Skip to main content
SpringerLink
Log in

Shear-induced undulation of smectic-\(\mathsf{A}\): Molecular dynamics simulations vs. analytical theory

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

Abstract.

Experiments on a variety of systems have shown that layered liquids are unstable under shear even if the liquid layers are planes of constant velocity. We investigate the stability of smectic-A like liquids under shear using Molecular Dynamics simulations and a macroscopic hydrodynamic theory (including the layer normal and the director as independent variables). Both methods show an instability of the layers, which sets in above a critical shear rate. We find a remarkable qualitative and reasonable quantitative agreement between both methods for the spatial homogeneous state and the onset of the instability.

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. O. Diat, D. Roux, F. Nallet, J. Phys. II France 3, 1427 (1993)

    Article  Google Scholar 

  2. S. Müller, C. Börschig, W. Gronski, C. Schmidt, D. Roux, Langmuir 15, 7558 (1999)

    Article  Google Scholar 

  3. J.I. Escalante, H. Hoffmann, Rheol. Acta 39, 209 (2000)

    Article  Google Scholar 

  4. J. Zipel, F. Nettesheim, P. Linder, T.D. Le, U. Olsson, W. Richtering, Europhys. Lett. 53, 335 (2001)

    Article  Google Scholar 

  5. F. Nettesheim, J. Zipfel, U. Olsson, F. Renth, P. Lindner, W. Richtering, Langmuir 19, 3603 (2003)

    Article  Google Scholar 

  6. J. Zipfel, P. Lindner, M. Tsianou, P. Alexandridis, W. Richtering, Langmuir 15, 2599 (1999)

    Article  Google Scholar 

  7. R.G. Horn, M. Kléman, Ann. Phys. France 3, 229 (1978)

    Google Scholar 

  8. C.R. Safinya, E.B. Sirota, R.J. Plano, Phys. Rev. Lett. 66, 1986 (1991)

    Article  Google Scholar 

  9. P. Panizza, P. Archambault, D. Roux, J. Phys. II France 5, 303 (1995)

    Article  Google Scholar 

  10. V.K. Gupta, R. Krishnamoorti, Z.-R. Chen, J.A. Kornfield, S.D. Smith, M. Satkowski, J.T. Grothaus, Macromolecules 29, 875 (1996)

    Article  CAS  Google Scholar 

  11. U. Wiesner, Macromol. Chem. Phys. 198, 3319 (1997)

    Article  Google Scholar 

  12. J.H. Laurer, B. Scott Pinheiro, D.L. Polis, K.I. Winey, Macromolecules 32, 4999 (1999)

    Article  CAS  Google Scholar 

  13. J.L. Zryd, W.R. Burghardt, Macromolecules 31, 3656 (1998)

    Article  Google Scholar 

  14. H. Leist, D. Maring, T. Thurn-Albrecht, U. Wiesner, J. Chem. Phys. 110, 8225 (1999)

    Article  Google Scholar 

  15. D.L. Polis, S. Smith, N.J. Terrill, A.J. Ryan, D.C. Morse, K.I. Winey, Macromolecules 32, 4668 (1999)

    Article  CAS  Google Scholar 

  16. L. Noirez, A. Lapp, Phys. Rev. Lett. 78, 70 (1997)

    Article  Google Scholar 

  17. L. Noirez, Phys. Rev. Lett. 84, 2164 (2000)

    Article  Google Scholar 

  18. J. Zipfel, J. Berghausen, G. Schmidt, P. Lindner, P. Alexandridis, M. Tsianou, W. Richtering, Phys. Chem. Chem. Phys. 1, 3905 (1999)

    Article  Google Scholar 

  19. P.G. de Gennes, Solid State Commun. 10, 753 (1972)

    Article  Google Scholar 

  20. P.C. Martin, O. Parodi, P.S. Pershan, Phys. Rev. A 6, 2401 (1972)

    Article  Google Scholar 

  21. P.G. de Gennes, J. Prost, The Physics of Liquid Crystals (Clarendon Press, Oxford, 1993)

  22. H. Pleiner, H.R. Brand, in Pattern Formation in Liquid Crystals, edited by A. Buka, L. Kramer (Springer, New York, 1996), Chap. 2, Hydrodynamics and Electrohydrodynamics of Liquid Crystals

