Attenuation of Sound Resulting from Ionic Relaxation

Abstract

Slowness in the rearrangement of ion configuration under acoustic perturbation should cause sound absorption in ionic solutions. This mechanism investigated from the standpoint of the Debye-Ḧckel theory of strong electrolytes. The electrostatic part of the free energy of the solution is formulated in terms of temperature, volume, and an ion configuration function. The partial derivative of this expression with respect to volume gives the electrostatic component of pressure. A rate equation for change of ion concentration at a point enables us to find the variation in the ion configuration function with a small harmonic fluctuation in volume. Since the pressure is expressed in terms of the configuration function, this leads readily to the relaxational bulk modulus connected with rearrangement. The rate equation involves a parameter which in interionic theory has been identified as the relaxation time of the ionic atmospheres and can be evaluated from conductivity data. A calculation made for MgSO4 solutions sets the relaxation frequencies for 0.001 and 0.01 molal concentrations at 21 and 143 mc, respectively, and shows the maxima in the wavelength absorption coefficients to be 20 and 660× 10−9 respectively. The recently reported much higher excess absorptions for MgSO4 at lower frequencies are thus due to processes other than ionic relaxation.