Skip to main content
SpringerLink
Log in

Strongly anisotropic elastic moduli of nematic elastomers: Analytical expressions and nonlinear temperature dependence

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

Abstract.

Exact formulae for the elastic moduli of the nematic elastomers are obtained by the implicit function method based on somewhat general energy functions. The formulae indicate that both the moduli parallel and perpendicular to the director of the nematic elastomers are smaller than the modulus of the classical elastomers because of the mechanical-nematic coupling. Moreover, the moduli are generally anisotropic due to the biaxiality induced by stretching the nematic elastomers perpendicular to the director. Then we get the explicit analytical expressions of the parallel and perpendicular moduli by making use of the Landau-de Gennes free energy and the neo-classical elastic energy. Very different from the classical elastomers, they are both strongly nonlinear functions of the temperature in the nematic phase. Furthermore, their ratio, the degree of anisotropy, changes with the temperature as well. The results agree qualitatively with some experiments. Better quantitative agreement is obtained by some modifications of the constitutive relation of the elastic energy.

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. Warner, E.M. Terentjev, Liquid Crystal Elastomers (Clarendon Press, Oxford, 2003)

  2. H.R. Brand, H. Pleiner, P. Martinoty, Soft Matter 2, 182 (2006)

    Article  Google Scholar 

  3. P.G. de Gennes, J.P. Prost, The Physics of Liquid Crystals (Oxford University Press, Oxford, 1994)

  4. J. Schatzle, W. Kaufhold, H. Finkelmann, Makromol. Chem. 190, 3269 (1989)

    Article  Google Scholar 

  5. W. Kaufhold, H. Finkelmann, Makromol. Chem. 192, 2555 (1991)

    Article  Google Scholar 

  6. D.L. Thomsen III, P. Keller, J. Naciri, R. Pink, H. Jeon, D. Shenoy, B.R. Ratna, Macromolecules 34, 5868 (2001)

    Article  ADS  Google Scholar 

  7. J. Naciri, A. Srinivasan, B. R. Ratna, in Proc. SPIE, Vol. 5385, edited by Y. Bar-Cohen (SPIE, Bellingham, WA, 2004), p. 548

  8. P. Bladon, M. Warner, Macromolecules 26, 1078 (1993)

    Article  ADS  Google Scholar 

  9. H.R. Brand, O. Müller, Macromol. Theory Simul. 11, 154 (2002)

    Article  Google Scholar 

  10. G.R. Mitchell, F.J. Davis, W. Guo, Phys. Rev. Lett. 71, 2947 (1993)

    Article  ADS  Google Scholar 

  11. I. Kundler, H. Finkelmann, Macromol. Chem. Phys. 199, 677 (1998)

    Article  Google Scholar 

  12. F. Zhang, P.A. Heiney, Phys. Rev. E 73, 021701 (2006)

    Article  ADS  Google Scholar 

  13. H. Finkelmann, E. Nishikawa, G.G. Pereira, M. Warner, Phys. Rev. Lett. 87, 015501 (2001)

    Article  ADS  Google Scholar 

  14. A.R. Tajbakhsh, E.M. Terentjev, Eur. Phys. J. E 6, 181 (2001)

    Article  Google Scholar 

  15. H. Hirschmann, P.M.S. Roberts, F.J. Davis, W. Guo, C.D. Hasson, G.R. Mitchell, Polymer 42, 7063 (2001)

    Article  Google Scholar 

  16. J. Küper, H. Finkelmann, Macromol. Chem. Rapid. Commun. 12, 717 (1991)

    Article  Google Scholar 

  17. H. Finkelmann, A. Greve, M. Warner, Eur. J. Phys. E 5, 281 (2001)

    Article  Google Scholar 

  18. E.M. Terentjev, M. Warner, Eur. Phys. J. E 4, 343 (2001)

    Article  Google Scholar 

  19. S.M. Clarke, A.R. Tajbakhsh, E.M. Terentjev, M. Warner, Phys. Rev. Lett. 86, 4044 (2001)

    Article  ADS  Google Scholar 

  20. P. Martinoty, P. Stein, H. Finkelmann, H. Pleiner, H.R. Brand, Eur. Phys. J. E 14, 311 (2004)

    Article  Google Scholar 

  21. G.G. Pereira, M. Warner, Eur. Phys. J. E 5, 295 (2001)

    Article  Google Scholar 

  22. P. Bladon, E.M. Terentjev, M. Warner, Phys. Rev. E 47, R3838 (1993)

    Article  ADS  Google Scholar 

  23. S.M. Clarke, A. Hotta, A.R. Tajbakhsh, E.M. Terentjev, Phys. Rev. E 64, 061702 (2001)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanics and Engineering Science, Fudan University, 200433, Shanghai, China

    Z. Zeng, L. Jin & Y. Huo

Authors
  1. Z. Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Y. Huo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Y. Huo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zeng, Z., Jin, L. & Huo, Y. Strongly anisotropic elastic moduli of nematic elastomers: Analytical expressions and nonlinear temperature dependence. Eur. Phys. J. E 32, 71–79 (2010). https://doi.org/10.1140/epje/i2010-10599-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epje/i2010-10599-9

Keywords

Search

Navigation