Physical insights into uranyl diffusion and sorption in bentonite: Theoretical and molecular dynamics study

Abstract

Mechanistic understanding of diffusion and sorption of radionuclides and metals in clay-based engineered barriers is essential to develop models and define parameters for transport calculations for the safety analysis of disposal systems. Here we studied diffusion of uranyl (UO22+) species in the clay interparticle pore or macropores of bentonite clay by means of molecular dynamics simulation (MDS) for pore sizes ranging from 8.37 to 33.5 nm. The conceptual model of the clay pore system considered diffusion as a combination of pore diffusion (Dp) and surface diffusion DS (i.e. diffusion of adsorbed cations within the electrical double layer of the clay surfaces), from which the apparent diffusion Da was calculated as the weighted sum of Dp and DS, using a weighing factor f calculated as the ratio of adsorbed to total UO22+ in the system. Diffusivities at equilibrium for the largest pore size of 33.5 nm were: Da=7.37×10−10 m2 s−1, Dp=1.14×10−9 m2 s−1, and Ds=1.97×10−13 m2 s−1. The Ds was several orders of magnitude smaller than Dp. This was evident from the much smaller gradient of the mean-square displacement vs time lag curve for the adsorbed species than that of the species in the pore space. We found a remarkable consistency between our theoretical derivation and independent MDS evidence. For the slit-shaped interparticle pore, the retardation factor Rf was found to be the reciprocal of the unabsorbed fraction (Rf=1/1−f) and the capacity factor α was a ratio of the porosity to the unadsorbed fraction (α=ε1−f) or the ratio of the diffusant density in the bulk sample to the corresponding density in the pore solution. MD simulations of diffusion and sorption processes can be applied to other transport related problems at continuum scale, pore scale and molecular scale, such as for improved modelling of global elemental cycles, CO2 geosequestration, or the performance of desalination membranes.