Skip to main content
SpringerLink
Log in

Polar nano-rods under shear: From equilibrium to chaos

  • Regular Article
  • Published:
The European Physical Journal E Aims and scope Submit manuscript

Abstract.

The orientational dynamics of rod-like particles with permanent (electric or magnetic) dipole moments in a plane Couette shear flow is investigated using mesoscopic relaxation equations combined with a generalized Landau free energy. The free energy contribution due to the coupling between average alignment and dipole orientation is derived on a microscopic basis. Numerical results of the resulting eight-dimensional dynamical system are presented for the case of longitudinal dipoles and thermodynamic conditions where the equilibrium state is a (polar or non-polar) nematic. Solution diagrams reveal presence of a large variety of periodic, transient chaotic, and chaotic dynamic states of the average alignment and dipole moment, respectively, appearing as a function of Deborah number and tumbling parameter. Compared to rods without dipoles we observe a significant preference of out-of-plane kayaking-tumbling states and, generally, a higher sensitivity to the initial conditions including bistability. We also demonstrate that the average (electric) dipole moment characterizing most of the observed states yields electrodynamic (magnetic) fields of measurable strength.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Grosso, R. Keunings, S. Crescitelli, P.L. Maffettone, Phys. Rev. Lett. 86, 3184 (2001).

    Article  ADS  Google Scholar 

  2. G. Rienäcker, M. Kröger, S. Hess, Phys. Rev. E 66, 040702(R) (2002).

    Article  ADS  Google Scholar 

  3. G. Rienäcker, M. Kröger, S. Hess, Physica A 315, 537 (2002).

    Article  ADS  Google Scholar 

  4. S. Hess, M. Kröger, J. Phys.: Condens. Matter 16, 3835 (2004).

    Article  ADS  Google Scholar 

  5. B. Chakrabarti, M. Das, C. Dasgupta, S. Ramaswamy, A.K. Sood, Phys. Rev. Lett. 92, 055501 (2004).

    Article  ADS  Google Scholar 

  6. M.G. Forest, Q. Wang, R. Zhou, Rheol. Acta 86, 80 (2004).

    Article  Google Scholar 

  7. Y.-G. Tao, W.K. den Otter, W.J. Briels, Phys. Rev. Lett. 95, 237802 (2005).

    Article  ADS  Google Scholar 

  8. Y.-G. Tao, W.K. den Otter, W.J. Briels, J. Chem. Phys. 124, 204902 (2006).

    Article  ADS  Google Scholar 

  9. Y.-G. Tao, W.K. den Otter, J.K.G. Dhont, W.J. Briels, J. Chem. Phys. 124, 134906 (2006).

    Article  ADS  Google Scholar 

  10. Y.-G. Tao, PhD Thesis, University of Twente (2006).

  11. J.K.G. Dhont, W.J. Briels, Rod-like Brownian particles in shear flow, in Soft Matter: Complex Colloidal Suspensions, edited by G. Gompper, M. Schick, Vol. 2 (Wiley-VCH, 2006).

