Theoretical study on the sound absorption of electrolytic solutions. II. Assignments of relaxations

The theory on the ultrasonic absorption spectrum of electrolytic solutions recently proposed by us is applied to the model system that resembles to the aqueous solution of MgSO4. The charges on ions are reduced to +/-1.5e in order to obtain the equilibrium structure by the integral equation theory. The theory reproduces the existence of two relaxations around 100 kHz and 1 GHz. The physical origin of the relaxation is analyzed based on the theoretical expression. The slower relaxation is shown to originate in the formation of contact ion pair, in harmony with the conventional assignment. The amplitude of this relaxation agrees with the experimental one fairly well. The absorption cross section is a weakly increasing function of the concentration of the salt in theory, whereas it depends little on the concentration in experiment, which is ascribed to the weaker association of the pair in the theory. The deviation from the Debye relaxation is found for the faster process, and the concentration dependence is small. The analysis shows that this relaxation stems from the coupling between the pressure and the long-range concentration fluctuation, and the concentration independence and the non-Debye relaxation are explained based on the theoretical analysis. In particular, the theory demonstrates that this process has the t(-3/2) tail in the time domain, which is confirmed by numerical calculation. The deviation of the theoretical relaxation amplitude from the experimental one is elucidated in terms of the theoretical expression of the coefficient.