Dubois-Violette, de Gennes, and Parodi Model

The Helfrich theory was extended by Dubois-Violette, de Gennes, and Parodi [17] to cover the AC field. The geometrical conditions are still the same. In the distorted state, the molecules are deflected by a small angle 0 in the xz plane. The most important parameter from the point of view of charge accumulation is not exactly 0, but rather the curvature v = 30/3x of the molecular pattern y/ and the charge density, q, are used as fundamental variables. 

The equation also shows that the threshold voltage is independent of the thickness of the cell and increases with an increase in the frequency, finally becoming very large on approaching the cut-off frequency, C0(., where 

When 0) reaches the cut-off frequency the threshold field becomes very large, (oT reaches 1 and the curvature y/ becomes time dependent henee the low frequency calculations are not valid 

In the high frequency regime (oxo ), the molecular pattern oscillates while the charges are static for this reason, the regime 

The Carr-Helfrich theory and its extension to AC field by the Orsay group have been verified experimentally by several workers and they found good agreement with the theory [8-12, 16-28, 33, 34, 39-41]. Besides the above-mentioned theories, attempts have been made by other workers [41-43]. Some of these are beautifully reviewed by Goosen [8], Dubois-Violette et al. [9], Chandrasekhar [11], and Blinov [28]. 

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Figure 4. Threshold voltage of the AC instabilities for MBBA. Region I -conduction regime (Williams domains) Region II - dielectric regime (chevrons). Pull line from Dubois-Violette, de Gennes, and Parodi model. After Orsay Liquid Crystal Group [17, 23].

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