Direct measurement of orientation correlations in a two-dimensional liquid-crystal system.

Abstract

The behavior of a two-dimensional orientation field has been studied directly in space and time. In a freely suspended thin film of tilted smectic liquid crystal the local projection onto the film plane of the molecular orientation averaged through the film forms a two-dimensional (2D) vector field C^(x,y) with local orientation \ensuremath{\Phi}(x,y). This orientation field was imaged in real space by depolarized reflection microscopy. By probing the light at two distinct (x,y) locations in the image and employing cross-correlation intensity-fluctuation spectroscopy, we have measured the space-time behavior of ${\ensuremath{\sigma}}^{2}$(\ensuremath{\rho},\ensuremath{\tau})\ensuremath{\equiv}〈\ensuremath{\Vert}\ensuremath{\Phi}(0,0) -\ensuremath{\Phi}(\ensuremath{\rho},\ensuremath{\tau})${\ensuremath{\Vert}}^{2}$〉. At large \ensuremath{\tau}, \ensuremath{\sigma} increases logarithmically with \ensuremath{\tau}, consistent with the expected diffusional dynamics and thermally excited fluctuation spectrum of \ensuremath{\Phi}. This logarithmic (Landau-Peierls) divergence confirms that this 2D orientational system is at its lower marginal dimensionality. In addition, by fitting the behavior of ${\ensuremath{\sigma}}^{2}$(\ensuremath{\rho},\ensuremath{\tau}), we extract the 2D orientational diffusion constants for splay and bend in both the smectic-C and smectic-I phases.