Shear and flexoelectric deformation effects on the dynamic structure factor of a nematic liquid crystal

We use a fluctuating hydrodynamic description to calculate the orientation (director) correlation function of hydrodynamic fluctuations for a nematic liquid crystal in a non-equilibrium steady state (NESS). This state is produced by both, a planar shear flow and an external uniform electric field, which induces an elastic deformation through the so-called flexoelectric effect. We analyze the effects of these external gradients to estimate the changes on the light scattering spectrum produced by both gradients with respect to its equilibrium shape. We find that these non-equilibrium effects induce long-range effects on the orientation correlation with a k-dependence k−2k−2 and k−3k−3, respectively, giving rise to an asymmetry of the spectrum. This consists of an increment of its maximum and a displacement in the frequency shift space. These changes are proportional to the magnitude of the external gradients and also depend on the relative orientation of the gradients with respect to the wave vector. We find that for MBBA, the shear flow can produce significant increases on the dynamic structure factor of 9.6%, for normalized velocity gradients of the order 0.1–0.5. The flexoelectric effect produces only small changes on the structure factor, which are about two orders of magnitude smaller with respect to those due to the presence of the shear flow. Our analysis suggests that the effects produced on dynamic correlations by the flexoelectric effect would be hard to observe experimentally, while those due to the shear flow might be detectable.