial and academic relevance [1][2][3][4][5][6][7][8][9][10][11][12][13] . The diffusion of sodium chloride through granular soil bed is important in understanding the ground water contamination from solid waste landfills 14 .…”

Non-monotonic size dependence of diffusion and levitation effect: A mode-coupling theory analysis

“…This study is done in order to understand the non monotonic size dependence of diffusion of small solutes which was earlier found in simulation studies [9]. In the earlier simulation and experimental studies the diffusion of small solute particles in porous zeolite structures [13][17], pure solvents [9] and ionic medium [14] have predicted that the non monotonic size dependence of diffusion is a generic phenomena, independent of the nature of the solvent.…”

“…The solute tends to spend longer time bound to one side of the neck or one solvent particle (in case of LJ solvent), which leads to lower diffusion constant. In experiments, simulations and also in theoretical studies such maximum in diffusivity for ion diffusion in polar solvent has been found [12] [13][14][15][16] [17]. All these studies show that the non monotonic size dependence of diffusion is a generic phenomena independent of the nature of the solvent.…”

“…Yashonath and co-workers have connected this behaviour to levitation effect [8][9][10][11][12][13][14]. They have found that when a solute size is approximately similar to the size of the zeolitic pore or in case of pure solvent, the size of the neck of the solvent cage then the solute particle feels a symmetric attraction from all directions and thus levitates through the pore and diffuses faster.…”