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Influence of tetrahedral order on ferromagnetic gel phases

  • Tilen Potisk
  • Harald PleinerEmail author
  • Helmut R. Brand
Open Access
Regular Article
  • 128 Downloads

Abstract.

We investigate the macroscopic dynamics of gels with tetrahedral/octupolar symmetry, which possess in addition a spontaneous permanent magnetization. We derive the corresponding static and dynamic macroscopic equations for a phase, where the magnetization is parallel to one of the improper fourfold tetrahedral symmetry axes. Apart from elastic strains, we take into account relative rotations between the magnetization and the elastic network. The influence of tetrahedral order on these degrees of freedom is investigated and some experiments are proposed that are specific for such a material and allow to indirectly detect tetrahedral order. We also consider the case of a transient network and predict that stationary elastic shear stresses arise when a temperature gradient is applied.

Graphical abstract

Keywords

Soft Matter: Liquid crystals 

Notes

Acknowledgments

Open Access funding provided by Max Planck Society.

References

  1. 1.
    R.E. Rosensweig, Ferrohydrodynamics (Cambridge University Press, Cambridge, 1985)Google Scholar
  2. 2.
    S. Odenbach, J. Phys.: Condens. Matter 16, R1135 (2004)Google Scholar
  3. 3.
    H.-W. Müller, M. Liu, Phys. Rev. E 64, 061405 (2001)CrossRefGoogle Scholar
  4. 4.
    B. Huke, M. Lücke, Rep. Prog. Phys. 67, 1731 (2004)CrossRefGoogle Scholar
  5. 5.
    P. Ilg, E. Coquelle, S. Hess, J. Phys.: Condens. Matter 18, S2757 (2006)Google Scholar
  6. 6.
    V.I. Zadorozhnii, A.N. Vasilev, V.Yu. Reshetnyak, K.S. Thomas, T.J. Sluckin, Europhys. Lett. 73, 408 (2006)CrossRefGoogle Scholar
  7. 7.
    S. Mahle, P. Ilg, M. Liu, Phys. Rev. E 77, 016305 (2008)CrossRefGoogle Scholar
  8. 8.
    S.D. Peroukidis, S.H.L. Klapp, Phys. Rev. E 92, 010501 (2015)CrossRefGoogle Scholar
  9. 9.
    M. Zrínyi, Trends Polym. Sci. 5, 280 (1997)Google Scholar
  10. 10.
    Z. Varga, J. Fehér, G. Filipcsei, M. Zrínyi, Macromol. Symp. 200, 93 (2003)CrossRefGoogle Scholar
  11. 11.
    M. Zrínyi, L. Barsi, A. Büki, J. Chem. Phys. 104, 8750 (1996)CrossRefGoogle Scholar
  12. 12.
    M. Zrínyi, F. Horkay, J. Intell. Mater. Syst. Struct. 4, 190 (1993)CrossRefGoogle Scholar
  13. 13.
    M. Babincová, D. Leszczynska, P. Sourivong, P. Čičmanec, P. Babinec, J. Magn. & Magn. Mater. 225, 109 (2001)CrossRefGoogle Scholar
  14. 14.
    E. Jarkova, H. Pleiner, H.-W. Müller, H.R. Brand, Phys. Rev. E 68, 041706 (2003)CrossRefGoogle Scholar
  15. 15.
    G. Pessot, P. Cremer, D.Y. Borin, S. Odenbach, H. Löwen, A.M. Menzel, J. Chem. Phys. 141, 124904 (2014)CrossRefGoogle Scholar
  16. 16.
    S. Huang, G. Pessot, P. Cremer, R. Weeber, C. Holm, J. Nowak, S. Odenbach, A.M. Menzel, G.K. Auernhammer, Soft Matter 12, 228 (2016)CrossRefGoogle Scholar
