Statistical-mechanical theory of ultrasonic absorption in molecular liquids

We present results of the theoretical description of ultrasonic phenomena in molecular liquids. In particular, we are interested in the development of a microscopical, i.e., statistical-mechanical, framework capable of explaining the long living puzzle of excess ultrasonic absorption in liquids. Typically, an ultrasonic wave in a liquid can be generated by applying a periodically alternating external pressure with an angular frequency that corresponds to the ultrasound. If the perturbation introduced by such a process is weak, its statistical-mechanical treatment can be done with the use of a 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 first-order memory kernels, while equilibrium properties such as site-site static structure factors, and direct and total correlation functions are deduced from the integral equation theory of molecular liquids known as RISM, or one of its generalizations. All of the formalism is phrased in a general manner, hence the results obtained are expected to work for arbitrary types of molecular liquids including simple, ionic, polar, and nonpolar liquids.