Ion dynamics in compacted clays: derivation of a two-state diffusion-reaction scheme from the lattice Fokker-Planck equation.

We show how a two-state diffusion-reaction description of the mobility of ions confined within compacted clays can be constructed from the microscopic dynamics of ions in an external field. The diffusion-reaction picture provides the usual interpretation of the reduced ionic mobility in clays, but the required partitioning coefficient K(d) between trapped and mobile ions is generally an empirical parameter. We demonstrate that it is possible to obtain K(d) from the microscopic dynamics of ions interacting with the clay surfaces by evaluating the ionic mobility using a novel lattice implementation of the Fokker-Planck equation. The resulting K(d) allows a clear-cut characterization of the trapping sites on the clay surfaces and determines the adsorption/desorption rates. The results highlight the limitations of standard approximation schemes and pinpoint the crossover from jump to Brownian diffusion regimes.

Frequency-dependent dielectric permittivity of salt-free charged lamellar systems.

We present a new model to analyze dielectric spectroscopy measurements on charged lamellar systems, with the following improvements with respect to the hitherto available models: (i) it does not rely on the hypothesis of local electro-neutrality, and allows to treat the salt-free case; (ii) the chemical exchange governing the partition between free and bound ions is properly taken into account; (iii) a fully analytical solution is provided. The variation of the frequency-dependent dielectric permittivity with both thermodynamic and kinetic characteristics of the free-bound ion equilibrium is presented. In particular, the relative weights of both relaxation modes (exchange and transport), and their characteristic frequencies are discussed. This study opens the way to the analysis of systems for which the usual models are irrelevant, such as salt-free clay gels or membranes.