chapter  4
71 Pages

Instabilities

WithEpifanio G. Virga

This chapter focuses on the most classical instabilities driven by electric or magnetic fields. If the optic axis is somehow prescribed on the boundary of the region occupied by the liquid crystal, then the elastic free energy competes against the electric or the magnetic energy and the orientation field that minimizes the total free energy functional may be strongly affected by the applied field. The chapter also focuses on an instability which occurs in cholesteric liquid crystals. It actually consists in a transition which changes cholesterics into nematics with no change in the temperature, but in the presence of a magnetic field, whose strength exceeds a critical value. The chapter considers an instability which was discovered by V. Freedericks and explained by H. Zocher within his continuum theory of liquid crystals. The effect discussed by R. B. Meyer is reminiscent of the piezo-electric effect that occurs in solid crystals. This is why De Gennes has suggested calling Meyer’s effect flexo-electric.