Sound absorption in nonelectrolyte aqueous solutions

Abstract

We indicate that the curve fitting for Debye-type relaxation spectrum of sound absorption (SA) cannot sufficiently account for the observed data of nonelectrolyte aqueous solutions (NEAS). To solve these problems, we introduce the distribution function of relaxation time [DFRT, F(τ)] from a diffusion equation of concentration fluctuations using the fluctuation dispersion theory. The SA expression is described by four-adjustable parameters. By use of the mixtures of 1-propanol, t-butanol, and monobutyl triethylene glycol with water, our calculation of SA shows the best fit between the observed and calculated curves, compared with other models. It was found that at lower frequencies the SA behaves as the square root of frequency. The approximate expression of DFRT was expressed in terms of a power law of relaxation time, F(τ)∝τ−γ, which is the same as the expression of dielectric relaxation by Matsumoto and Higashi. Our exponent (γ) of relaxation time is varied from 5/2 in hydrophilic solutes to 3/2 in hydrophobic solutes. The power (γ) of relaxation time was regarded as a parameter to explain the hydrophobic and hydrophilic in the dissolved states of a solute. Our SA expression of γ=5/2 for solutes of a small correlation length leads to that of Romanov–Solov’ev, where the value of 5/2 is that of the Debye distribution for the relaxation time in the Romanov–Solov’ev model.