  17. 17.
    D. Collin, G.K. Auernhammer, O. Gavat, P. Martinoty, H.R. Brand, Macromol. Rapid Commun. 24, 737 (2003)CrossRefGoogle Scholar
  18. 18.
    S. Bohlius, H.R. Brand, H. Pleiner, Phys. Rev. E 70, 061411 (2004)CrossRefGoogle Scholar
  19. 19.
    L.G. Fel, Phys. Rev. E 52, 702 (1995)CrossRefGoogle Scholar
  20. 20.
    L.G. Fel, Phys. Rev. E 52, 2692 (1995)CrossRefGoogle Scholar
  21. 21.
    L. Radzihovsky, T.C. Lubensky, Europhys. Lett. 54, 206 (2001)CrossRefGoogle Scholar
  22. 22.
    T.C. Lubensky, L. Radzihovsky, Phys. Rev. E 66, 031704 (2002)MathSciNetCrossRefGoogle Scholar
  23. 23.
    B. Mettout, Phys. Rev. E 74, 041701 (2006)MathSciNetCrossRefGoogle Scholar
  24. 24.
    L. Longa, G. Pajak, T. Wydro, Phys. Rev. E 79, 040701 (2009)CrossRefGoogle Scholar
  25. 25.
    K. Trojanowski, G. Pajak, L. Longa, T. Wydro, Phys. Rev. E 86, 011704 (2012)CrossRefGoogle Scholar
  26. 26.
    L. Longa, K. Trojanowski, Acta. Phys. Pol. B 44, 1201 (2013)CrossRefGoogle Scholar
  27. 27.
    H.R. Brand, H. Pleiner, P.E. Cladis, Eur. Phys. J. E 7, 163 (2002)Google Scholar
  28. 28.
    P.E. Cladis, H. Pleiner, H.R. Brand, Eur. Phys. J. E 11, 283 (2003)CrossRefGoogle Scholar
  29. 29.
    H.R. Brand, P.E. Cladis, H. Pleiner, Ferroelectrics 315, 165 (2005)CrossRefGoogle Scholar
  30. 30.
    H.R. Brand, H. Pleiner, P.E. Cladis, Physica A 351, 189 (2005)CrossRefGoogle Scholar
  31. 31.
    H. Pleiner, P.E. Cladis, H.R. Brand, Eur. Phys. J. E 20, 257 (2006)CrossRefGoogle Scholar
  32. 32.
    H.R. Brand, H. Pleiner, Eur. Phys. J. E 31, 37 (2010)CrossRefGoogle Scholar
  33. 33.
    H. Pleiner, H.R. Brand, Eur. Phys. J. E 37, 11 (2014)CrossRefGoogle Scholar
  34. 34.
    G. Pelzl, A. Eremin, S. Diele, H. Kresse, W. Weissflog, J. Mater. Chem. 12, 2591 (2002)CrossRefGoogle Scholar
  35. 35.
    V. Bourny, V. Lorman, J. Pavel, B. Mettout, H.T. Nguyen, Ferroelectrics 276, 127 (2002)CrossRefGoogle Scholar
  36. 36.
    W. Weissflog, M.W. Schröder, S. Diele, G. Pelzl, Adv. Mater. 15, 630 (2003)CrossRefGoogle Scholar
  37. 37.
    T. Niori, J. Yamamoto, H. Yokoyama, Mol. Cryst. Liq. Cryst. 409, 475 (2004)CrossRefGoogle Scholar
  38. 38.
    M.W. Schroeder, S. Diele, G. Pelzl, W. Weissflog, ChemPhysChem 2004, 99 (2004)CrossRefGoogle Scholar
  39. 39.
    D. Wiant, J.T. Gleeson, N. Eber, K. Fodor-Csorba, A. Jakli, T. Toth-Katona, Phys. Rev. E 72, 041712 (2005)CrossRefGoogle Scholar
  40. 40.
    J. Harden, B. Mbanga, N. Eber, K. Fodor-Csorba, S. Sprint, J.T. Gleeson, A. Jakli, Phys. Rev. Lett. 97, 157802 (2006)CrossRefGoogle Scholar
  41. 41.
    D. Wiant, S. Stojadinovic, K. Neupane, S. Sharma, K. Fodor-Csorba, A. Jakli, J.T. Gleeson, S. Sprunt, Phys. Rev. E 73, 030703 (2006)CrossRefGoogle Scholar
  42. 42.
