Nematic liquid crystal elastic constant approximation

The energy scale of an elastic distortion around a particle is of order KR, where iC is a typical elastic constant of the nematic liquid crystal [19] and R is the radius of the particle. For a thermotropic liquid crystal, K is approximately 10 N, and for a colloidal particle, i is approximately one micron thus the energy scale is a few thousands k TyWhere is the Boltzmann constant and T the temperature. As a result, the entropy of the particles is negligible compared to the elastic interactions. Under these conditions, the structures formed due to attractive interactions remain stable against thermal fluctuations. 

We consider the possible deformations of a nematic liquid crystal confined between two parallel substrates with tangential anchoring condition (parallel to the substrates but no preferred direction on the plane of the substrate). We use the one elastic constant approximation (A n = K22 = Kss = K), the elastic energy is given by... 

In case of nematic liquid crystals, in one elastic constant approximation. 

We now investigate the Couette flow of a nematic liquid crystal in precisely the same type of experiment discussed above for an anisotropic fluid described in Fig. 5.8 and in essence follow the work of Atkin and Leslie [6]. The one-constant approximation for the nematic elastic energy will be assumed in order to simplify the presentation ... 

The constants iFi=i-3 are the Frank elastic constants and correspond to the three fundamental deformations of the director field splay, twist and bend. Then-magnitude is of the order of 10 N, which is a fairly small value, meaning that on a length scale of several hundred microns (a typical size of a bulk sample), the nematic liquid crystal can easily deform or be deformed. It should be added that the Frank elastic constants depend on the order in the liquid crystal, being approximately proportional to 5. Consequently, the Frank constants Ki are temperature dependent and increase with decreasing temperature. 

---