Experimental method research on transverse flexoelectric response of poly(vinylidene fluoride)

Abstract

Flexoelectricity describes the strain-gradient-induced electric polarization existing in dielectric materials. The coefficient that exists between the strain-gradient and the induced electric polarization defines the flexoelectric coefficient tensor. It is necessary to analyze different experimental methods to evaluate the procedure of measuring the transverse flexoelectric coefficient tensor component. In this work, the transverse flexoelectric coefficient tensor component of poly(vinylidene fluoride) (PVDF) is studied using three different experimental methods and the effects of the mentioned methods are evaluated. The results presented in this work are helpful for the design of experiments of different dielectric materials, including ceramics and polymers on flexoelectricity.

Investigation of the 2312 flexoelectric coefficient component of polyvinylidene fluoride: Deduction, simulation, and mensuration

“…In this description, the gradient of the electric polarization-induced stress contributes to the deformation of the material, and enhances the general deformation, especially in the dielectrics with high dielectric constants and in smaller scales. Considering the low dielectric constant, the macro-scale of the designed specimen, and the previously measured electric polarization magnitudes 28 – 30 , this coupling effect is negligible in this study, hence Hooke’s law is adopted for the analysis of the stress-strain relationship. In the elastic regime, the shear strain γϕ z is proportional to the shear stress simply by applying the shear modulus G 31 , 32 …”

“…When a small twisting moment is imposed upon the sandwich specimen, shear strain is generated in both PVDF parts and the rectangular epoxy. According to theoretical deduction, the shear angles ϕ of the PVDF parts and the epoxy can be calculated using the following equations 30 , 31 : where M , I , G , and the subscripts c and r are the magnitudes of torque, the polar moment of inertia, shear modulus, the cylindrical parts and epoxy, respectively. l and D represent the length and diameter of the cylindrical bar, while h and b define the long and short side of the rectangular electrode.…”

“…In our previous work, experimental approaches have been developed to assessing the flexoelectric coefficient components μ 1211 and μ 3121 of polymers. As an example, these methods were applied to PVDF, and μ 1211 and μ 3121 were measured in the magnitude of 10 −10 C/m and 10 −8 C/m, respectively 28–30 . It is worth emphasizing that all those measured values are effective flexoelectric coefficients, for the following reasons.…”

Ultrahigh flexoelectric effect of 3D interconnected porous polymers: modelling and verification

“…where μ ijkl is the flexoelectric coefficient along l direction of the strain gradient that the elastic strain ε ij induced along x k direction 40 . Therefore, regardless of the macro geometry of the sample and the loading form, the remarkable flexoelectric response can be obtained.…”

Modeling flexoelectricity in soft dielectrics at finite deformation

“…Flexoelectric effects have been observed and widely studied in hard materials (Tolpygo, 1963, Kogan, 1964, Hong and Vanderbilt, 2011, Resta, 2010, Maranganti et al, 2006, mainly crystalline ceramics such as ferroelectric perovskites (Zubko et al, 2007, Ma and Cross, 2001a, Fu et al, 2006, Ma and Cross, 2001b, 2003. However, they are also present in soft materials, such as liquid crystals (Meyer, 1969, Petrov, 1975, Prost and Marcerou, 1977, Harden et al, 2006, Trabi et al, 2008, cellular membranes (Petrov et al, 1989, Todorov et al, 1991, 1994, Sun, 1997, Petrov, 2002 and polymers (Breger et al, 1976, Marvan and Havránek, 1998, Baskaran et al, 2011, Deng et al, 2014c, Zhang et al, 2016b, Zhou et al, 2017.…”