Performance indexes for flexoelectricity in transverse and longitudinal modes

Abstract

Flexoelectric energy conversion, due to its universality and size dependence, is a potential candidate for applications in self-sustainable micro-electromechanical systems/nano-electromechanical systems. This study presents the performance indices for assessing flexoelectricity-driven energy conversion in micro-scale piezoelectric (non-centrosymmetric) and non-piezoelectric (centrosymmetric) dielectric materials. Electromechanical coupling coefficients for geometry selection and figures of merit for material selection for the two most common modes of operations, i.e., transverse mode as in bending of beams and longitudinal mode as in the compression of non-uniform cross section structures, are derived. An interplay of flexoelectricity and piezoelectricity in different circumstances is assessed for three different materials, namely, barium titanate (BaTiO3), Er-doped BST ceramic (Ba1-xTi0.96Sn0.04O3 + x mol. % Er), and polyvinylidene difluoride (PVDF), for transverse and longitudinal modes. In the transverse mode, BaTiO3 and BST are found to dominate at a beam thickness of 5 μm, while at 100 μm, PVDF shows substantially higher magnitudes of electromechanical coupling coefficients. A similar trend for the electromechanical coupling coefficient is observed in the longitudinal mode. PVDF has a very low magnitude of figure of merit in the transverse mode as compared to the other two materials (0.65% of BST and 0.71% of BaTiO3), while in the longitudinal mode, the figure of merit of PVDF exceeds the other two materials by a large magnitude (197 times of BST and 285 times of BaTiO3).