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Robustness of the periodic and chaotic orientational behavior of tumbling nematic liquid crystals.

The dynamical behavior of molecular alignment strongly affects physical properties of nematic liquid crystals. A theoretical description can be made by a nonlinear relaxation equation of the order parameter and leads to the prediction that rather complex even chaotic orientational behavior occur. Here the influence of fluctuating shear rates on the orientational dynamics especially on chaotic solutions is discussed. With the help of phase portraits and time evolution diagrams, we investigated the influence of different fluctuation strengths on the flow aligned, isotropic, and periodic solutions. To explore the effect of fluctuations on the chaotic behavior, we calculated the largest Lyapunov exponent for different fluctuation strengths. We found in all cases that small fluctuations of the shear rate do not affect the basic features of the dynamics of tumbling nematics. Furthermore, we present an amended potential modeling the isotropic to nematic transition and discuss the equivalence and difference to the commonly used Landau-de Gennes potential. In contrast to the Landau-de Gennes potential, our potential has the advantage to restrict the order parameter to physically admissible values. In the case of extensional flow, we show that the amended potential leads for increasing extensional rate to a better agreement with experimental results.