Rotational Dynamics and Light-scattering in Super-cooled Molecular Liquids

TL;DR

This paper develops a theoretical framework for understanding the orientational dynamics and light-scattering spectra of super-cooled molecular liquids, extending previous models to molecules of arbitrary shape and including hydrodynamic effects.

Contribution

It introduces a rigorous projection-operator-based derivation of constitutive equations for arbitrary rigid molecules, incorporating hydrodynamic fluctuations and detailed memory-kernel analysis.

Findings

Derived constitutive equations for arbitrary-shaped molecules.

Formulated light-scattering spectra including Rayleigh-line.

Provided a mathematically rigorous treatment of correlation-function Laplace-transforms.

Abstract

Constitutive equations for the long-wavelength behaviour of the orientational dynamics of a super-cooled liquid are derived using a projection-operator technique and resulting expressions for light-scattering spectra are formulated. We thus extend recent studies for axially symmetric molecules to the general case of arbitrarily shaped rigid molecules. The second part of the discussion considers hydrodynamic energy-fluctuations and thus arrives at expressions for light-scattering spectra which also include a Rayleigh-line. The role of the memory-kernels in the theory is treated in detail. In particular, the derivation of a theory that formally resembles earlier approaches to the problem is presented using a mathematically rigorous description of the Laplace-transforms of correlation-functions.