Vibrational Fréedericksz transition in liquid crystals

Our aim is to show the possibility of a "vibrational Fréedericksz's transition" in nematic liquid crystals (LCs) consisting of asymmetric molecules (in the absence of the reflectional symmetry for the director field). For this purpose we study the effects of the external high-frequency vibrations imposed on LCs by employing the rigorous two-timing asymptotic averaging method to the governing LC equations in their most general form. We restrict our attention only to translational mechanical vibrations of an incompressible LC medium as a whole, so our vibrations are not related to acoustical waves. We show that the averaged "vibrogenic" torque acted on the director field is mathematically equivalent to the torque caused by an external magnetic field. This equivalence leads us to the key conclusion that the high-frequency mechanical vibrations can cause the vibrational Fréedericksz's transition. Our evaluation of the relevant physical parameters shows that this phenomenon can be observed in laboratory experiments.