Vapor Transport in a Porous Smectite Clay: From Normal to Anomalous Diffusion

Abstract:

Smectite clays are widely found on the Earth surface. They are porous materials possessing a connected mesoporosity in the micrometer range, in-between mineral grains, and a nanoporosity inside the grains. These grains are stacks of individual 1 nm-thick clay particles (the layers) and have the ability to swell by incorporating H₂O molecules (or other molecules such as CO₂) in-between the layers, depending on the ambiant temperature and on the humidity present in the mesoporosity surrounding the grain. Imposing a gradient of relative humidity H along a temperature- controlled dry sample of smectite clay, we investigate the diffusive transport of water molecules in vapor phase through the material. As water molecules diffuse through the mesoporosity, some of them intercalate into the nanoporosity, causing the grains to swell and therefore a decrease in the mesoporous volume available for vapor diffusion. These two effects render the transport process potentially anomalous; we monitor it using space- and time-resolved X-ray diffraction at a synchrotron source. Indeed, water absorption into the nano-layered grains changes the interlayer repetition distance (d-spacing) of the stacks, which is seen as a horizontal translation of a peak in the diffraction data. A calibration experiment performed under controlled constant temperature and controlled humidity level all around the sample, varying H by steps, has allowed us to map the monotonous evolution of d as a function of H. By mapping d in space and time in the transport experiments we thus obtain humidity H(x) profiles along the direction of the initial humidity gradient, at regular time intervals t. To model the data we consider a one-dimensional effective diffusion process described by a fractional time diffusion equation with a diffusion coefficient that depends on humidity. It is possible to rescale all humidity profiles onto a single master curve as a function of (x/t)^γ/2, where γ is the exponent characteristic of the fractional derivative. We observe that when the clay sample is prepared with sodium cations intercalated in the nano-porosity, vapor transport is normal (γ=2), while if the interlayer cation is lithium the transport is strongly subdiffusive. In both cases we also obtain the dependence of the effective diffusion coefficient on humidity.