  12. J. Mewis, M. Mortier, J. Vermant, P. Moldenaers, Macromolecules 30, 1323 (1997).

    Article  ADS  Google Scholar 

  13. M.P. Lettinga, Z. Dogic, H. Wang, J. Vermant, Langmuir 21, 8048 (2005).

    Article  Google Scholar 

  14. R.G. Larson, The Structure and Rheology of Complex Fluids (Oxford University Press, Oxford, UK, 1999).

  15. S. Grandner, S. Heidenreich, P. Ilg, S.H.L. Klapp, S. Hess, Phys. Rev. E 75, 040701(R) (2007).

    Article  ADS  Google Scholar 

  16. A.Y. Zubarev, L.Y. Iskakova, Physica A 229, 188 (1996).

    Article  ADS  Google Scholar 

  17. A.L. McClellan, Tables of Experimental Dipole Moments (W. H. Freeman & Co., San Francisco, 1963).

  18. H.H. Wesink, G.J. Vroege, Phys. Rev. E 72, 031708 (2005).

    Article  ADS  Google Scholar 

  19. G.J. Vroege, D.M.E. Thies-Weesie, A.V. Petukhov, B.J. Bemaire, P. Davidson, Adv. Mater. 18, 2565 (2005).

    Article  Google Scholar 

  20. Y. Qi, L. Zhang, W. Wen, J. Phys. D.: Appl. Phys. 36, L10 (2003).

  21. V.N. Manoharan, M.T. Elsesser, D.J. Pine, Science 301, 483 (2003).

    Article  ADS  Google Scholar 

  22. C.G. Gray, K.E. Gubbins, Theory of Molecular Fluids, Vol. 1 (Oxford University, London, 1984).

  23. P.G. de Gennes, J. Prost, The Physics of Liquid Crystals, 2nd ed. (Oxford University, London, 1995).

  24. S. Hess, Z. Naturforsch. 30a, 728 (1975).

    ADS  Google Scholar 

  25. S. Hess, Z. Naturforsch. 31a, 1034 (1976).

    ADS  Google Scholar 

  26. S. Hess, P. Ilg, Rheol. Acta 44, 465 (2005).

    Article  Google Scholar 

  27. P. Ilg, S. Hess, J. Non-Newtonian Fluid Mech. 134, 2 (2006).

    Article  MATH  Google Scholar 

  28. H. Pleiner, E. Jarkova, H.-W. Müller, H.R. Brand, Magnetohydrodynamics 37, 254 (2001).

    ADS  Google Scholar 

  29. H. Pleiner, E. Jarkova, H.-W. Müller, H.R. Brand, J. Magn. & Magn. Mater. 252, 147 (2002).

    Article  ADS  Google Scholar 

  30. G.M. Range, S.H.L. Klapp, Phys. Rev. E 69, 041201 (2004).

    Article  ADS  Google Scholar 

  31. G.M. Range, S.H.L. Klapp, Phys. Rev. E 70, 031201 (2004).

    Article  ADS  Google Scholar 

  32. S. Klapp, F. Forstmann, Europhys. Lett. 38, 663 (1997).

    Article  ADS  Google Scholar 

  33. B. Groh, S. Dietrich, Phys. Rev. Lett. 72, 2422 (1994).

    Article  ADS  Google Scholar 

  34. S. Hess, I. Pardowitz, Z. Naturforsch. 36a, 554 (1981).

    MathSciNet  ADS  Google Scholar 

  35. C. Pereira Borgmeyer, S. Hess, J. Non-Equilib. Thermodyn. 20, 359 (1995).

    Article  MATH  Google Scholar 

  36. G. Rienäcker, S. Hess, Physica A 267, 294 (1999).

    Article  Google Scholar 

  37. S. Hess, Z. Naturforsch. 30a, 1224 (1975).

    ADS  Google Scholar 

  38. M. Doi, Ferroelectrics 30, 247 (1980).

    Google Scholar 

  39. M. Doi, J. Polym. Sci. Polym. Phys. 19, 229 (1981).

    Article  Google Scholar 

  40. G. Rienäcker, PhD Thesis, Technical University Berlin (2000).

  41. For the decomposition of $\mathbf{a}$ into five independent components see, e.g., P. Kaiser, W. Wiese, S. Hess, J. Non-Equilib. Thermodyn. 17, 153 (1992).

    Article  Google Scholar 

  42. A. Wolf, J.B. Swift, H.L. Swinney, J.A. Vastano, Physica D 16 285 (1985).

  43. R.G. Larson, H.C. Öttinger, Macromolecules 24, 6270 (1991).

    Article  ADS  Google Scholar 

  44. S. Heidenreich, P. Ilg, S. Hess, Phys. Rev. E 75, 066302 (2007).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, Sekr. PN 7-1, Technische Universität Berlin, Hardenbergstraße 36, D-10623, Berlin, Germany

    S. Grandner, S. Heidenreich, S. Hess & S. H. L. Klapp

  2. Stranski-Laboratorium für Physikalische und Theoretische Chemie, Sekr. C7, Technische Universität Berlin, Straße des 17. Juni 115, D-10623, Berlin, Germany

    S. Grandner & S. H. L. Klapp

Authors
  1. S. Grandner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Heidenreich
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Hess
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. H. L. Klapp
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grandner, S., Heidenreich, S., Hess, S. et al. Polar nano-rods under shear: From equilibrium to chaos. Eur. Phys. J. E 24, 353–365 (2007). https://doi.org/10.1140/epje/i2007-10246-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epje/i2007-10246-8

PACS.

Search

Navigation