Strain gradient induced electric polarization in <i>α</i>-phase polyvinylidene fluoride films under bending conditions

Baskaran, Sivapalan; He, Xiangtong; Wang, Yu; Fu, John Y.

doi:10.1063/1.3673817

Cited by 68 publications

(51 citation statements)

References 19 publications

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“…We did not find evidence for giant flexoelectric coefficients of up to 82 lC/m as reported by Baskaran et al with nominally unpoled samples of PVDF. [15][16][17] Although they corrected their data for piezoelectric contributions, a small error in the correction may have had a large effect on the extracted value of the flexoelectric coefficient, as we found in our studies.…”

supporting

confidence: 60%

“…14 Nevertheless, Baskaran et al have reported high values for the flexoelectric coefficient l up to 82 lC/m in nominally nonferroelectric PVDF samples. [15][16][17] It is difficult, however, to rule out piezoelectric contributions from residual ferroelectric beta and delta phases, because PVDF is, in general, a polymorphous material, 14,18,19 containing a substantial amorphous component 20 and various crystalline phases that depend strongly on synthesis and sample preparation procedures. [21][22][23] Therefore, we have made a study of thin films of VDF copolymer and a VDF terpolymer, which allow us to compare the flexoelectric response in three distinct states-ferroelectric, paraelectric, and relaxor.…”

mentioning

confidence: 99%

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Measurement of the flexoelectric response in ferroelectric and relaxor polymer thin films

Poddar¹,

Ducharme²

2013

Appl. Phys. Lett.

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supporting

confidence: 60%

mentioning

confidence: 99%

Measurement of the flexoelectric response in ferroelectric and relaxor polymer thin films

Poddar¹,

Ducharme²

2013

Appl. Phys. Lett.

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“…Flexoelectricity has been experimentally confirmed in several crystalline materials such as NaCl, strontium titanate, and ferroelectrics like barium titanate, among others [17][18][19][20][21]. Some recent experiments have also measured a flexoelectric response in several polymers [22][23][24].…”

Section: What Are Some Examples Of Real Materials In Which Flexoelectmentioning

confidence: 91%

Flexoelectricity: A Perspective on an Unusual Electromechanical Coupling

Krichen

Sharma

2016

Journal of Applied Mechanics

178

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The ability of certain materials to convert electrical stimuli into mechanical deformation, and vice versa, is a prized property. Not surprisingly, applications of such so-called piezoelectric materials are broad-ranging from energy harvesting to self-powered sensors. In this perspective, written in the form of question-answers, we highlight a relatively understudied electromechanical coupling called flexoelectricity that appears to have tantalizing implications in topics ranging from biophysics to the design of next-generation multifunctional nanomaterials.A uniform mechanical strain electrically polarizes a piezoelectric material. There is extensive literature on the formal development of the phenomenological theory of piezoelectricity; however, simply put, this phenomenon may be described by the following linearized relation between the components of the polarization vector (P) and the strain tensor (e): P i d ijk e jk . The piezoelectric property tensor (d) is third order. Group theory states that only noncentrosymmetric crystals may exhibit properties dictated by third-order tensors [1], and accordingly, common insulators which possess a centrosymmetric crystal structure, such as Si and NaCl, are nonpiezoelectric.However, as schematically alluded to in Fig. 1, a nonuniform strain may break the mirror symmetry even in otherwise centrosymmetric crystals. The relation of the polarization to the extent of the nonuniformity of the strain field, or strain gradient, is known as flexoelectricity: P i d ijk e jk þ f ijkl ð@e jk =@x l Þ, where f ijkl are the components of the so-called flexoelectric tensor. While the piezoelectric property is nonzero only for selected materials, the strain gradient-polarization coupling (i.e., flexoelectricity tensor) is in principle nonzero for all (insulating) materials. This implies that under a nonuniform strain, all dielectric materials are capable of producing a polarization. The reader is referred to the following articles for further information: Refs. [2][3][4][5][6][7][8][9].

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“…B (83) which holds ∀ u , v , C u ∈ R + . Let us consider now the mesh-dependent constants K u , K v , K C u ∈ R + such that t(δu) 2 L 2 (Ω c ∩∂Ω u ) ≤ K u Ω c ∩Ω σ i j (δu)ε i j (δu) +σ i jk (δu)ε i j,k (δu) dΩ, (84a) r(δu) 2 L 2 (Ω c ∩∂Ω v ) ≤ K v Ω c ∩Ω σ i j (δu)ε i j (δu) +σ i jk (δu)ε i j,k (δu) dΩ,…”

Section: Appendix B Materials Tensorsmentioning

confidence: 97%

An immersed boundary hierarchical B-spline method for flexoelectricity

Codony

Marco

Fernández‐Méndez

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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This paper develops a computational framework with unfitted meshes to solve linear piezoelectricity and flexoelectricity electromechanical boundary value problems including strain gradient elasticity at infinitesimal strains. The high-order nature of the coupled PDE system is addressed by a sufficiently smooth hierarchical B-spline approximation on a background Cartesian mesh. The domain of interest is embedded into the background mesh and discretized in an unfitted fashion. The immersed boundary approach allows us to use B-splines on arbitrary domain shapes, regardless of their geometrical complexity, and could be directly extended, for instance, to shape and topology optimization. The domain boundary is represented by NURBS, and exactly integrated by means of the NEFEM mapping. Local adaptivity is achieved by hierarchical refinement of B-spline basis, which are efficiently evaluated and integrated thanks to their piecewise polynomial definition. Nitsche's formulation is derived to weakly enforce essential boundary conditions, accounting also for the non-local conditions on the non-smooth portions of the domain boundary (i.e. edges in 3D or corners in 2D) arising from Mindlin's strain gradient elasticity theory. Boundary conditions modeling sensing electrodes are formulated and enforced following the same approach. Optimal error convergence rates are reported using high-order B-spline approximations. The method is verified against available analytical solutions and well-known benchmarks from the literature.

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Strain gradient induced electric polarization in α-phase polyvinylidene fluoride films under bending conditions

Cited by 68 publications

References 19 publications

Measurement of the flexoelectric response in ferroelectric and relaxor polymer thin films

Measurement of the flexoelectric response in ferroelectric and relaxor polymer thin films

Flexoelectricity: A Perspective on an Unusual Electromechanical Coupling

An immersed boundary hierarchical B-spline method for flexoelectricity

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