Dynamic Properties of Chiral Nematics

The static theory discussed in the previous section describes the equilibrium situation in chiral nematics very well - in general, theory and experiment are in good accord. The dynamic situation is less clear. On the molecular scale, the chiral nematic and nematic phases are identical the question then becomes, how does the macroscopic twist or helicity modify the vector stress tensor of the achiral nematic phase defined by the so-called [109] Leslie friction coefficients a -a T Experimentally, viscosity coefficients that are then related to the Leslie coefficients are measured in a way that depends specifically on the experiment being used to determine them. The starting point for discussion of dynamic properties is to use classical mechanics to describe the time dependencies of the director field n (r, t), the velocity field v (r, t), and their interdependency. Excellent reviews of this, for achiral nematics, are to be found in [59,109, 

As discussed in Sec. 2.2.2.1, the foundations of the continuum model were laid by Oseen [61] and Zocher [107] some seventy years ago, and this model was reexamined by Frank [65], who introduced the concept of curvature elasticity to describe the equilibrium free energy. This theory is used, to this day, to determine splay, twist, and bend distortions in nematic materials. The dynamic models or how the director field behaves in changing from one equilibrium state to another have taken much longer to evolve. This is primarily due to the interdependency of the director it (r, t) and v (r, /) fields, which in the case of chiral nematics is made much more complex due to the long-range, spiraling structural correlations. The most widely used dynamic theory for chiral 

The chiral nematic is considered incompressible, i.e., of constant density p with a nonpolar unit director n (i.e., i = 1). This implies that the external forces and fields responsible for the elastic deformation, viscous flow, etc., are much weaker than the intermolecular forces giving rise to the local order, i.e., between the chiral molecules. We will consider a volume of material V bounded by a surface 5 v and O) represent linear velocity and local angular velocity, respectively, i.e.. 

Conversion of surface integrals into volume integrals and rearranging leads to the conservation laws in the following differential form, 

Here iV, may be interpreted as the angular velocity of the director relative to that of the bulk fluid, and it should be noted that ty is asymmetric. 

---

A purely organic chiral nitroxide which shows liquid crystalline behaviour as well as intriguing magnetic properties and a dependence on the enantiomeric nature has been reported [180]. The reason for studying the compounds was to increase the sensitivity of mesophases to magnetic and electric fields. The racemic modification of the radical, which displays a nematic phase, proved to be more sensitive to alignment than the cholesteric phase with the enantiomers present. It was proposed that the compounds may also be used to study the dynamic nature of mesophases by electron paramagnetic resonance spectroscopy. 

In addition to thermotropic nematic liquid crystals, others such as chiral, smectic and lyotropic liquid crystals have been investigated and their dynamics and orienting properties studied. The structure of the tilted phase of a chiral liquid crystal has been investigated by means of the line-shape... 

---