Theory of polarized fluorescent emission in uniaxial liquid crystals

Abstract

The theory for the fluorescence emission anisotropy [r(t)] of a cylindrical probe in a macroscopically aligned uniaxial liquid crystal (e.g., an oriented membrane) is developed for the situation where the equilibrium orientational distribution of the probes is not random. Expressions are derived for r(0) and r(∞) involving equilibrium averages for the general case where the emission and absorption dipoles and the major axis of the probe are not parallel. The rotational motion of the probe is described as diffusion in a potential which is consistent with the equilibrium distribution (i.e., using the Smoluchowski equation). Both the short time behavior and the time integral of r(t) are explicitly expressed in terms of equilibrium averages. It is shown how these limits can be used to construct useful approximations for the time dependence of r(t), and how the diffusion constant can be obtained for the short time behavior of r(t).