    D. Wiant, K. Neupane, S. Sharma, J.T. Gleeson, S. Sprunt, A. Jakli, N. Pradhan, G. Iannacchione, Phys. Rev. E 77, 061701 (2008)CrossRefGoogle Scholar
  43. 43.
    T. Ostapenko, D.B. Wiant, S.N. Sprunt, A. Jakli, J.T. Gleeson, Phys. Rev. Lett. 101, 247801 (2008)CrossRefGoogle Scholar
  44. 44.
    Y. Jang, R. Balachandran, C. Keith, A. Lehmann, C. Tschierske, J.K. Vij, Soft Matter 8, 10479 (2012)CrossRefGoogle Scholar
  45. 45.
    F. Vita, I.F. Placentino, C. Ferreo, G. Singh, E.T. Samulski, O. Francescangeli, Soft Matter 9, 6475 (2013)CrossRefGoogle Scholar
  46. 46.
    M. Jasinski, D. Pociecha, H. Monobe, J. Szczytko, P. Kaszynski, J. Am. Chem. Soc. 136, 14658 (2014)CrossRefGoogle Scholar
  47. 47.
    O.N. Kadkin, E.H. Kim, Y.J. Rha, S.Y. Kim, J. Taem, M.-G. Choi, Chem. Eur. J. 15, 10343 (2009)CrossRefGoogle Scholar
  48. 48.
    E.H. Kim, O.N. Kadkin, S.Y. Kim, J. Taem, M.-G. Choi, Eur. J. Inorg. Chem. 2011, 2933 (2011)CrossRefGoogle Scholar
  49. 49.
    H. Pleiner, H.R. Brand, Braz. J. Phys. 46, 565 (2016)CrossRefGoogle Scholar
  50. 50.
    T. Potisk, H. Pleiner, H.R. Brand, Phys. Rev. E 98, 042703 (2018)CrossRefGoogle Scholar
  51. 51.
    H.R. Brand, H. Pleiner, Eur. Phys. J. E 40, 34 (2017)CrossRefGoogle Scholar
  52. 52.
    C. Dressel, T. Reppe, M. Prehm, M. Brautzsch, C. Tschierske, Nat. Chem. 6, 971 (2014)CrossRefGoogle Scholar
  53. 53.
    C. Dressel, W. Weissflog, C. Tschierske, Chem. Commun. 51, 15850 (2015)CrossRefGoogle Scholar
  54. 54.
    M. Alaasar, M. Prehm, Y. Cao, F. Liu, C. Tschierske, Angew. Chem. Int. Ed. 55, 312 (2016)CrossRefGoogle Scholar
  55. 55.
    H. Temmen, H. Pleiner, M. Liu, H.R. Brand, Phys. Rev. Lett. 84, 3228 (2000)CrossRefGoogle Scholar
  56. 56.
    H. Pleiner, M. Liu, H.R. Brand, Rheol. Acta 39, 560 (2000)CrossRefGoogle Scholar
  57. 57.
    A.M. Menzel, H. Pleiner, H.R. Brand, J. Chem. Phys. 126, 234901 (2007)CrossRefGoogle Scholar
  58. 58.
    A. Menzel, H. Pleiner, H.R. Brand, J. Appl. Phys. 105, 013503 (2009)CrossRefGoogle Scholar
  59. 59.
    A. Menzel, H. Pleiner, H.R. Brand, Eur. Phys. J. E 30, 371 (2009)CrossRefGoogle Scholar
  60. 60.
    H. Pleiner, H.R. Brand, Hydrodynamics and Electrohydrodynamics of Nematic Liquid Crystals, in Pattern Formation in Liquid Crystals, edited by A. Buka, L. Kramer (Springer, New York, 1996)Google Scholar
  61. 61.
    H.R. Brand, H. Pleiner, Eur. Phys. J. E 37, 122 (2014)CrossRefGoogle Scholar
  62. 62.
    P.C. Martin, O. Parodi, P.S. Pershan, Phys. Rev. A 6, 2401 (1972)CrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 License (https://doi.org/creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  • Tilen Potisk
    • 1
  • Harald Pleiner
    • 2
    Email author
  • Helmut R. Brand
    • 1
  1. 1.Department of PhysicsUniversity of BayreuthBayreuthGermany
  2. 2.Max Planck Institute for Polymer ResearchMainzGermany

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