Statistical-mechanical theory of ultrasonic absorption in molecular liquids

TL;DR

This paper develops a statistical-mechanical framework to explain ultrasonic absorption in molecular liquids, linking microscopic site-site correlations to macroscopic ultrasonic response.

Contribution

It introduces a general theoretical approach using mode-coupling and integral equation theories to predict ultrasonic absorption based on molecular structure and correlations.

Findings

Derived expressions for ultrasonic absorption coefficients in terms of static and dynamic correlation functions.

Implemented mode-coupling approximation for site-site memory kernels.

Applicable to various types of molecular liquids, including ionic and polar liquids.

Abstract

We present results of theoretical description of ultrasonic phenomena in molecular liquids. In particular, we are interested in the development of microscopical, i.e., statistical-mechanical framework capable to explain the long living puzzle of the excess ultrasonic absorption in liquids. Typically, ultrasonic wave in a liquid can be generated by applying the periodically alternating external pressure with the angular frequency that corresponds to the ultrasound. If the perturbation introduced by such process is weak - its statistical-mechanical treatment can be done with the use of the linear response theory. We treat the liquid as a system of interacting sites, so that all the response/aftereffect functions as well as the energy dissipation and generalized (wave-vector and frequency dependent) ultrasonic absorption coefficient are obtained in terms of familiar site-site static and time correlation functions such as static structure factors or intermediate scattering functions. To express the site-site intermediate scattering functions we refer to the site-site memory equations in the mode-coupling approximation for the first-order memory kernels, while equilibrium properties such as site-site static structure factors, direct and total correlation functions are deduced from the integral equation theory of molecular liquids known as RISM or one of its generalizations. All the formalism is phrased in a general manner, hence the obtained results are expected to work for arbitrary type of molecular liquid including simple, ionic, polar, and non-polar liquids.