Director defined

The director defines the local optical axis. The most obvious indication of the anisotropy of nematics is their birefringence. Since nematics are composed of elongated molecules their extraordinary refractive index ng is always larger than the ordinary one Ho, i.e. nematics have a positive optical anisotropy Ua = Ue — Ho- When light is passing through a nematic layer, an optical path difference... 

The above is a quick summary of the relevant hydrodynamic equations for a simple fluid. The behaviour of a nematic liquid crystal is more complex in that the stress tensor is now non-symmetric. Another variable that is introduced is the director, , defined by a unit vector, where n —Allied to these constraints, one defines the rate of rotation of the director with respect to the background fluid by... 

Figure 6.8 A magnetic field H is applied across a sample of depth d of SmC liquid crystal in the bookshelf geometry, as shown. For simplicity, the director is assumed to be strongly anchored at the surfaces in such a way that 0(0) = 0(d) = 0 where 0(z) is the orientation angle of the c-director defined by (6.120)2 this indicates that the director makes an in-plane surface twist angle j3 = 0 to the x-axis at the boundaries, equivalent to the constant smectic tilt angle. Other values for are feasible see page 279. (a) When H < where He is the F eedericksz threshold defined by (6.143), only 0 = 0 is available and the director alignment is uniformly constant across the sample, (b) There is a Freedericksz transition at H = He and for H > He the c-director reorients within the 2/2 -plane, as shown schematically.

An orientational order parameter can be defined in tenns of an ensemble average of a suitable orthogonal polynomial. In liquid crystal phases with a mirror plane of symmetry nonnal to the director, orientational ordering is specified. 

If we compare with figure C2.2.I I, we can see that this defonnation involves bend and splay of the director field. This field-induced transition in director orientation is called a Freedericksz transition [9, 106, 1071. We can also define Freedericksz transitions when the director and field are both parallel to the surface, but mutually orthogonal or when the director is nonnal to the surface and the field is parallel to it. It turns out there is a threshold voltage for attaining orientation in the middle of the liquid crystal cell, i.e. a deviation of the angle of the director [9, 107]. For all tliree possible geometries, the threshold voltage takes the fonn [9, 107]... 

A similar effect occurs in highly chiral nematic Hquid crystals. In a narrow temperature range (seldom wider than 1°C) between the chiral nematic phase and the isotropic Hquid phase, up to three phases are stable in which a cubic lattice of defects (where the director is not defined) exist in a compHcated, orientationaHy ordered twisted stmcture (11). Again, the introduction of these defects allows the bulk of the Hquid crystal to adopt a chiral stmcture which is energetically more favorable than both the chiral nematic and isotropic phases. The distance between defects is hundreds of nanometers, so these phases reflect light just as crystals reflect x-rays. They are called the blue phases because the first phases of this type observed reflected light in the blue part of the spectmm. The arrangement of defects possesses body-centered cubic symmetry for one blue phase, simple cubic symmetry for another blue phase, and seems to be amorphous for a third blue phase. 

Liquid crystal displays depend upon the reorientation of the director , the defining alignment vector of a population of liquid crystalline molecules, by a localised applied electric field between two glass plates, which changes the way in which incident light is reflected directional rubbing of the glass surface imparts a... 

The anisotropy of the liquid crystal phases also means that the orientational distribution function for the intermolecular vector is of value in characterising the structure of the phase [22]. The distribution is clearly a function of both the angle, made by the intermolecular vector with the director and the separation, r, between the two molecules [23]. However, a simpler way in which to investigate the distribution of the intermolecular vector is via the distance dependent order parameters Pl+(J") defined as the averages of the even Legendre polynomials, PL(cosj r)- As with the molecular orientational order parameters those of low rank namely Pj(r) and P (r), prove to be the most useful for investigating the phase structure [22]. 

The successful chairmanship and the apparent qualities of personnel management landed several offers of deanships in Yngve s lap. He decided, to my delight, to remain a dedicated scientist. Administrative obligations remained, he assumed the role of Director of the Quantum Theory Project in 1983 and led this rather informal association of faculty members from Chemistry and Physics to be established, in 1987, as the "Institute for Theory and Computation in Molecular and Materials Sciences" with a well defined position in the University system. This was another demonstration of the ability to create coherence and commitment amongst a body of strong minded people with diverse interests. It is a consequence that Florida remains a world renowned hub of quantum chemistry activities. 

The mesophases of calamitic mesogens are classified in two groups nematic and smectic. The nematic mesophase (N) is characterized by an orientational order of the molecules that are aligned along a preferred direction (defined by a director n) (Figure 8.2). The molecules can slide and move in the nematic mesophase (while roughly keeping their molecular orientation) and rotate around their main axis. This is the less ordered mesophase and it is usually very fluid. 

In the smectic mesophases the molecules are oriented, as in a nematic mesophase, with their principal axis roughly parallel to the director, but they are also defining layers. These layers can be perpendicular to the director, as in the smectic A mesophase (SmA), or tilted, as in the smectic C (SmC). The SmA and SmC mesophases are the less ordered and more common smectic mesophases. Other less common types of smectic mesophases are known, which differ in the degree or kind of molecular ordering within and between the layers [2]. 

The format of the final report from a study is closely defined and the Study Director is responsible for its production. The test item and name of the study must be clearly identified, along with the start and end date. It has to be accompanied by a statement from the Quality Assurance unit that the study and any critical aspects of the work have been conducted to the requirements of GLP principles. It will contain the names of all those involved with the study and their address this includes the Study Director, the Principal Investigator, and all the scientists... 

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