Nanoscale Flexoelectricity

Abstract

Electromechanical effects are ubiquitous in biological and materials systems. Understanding the fundamentals of these coupling phenomena is critical to devising next-generation electromechanical transducers. Piezoelectricity has been studied in detail, in both the bulk and at mesoscopic scales. Recently, an increasing amount of attention has been paid to flexoelectricity: electrical polarization induced by a strain gradient. While piezoelectricity requires crystalline structures with no inversion symmetry, flexoelectricity does not carry this requirement, since the effect is caused by inhomogeneous strains. Flexoelectricity explains many interesting electromechanical behaviors in hard crystalline materials and underpins core mechanoelectric transduction phenomena in soft biomaterials. Most excitingly, flexoelectricity is a size-dependent effect which becomes more significant in nanoscale systems. With increasing interest in nanoscale and nano-bio hybrid materials, flexoelectricity will continue to gain prominence. This Review summarizes work in this area. First, methods to amplify or manipulate the flexoelectric effect to enhance material properties will be investigated, particularly at nanometer scales. Next, the nature and history of these effects in soft biomaterials will be explored. Finally, some theoretical interpretations for the effect will be presented. Overall, flexoelectricity represents an exciting phenomenon which is expected to become more considerable as materials continue to shrink.

Fundamentals of flexoelectricity in solids

“…This method was used by Fu and coworkers to measure the converse flexoelectric effect and thus estimate the flexoelectric coefficientμ 11 for BST, which was found to be in excellent agreement with measurements of the direct flexoelectric effect [31]. A similar method was also used by Hana et al to study converse flexoelectricity in PbMg 1/3 Nb 2/3 O 3 -PbTiO 3 [33,107].…”

“…Namely, as follows from equation (5), under the short-circuited conditions (E = 0), strain induces polarization while, as follows from equation (6), under the mechanically free conditions (σ = 0), polarization induces strain. However, equations (10) and (11) suggest a certain asymmetry between the direct and converse flexoelectric effects: as clear from equations (10) and (11), in the absence of an electric field, a strain gradient induces homogeneous polarization while, for the converse effect, in a mechanically free sample, homogeneous polarization does not induce a strain gradient. This asymmetry provoked a judgment that a sensor based on the flexoelectric effect will not behave as an actuator [7].…”

“…An approximate form of the constitutive equations (10) and (11), where the last rhs term in (10) is neglected and equation (11) is rewritten in terms of E, neglecting the appearing contribution ∝ ∂ 2 u ik ∂x j ∂x l , is also used [7]:…”

“…Judging from the number of publications on flexoelectricity in solids (figure 1), the total volume of activity in the field is still modest but the field is evolving rapidly. Several reviews have already been published on flexoelectricity in solids [5][6][7][8][9][10][11][12], some of them quite recently. Based on these publications, one finds the big picture of the field, which leaves a mixed impression.…”

Interesting Evidence for Template‐Induced Ferroelectric Behavior in Ultra‐Thin Titanium Dioxide Films Grown on (110) Neodymium Gallium Oxide Substrates

“…a flexoelectric effect [36] ) may also be having an effect in breaking the symmetry along the c-axis, and stabilising a single domain state in the thinnest films. Lee at al.…”