Light Scattering Studies of Molecular Orientation Fluctuations in Two Dimensions

Abstract

The static and dynamic behavior of the two dimensional orientation field of molecules in the plane of thin, freely-suspended smectic C liquid crystal films is effectively studied by light scattering. Films of 1 to 10 layers in thickness (30Å per layer) have been studied. Thin smectic C (SC) films are a nearly ideal physical representation of the Classical Continuous XY Model. Light scattering with well-defined wave-vector has been used to study the dispersion relations for the two allowed orientation fluctuation modes in two dimensions (bend and splay). These exhibit Frank-like elastic behavior with, in ferroelectric SC films, an additional term in the bend mode dispersion relation due to polarization space charge interaction effects. Exploitation of this latter term allows the absolute measurement of the polarization, elastic constants, and viscosities. The Frank elastic constants decrease with increasing temperature to values comparable to those predicted for the Kosterlitz-Thouless transition at which point a phase transition to an isotropic (smectic A) film is found to occur. Measurements of the 2-d elastic constants vs. film thickness shows that, 3-d Frank elasticity is dispersive (nonlocal) at wave vectors q ~ 10⁶cm⁻¹. Light scattering studies which employ the collection of a broad distribution of wave vectors have also been carried out. These allow the direct visualization of the 2-d molecular orientational field, a feature unique to these systems. The static and dynamic behavior of spontaneous and field induced point and line defects has been investigated using this method. It has also been used to study directly the fluctuations in the average local orientation which show contributions of modes having inverse wavevectors ranging from the size of the averaging area to the size of the sample.