A study of periodic transitions in smectic C liquid crystals

We present a dynamical study of the instabilities that ensue when a relatively large magnetic field is applied suddenly across a sample of smectic liquid crystal held between parallel plates. We consider the case when the smectic layers are initially aligned parallel to the bounding plates, and the applied field is also parallel to the plates but normal to the initial average molecular orientation within the layers. Our linearized dynamical analysis for this situation confirms the prediction of static theory that there is a threshold field beyond which a Freedericksz transition occurs. Additionally, however, it is shown here that there is a second threshold beyond which a spatially periodic (rather than homogeneous) transition occurs, leading to a striped pattern; such patterns are likely to be of concern in the construction of smectic display devices. For both types of instability a bulk velocity ('backflow') is induced. Both strong anchoring and weak anchoring are considered, and expressions are obtained for the threshold fields and for the growth rates in the various cases. Attention is focussed on the smectic CM phase, though analogous results should be valid for more general smectic phases.