  23. M. Delaye, R. Ribotta, G. Durand, Phys. Lett. A 44, 139 (1973)

    Article  Google Scholar 

  24. N.A. Clark, R.B. Meyer, Appl. Phys. Lett. 22, 493 (1973)

    Article  Google Scholar 

  25. P. Oswald, S.I. Ben-Abraham, J. Phys. France 43, 1193 (1982)

    Google Scholar 

  26. G.K. Auernhammer, H.R. Brand, H. Pleiner, Rheol. Acta 39, 215 (2000)

    Article  Google Scholar 

  27. G.K. Auernhammer, H.R. Brand, H. Pleiner, Phys. Rev. E 66, 061707 (2002)

    Article  Google Scholar 

  28. R. Bruinsma, Y. Rabin, Phys. Rev. A 45, 994 (1992)

    Article  Google Scholar 

  29. A.G. Zilman, R. Granek, Eur. Phys. J. B 11, 593 (1999)

    Article  Google Scholar 

  30. D.R.M. Williams, F.C. MacKintosh, Macromolecules 27, 7677 (1994)

    Google Scholar 

  31. G.H. Frederickson, J. Rheol. 38, 1045 (1994)

    Article  Google Scholar 

  32. V. Kumaran, S. Jariwala, S. Hussain, Chem. Eng. Sci. 56, 5663 (2001)

    Article  Google Scholar 

  33. T. Soddemann, B. Dünweg, K. Kremer, Eur. Phys. J. E 6, 409 (2001)

    Article  Google Scholar 

  34. H. Guo, K. Kremer, T. Soddemann, Phys. Rev. E 66, 061503 (2002)

    Article  Google Scholar 

  35. P.G. de Gennes, Mol. Cryst. Liq. Cryst. 21, 49 (1973)

    Google Scholar 

  36. J.D. Litster, J. Als-Nielson, R.J. Birgeneau, S.S. Dana, D. Davidov, F. Garcia-Golding, M. Kaplan, C.R. Safinya, R. Schaetzing, J. Phys. Colloq. France 40, C3-339 (1979)

  37. S. Garoff, R.B. Meyer, Phys. Rev. Lett. 38, 848 (1977)

    Article  Google Scholar 

  38. S.R. de Groot, P. Mazur, Non-equilibrium Thermodynamics (North-Holland, Amsterdam, 1962)

  39. D. Forster, Hydrodynamic Fluctuations, Broken Symmetries, Correlation Functions (W.A. Benjamin, Reading, Massachusetts, 1975)

  40. H. Guo, K. Kremer, J. Chem. Phys. 119, 9308 (2003)

    Article  Google Scholar 

  41. D. Morse, S. Milner, Phys. Rev. E 47, 1119 (1993)

    Article  Google Scholar 

  42. F. Müller-Plathe, Phys. Rev. E 59, 4894 (1999)

    Article  Google Scholar 

  43. T. Soddemann, B. Dünweg, K. Kremer, Phys. Rev. E 68, 046702 (2003)

    Article  Google Scholar 

  44. P. Español, P. Warren, Europhys. Lett. 30, 191 (1995)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Max-Planck-Institut für Polymerforschung, 55021, Mainz, Germany

    Th. Soddemann, G. K. Auernhammer, H. Guo, B. Dünweg & K. Kremer

  2. Theoretische Physik III, Universität Bayreuth, 95440, Bayreuth, Germany

    G. K. Auernhammer

Authors
  1. Th. Soddemann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. K. Auernhammer
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. B. Dünweg
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. K. Kremer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Th. Soddemann.

Additional information

Received: 2 October 2003, Published online: 9 March 2004

PACS:

61.30.Dk Continuum models and theories of liquid crystal structure - 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 05.70.Ln Nonequilibrium and irreversible thermodynamics - 83.10.Rs Computer simulation of molecular and particle dynamics - 83.50.Ax Steady shear flows, viscometric flow

Th.Soddemann : Present address: Rechenzentrum der Max-Planck-Gesellschaft, Boltzmannstrasse 2, 85748 Garching, Germany

Rights and permissions

Reprints and permissions

About this article

Cite this article

Soddemann, T., Auernhammer, G.K., Guo, H. et al. Shear-induced undulation of smectic-\(\mathsf{A}\): Molecular dynamics simulations vs. analytical theory. Eur. Phys. J. E 13, 141–151 (2004). https://doi.org/10.1140/epje/e2004-00045-0

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1140/epje/e2004-00045-0

Keywords

Search

Navigation