Light Scattering and the Coupling of Molecular Reorientation and Hydrodynamic Modes

Abstract

Distribution of reorientational times of optically anisotropic molecular liquids from depolarized lightscattering studiesA statistical theory, based on linear response theory, is presented to describe the coupling between molecular reorientation and both longitudinal and shear hydrodynamic modes in liquids, and the effect of this coupling on the depolarized light scattering spectrum. The theory is valid if molecular reorientation takes place by rotational diffusion. The "doublet" features of the observed spectra are explained and both the VH and Hll depolarized spectra can be understood in terms of one nonhydrodynamic parameter which depends upon the anisotropic intermolecular potential. Although the longitudinal modes contain traveling waves which couple to the molecular reorientation and give rise to depolarized Brillouin doublets, the doublet due to the coupling to the shear modes arises from purely dissipative motion and not from shear waves.

Light scattering by transverse waves in supercooled liquids and application to metatoluidine

“…The original papers of Keyes and Kivelson [6] and of Andersen and Pecora [7] were the first to propose a twovariable theory which could explain the existence of the Rytov dip at high temperature and its change into propagative transverse modes at lower temperatures. They did not make use of an equation of motion for the mass current density (Eq.…”

“…Both Keyes and Kivelson [6] and Andersen and Pecora [7] used, for the additional variable which has to enter into the stress tensor associated with Π ij (σ ij = −Π ij ) a symmetrical 2nd rank tensor which was assumed to describe a polarizability density (or, more accurately, the traceless part of the fluctuation of such a quantity). In order to write down the corresponding equations of motion, they made use of the Zwanzig-Mori formalism, introducing the symmetry properties of the correlation functions of this variable and of the momentum density rather than writing the explicit form of σ ij (r, t).…”

“…At first, it was thought that this spectrum was the superposition of the rotational spectrum described above and of transverse propagative modes originating from the Maxwell viscoelastic effect. Shortly after, Keyes and Kivelson [6] and Andersen and Pecora [7] pointed out the necessity of taking into account the orientational dynamics of the molecules and their coupling with the shear motion. In both cases, as well as in all the following publications taking orientational dynamics into account, the solution was based upon a semi-phenomenological approach to the problem: writing down equations describing this rotation translation coupling, they showed that the interpretation given in [3,4] was incorrect: through a negative interference effect, the narrow diffuse shear mode, with a linewidth proportional to the static shear viscosity, was subtracted from the broad reorientational spectrum: viscoelasticity did not play any role in the explanation of these low viscosity experiments.…”

“…[10][11][12][13][14]), each one introducing some additional internal mode, i.e. adding at least one more equation containing a linear coupling between this new variable, or its time derivative, and the variables already introduced in [6] or [7]. These models will be briefly reviewed in Section 5 but we must stress here that their fundamental and common characteristic was that, as in the original models [6,7], they assumed, at least formally, that the rotation-translation coupling was instrumental in producing the propagation of transverse modes at low temperature, ignoring the fact that, even in a simple fluid, transverse modes do propagate for high enough frequencies.…”

Collective Excitations in Supercritical Fluids

“…Extensive studies of generalized collective modes [21,22] showed a convergence of the GCM eigenvalues with systematic extension of the set of dynamic variables up to the third time derivatives of the hydrodynamic ones. The GCM methodology is very close to the generalized hydrodynamic theory by Kivelson and Keyes [23,24] developed for molecular fluids. The microscopic theory of extended collective modes enables correct description of the hydrodynamic modes as well as of the well-defined short-wavelength collective excitations for large wave numbers [25,26].…”