Hostname: page-component-6bf8c574d5-vmclg Total loading time: 0 Render date: 2025-02-23T06:31:59.287Z Has data issue: false hasContentIssue false
  • English
  • Français

Elastic director vibrations in nematic liquid crystals

Published online by Cambridge University Press:  13 November 2014

STEFANO S. TURZI
STEFANO S. TURZI*
Affiliation:
Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy email: stefano.turzi@polimi.it
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Recently Biscari, DiCarlo and Turzi [Anisotropic wave propagation in nematic liquid crystals, Soft Matter 10, 8296–8307.] proposed a theory for nematoacustics which models nematic liquid crystals as nematic elastomers with molecular relaxation. Here, we extend the analysis of this theory to account for the director motion possibly induced by the propagation of a sound wave. We find that the director vibration is related to the - usually small - anisotropy of the molecular distribution, thus providing a justification to the relative high ultrasonic intensities required to observe non-negligible acousto-optic responses.

Keywords

Liquid crystals (76A15)Anisotropy (74E10)Viscoelastic fluids (76A10)Hydroacoustics (76Q05)
Type
Papers
Information
European Journal of Applied Mathematics , Volume 26 , Issue 1 , February 2015 , pp. 93 - 107
Copyright
Copyright © Cambridge University Press 2014 

References

[1]Berardi, R., Emerson, A. P. J. & Zannoni, C. (1993) Monte-carlo investigations of a Gay-Berne liquid crystal. J. Chem. Soc. Faraday Trans. 89, 4069–4078.CrossRefGoogle Scholar
[2]Biscari, P., DiCarlo, A. & Turzi, S. S. (2014) Anisotropic wave propagation in nemaric liquid crystals. Soft Matter 10, 8296–8307.CrossRefGoogle ScholarPubMed
[3]Bladon, E. M., Terentjev, P. & Warner, M. (1994) Deformation-induced orientational transitions in liquid crystals elastomer. J. Phys. II France 4, 75–91.Google Scholar
[4]de Gennes, P. & Prost, J. (1995) The Physics of Liquid Crystals, 2nd. edn.Oxford University Press, Oxford.Google Scholar
[5]De Matteis, G. & Virga, E. G. (2011) Director libration in nematoacoustics. Phys. Rev. E 83, 011703.CrossRefGoogle ScholarPubMed
[6]DeSimone, A., DiCarlo, A. & Teresi, L. (2007) Critical voltages and blocking stresses in nematic gels. Eur. Phys. J. E 24, 303–310.CrossRefGoogle ScholarPubMed
[7]DeSimone, A. & Teresi, L. (2009) Elastic energies for nematic elastomers. Eur. Phys. J. E 29, 191–204.CrossRefGoogle ScholarPubMed
[8]DiCarlo, A. (2005) Surface and Bulk Growth Unified, in “Mechanics of Material Forces”, Steinmann, P. and Maugin, G. A. (Editors) Springer, pp. 56–64.Google Scholar
[9]DiCarlo, A. & Quiligotti, S. (2002) Growth and balance. Mech. Res. Commun. 29, 449–456.CrossRefGoogle Scholar
[10]Greanya, V. A., Spector, M. S., Selinger, J. V., Weslowski, B. T. & Shashidhar, R. (2003) Acousto-optic response of nematic liquid crystals. J. Appl. Phys. 94, 7571–7575.CrossRefGoogle Scholar
[11]Kim, Y. J. & Patel, J. S. (1999) Acoustic generation in liquid crystals. Appl. Phys. Lett. 75, 1985–1987.CrossRefGoogle Scholar
[12]Lord, A. E. Jr. & Labes, M. M. (1970) Anisotropic ultrasonic properties of a nematic liquid crystal. Phys. Rev. Lett. 25, 570–572.CrossRefGoogle Scholar
[13]Malanoski, A. P., Greanya, V. A., Weslowski, B. T., Spector, M. S., Selinger, J. V. & Shashidhar, R. (2004) Theory of the acoustic realignment of nematic liquid crystals. Phys. Rev. E 69, 021705.CrossRefGoogle ScholarPubMed
[14]Mullen, M. E., Lüthi, B. & Stephen, M. J. (1972) Sound velocity in a nematic liquid crystal. Phys. Rev. Lett. 28, 799–801.CrossRefGoogle Scholar
[15]Rajagopal, K. R. & Srinivasa, A. R. (1998) Mechanics of the inelastic behavior of materials. Part I: Theoretical underpinnings. Int. J. Plast. 14, 945–967.CrossRefGoogle Scholar
[16]Rajagopal, K. R. & Srinivasa, A. R. (1998) Mechanics of the inelastic behavior of materials. Part II: Inelastic response. Int. J. Plast. 14, 969–995.CrossRefGoogle Scholar
[17]Rajagopal, K. R. & Srinivasa, A. R. (2004) On the thermomechanics of materials that have multiple natural configurations. Part I: Viscoelasticity and classical plasticity. Z. Angew. Math. Phys. 55, 861–893.CrossRefGoogle Scholar
[18]Sandhu, J. S., Schmidt, R. A. & L ARivière, P. J. (2009) Full-field acoustomammography using an acousto-optic sensor. Med. Phys. 36, 2324–2327.CrossRefGoogle ScholarPubMed
[19]Sandhu, J. S., Wang, H. & Popek, W. J. (2000) Liquid crystal-based acoustic imaging. Proc. SPIE 3955, 94–108.CrossRefGoogle Scholar
[20]Selinger, J. V., Spector, M. S., Greanya, V. A., Weslowski, B., Shenoy, D. & Shashidhar, R. (2002) Acoustic realignment of nematic liquid crystals. Phys. Rev. E 66, 051708.CrossRefGoogle ScholarPubMed
[21]Sonnet, A. M., Maffettone, P. L. & Virga, E. G. (2004) Continuum theory for nematic liquid crystals with tensorial order. J. Non-Newtonian Fluid Mech. 119, 51–59.CrossRefGoogle Scholar
[22]Sonnet, A. M. & Virga, E. G. (2001) Dynamics of dissipative ordered fluids. Phys. Rev. E 64, 031705.CrossRefGoogle ScholarPubMed
[23]Stewart, I. (2004) The Static and Dynamic Continuum Theory of Liquid Crystals: A Mathematical Introduction, 1st. edn., Taylor & Francis, London,.Google Scholar
[24]Virga, E. G. (2009) Variational theory for nematoacoustics. Phys. Rev. E 80, 031705.CrossRefGoogle ScholarPubMed
[25]Warner, M. & Terentjev, E. M. (1996) Nematic elastomers–-a new state of matter?. Prog. Polym. Sci. 21, 853–891.CrossRefGoogle Scholar
[26]Warner, M. & Terentjev, E. M. (2003) Liquid Crystal Elastomers, Oxford Science Publications, Oxford.CrossRefGoogle ScholarPubMed