Determination of the Number of Free Water Molecules in Aqueous Solutions on the Basis of Interrelated Consideration of the Polarization Processes in Water in the THz Frequency Range

The structure of aqueous solutions has been studied for a long time; however, many things still remain unclear. One of the ways to describe the water structure is the statistical approach, within which the distribution of water molecules over mobility, connectivity, number of hydrogen bonds, etc. is analyzed. An important parameter in this consideration is the equilibrium number of free water molecules, which are not bound by hydrogen bonds and do not enter the composition of hydrate shells. There are not any completely justified approaches for calculating the fraction of free water molecules in solutions. Aqueous solutions are known to have a weak band of the relaxation type (differing from the classical Debye relaxation band) in the THz frequency range. This band is assigned to the orientational relaxation of free water molecules. In this paper we theoretically consider the process of orientational relaxation of free water molecules in an aqueous solution in the THz range. The theory is based on the Onsager polarization model, modified for application in the THz range. The field screening due to the higher frequency polarization processes is taken into account. Particular attention is paid to the field screening due to the orientational polarization of bound water molecules. Based on this consideration the ratio between the fractions of free water molecules in solution and the parameters of spectral bands of water molecular dynamics is obtained. The calculated numbers of free water molecules, obtained within the proposed theory and other known (simpler) approaches, are compared for some solutions. It is shown that, if the field screening is taken into account when considering the orientational polarization of free water molecules, their number increases. For example, the number of free molecules for liquid water at 25°С, with complete consideration of screening, is about 9%.