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

Abstract

Flexoelectric effects hold promising applications in sensing, actuating, and energy capturing, and thus it is demanded to measure the flexoelectric coefficient tensors of dielectric materials accurately. In this work, an approach to measuring the effective flexoelectric coefficient tensor component μ 2312 of polymeric materials is developed by imposing a torque load upon a half cylindrical specimen. It is proven that μ 2312 can be calculated by assessing the electric charge on the axial plane and the strain gradient along the radial direction, both induced by the torque. To overcome the difficulty in experimental measurements, the relationship between the strain gradient and torque is deduced theoretically and further verified with finite element analysis. This approach is applied to testing bars machined from bulk polyvinylidene fluoride (PVDF). Potential errors from the piezoelectric effects and the non-uniform strain gradient are discussed to verify the validity of the measurement. The experimental results show good reproducibility and agreement with other measured effective flexoelectric tensor components of PVDF. This work indicates a potential application of PVDF-based mechanical sensors and provides a method to investigate the effective flexoelectric coefficient component of polymers.

Asymptotic Homogenization Applied to Flexoelectric Rods

“…Recent papers have established detailed descriptions of their experiments to determine the flexoelectric properties of PVDF. More precisely, References [44] and [45] describe experiments to find the effective flexoelectric components μ1123 and μ2312 of the fourth order tensor μijkl for polyvinylidene fluoride. On account of the great difficulty in obtaining some experimental measurements, the relationship between the strain gradient and torque is deduced theoretically and further verified with finite element analysis.…”

“…On account of the great difficulty in obtaining some experimental measurements, the relationship between the strain gradient and torque is deduced theoretically and further verified with finite element analysis. The approach is applied to test responses in bars machined from bulk polyvinylidene fluoride [45]. On the other hand, in Reference [46], the flexoelectricity of prototypical semicrystalline polymer, α-phase PVDF, films are investigated.…”

Flexoelectricity in dielectrics: Materials, structures and characterizations

“…This material has been the one that was measured for the components of its flexoelectric coefficient matrix, including 1211 ; 3121 ; 2312 and 1123 . [26][27][28][29] In addition to this shear component, the giant transverse and longitudinal flexoelectric coefficients in PVDF were observed. 15,[30][31][32] The difference apart from the flexoelectric characterization for solid material is that the residual piezoelectricity cannot be ignored for PVDF.…”

Compact explicit matrix representations of the flexoelectric tensor and a graphic method for identifying all of its rotation and reflection symmetries

“…The flexoelectric effects can be produced in a multitude of situations, for example, in bending crystal plates 1 , nanobeams and nanowires [2][3][4] or when stretching thin films 5 on liquid crystals 6 and on elastomers 7 . The flexoelectric constants describing the flexoelectric effects of some dielectric materials were observed and measured in a direct or indirect way in a few experimental works such as those made by Ma and Cross 8-10 and Zubko et al 11 for various perovskites which exhibit unusually high flexoelectricity, the ones of Kalinin and Meunier 12 and Naumov et al 13 for low-dimensional structures like nanographitic systems and two-dimensional boronnitride sheets or by Zhang et al 14,15 , Chu and Salem 16 and Zhou et al 17 for dielectric materials and polymers a) Corresponding author Tel: 33 (0) 160 957 797; Fax: 33 (0) 160 957 799; Email: hung.le-quang@univ-eiffel.fr such as TiO 2 ceramics and the polyvinylidene fluoride (PVDF). In parallel with these experimental works, theoretical studies were also conducted to demonstrate the size-dependent flexoelectric properties and surface effect of dielectric materials/structures in nanoscale, for example, by Sahin and Dost 18 , Tagantsev 19,20 , Yurkov and Tagantsev 21 , He et al 22 , Qi et al 23 and Bai et al 24 .…”