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Book	S. Hess, M. Kröger Regular and chaotic rheological behavior of tumbling polymeric liquid crystals in: Computer simulations bridging liquid crystals and polymers , Eds. P. Pasini, C. Zannoni, S. Zumer ISBN 1-4020-2758-3 NATO Sci. Ser. II Math. Phys. Chem. Vol. 177, Kluwer, Dordrecht (2005) 295-333
The rheological properties of nematic liquid crystalline polymers are strongly affected by the dynamic behavior of the molecular alignment. Starting from a closed nonlinear inhomogeneous relaxation equation for the five components of the alignment tensor which, in turn, can be inferred from a generalized Fokker-Planck equation, it has recently been demonstrated (G. Rienäcker, M. Kröger, and S. Hess, Phys. Rev. E 66 040702 (R) (2002); Physica A 315, 537, (2002)) that the rather complex orientation behavior of tumbling nematics can even be chaotic in a certain range of the relevant control variables, viz. the shear rate and tumbling parameter. 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 both for imposed constant shear rate and constant shear stress. Orientational and rheological properties are presented as function of the shear rate. The transitions between different dynamic states are detected and discussed. Representative examples of alignment orbits and rheological phase portraits give insight into the dynamic behavior. @book{SHess2005, author = {S. Hess, M. Kröger }, title = {Regular and chaotic rheological behavior of tumbling polymeric liquid crystals in: Computer simulations bridging liquid crystals and polymers , Eds. P. Pasini, C. Zannoni, S. Zumer }, volume = {}, year = {2005}, publisher = {ISBN 1-4020-2758-3 NATO Sci. Ser. II Math. Phys. Chem. Vol. 177, Kluwer, Dordrecht }