Regular and Chaotic Rheological Behavior of Tumbling Polymeric Liquid Crystals
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.
KeywordsShear Rate Phase Portrait Nematic Phase Normal Stress Difference Constant Shear Rate
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- R.G. Larson, The Structure and Rheology of Complex Fluids, Oxford University Press, Oxford, UK, 1999.Google Scholar
- G. Rienäcker, Orientational dynamics of nematic liquid crystals in a shear flow, Thesis TU Berlin, 2000; Shaker Verlag, Aachen, Germany, 2000.Google Scholar
- S. Hess, Flow alignment of a colloidal solution which can undergo a transition from the isotropic to the nematic phase (Liquid crystal), in: Electro-optics and dielectrics of macromolecules and colloids, ed. B.R. Jennings, Plenum Publ. Corp., New York, 1979.Google Scholar
- M. Doi, Ferroelectrics, 30:247, 1980; J. Polym. Sci. Polym. Phys. Ed., 19:229, 1981.Google Scholar
- M. G. Forest, Q. Wang, and R. Zhou, Rheol. Acta, 2004) in press; S. Fielding and P. Olmsted, preprint: arXiv.org/abs/cond-mat/0310658; B. Chakrabarti, M. Das, C. Dasgupta, S. Ramaswamy, and A.K. Sood, preprint: arXiv:cond-mat/0311101 vl.Google Scholar
- G. Marrucci, Macromolecules, 24:4176, 1991; G. Marrucci and P. L. Maffettone, ibid., 22:4076, 1989; J. Rheol., 34:1217, 1990; P. L. Maffettone, A. Sonnet, and E. G. Virga, J. Non-Newtonian Fluid Mech., 90:283, 2000; P. L. Maffettone and S. Crescitelli, ibid., 59:73, 1995; J. Rheol., 38:1559, 1994; Y. Farhoudi and A. D. Rey, ibid., 37:289, 1993; Q. Wang, ibid., 41:943, 1997; N. C. Andrews, A. J. McHugh, and B. J. Edwards, ibid., 40:459, 1996; P. Ilg, I.V. Karlin, M. Kröger, and H.C. Öttinger, Physica A, 319:134, 2003.CrossRefADSGoogle Scholar
- A. Peterlin and H. A. Stuart, Hand-und Jahrbuch der Chemischen Physik, Vol. 8, 113, Ed. Eucken-Wolf, 1943.Google Scholar
- C. Zannoni, Liquid crystal observables: static and dynamic properties, in Advances in the computer simulations of liquid crystals, P. Pasini and C. Zannoni, eds., Kluwer Academic Publisher, Dordrecht (2000.Google Scholar
- G. G. Fuller, Optical Rheometry of Complex Fluids Oxford University Press, New York, 1995.Google Scholar