On the flexoelectricity in Polyvinylidene fluoride films
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On the flexoelectricity in Polyvinylidene fluoride films Xiangtong He, Sivapalan Baskaran, and John Y. Fu Department of Mechanical and Aerospace Engineering, The State University of New York at Buffalo, Buffalo, NY 14260, U.S.A. ABSTRACT It is well known that there is a linear electro-mechanical coupling under equilibrium thermodynamics in certain crystalline materials with non-centrosymmetric structures. Since Kogan and Meyer published their seminal papers in 1960s [1, 2], people have gradually realized that an inhomogeneous electro-mechanical coupling also exists in insulating materials, which is often called flexoelectricity. The physical mechanism of flexoelectricity in solid crystalline dielectrics is well known and its phenomenological model can be derived from the electromechanical energy coupling under equilibrium thermodynamics, whereas flexoelectricity in liquid crystals is closely related to the geometrical asymmetry of mesogen molecules or the shape polarity but the relation between the flexoelectric coefficients and molecular structures is far from being understood. Theoretically, flexoelectricity in polymers is similar to that in liquid crystals, which is largely dependent on rotation of molecules; therefore, the flexoelectric responses of polymers are complicated and might be different under external perturbations, such as tensile stretching, bending, electric field poling, etc. In this report, we will discuss experimental observations of the giant direct flexoelectric effect in certain polyvinylidene fluoride (PVDF) films under tensile stretching conditions. Our experimental studies indicate that the physical mechanism behind flexoelectricity in polymers might be more complicated than the one proposed for solid crystalline dielectrics. INTRODUCTION In solid crystalline dielectric materials, the phenomenon that the electric polarization ܲ can be induced under the application of a uniform strain ݁ is defined as the direct piezoelectric effect. It is well known that only the materials with the non-centrosymmetric crystal structures possess piezoelectricity since the piezoelectric coefficient is a third-rank tensor ݀ . However, the polarization ܲ can also be induced under non-uniform deformation even in the materials with centrosymmetric crystal structures; this is because the symmetry of their crystalline structures can be broken by the applied inhomogeneous strain field. Such an effect is called flexoelectricity, which is represented by a fourth rank tensor ߤ . Based on Kogan’s work, the constitutive equation of flexoelectricity can be written as [1] (1)
ܲ ൌ ߤ ߘ ܵ
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where ߘ represents the gradient with respect to the direction ݈, ܵ is the applied strain. Flexoelectricity in a liquid crystal is defined as the generation of electric polarization ܲௗ , when the asymmetric structure of ordered molecules undergoes distortion such as splay or bend. This linear energy coupling between deformation and polarization was proposed in 1969 by Meyer, which can be written as [2] (2)
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