BS in Physics
Liquid crystal systems show strong responses to small changes in both temperature and electric field. Changing these conditions can result in phase shifts and other similar behaviors. We study several theoretical models of smectic liquid crystals. The ideas and notation are first developed in basic polynomial models used to describe liquid crystal systems dependent only on temperature. Specifically, smectic-C to smectic-A phase transitions are examined in a fourth-order polynomial model. The bifurcations in the nonlinear equations are shown to correspond to the phase transi- tions in the system. Similar analytic techniques are then applied to a more complex model, based on the work of Schaub and Mukamel. This model, which includes terms for electric field depen- dance and chirality, describes smectic-C* liquid crystal molecules wound into helixes. Increasing temperature and electric field strength tends to "unwind" the helixes into the smectic-A or smectic- C state. The phase transition from the smectic-C* phase to smectic-A phase is identified analytically in the special case of zero electric field. Numeric analysis of the system in general is undertaken with bvp5c, a Matlab boundary value problem solver. The region of transition from smectic-C* to smectic-C is mapped using numeric solutions, and specific areas of interest wherein the phase transition changes in nature are highlighted.