Orientational/translational relaxation in aqueous electrolyte solutions: a molecular model for microwave/far-infrared ranges

Abstract

A model is given where the complex permittivity of an electrolyte solution is calculated as a superposition of the contributions due to the translation of ions and the reorientation of water molecules, which occur in intermolecular potential wells during the lifetime of local order in liquids. Simple analytical expressions are found for the contributions of cations and anions to the linear-response spectral function. The one-dimensional rectangular potential well with perfectly elastic walls is considered. The contribution of water molecules to the orientational relaxation was calculated in terms of a hybrid model using the approach given recently in a book by Gaiduk (Dielectric Relaxation and Dynamics of Polar Molecules, World Scientific, Singapore, 1999). A modification of this model is also suggested in which the walls of the potential well undergo rather slow vibration. If the angular frequency ω is much less than the plasma frequency ω_p of an ion, then the theory yields a nearly constant real part σ′ of the complex ionic conductivity σ(ω), while its imaginary part σ″ is very small. Large variations with ω of both parts of σ are predicted to occur at millimetre/submillimetre wavelengths, when ω approaches ω_p. Wideband (up to 1000 cm⁻¹) theoretical spectra of the complex permittivity and absorption coefficient are calculated for NaCl–water and KCl–water solutions. The theory predicts that an additional loss/absorption could arise in the far-infrared (FIR) spectral range, if the mean ionic lifetime τ_ion is much longer than the lifetime τ of the bulk water molecules.