Flexoelectricity converse

Flexoelectricity involves two degrees of freedom of the BLM electrical and mechanical. The system is amenable to simultaneous electrical and optical investigation of mechanical-to-electrical-energy conversion mediated by a bi-molecularly thin membrane. BLMs themselves are unlikely to be used as device components. They offer, however, an eminently suitable means for conducting the fundamental studies which are necessary for the full potential of the membrane-mimetic approach to advanced materials to be realized. 

Converse flexoelectric effects (i.e. voltage-generated curving) have been demonstrated in uranyl-acetate-stabilized phosphatidylserine BLMs by real-time stroboscopic interferometric measurements the obtained satisfactory agreement between the converse and the direct (i.e. curvature-generated voltage) flexoelectric coefficients have been in accord with the Maxwell relationship [8]. 

In the following sections of this chapter we will summarize the direct, as well as the converse, flexoelectric measurements in fluid and elastomeric (dry or swollen) bent-core nematic liquid crystals, and try to explain these observations using the structural model outlined above. 

Although most of the scientists working on liquid crystals may think that flexoelectricity is a special property of liquid crystals, it was actually first discussed in 1964 for crystals as a response to strain (stress) gradients. The direct and converse flexoelectric coupling constants Cijki were described with a fourth-rank tensor, as... 

Converse flexoelectric studies of lyotropic liquid crystals, such as vesicles, is still an active subject. Notably, the sensory mechanism of outer hair cell composite membranes " can be understood by the flexoelectric properties of the lipid bilayer. The converse of this effect, i.e., a voltage-generated curvature, has also been observed and was discussed by Todorov et Another related phenomenon is the ferroelectricity which results from the tilted layered structures of chiral molecules, which has been discussed extensively since the 1980s.Ferroelectric phases are called... 

We note here that, though the substrate curvature due to the converse giant flexoelectric effect could be observed, detection of the converse flexoelectric effect of calamitic nematics using the same geometry cannot be... 

A possible clue for resolving the problem of giant versus normal flexoelectricity of BC nematics may lie in recent observations of converse giant flexoelectricity. As flexoelectricity is a linear phenomenon, the deformation of the substrates is expected to be proportional to the applied voltage. In this experiment, however, no flexing was detected below a critical voltage corresponding to a critical electric field of IV/itm. This may be interpreted that the cluster contribution to flexoelectricity requires a threshold... 

Summarizing, experimental observations suggest that the giant (direct or converse) flexoelectricity of bent-core nematics is related to the polar smectic clusters occurring in them. In order to explore the exact mechanism for how clusters contribute to the flexoelectric response, further experimental and theoretical studies are needed. 

Efficient energy conversion has been demonstrated under dynamic flexing conditions (using a nanoscale cantilever beam ). Disadvantageously, however, ceramics are fragile and difficult to stress, cannot maintain a large bend and suffer from fatigue in a dynamic environment. Furthermore, flexoelectric crystals must have a suitable shape, which makes the fabrication process for crystalline or ceramic solid materials much more difficult. 

A.T. Todorov, A.G. Petrov and J.H. Fendler, First observation of the converse flexoelectric effect in bilayer lipid membranes, J. Phys. Chem. 98(12), 3076-3099, (1994). doi 10.1021/jl00063a004... 

J.Y. Fu, Z. Zhu and L.E. Cross, Experimental studies of the converse flexoelectric effect induced by inhomogeneous electric field in a barium strontium titanate composition, J. Appl. Phys. 100(2), 024112/1-6, (2006). 

The theory and experiments of lyotropic and biomembrane flexoelectricity are reviewed. Flexoelectricity is a reciprocal relation between electricity and mechanics in soft lyotropic systems, i.e., between curvature and polarization. Experimental evidence of model and biomembrane flexoelectricity (including the direct and the converse flexoelectric effects) is reported. The biological implications of flexoelectricity are underlined. Flexoelectricity enables membrane structures to function like soft micromachines and nanomachines, sensors and actuators, thus providing important input to nanoionics apphcations. Nanobio examples include membrane transport, membrane contact, mechanosensitiv-ity, electromotility, hearing, nerve conduction, etc. 

As in the piezoelectricity of solids, flexoelectricity also manifests as a direct effect [f, Eq. (6.4)] and a converse effect [f, Eq. (6.5)], with an electric field-induced curvature ... 

Exploring the molecular mechanisms of flexoelectricity is a central task of the liquid crystal approach in membrane biophysics. 43,15-21 pjjg flexoelectric coefficient can be represented as an integral over the curvature derivative of the distribution of the normal component of polarization P z, c+) across the membrane (c+ = ci - - C2 is the total curvature). Both direct and converse flexocoefficients can be expressed in this manner and these can be shown to be equal ... 

Mechanical tension may be due to a converse-flexoelectric area dilatation induced by the photopotential, as analysed above [c/. Eq. (6.16)]. The photopotential is due to the pH gradient because of the ferricyanide photochemical reactions. The increase of membrane tension above a certain threshold can open the ion channels thus dissipating the pH gradient returning the membrane tension back to zero (at this instant extensive form fluctuations, cf. Fig. 6.10, are thermally excited), so that the channels close and the cycle repeats. Under this scenario it is clear that the whole photo-... 

A. Todorov, Experimental Investigations of Direct and Converse Flexoelectric Effect in BUayer Lipid Membranes, PhD Thesis, Syracuse University, 1993. 

The second application uses the converse flexoelectric effect, i.e. a field-induced splay-bend distortion, to generate a fast, symmetric and thresholdless linear electro-optic effect in a cholesteric liquid crystal. 

As has been shown, the splay and bend distortions of a nematic create electric polarization. There is also a converse effect the external electric field causes a distortion due to the flexoelectric mechanism. For example, if the banana-shape molecules with transverse dipoles are placed in the electric field, the dipoles are partially aligned along the field and their banana shape induces some bend. This effect takes place even in nematics with zero dielectric anisotropy. 

Fig. 11.27 Converse flexoelectric effect (a) Structure of the electrooptical cell, (b) Distribution of the director angle over the cell thickness pictured by lower straight lines for zero (solid line) and finite (dot line) anchoring energies, respectively. The upper curves show spatial dependence of two principal refraction indices no (dash line) and (z) (solid line)...

Fig. 11.29 Conversed flexoelectric effect in cells with homeotropic (a) and homogeneous (b) director alignment and electric field applied along the cell normal. Weak anchoring energy at the bottom plate allows the flexoelectric deflection of the director 3 at the surface propagating up in the vertical direction (e = 0)...

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