Calculation of the microwave and far-infrared spectra of aqueous electrolyte solutions from a molecular model. On the ionic-conductivity dispersion σ(ω)

Abstract

Abstract A simple model of dielectric response due to the three-dimensional motion of ions inside a spherical ideally reflecting sheath is suggested. The present model termed the sphere-confined ionic (SCI) model is combined with the so called hybrid model, previously used to describe dipolar orientational relaxation [ see Dielectric Relaxation and Dynamics of Polar Molecules by V. I. Gaiduk (World Scientific, Singapore, 1999) ]. The wideband (up to 1000 cm−1) complex permittivity ɛ(ω) and absorption α(ω) spectra of NaCl-water and KCl-water diluted solutions are calculated as the sum of the contributions due to cations and anions and to reorientation of polar H2O molecules. A modification of this model is also suggested, in which the walls may also vibrate. The parametrisation of the ionic model is made taking account of the experimental value σs of the static conductivity; the ionic contributions σ±s due to anions and cations are calculated, as well as ionic self-diffusion coefficients and mobilities. The positive (for NaCl) and negative (for KCl) hydration are described in terms of respectively increasing and decreasing τ(CM) concentration dependencies of the lifetimes fitted for water molecules. The frequency dependence of the electric conductivity is estimated for a relatively low electrolyte concentration. If the frequency ω is much less than the ionic plasma frequency ωp, then the real part σ′ of the complex ionic conductivity is close to its static value σs, while the imaginary part σ″ is close to zero. In the high-frequency region (at millimetre/submillimetre wavelengths) the σ(ω)-spectrum has resonant-like behaviour. The ionic contribution σɛ″ion = σπω (ω)/ω to the total loss and the corresponding contribution to the absorption coefficient α(ω) is pronounced in the microwave and in the FIR ranges, if the lifetime of the hydration sheath around an ion is much longer than that of the bulk water in the local-order configuration.