  Soft robotics requires materials that are capable of large deformation and
amenable to actuation with external stimuli such as electric fields. Energy
harvesting, biomedical devices, flexible electronics and sensors are some other
applications enabled by electro-active soft materials. The phenomenon of
flexoelectricity is an enticing alternative that refers to the development of
electric polarization in dielectrics when subjected to strain gradients. In
particular, flexoelectricity offers a direct linear coupling between a highly
desirable deformation mode (flexure) and electric stimulus. Unfortunately,
barring some exceptions, the flexoelectric effect is quite weak and rather
substantial bending curvatures are required for an appreciable
electro-mechanical response. Most experiments in the literature appear to
confirm modest flexoelectricity in polymers although perplexingly, a singular
work has measured a "giant" effect in elastomers under some specific
conditions. Due to the lack of an understanding of the microscopic
underpinnings of flexoelectricity in elastomers and a commensurate theory, it
is not currently possible to either explain the contradictory experimental
results on elastomers or pursue avenues for possible design of large
flexoelectricity. In this work, we present a statistical-mechanics theory for
the emergent flexoelectricity of elastomers consisting of polar monomers. The
theory is shown to be valid in broad generality and leads to key insights
regarding both giant flexoelectricity and material design. In particular, the
theory shows that, in standard elastomer networks, combining stretching and
bending is a mechanism for obtaining giant flexoelectricity, which also
explains the aforementioned, surprising experimental discovery.
