Measurement of the dielectric relaxation property of water-ion loose complex in aqueous solutions of salt at low concentrations

Electrolytes and their dissociated ions are thought to form positive or negative hydration layers around them. In this study, we have developed a method to determine the volume and the dielectric relaxation property (relaxation frequency f_c, dispersion intensity δ) of the water hydrating ions in salt solutions. The method consists of four steps: (1) By use of a high-resolution microwave dielectric spectroscopy technique, the dielectric spectra of sample salt solution and bulk water are measured in pair. (2) The dielectric spectrum of solutes (ions) with water layers for a given volume fraction φ is then calculated from each pair of dielectric spectra of a sample salt solution and reference water according to the Hanai mixture theory. (3) Each spectrum of solutes with water layers at a given 0 is decomposed into a few Debye relaxation functions and the bulk water component. (4) The volume fraction φ is operationally decreased from 0.5, and steps (2) and (3) are repeated at each φ until the bulk water component vanished. Then the volume fraction of the hydrated solutes (ions) in solution is determined. The method was applied to NaF and NaCl solutions. As a result the different spectral intensity was nearly proportional to the salt concentration below 0.2 M in the frequency range of 3-26 GHz. The hydration number N^h, and the dielectric relaxation property of the hydration layer for each salt solution was successfully determined as (f_cl, δ₁, N _h)= (18.7, 44.9, 27.9) for NaCl and (f_cl, δ₁, f_c2, δ₂, N_h) = (26.0, 6.70, 5.64, 19.2) for NaF.