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

Smectite clays are widely found on the Earth surface. They possess a connected mesoporous space in the micrometer range, and nanopores inside the mineral grains. The grains are stacks of individual 1 nm-thick clay particles (the layers) with 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 relative humidity (RH) present in the mesoporous space surrounding the grain. Imposing a gradient of RH 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 mesoporous space, (i) some of them intercalate into the nanopores, (ii) causing the grains to swell and the separation of clay grains into particles of smaller thickness. From (ii) results a change in the geometry of the mesoporous space, with a decrease in the mesoporous volume available for vapor diffusion. These two effects (i and ii) 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 in the diffraction data. A separate calibration experiment allows mapping this monotonous evolution of d as a function of the RH. By measuring d in space and time in the transport experiments we thus record the time evolution of RH profiles along the direction of the initial RH gradient. To model the data we consider a 1D effective diffusion process described by a fractional time diffusion equation with a diffusion coefficient that depends on the RH. It is possible to rescale all RH 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 nanopores, vapor transport is normal (γ=2), while if the interlayer cation is lithium the transport is strongly subdiffusive. This is explained by the different dynamics of cation intercalation in these two clays. In both cases we also obtain the dependence of the effective diffusion coefficient on relative humidity.