Disorder influence on linear dichroism analyses of smectic phases

Linear dichroism, the unequal absorption of parallel and perpendicular linear polarized light, is often used to determine the anisotropic ordering of rodlike polymers in a smectic phase, such as helices in a lipid bilayer. It is a measure of two properties of the sample: 1), orientation of the chromophore transition dipole moment (TDM) and 2), disorder. Since it is the orientation of the chromophore TDM that is needed for high resolution structural studies, it is imperative to either deconvolve sample disorder, or at a minimum, estimate its effect upon the calculated TDM orientation. Herein, a rigorous analysis of the effects of disorder is undertaken based on the recently developed Gaussian disorder model implemented in linear dichroism data. The calculation of both the rod tilt and rotational pitch angles as a function of the disorder and dichroism, yield the following conclusions: Disorders smaller than 5° have a vanishingly small effect on the calculated polymer orientation, whereas values smaller than 10° have a negligible effect on the calculated parameters. Disorders larger than 10° have an appreciable effect on the calculated orientational parameters and as such must be estimated before any structural characterization. Finally the theory is tested on the HIV vpu transmembrane domain, employing experimental mosaicity measurements from x-ray reflectivity rocking scans and linear dichroism.