Dynamics of orientational fluctuations of molecules near a liquid-solid interface: A Landau-Ginzburg description

We present a theory of the frequency spectrum of orientational fluctuations of molecules in a liquid which are near a solid interface at which the molecules are rigidly pinned, with the consequence that there will be orientational order induced in the fluid in the vicinity of the solid interface. It is argued that the fluctuations in orientation in this region may be probed by light scattering spectroscopy, under conditions where the incident light suffers total internal reflection from the boundary. Our theory is based on a time-dependent Landau-Ginzburg equation for the fluctuating part $\delta Q(\overrightarrow{\mathrm{x}},t)$ of the orientational-order parameter; the pinning of the molecules at the interface leads to orientational order near the interface, we assume, is described by an order parameter $\overline{Q}\mathrm{}\left(z\right)\mathrm{}$ which falls exponentially as one moves into the liquid. We have carried out a series of calculations of the light scattering spectrum, in the reflection geometry, for the liquid crystal $p$-methoxybenzylidene-$p$-($n$-butyl)aniline in contact with a dielectric substrate. As the temperature of the nematicisotropic phase transition is approached from above, pinning of the order parameter can lead to a substantial enhancement in the strength of the central peak in the light scattering spectrum observed in this geometry.