Mesoscopic collective dynamics in liquids and the Dual Model

Abstract

In the present article it is shown how a series of experimental evidences and theoretical developments on liquid modelling, gathered for the first time, can all be framed in a mesoscopic view of liquids that are hypothesized as constituted by a population of wave packets, responsible for the propagation of elastic and thermal perturbations, and of dynamic aggregates of molecules, in continuous re-arrangement, diving in an ocean of amorphous, disordered liquid. This model, dubbed Dual Model of Liquids, is complementary to the Phonon theory of Liquid Thermodynamics, recently proposed by an independent group. The pseudo-crystalline dynamic structures, whose presence in liquids is evidenced by high energy inelastic scattering experiments, interact with a statistical population of harmonic elastic waves and anharmonic wave-packets propagating within and among the structures themselves, respectively. The expression for the interaction term is derived from “first principles” based on general considerations related to the pressure exerted by elastic waves travelling in condensed media. The anharmonic character of the interaction allows the exchange not only of energy but also of momentum between wave packets and clusters, thus determining both the displacement of the latter within the medium, and the redistribution of the energy between external, or translatory degrees of freedom of the clusters, and internal collective, vibratory degrees. Using these concepts it is possible to calculate some dynamic and thermodynamic quantities concerning the dynamics of liquids. Moreover, the interpretation of the relaxation times of the processes involved in momentum and energy transport is given, their Order-of-Magnitude is calculated, and the way in which these times are involved in the different phases of the collective dynamics of liquids is discussed. A comparison is provided with results obtained in the frame of PLT and with the forecasts for the visco-elastic transition regions. In the last part of the paper, some experiments are suggested that should be performed to provide additional details to the model.

Isochoric specific heat in the Dual Model of Liquids and comparison with the Phonon theory of Liquid Thermodynamics

“…The pool of energy stored into the cluster will be released after a time lag R  . Depending on the OoM of such time interval, the events of Figure 1 can be considered elastic, quasi-elastic or inelastic [1,3,12,21].…”

“…In a previous paper [1] the mesoscopic model of liquids dubbed Dual Model of Liquids (DML) has been introduced. It assumes a liquid be a system made up of molecules arranged in solid-like dynamic structures in continuous rearrangement, swimming in an ocean of amorphous liquid.…”

“…Figure 2 is a close-up of the first part of the wave-packet  particle interaction shown in Figure 1a, that lasting p  . wp  is the extension of the wave-packet and p d that of the liquid particle [1].…”

“…Examples are the thermal conductivity, the thermal diffusivity, the specific heat, etc.. The evaluation of the order of magnitude of the particle and phonon mean free paths and in particular of the relaxation times involved in their interactions, have also been provided [1].…”

“…where  is the medium density, V C the isochoric specific heat per unit mass, wp Ν the number of wave-packets per unit of volume 1 , and wp  their average energy (here and in the rest of the paper, the two brackets indicate the average over a statistical ensemble of the quantity inside them).…”