Perturbative analysis of the nematic director reorientation dynamics induced by a magnetic field rotation in confined media

We present a theoretical study of the nematic director field reorientation dynamics induced by the magnetic field rotation as a function of the magnetic field intensity, the field rotation time and the angle of rotation. A nematic monodomain sample with positive anisotropy of the magnetic susceptibility between two parallel plates with planar boundary conditions and rigid anchoring is studied. The director remains in a plane (parallel to the plates) defined by its initial orientation and the final magnetic field direction. The cases of thin and thick sample dimensions in the direction perpendicular to the director spanning plane are considered in this work. It is found that the (thermally excited) periodic modes are amplified during the director reorientation process only if the magnetic field deviates from the initial director by more than a critical angle ac(B, tr) where B is the magnetic induction and tr is the magnetic induction rotation time. In the case of large plate separation, ac increases with increasing tr at fixed field and with increasing field at fixed tr in the range of fields studied. For the thin sample case, ac increases with increasing tr at fixed field and passes through a minimum with increasing field at fixed tr. In both cases the wave vector increases monotonously with the magnetic field intensity at constant final field orientation a0 and constant tr. At constant field and tr the selected mode's amplitude and wave vector increase with increasing a0, reaching a maximum value for a0 slightly above p/2, also in both cases.