Scaling relations of dynamic hysteresis in pristine and BiFeO3 particle embedded P(VDF-TrFE) flexible ferroelectric membranes

The domain reversal dynamics of the pristine and 10 wt. % BiFeO3 nanoparticle-embedded P(VDF-TrFE) (polyvinylidene fluoride-trifluoroethylene) flexible ferroelectric membranes were investigated. A scaling relation of A∝fαE0β relevant to the domain reversal dynamics was eventually determined. The pristine P(VDF-TrFE) flexible membrane takes the form of A∝f0.04077E00.39748 in stage III of high electric fields. Nevertheless, for BiFeO3-embedded P(VDF-TrFE) [BFO/P(VDF-TrFE)] flexible membranes, the relations are developed as A∝f−0.3326E02.74911 in the low electric fields of stage I and as A∝f0.04309E01.04872 in stage III separately. The negative α indicates that more and more domain reversal lags behind the alternating periodic electric field in stage I. Instead, in stage III, the positive α indicates that most domain reversals can occur anytime whatever the alternating speed of electric fields is. Analogously, the positive β indicates that at any selected frequency, domains can flip at an external electric field. Abnormally, for the pristine P(VDF-TrFE) membrane, the scaling relation in the first E0 stage is broken, reflecting only dielectric contributions this time. The dynamic scaling data are significant for the micromechanism accomplishments of copolymers and for the designs of flexible electric devices.