Field-Induced Order in Nematic Liquid Crystals

Abstract

The effect of an external magnetic field on the orientational order of a nematic liquid crystal has been examined using both Landau-de Gennes and Maier-Saupe theories. In the Maier-Saupe approach a rotationally invariant form of the pseudo-potential is introduced, which in the absence of an external field leads to three degenerate isomorphic solutions for the order parameter, corresponding to alignment along three principal axes; a similar result is obtainable from the Landau-de Gennes theory. Application of a magnetic field lifts the degeneracy of these solutions, and for materials having a positive diamagnetic susceptibility anisotropy, the uniaxial solution with alignment along the field direction is always energetically favorable. For materials with a negative susceptibility anisotropy, a biaxial solution minimizes the free energy at low temperatures, but on increasing the temperature there is a transition from a biaxial phase to an uniaxial phase. The field dependence of the transition temperatures is evaluated, and for positive materials there is a critical field, corresponding to a second order transition above which the nematic and isotropic phases are indistinguishable. A contrasting behavior is predicted for negative materials, and above a certain critical field the biaxial/uniaxial transition changes from first order to second order. For weakly ordered systems it is shown that the Landau-de Gennes expression for the free energy is identical to that obtained from the Maier-Saupe theory. However, for more ordered systems, the results of the two approaches differ, and in particular the Maier-Saupe theory predicts a susceptibility divergence temperature T* which increases with applied field, in agreement with recent experiments.