  It has been well known that flexoelectricity can be exploited to generate an
analogous piezoelectric response in non-piezoelectric materials. For the direct
flexoelectric effect, the induced electric polarization is linearly
proportional to the applied strain gradient. Therefore, it is logical to expect
that such a piezoelectric response would be enhanced in the materials with
reduced dimensions. In this paper, we will report our experimental observation
of such a gradient scaling phenomenon of piezoelectricity in non-piezoelectric
polyvinylidene fluoride (PVDF) films.
