Tilt and Twist Equilibrium Solutions

The above simple equilibrium solutions motivate the search for more general solutions which contain these elementary ones as special cases. To this end it is natural to seek equilibrium solutions when the director is of the form 

Setting 0 =9 and 62 = 4 o. the equilibrium equations (2.221) easily gives the two coupled Euler equations 

These coupled nonlinear equations eire the key governing equations. It is possible to proceed further. First observe that 

multiplying both sides of equation (3.21) by ff and employing the identity (3.25) allows us to rewrite (3.21) as 

To simphfy the presentation in this Section on tilt and twist equilibrium solutions we shall henceforth assume that the elastic constants i i, K2 and K3 are all strictly positive (recall that they are necessarily non-negative by Ericksen s inequalities (2.58)). 

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The notation used in Section 3.2.2 based on Fig. 3.3 on page 60 to obtain the tilt and twist equilibrium solutions in the absence of any fields will be used again here. Figure 3.18, which follows that given in the short review by Scheuble [243], describes the geometrical set-up and illustrates the principle mechanism by which a twisted nematic display works further comments on this type of display will be made at the end of this Section. 

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