Elastic constants nematics

Allen M P, Warren M A, Wilson M R, Sauron A and Wiliam S 1996 Molecular dynamics calculation of elastic constants in Gay-Berne nematic liquid crystals J. Chem. Phys. 105 2850-8... 

Figure C2.2.11. (a) Splay, (b) twist and (c) bend defonnations in a nematic liquid crystal. The director is indicated by a dot, when nonnal to the page. The corresponding Frank elastic constants are indicated (equation(C2.2.9)).

The factors Kn are elastic constants for the nematic phase and Icb is the Boltzmann constant. Therefore a combination of molecular electronic structure, orientational order and continuum elasticity are all involved in determining the flexoelectric polarisation. Polarisation can also be produced in the presence of an average gradient in the density of quadrupoles. This is... 

In simple single-site liquid crystal models, such as hard-ellipsoids or the Gay-Berne potential, a number of elegant techniques have been devised to calculate key bulk properties which are useful for display applications. These include elastic constants for nematic systems [87, 88]. However, these techniques are dependent on large systems and long runs, and (at the present time) limitations in computer time prevent the extension of these methods to fully atomistic models. 

Note 3 The names of Oseen, Zocher, and Frank are associated with the development of the theory for the elastic behaviour of nematics and so the elastic constants may also be described as the Oseen-Zocher-Frank constants, although the term Frank constants is frequently used. 

For a nematic LC, the preferred orientation is one in which the director is parallel everywhere. Other orientations have a free-energy distribution that depends on the elastic constants, K /. The orientational elastic constants K, K22 and K33 determine respectively splay, twist and bend deformations. Values of elastic constants in LCs are around 10 N so that free-energy difference between different orientations is of the order of 5 x 10 J m the same order of magnitude as surface energy. A thin layer of LC sandwiched between two aligned surfaces therefore adopts an orientation determined by the surfaces. This fact forms the basis of most electrooptical effects in LCs. Display devices based on LCs are discussed in Chapter 7. 

It has been shown 65,68) that the threshold voltage is a function of the dielectric anisotropy Ae and the elastic constants of splay (ku), twist (k22) and bend (k33) deformation of the nematic phase (Fig. 17) ... 

Fig. 17a-c. Elastic constants for a splay b twist c bend deformations of a nematic phase. The full lines represent the director... 

The theory of nematic liquid crystal deformation, forced by an electric field is well developed and permits to establish the relationship between the threshold voltage U, causing sample orientation, with Ae and elasticity constants of a liquid crystal (Kn). For the main S and B types of deformation the equation is the following27 ... 

U values are substantially higher (U = 20-60 V). This was interpreted to be a result of significant differences in elastic constants of polymeric nematics with varying spacer lengths. 

Kundu B, PratibhaR, MadhusudanaNV (2007) Anomalous temperature dependence of elastic constants in the nematic phase of binary mixtures made of rodlike and bent-core molecules. Phys Rev Lett 99 247802-1-4... 

The big difference between normal isotropic liquids and nematic liquids is the effect of anisotropy on the viscous and elastic properties of the material. Liquid crystals of low molecular weight can be Newtonian anisotropic fluids, whereas liquid crystalline polymers can be rate and strain dependent anisotropic non-Newtonian fluids. The anisotropy gives rise to 5 viscosities and 3 elastic constants. In addition, the effective flow properties are determined by the flow dependent and history dependent texture. This all makes the rheology of LCPs extremely complicated. 

The three elastic constants are the Frank elastic constants, called after Frank, who introduced them already in 1958. They originate from the deformation of the director field as shown in Fig. 15.52. A continuous small deformation of an oriented material can be distinguished into three basis distortions splay, twist and bend distortions They are required to describe the resistance offered by the nematic phase to orientational distortions. As an example, values for Miesowicz viscosities and Frank elastic constants are presented in Table 15.10. It should be mentioned that those material constants are not known for many LCs and LCPs. Nevertheless, they have to be substituted in specific rheological constitutive equations in order to describe the rheological peculiarities of LCPs. Accordingly, the viscosity and the dynamic moduli will be functions of the Miesowicz viscosities and/or the Frank elastic constants. Several theories have been presented that are more or less able to explain the rheological peculiarities. Well-known are the Leslie-Ericksen theory and the Larson-Doi theory. It is far beyond the scope of this book to go into detail of these theories. The reader is referred to, e.g. Aciemo and Collyer (General References, 1996). 

The spatial and temporal response of a nematic phase to a distorting force, such as an electric (or magnetic) field is determined in part by three elastic constants, kii, k22 and associated with splay, twist and bend deformations, respectively, see Figure 2.9. The elastic constants describe the restoring forces on a molecule within the nematic phase on removal of some external force which had distorted the nematic medium from its equilibrium, i.e. lowest energy conformation. The configuration of the nematic director within an LCD in the absence of an applied field is determined by the interaction of very thin layers of molecules with an orientation layer coating the surface of the substrates above the electrodes. The direction imposed on the director at the surface is then... 

Figure 2.9 Schematic representation of the elastic constants for splay, twist and bend, ku, k22 und kjs, respectively, of a nematic phase.

Therefore, switch-off times are independent of the field strength and directly dependent on material parameters, such as viscosity coefficients and elastic constants, and the cell configuration. Therefore, they are often three or four orders of magnitude larger than the switch-on times. However, sophisticated addressing techniques can produce much shorter combined response times ( on + off The nematic director should be inclined, e.g. 1° pretilt,... 

Table 3.18 Transition temperatures (°C), elastic constants (ku, k22, kjj, 10 N), dielectric anisotropy ( e), dielectric constant measured perpendicular to the director (b2.)> birefringence ( n), refractive index measured parallel and perpendicular to the director ( ng and xto), viscosity (yi, mm s ), threshold voltage (V), rate of change of voltage with temperature (%°C ) and twist angle (°) measured at 20° C unless otherwise stated for three typical nematic mixtures for STN-LCDs ...

The application of an electric field above the threshold value results in a reorientation of the nematic liquid crystal mixture, if the nematic phase is of negative dielectric anisotropy. The optically active dopant then applies a torque to the nematic phase and causes a helical structure to be formed in the plane of the display. The guest dye molecules are also reoriented and, therefore, the display appears coloured in the activated pixels. Thus, a positive contrast display is produced of coloured information against a white background. The threshold voltage is dependent upon the elastic constants, the magnitude of the dielectric anisotropy, and the ratio of the cell gap to the chiral nematic pitch ... 

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