Dynamics of the Freedericksz transition

We consider the dynamics of the Freedericksz transition in the splay geometry upon the removal of the applied field [24-27]. Initially the liquid crystal director is aligned vertically by the applied field, as shown in Figure 5.17(a). When the applied field is removed, the liquid crystal relaxes back to the homogeneous state. The rotation of the molecules induces a macroscopic translational motion known as the backflow effect. The velocity of the flow is... 

This form of threshold has been obtained and discussed by Pelzl, Schiller and De-mus [219], who also go on to discuss their theoretical and experimental results for some SmC materials. Although the dynamic theory for SmC liquid crystals has yet to be reached in Section 6.3, it seems appropriate to record here that these authors additionally considered switch-on and switch-off times (rise and decay times, respectively) and arrived at results analogous to those for a nematic liquid crystal given by equations (5.420) and (5.424) which were encountered when the dynamics of the Freedericksz transition for nematic liquid crystals was discussed in Section 5.9.1. These results for SmC are... 

Although the dynamics of Freedericksz transition in splay geometry, bend geometry, and twisted geometry is more complicated, the response time is still of the same order and has the same cell thickness dependence. The rotational viscosity coefficient is of the order O.IN - s/m. When the elastic constant is 10 "N and the cell thickness is 10pm, the response time is of the order 100 ms. Faster response times can be achieved by using thinner cell gaps. 

The dynamic behavior of the optical-field-in-duced Freedericksz transition is also analogous to the dc case. The initial response of the induced molecular reorientation to the laser switch-on and the long-time response to the laser switch-off are both exponential with relaxation times Tqjj and Toff, respectively. 

Oseen [1] and Frank [2] far before the development of LCD technology. The dynamic continuum theory of nematics, which is frequently called the nematodynamics, was developed by Ericksen [3] and Leslie [4] (hereafter referred to as E-L theory) based on the classical mechanics just in time for the upsurge of LCD technology. In conjunction with the electrodynamics of continuous media, the static and dynamic continuum mechanics of Oseen-Erank and E-L theory provided theoretical tools to analyze quantitatively key phenomena, e.g., Freedericksz transition of various configurations and associated optical switching characteristics. For the details of E-L theory [5-7] and its development [9,10], please refer to the articles cited. 

The dissipative coefficient yi on the right-hand side of (7.32) is called the rotational viscosity and plays a major role in the dynamics of Freedericksz transition. Since entropy production is positive, we have... 

Application of external electric field in the direction parallel to the liquid crystal rich planes breaks the intrinsic axial symmetry of the nematic director field within the droplets. This causes a slowing down of orientational fluctuations similar to the case of Freedericksz transition in planar nematic cells [29-31]. For E = Eqb the dynamic equation for the fluctuations (4.5) becomes... 

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