Chaotic and regular shear-induced orientational dynamics of nematic liquid crystals

Based on a relaxation equation for the alignment tensor characterizing the molecular orientation in liquid crystals under flow we present results for the full orientational dynamics of homogeneous liquid crystals in a shear flow. We extend the analysis of the symmetry-adapted states by Rienäcker and Hess (Physica A 267 (1999) 294), which invoke only 3 of the 5 components of the tensor to full alignment. The steady and transient states of reduced model are preserved in this more general description, except for log-rolling, which turns out to be unstable in the range of parameters considered. However, the states reported earlier are only stable within a certain range of the parameters and there is a variety of new, symmetry-breaking transient states with the director out of the shear plane, which partially coexist with the in-plane states. The new, out-of-plane states can be divided in two classes: simple periodic and complex orbits. The first class consists of a kayaking-tumbling and a kayaking-wagging state, where the projection of the director onto the shear plane describes a tumbling or wagging motion, respectively. The second class of states, which can be found only in a small parameter range, consists of a variety of either complicated periodic or irregular, chaotic orbits. Both an intermittency route and a period-doubling route to chaos are found. A link to the corresponding rheological properties is made.