Magnetic field induced bistability in nematics and cholesterics: general deformations

Abstract

Abstract The continuum theory is used for studying magnetic field (H) induced orientational bistability of the director field (n) of a nematic with positive diamagnetic susceptibility anisotropy (χa) the nematic being confined between two plane parallel plates. The rigid anchoring hypothesis is utilized for investigating the effect of variation of magnetic tilt on the nature of change of director deformation described by two distortion angles. Such general deformations can result, for instance, when H is slowly rotated in a plane whose normal does not coincide with the normal to the sample planes. The bistability width w b (the range of magnetic tilt angle over which two different equilibrium configurations can exist) depends upon various parameters such as the elastic ratios, the angle of inclination of n at the boundaries and the twist in the ground state. In particular, the nature of change of distortion exhibits certain new features when n is pretilted at the sample boundaries. Scaling analysis indicates that w b should be independent of the sample thickness at a given reduced field. Linear time dependent perturbation analysis shows that where bistability is associated with discontinuous orientational change, the static deformation is susceptible to instability near the edges of the bistable region. Scaling analysis of the general dynamical equations indicates that even at the same reduced field we cannot rule out a strong dependence of the time of transition between deformation states on sample thickness. When the nematic has χa<0, a threshold magnetic tilt may exist separating two different types of distortion; this is indicated by the time independent perturbation analysis. The possible effects of an additional electric field are briefly discussed. In the light of recent experimental evidence it seems interesting to generalize the rotating field (or sample) experiments discussed in an earlier paper.