Regular and Chaotic Rheological Behavior of Tumbling Polymeric Liquid Crystals

  • Siegfried Hess
  • Martin Kröger
Part of the NATO Science Series II: Mathematics, Physics and Chemistry book series (NAII, volume 177)


The theological 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 theological 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 theological 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 theological phase portraits give insight into the dynamic behavior.


Shear Rate Phase Portrait Nematic Phase Normal Stress Difference Constant Shear Rate 
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Copyright information

© Kluwer Academic Publishers 2005

Authors and Affiliations

  • Siegfried Hess
    • 1
  • Martin Kröger
    • 2
  1. 1.Institute für Theoretische PhysikTechnische Universitlt BerlinBerlinGermany
  2. 2.Polymer Physics, Materials ScienceETH Zentrum, ML H18ZürichSwitzerland

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