An analytical model for probing ion dynamics in clays with broadband dielectric spectroscopy

A simple two-state model is proposed to explicitly derive the ionic contribution to the frequency-dependent dielectric permittivity of clay. This model is based on a separation of time scales and accounts for two possible solvation modes (inner/outer-sphere complexes) for ions in the interlayer spacing and a possible chemical exchange between both forms. The influence on the permittivity of thermodynamic (distribution constant K-d) and dynamic (diffusion coefficient, chemical relaxation rate) parameters is discussed. In turn, this model is used to analyze experimental data obtained with Na-montmorillonite for two relative humidities. The values of the parameters extracted from these measurements, and their variation with water content, show that the proposed model is at least reasonable.