Nonlinear bending deformation of soft electrets and prospects for engineering flexoelectricity and transverse (d31) piezoelectricity†
Soft materials that exhibit electromechanical coupling are an important element in the development of soft robotics, flexible and stretchable electronics, energy harvesters, sensor and actuators. Truly soft natural piezoelectrics essentially do not exist and typical dielectric elastomers, predicated on electrostriction and the Maxwell stress effect, exhibit only a one-way electromechanical coupling. Extensive research however has shown that soft electrets i.e. materials with embedded immobile charges and dipoles, can be artificially engineered to exhibit a rather large piezoelectric-like effect. Unfortunately, this piezoelectric effect—large as it may be—is primarily restricted to an electromechanical coupling in the longitudinal direction or what is referred colloquially as the d33 piezoelectric coefficient. In sharp contrast, the transverse piezoelectric property (the so-called d31 coefficient) is rather small. This distinction has profound implications since these soft electrets exhibit negligible electromechanical coupling under bending deformation. As a result, the typically engineered soft electrets are rendered substantively ill-suited for energy harvesting as well as actuation/sensing of flexure motion that plays a critical role in applications like soft robotics. In this work, we analyze nonlinear bending deformation of a soft electret structure and examine the precise conditions that may lead to a strong emergent piezoelectric response under bending. Furthermore, we show that non-uniformly distributed dipoles and charges in the soft electrets lead to an apparent electromechanical response that may be ambiguously and interchangeably interpreted as either transverse piezoelectricity or flexoelectricity. We suggest pragmatic routes to engineer a large transverse piezoelectric (d31) and flexoelectric coefficient in soft electrets. Finally, we show that in an appropriately designed soft electret, even a uniform external electric field can induce curvature in the structure thus enabling its application as a bending actuator.