Dynamics of Frederiks Transition

It is simpler to examine the dynamics of the Frederiks effect for the experimental geometry of Fig. 11.15c, since a pure twist distortion is not accompanied by the backflow effect (see the next Section). For a twist distortion we operate with the azimuthal director angle tp(z) (sintp riy) and the equation for rotation of the director that expresses the balance of elastic, magnetic field and viscous torques is given by 

the first two terms came from minimisation procedure of the free energy, see Eqs. (8.15) and (11.43) and the viscous term was discussed earlier, see Eqs. (9.31) and (9.32) [21]. In terms of the phase transition theory, Eq. (11.63) may be regarded as the Landau-Khalatnikov equation discussed in Section 6.5.1. It describes the director rotation in magnetic field H with rotational viscosity yi = 2 — 3 and without the director inertia term. In the limit of small (p-angles, it reduces to the linear form  

11 Optics and Electric Field Effects in Nematic and Smectic A Liquid Crystals Yl Yi 

---