Molecule pear-shaped

Fig. 4. Tentative allocation of probe binding sites within the three-dimensional structure of Ca -ATPase derived from vanadate-induced E2-type crystals. The top picture is the projection view of the Ca -ATPase down the x-axis, revealing the pear-shaped contours of ATPase molecules. The maximum length of the cytoplasmic domain to the tip of the lobe is =r65A. In the middle and bottom pictures the same structure is viewed down the x-axis, revealing the gap between the bridge and the bilayer surface and the connections between ATPase molecules in neighboring dimer chains. The proposed binding sites for lAEDANS and FITC are indicated. The bottom right picture is the same structure viewed down the y-axis. Adapted from Taylor et al. [90].

J. Stelzer, R. Berardi and C. Zannoni, Flexoelectric effects in liquid crystals formed by pear-shaped molecules. A computer simulation study, Chem. Phys. Lett. 299(1), 9-16, (1999). doi 10.1016/S0009-2614(98)01262-7... 

In addition to the pear-shaped molecules, bent-shaped molecules were used to illustrate the dipolar origin of the flexoelectric effects in nematic liquid crystals. It was assumed that the constituent molecules of the nematic liquid crystals are free to rotate around their axes, and in the absence of electric fields, their dipole moments average out so the net polarization of the material is zero. However, when liquid crystals made from polar pear- or banana-shaped molecules are subjected to splay or bend deformations, respectively, they can become macroscopically polar, because the polar structures correspond to a more efficient packing of the molecules. It follows from symmetry considerations that the deformation-induced fiexo-electric polarization Pa can be written as ... 

In precisely the same way, a spontaneously splay-deformed structure must correspond to the equilibrium condition with finite coefficient fsTi 7 0 in tensor (8.13). The corresponding term should be added to the splay term with (divn). If the molecules have, e.g., pear shape they can pack as shown in Fig. 8.7b. In this case, the local symmetry is Coov (conical) with a polar rotation axis, which is compatible with existence of the spontaneous polarization. However, such packing is unstable, as seen in sketch (b), and the conventional nematic packing (a) is more probable. The splayed stmcture similar to that pictured in Fig. 8.7b can occur close to the interface with a solid substrate or when an external electric field reduces the overall symmetry (a flexoelectric ejfecf). 

Fig. 8.7 Packing of conical pear-shape) molecules in the conventional nematic phase (a) and in a hypothetical polar nematic phase (b)...

Fig. 11.24 Dipolar flexoelectric polarization. Pear-shape and banana-shape molecules in undistorted nematic liquid crystals without any polar axes (a) and appearance of polar axes and flexoelectric polarization along the z-direction in the same nematics due, correspondingly, splay and bend distortion (b)...

In the case of pear-shaped molecules, the value of the induced polarization is proportional to the splay deformation V n, and its direction is along n. In the case of the banana-shaped molecules, the induced polarization is proportional to the bend deformation n xVxn. Including both cases, the induced polarization is given by... 

It is well known that a nematic liquid crystal is nonpolar as a result of the free or hindered rotation of its constituent molecules around their axes. In the absence of an external field the distribution of the dipoles in an undistorted nematic liquid crystal has a nonpolar cylindrical symmetry. This is shown schematically in Fig. 4.29(a). However, as Meyer [183] has shown, a polar axis can arise in a liquid crystal made up of polar pear-shaped molecules when it is subjected to splay deformations, or in a liquid crystal made up of banana-shaped molecules subjected to bend deformations. In this case, the polar structure corresponds to closer packing of the molecules (Fig. 4.29(b)). Thus, the external mechanical deformation of the nematic liquid crystal results in the occurrence of a charge at electrodes perpendicular to the polar axis, i.e., there is a similarity to the piezoelectric effect in solid crystals. 

The most direct method of finding the coefficient en would be to fill the space between the metallic coaxial cylinders with a liquid crystal having pear-shaped molecules, with the surfaces of the cylinders having been pretreated for homeotropic orientation and to measure the potential difference between the cylinders. In fact, because of the difference in radii of the cylinders, the nematic liquid crystal structure proves to be splay deformed, and if the molecules have even a small longitudinal dipole moment the plates of the coaxial capacitor would be charged. However, despite its apparent simplicity, this experiment is, in fact, complicated because of the screening of the potential caused by the flexoelectric effect by firee charges from the liquid crystal and the atmosphere. 

FIGURE 4.33. Calculation of the flexoelectric coefficients for (a) pear-shaped molecules (b) banana-shaped molecules and (c) the quadrupole model of the flexoelectric effect [200]. 

Illustration of the flexoelectricity assuming polar noncentrosymmetric molecules. Upper row pear-shape molecules Bottom row banana-shape molecules. (After Meyer. 

Molecular models for (a) pear-shape molecules (b) banana-shape molecules, used for calculation of flexoelectric coefficients. 

Note 2 The molecular origins of dipolar flexo-electricity are the particular shape anisotropy (e.g., resembling a pear or banana) of the molecules, each of which must also possess a permanent dipole moment. 

Fig. 32. Schematic representation of the flexo-electric effect, (a) The structure of an undeformed nematic liquid crystal with pear- and banana-shaped molecules (b) the same liquid crystal subjected to splay and bend deformations, respectively.

Let us look at Fig. 11.24. In the upper two sketches, we can see undistorted nematic liquid crystals with pear- and banana-shape molecules. Such nematics in the bulk... 

Figure 15.1 shows the three ways the atoms of a crystalline solid can be arranged. As a molecule goes from a simple cubic structure to a face-centered cubic structure, the density increases. The less space between the atoms, the more tightly packed the entire molecule, and the harder and less flexible. Unlike amorphous solids, a lattice structure provides for predictable breaks along set lines. This is the reason why diamonds and gemstones can be cut into facets. The round, oval, pear, emerald cut, and diamond-shaped cuts used in jewelry can be cut by dilferent gem cutters all over the world due to their characteristic lattice structures. 

The molecular-statistical approach to calculating the flexoelectric coeflS-cients was developed independently in [198, 199]. Parameters a, 6, and Oq are introduced to define the pear or banana shape of the molecules (Fig. 4.33). Next, by specifying a definite splay or bend deformation, it is possible to calculate the fraction of the molecules which achieve the preferred orientation of their dipoles in order to ensure the maximum packing density. The excess number AN = — N-) of the molecules with dipole... 

Minimizing the total energy, F = F,. + now leads to pears, budding and a multitude of starfish vesicles, some of which are shown in Figure 7.3 [7], These shapes depend not just on the reduced volume v but on one more parameter which basically is the number difference of lipid molecules in the two layers. These shapes of lowest energy can be arranged in a two-dimensional phase diagram [15,18]. As... 

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