Director vector

Figure 7.2 Schematic representation of N, SmA and SmC calamitic mesophases with the corresponding director vector n.

Figure 7.3 Schematic representation of N and Colh discotic mesophases with the director vector n.

In Section 2.1 a parameter S, was defined which measures the degree to which all the chains in a multilayer lie parallel to one another and hence to the director vector which defines their average direction. A... 

The discotic phases can show also a complex polymorphism. Nematic and cholesteric-like, low viscosity phases have been reported recently. In these, the director vector is perpendicular to the plane of alignment of the flat molecules56) in contrast to the normal nematics and cholesterics where it is parallel to the molecular axis. Most frequently, however, discotics form columnar arrangements as shown in Fig. 10. The order within the columns may change from liquid to quasi-crystalline. The columns are then packed in hexagonal or tetragonal coordination, but are free to slide in the direction parallel to their axes S7). The viscosity of these more ordered discotics is considerably higher than the nematic discotics. 

Helical (or chiral) vector Ch defined from the director vectors (a-1) and (a2) of the graphene sheet by using a pair of integers (n, m) Ch = na-, + ma2 and chiral angle 0. Reprint from Carbon, vol. 33, No. 7, Dresselhaus M.S., Dresselhaus G., Saito R., Physics of carbon nanotubes, pages 883-891, Copyright (1995) with permission from Elsevier. 

Let us consider the ER signal due to the redox reaction of a surface-confined dye molecule. For simplicity, we assume that, for an electrode/adsorption layer incorporating a chromophore/solution interface, the absorption of the oxidized form is negligibly small, i.e. the oxidized form is colorless. We also assume that the electric dipole moment of the reduced form is of a single hnear dipole and that it has a unique director angle f with respect to the surface normal while its azimuthal angle is two-dimensionally isotropic (Fig. 2.15a). The angle

surface normal represents the molecular orientation. 

His theory is applicable to both isotropic and nematic phases, and so can be tested by the peak in viscosity with concentration, which it successfully predicts (see Figure 5 in [23]). Doi recognized a limitation in his theory, in that it assumes a spatially uniform system in which the director vector does not change with position. As will be seen in section 11.6, this is far from reality. Doi does not address negative in this work (it does not appear that he was aware of it), but notes that for small shear rates, normal stress is proportional to shear rate in isotropic solutions and to the square of the shear rate in the nematic phase. 

Figure 10. Schematic drawing of the Sp and Sj phases represented by unit cells in the real space, reciprocal lattices and WAXD patterns, (a, b, c and P are real lattice parameters, a, b and c are reciprocal lattice parameters. and Qy represent the components of the momentum transfer which are perpendicular ana parallel respectively to the smectic layers, ft is the director vector and x is an average rotation angle.)...

FIG. 1. Unperturbed director vector n perpendicular to the cell walls. The wave vector k of the light field makes an angle a with the normal to the cell wails. 

When, through melting, the solid becomes liquid, both types of ordering are completely lost, allowing free movement of the molecules, subsequently forming an isotropic solution. The Hquid crystal is an intermediate state between solid and liquid, in that the molecules are free to move as in a liquid. However, as they move, the moleades tend to remain oriented in a certain direction (Figure 14.2), their preferred direction of orientation being determined by the director vector [76]. 

Figure 5 Experimental 250 GHz EPR spectra from membrane samples of various DMPC.DMPS compositions. The membranes were fully hydrated and mechanically and aligned with the director vector perpendicular to the external magnetic field. All spectra were recorded at 10°C in the gel phase and are reproduced here from Barnes and Ereed ...

Figure 6 Experimental W-band (94.4 GHz) EPR spectra from mixed DMPC/DHPC bicelles labeled at 1 mol% with 5-doxylstearic acid. At the 40 °C temperature of the experiment the bicelles were found to spontaneously align in the external magnetic field of ca. 3.4 T. The top spectrum (A) is illustrative of the bicelle orientation in which the bilayer vector is perpendicular to the external magnetic field. Upon addition of lanthanide Tm, which binds to the bilayer in the polar head region and changes the sign of the magnetic susceptibility anisotropy, the bicelles are flipped by 90° resulting in the parallel orientation of the director vector vs. magnetic field (bottom spectrum B).

In the discotic nematic (No) phase (Fig. 16.3a), molecules have orientationally ordered arrangement of discs with no long-range translational order. This is the least order (usually high temperature) in the disc-like molecules (Kumar 2009). The nematic mesophase can be assimilated to a lamellar nematic liquid crystal, in which the director vector (an optical axis) is perpendicular to the average direction along which the flat molecules are aligned, as illustrated in Fig. 16.3a. 

S is the order parameter and gives a long-range order in terms of the molecular axis. (3 is the angle of the director inclined to the proton internuclear vectors. S is a statistical value and I represents the angle between the static magnetic field and the director vector. In this expression, the molecular axis and the director of the liquid crystal are considered to be parallel. When we adopt r = 2.45 A and (3 = 10°, as calculated from X-ray diffraction data, with Av = 9.7 kHz, we obtain S = 0.41 for the S-value of the aromatic protons of APAPA at 108 °C. 

---