# Flexoelectricity in Nematic and Smectic-A Liquid Crystals

 Title: Flexoelectricity in Nematic and Smectic-A Liquid Crystals Author: Prost, Jacques; Pershan, Peter S. Note: Order does not necessarily reflect citation order of authors. Citation: Prost, Jacques, and Peter S. Pershan. 1976. Flexoelectricity in nematic and smectic-A liquid crystals. Journal of Applied Physics 47(6): 2298-2312. Full Text & Related Files: Prost_Flexoelectricity.pdf (1.155Mb; PDF) Abstract: Flexoelectric effects are observed in both the nematic and smectic‐A phases of p‐butoxybenzal‐p‐($$\beta$$‐methylbutyl) aniline (BBMBA) and p‐cyano‐benzylidine‐p‐octyloxyaniline (CBOOA). This is the first reported observation of flexoelectricity in smectic phases. The use of a symmetric interdigital electrode in the homeotropic geometry facilitated the unambiguous separation of linear and quadratic electro‐optic effects. Both the interdigital electrodes and those liquid‐crystal deformations that are quadratic in the voltage act as optical diffraction gratings with a spacing that corresponds to the repeat distance d for adjacent electrodes. In contrast linear electro‐optic effects give rise to diffraction gratings with twice this spacing since adjacent electrodes have opposite voltages. Diffraction maxima due to the linear effects are halfway between the maxima due to the other effects. Using optical heterodyne detection, the intensity of the diffraction maxima believed to arise from the linear effect are indeed observed to be linear in the applied voltage $$V (\omega)$$. With homodyne detection the diffracted intensity is proportional to $$V (\omega)^2$$. Although previous discussions of flexoelectricity in nematics have been in terms of two flexoelectric coefficients $$e_{11}$$ and $$e_{33}$$, we present theoretical arguments that as long as $$\nabla \times E=0$$ there is only one true volume coefficient and that the other constant can always be included in surface effects. Our measurements of the volume coefficient $$f=e_{11}+e_{33}$$ are an order of magnitude larger than previously obtained values for $$e_{11}$$ and $$e_{33}$$. Measured values of f are also nearly independent of temperature, in contrast to previous theoretical models, and of similar magnitude in the smectic and nematic phases. Measurements of flexoelectric signals versus the frequency of the driving voltage obtain relaxation times for splaylike nematic fluctuations and undulation‐type smectic fluctuations. Published Version: doi:10.1063/1.323021 Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:10361967 Downloads of this work: