Calculation of the Proportion of Free Water Molecules in Aqueous Solutions Using the Parameters of Their Dielectric Permittivity in the Terahertz Range, Based on the Onsager Theory

Abstract

The question of the structure of aqueous solutions is one of the most fundamental and complex, while it is relevant to all natural science disciplines. An important parameter of the dynamically equilibrium structure of an aqueous solution is the number of free water molecules. To date, there are no reliable and fully justified methods for determining this parameter. Recently, the terahertz time-domain spectroscopy (THz-TDS) method has been developing. It makes it possible to record the spectra of the complex permittivity in the THz region, where an orientation relaxation band of free water molecules is detected for aqueous solutions. The purpose of this work is to establish the relationship of the parameters of THz dielectric permittivity with the number of free water molecules. For this purpose, the process of polarization of water in the THz region was theoretically considered using the formalism of electrodynamics of continuous media. The Onsager theory is taken as a basis and its development is carried out for the case of high-frequency fields. As a result, an analytical ratio was obtained for calculating the proportion of free water molecules in solutions. A comparison with other well-known, more simplified and poorly substantiated approaches is presented. Calculations of the fraction of free molecules for a number of aqueous solutions have been carried out. It can be argued that the first theoretically justified approach to calculating the population of free water molecules in a solution, which does not contain internal contradictions, is presented.