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.