Boundary nematics

There exists a maximum pressure beyond which the smectic A phase disappears (see Fig. Id). The p(7 )-phase boundary nematic-smectic A has an elliptic shape. Reentrant behavior has been found for many systems, and therefore several theoretical treatments have been considered to explain this phenomenon. The most successful is probably the frustrated spin-gas model, which also predicts the sensitivity to the number of carbon atoms in the alkyl chain of the molecule. ... 

The structures of phases such as the chiral nematic, the blue phases and the twist grain boundary phases are known to result from the presence of chiral interactions between the constituent molecules [3]. It should be possible, therefore, to explore the properties of such phases with computer simulations by introducing chirality into the pair potential and this can be achieved in two quite different ways. In one a point chiral interaction is added to the Gay-Berne potential in essentially the same manner as electrostatic interactions have been included (see Sect. 7). In the other, quite different approach a chiral molecule is created by linking together two or more Gay-Berne particles as in the formation of biaxial molecules (see Sect. 10). Here we shall consider the phases formed by chiral Gay-Berne systems produced using both strategies. 

Here, ry is the separation between the molecules resolved along the helix axis and is the angle between an appropriate molecular axis in the two chiral molecules. For this system the C axis closest to the symmetry axes of the constituent Gay-Berne molecules is used. In the chiral nematic phase G2(r ) is periodic with a periodicity equal to half the pitch of the helix. For this system, like that with a point chiral centre, the pitch of the helix is approximately twice the dimensions of the simulation box. This clearly shows the influence of the periodic boundary conditions on the structure of the phase formed [74]. As we would expect simulations using the atropisomer with the opposite helicity simply reverses the sense of the helix. 

Many other interesting examples of spontaneous reflection symmetry breaking in macroscopic domains, driven by boundary conditions, have been described in LC systems. For example, it is well known that in polymer disperse LCs, where the LC sample is confined in small spherical droplets, chiral director structures are often observed, driven by minimization of surface and bulk elastic free energies.24 We have reported chiral domain structures, and indeed chiral electro-optic behavior, in cylindrical nematic domains surrounded by isotropic liquid (the molecules were achiral).25... 

The coagulation process can now be considered in perspective of a ternary polymer-solvent-nonsolvent system, A schematic ternary phase diagram, at constant temperature, is shown in Figure 8. The boundaries of the isotropic and narrow biphasic (isotropic-nematic) regions are based on an extension of Flory s theory ( ) to a polymer-solvent-nonsolvent system, due to Russo and Miller (7). These boundaries are calculated for a polymer having an axial ratio of 100, and the following... 

Mesophase with a helicoidal supramolecular structure of blocks of molecules with a local smectic C structure. The layer normal to the blocks rotates on a cone to create a helix-like director in the smectic C. The blocks are separated by plane boundaries perpendicular to the helical axis. At the boundary, the smectic order disappears but the nematic order is maintained. In the blocks the director rotates from one boundary to the other to allow the rotation of the blocks without any discontinuity in the thermomolecular orientation. 

Chen s analysis is more accurate than the procedure in which the Onsager trial function is used with a(N) given by Eq. (18), but it is very involved to carry through. On the other hand, the Onsager trial function procedure is simple enough for practical purposes. As shown in Appendix A, it predicts the isotropic-nematic phase boundary concentrations that can be favorably compared with those by Chen s procedure. 

The Gaussian trial function for f(a) used by Odijk [6] is mathematically simpler than Onsager s and allows p to be expressed by the leading term of Eq. (22) and ct(N) to be derived analytically. However, it becomes less accurate as the orientation gets weaker. As shown in Appendix A, its use leads to the isotropic-nematic phase boundary concentrations largely different from those by Chen s method and hence is not always relevant for quantitative discussion. 

The equilibrium value of a in the nematic phase can be determined by minimizing AF. With Eq. (19) for AF from the scaled particle theory, S has been computed as a function of c, and the results are shown by the curves in Fig. 12. Here, the molecular parameters Lc and N were estimated from the viscosity average molecular weight Mv along with ML and q listed in Table 1, and d was chosen to be 1.40 nm (PBLG), 1.15 nm (PHIC), and 1.08 nm (PYPt), as in the comparison of the experimental phase boundary concentrations with the scaled particle theory (cf. Table 2). 

Chen [47] calculated the isotropic-nematic phase boundary concentrations using not any trial function but f(a) determined by an numerical-iteration procedure. This method is more rigorous than the one resorting to a trial... 

Lubensky TC, Renn SR (1990) Twist-grain-boundary phases near the nematic smectic-A smectic-C point in liquid crystals. Phys Rev A 41 4392-4401... 

The modulations of S in the linear analysis are maximum at the boundaries and in phase with the layer displacement u. The sign of the amplitude depends on the coupling to the velocity field (only the anisotropic part — /) [< is relevant) and on the coupling to the director undulations (via M , only for the nematic... 

The third electro-optical effect using calamitic nematic liquid crystals makes use of a flexoelectric effect manifested by a curved asymmetrical nematic medium. This corresponds to piezoelectricity in crystals. The existence of flexoelectricity in a nematic phase under certain boundary conditions was predicted in the late 1960s and then confirmed experimentally several years later. However, LCDs using this effect, such as bistable nematic displays are only in the development stage and as such they will not be discussed in this monograph. 

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