Mesoscopic Collective Dynamics in Liquids and the Dual Model

A microscopic vision is presented of a dual model of liquids (DML) starting from a solid picture. The task is accomplished first by showing how a series of experimental evidences and theoretical developments on liquid modeling, gathered for the first time, can be framed in a mesoscopic view of liquids, hypothesized as constituted by a population of dynamic aggregates of molecules, diving in an ocean of amorphous liquid. The pseudo-crystals interact with the rest of the liquid through harmonic elastic waves and anharmonic wave-packets propagating within and among the structures. The anharmonic interaction term is derived from “first principles”; it allows the exchange of energy and momentum between the wave packets and the molecule's clusters, determining the displacement of the latter within the medium, and the redistribution of the energy between external Degrees of Freedom (DoF) and internal collective degrees of the clusters. Among the novelties of this model is that it provides quantitative expressions of various extensive thermophysical properties. The introduction of the statistical number of excited DoF allows bypassing the problem of other dual models which are sometimes unable to correctly reproduce the expressions for those thermophysical quantities showing deviations due to the activation/de-activation of internal DoF. The interpretation of the relaxation times is given, their Order-of-Magnitude (OoM) calculated, and the way in which these times are involved in the different phases of the collective dynamics of liquids discussed. A comparison is provided with results obtained in the frame of Phonon theory of Liquid Thermodynamics, as well as the forecasts for the viscoelastic transition regions and with systems exhibiting k-gap. In the last part of the paper, theoretical insights and experiments are suggested as potential directions for future research and developments.