A model for the folding of freestanding ferroelectric films

Freestanding ferroelectric films offer many advantages over traditional substrate-attached thin films. It has been observed that, without the constraint of the rigid substrate, freestanding ferroelectric thin films may undergo a folding-unfolding transition under external electric field. The large displacement resulted in this folding-unfolding transition can be exploited to implement superelasticity in the thin films. A model based on the competition between the elastic bending force of the thin film and the electrostatic force from the surface charges on the periodic ferroelectric domains is formulated in this work. Effects of domain periodicity, polarization amplitude and the elastic property of the film on the folding-unfolding transition are studied. The model is then used to predict other ferroelectric thin films with similar superelastic behaviors.