Excitation flexoelectric

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-... 

According to Eq. (7.1) P is zero for the two cases of uniform director fields and pure twist. Hence both cases can serve as a zero state as far as flexoelectric excitations are concerned. It is important to note that a twist is not associated with a polarization (i.e. C2 is identically zero, cf. Fig. 7.2). An imstrained nematic has a centre of symmetry (centre of inversion). On the other hand, none of the elementary deformations - splay, twist or bend have a centre of symmetry. According to Curie s principle they could then be associated with the separation of charges analogous to the piezoeffect in solids. This is true for splay and bend but not for twist because of an additional symmetry in that case if we twist the adjacent directors in a nematic on either side of a reference point, there is always a two-fold symmetry axis along the director of the reference point. In fact, any axis perpendicular to the twist axis is such an axis. Due to this symmetry no vectorial property can exist perpendicular to the director. In other words, a twist does not lead to the separation of charges. This is the reason why twist states appear naturally in liquid crystals and are extremely common. It also means that an electric field cannot induce a twist just by itself in the bulk of a nematic. If anything it reduces the twist. A twist can only be induced in a situation where a field turns the director out of a direction that has previously been fixed by boundary conditions (which, for instance, happens in the pixels of an IPS display). 

The effect of flexoelectricity is also considerable in the case of a.c. excitation. References [88] suggest that it is the flexoelectric effect which transforms chevrons, initially perpendicular to the director, into a set of oblique rolls at a field which is very slightly above the threshold value (Fig. 5.10). 

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