Electrets in soft materials: Nonlinearity, size effects, and giant electromechanical coupling

Development of soft electromechanical materials is critical for several tantalizing applications such as soft robots and stretchable electronics, among others. Soft nonpiezoelectric materials can be coaxed to behave like piezoelectrics by merely embedding charges and dipoles in their interior and assuring some elastic heterogeneity. Such so-called electret materials have been experimentally shown to exhibit very large electromechanical coupling. In this work, we derive rigorous nonlinear expressions that relate effective electromechanical coupling to the creation of electret materials. In contrast to the existing models, we are able to both qualitatively and quantitatively capture the known experimental results on the nonlinear response of electret materials. Furthermore, we show that the presence of another form of electromechanical coupling, flexoelectricity, leads to size effects that dramatically alter the electromechanical response at submicron feature sizes. One of our key conclusions is that nonlinear deformation (prevalent in soft materials) significantly enhances the flexoelectric response and hence the aforementioned size effects.

Figure 1

A dielectric film under external electric field undergoes a deformation proportional to the square of the applied voltage difference across its thickness direction. The deformation results from the Coulombic force between the bound charges and dipoles generated at the opposing surfaces in response to the electric field. The deformation changes in magnitude with the variation of the applied voltage difference but not the direction.

Figure 2

Strain-voltage curves of the dielectric film: solid line shows conventional dielectrics; dashed line shows electrets.

Figure 3

The constituent of an electret: a layer of net charge is deposited between two different dielectric films.

Figure 4

A simplified model for the ferroelectret in which opposite charges are deposited on the surfaces of voids.

Figure 5

The variation of $d^{\mathrm{eff}}$ with respect to the applied voltage across the films.

Figure 6

The piezoelectric effect of the ferroelectret.

Figure 7

Size effect in electrets due to the flexoelectricity.