Regular and chaotic orientational and rheological behaviour of liquid crystals

The dynamic behaviour of the molecular alignment strongly affects the rheological properties of nematic liquid crystals. The closed nonlinear relaxation equation for the five components of the alignment tensor which was derived within the framework of irreversible thermodynamics and also inferred from a generalized Fokker–Planck equation led to the prediction (Rien¨ acker et al 2002 Phys. Rev. E 66 040702(R); Physica A 315 537) that the rather complex orientational behaviour of tumbling nematics can even be chaotic in a certain range of the relevant control variables. Here the rheological consequences, in particular the shear stress and the normal stress differences, as well as the underlying dynamics of the alignment tensor are computed and discussed. For selected state points, long time averages are evaluated for imposed shear rates. Orientational and rheological properties are presented. The transitions between different dynamic states are detected and discussed. Representative examples of alignment orbits and rheological phase portraits give insight into the dynamic behaviour.