An Electro-Chemo-Mechanical Theory With Flexoelectricity: Application to Ionic Conductivity of Soft Solid Electrolytes

Flexible batteries are gaining momentum in several fields, including wearable medical devices and biomedical sensors, flexible displays, and smartwatches. These energy storage devices are subjected to electro-chemo-mechanical effects. Here, we present a theoretical framework that couples diffusion and electromechanical theory with flexoelectricity. As an example, we investigate the effect of flexoelectricity on the ionic conductivity in soft materials. Our analytical results for a thin film made of a soft material reveal that the ionic conductivity is significantly higher at the nanoscale and decreases exponentially to approach the bulk value with increasing film thickness. Furthermore, we find that flexoelectricity reduces the ionic conductivity dramatically at film thickness smaller than the length scale associated with flexoelectricity. This behavior is attributed to the opposite directions of polarization induced by flexoelectricity and the flow of ions driven by the chemical potential. These findings shed light on the interplay between flexoelectricity and diffusion which would be paramount in designing miniaturized energy storage devices.