Chiral nematics order parameters

There are many parameters could affect the pitch of N -LCs, such as ionic strength, drying temperature, suspension concentration, magnetic field [22] and sonication [23, 24]. Interestingly, the chiral nematic orders can be retained after evaporation of the... 

Twisting a nematic structure around an axis perpendicular to the average orientation of the preferred molecular axes, one arrives at the molecular arrangement commonly called cholesteric (Kelker and Hatz, 1980). The twisted nematic phase is optically uniaxial, however with the axis perpendicular to the (rotating) director. Such a mesophase combines the basic properties of nematics with the implications of chirality The structure itself is chiral and as a consequence, a non-identical mirror image exists as it is shown schematically in Fig. 4.6-7. Besides the order parameters mentioned before, the essential characteristics of a cholesteric mesophase are the pitch, i.e., the period of the helical structure as measured along the twist axis, and its handedness, i.e., whether the phase is twisted clockwise or anticlockwise. 

The coefficient y is rotational viscosity of the director similar to coefficient yi for nematics. In fact, it does not include a factor of sin cp and, in the same temperature range, can be considerably larger than the viscosity ytp for the Gold-stone mode. This may be illustrated by Fig. 13.10 the temperature dependence of viscosities y and have been measured for a chiral mixture that shows the nematic, smectic A and smectic C phases [15]. The pyroelectric and electrooptic techniques were the most appropriate, respectively, for the measurements of ya and ytp describing the viscous relaxation of the amplitude and phase of the SmC order parameter. The result of measurements clearly shows that y is much larger than y and, in fact, corresponds to nematic viscosity yj. 

The orientational order of the cholesteric phase or chiral nematic phase is described as for the nematic phase, but a new parameter comes into a play. This parameter is the pitch of the cholesteric spiral P. The pitch is a measure of the... 

In a liquid crystal phase, the system remains a colloidal liquid, but the arrangement of the particles becomes ordered and periodic, and exhibits many of the attributes of a traditional solid crystal, despite having an order parameter far lower than that in a solid crystal. This difference can be seen in the latent heat of crystallisation, with a typical value for solid crystals of 250 J g , while liquid crystals have 5 J g . Understanding the control of these systems allows us to exploit chiral nematic liquid crystals to create artificial structural colour with biopolymers. 

The nematic phase is the simplest mesophase. It is described by the director n and the orientational order parameter S. In the nematic phase, the mesogens are arranged in such a way that their long axes lie preferentially in one direction (long-range orientational order). The long-range orientational order is responsible for the characteristic differences with respect to their isotropic melt. If the constituent compound is racemic, it is possible to form another phase from the enantiomericaUy pure compound. This is chiral nematic. 

Putting in some of the mathematical details [39], the Landau theory for the chiral nematic-isotropic transition has been described by de Gennes [2], who utilizes a tensor order parameter which is just the anisotropic part ,y(r) of the total dielectric tensor ,f(r) ... 

In this expression, the coefficients d, C, C2,P, and y are constants, while a = a T — T ) changes sign when T = T. The three terms with coefficients a, P, and y are just those terms which appear in the nematic free energy the Cl and C2 terms are order parameter gradients ( , ,/ = dEy/dxi) which are also allowed for nematics. The chiral term with coefficient d is forbidden in nematics—it contains the antisymmetric tensor Cyi and lacks nematic mirror symmetry. 

The refractive index data for n and n, calculated from n and (Eq. 11), may also be used to calculate the order parameter (5) in the chiral nematic phase using the Haller [56] technique with the Vuks local field correction factor [57] from... 

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