Criteria for Bistability and Hysteresis-Free Switching

In real SmC cells both Wf and W are finite. A finite azimuthal strength would create an additional surface torque trying to move the director from its angular positions at (p = 0 or p = ti to the easy axis z, Fig.13.13. On the cone surface, the minimum anchoring energy W corresponds to director position at (p = 7t/2 and the minima of are at p = 0 and (p = ti. But what will happen if Wf= It follows from Eqs. (13.37) that the sum of the two anchoring energies with equal amplitudes W 

As to dynamics of the response of a SSFLC cell to the alternating field, it is controlled by Eq. (13.38) with the viscous j dipldt torque added. When the helical stmcture of the SmC is unwound in a thin cell (a typical case) one can neglect the elastic torque d p/dx. If, in addition, the anchoring energies Wf and W are reasonably weak, the electric field torque would solely be balanced by the viscous torque  

the viscosity coefficient y, corresponds to the azimuthal motion of the director. From this equation, for small distortions, we immediately find the time of the response to an external field. 

For larger (p the response is not exponential, however, controlled by the same physical parameters with a numerical factor of 1-2. The viscosity y p can be found from the measurements of kinetics of the optical transmission. 

The electric voltage U is switched ON with polarity shown by (+) and (—) signs 

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