Strain-Induced Toroidal Polar States in Wrinkled Ferroelectric Polymer by Phase-Field Simulations

Wrinkled ferroelectric polymer films with out-of-plane deformation exhibit exotic strain fields that differ from those of conventional epitaxial film systems, offering a new path toward manipulating electrical and mechanical behaviors in ferroelectrics. However, the direct observation of the domain structure evolution in ferroelectric polymer films during continuous deformation is challenging with current experimental approaches. In this study, the strain-induced evolution of toroidal domain structures in organic poly(vinylidene fluoride-ran-trifluoroethylene) (P(VDF-TrFE)) films with concentric toroidal wrinkle patterns is comprehensively investigated using phase-field simulations. The results reveal morphology- and thickness-dependent toroidal polar topology in wrinkled P(VDF-TrFE) films. External strain loading can modulate this ferroelectric domain, which exhibits robust coupling behavior with a mixed strain field of periodic tensile and compressive strains. It is demonstrated that toroidal wrinkled ferroelectric films provide an effective and unique flexible platform for continuously controllable strain engineering in ferroelectrics and a theoretical framework with potential applications in flexible electronic devices.