Flexoelectricity

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Flexoelectricity is a property of a dielectric material where there is coupling between electrical polarization and a strain gradient. Flexoelectricity is closely related to piezoelectricity, but while piezoelectricity refers to polarization due to uniform strain, flexoelectricity refers specifically to polarization due to strain that changes from point to point in the material. This nonuniform strain breaks centrosymmetry, meaning that unlike in piezoelectricity, flexoelectric effects occur in both centrosymmetric and asymmetric crystal structures.^[1] Flexoelectricity is not the same as Ferroelasticity. Flexoelectricity plays a critical role in explaining many interesting electromechanical behaviors in hard crystalline materials and core mechanoelectric transduction phenomena in soft biomaterials.^[2] Most excitingly, flexoelectricity is a size-dependent effect that becomes more significant in nanoscale systems, such as crack tips. ^[3]

In common useage flexoelectricity is the generation of polarization due to a strain gradient; inverse flexoectricity is when polarization, often due to an applied electric field, generates a strain gradient. Converse flexoelectricity is where a polarization gradient induces strain in a material.^[4]

The electric polarization ${\displaystyle P_{i}}$ due to mechanical strain of ${\displaystyle \epsilon _{ij}}$ in a dielectric is given by

${\displaystyle P_{i}=e_{ijk}\epsilon _{jk}+\mu _{ijkl}{\frac {\partial \epsilon _{jk}}{\partial x_{l}}}}$

where the first term corresponds to the direct piezoelectric effect and the second term corresponds to the flexoelectric polarization induced by the strain gradient.

Here, the flexoelectric coefficient, ${\displaystyle \mu _{ijkl}}$, is a fourth-rank polar tensor and ${\displaystyle e_{ijk}}$ is the coefficient corresponding to the direct piezoelectric effect.

• Piezoelectricity
• Ferroelectricity
• Ferroelasticity
• Triboelectric effect

• Introduction to Flexoelectricity Archived 2009-03-06 at the Wayback Machine