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Macroscopic behavior of ferrocholesteric liquid crystals and ferrocholesteric gels and elastomers

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Abstract

We study the influence of macroscopic chirality on the macroscopic properties of superparamagnetic liquid crystals and gels. Specifically we derive macroscopic dynamic equations for ferrocholesteric low molecular weight (LMW) liquid crystals and for ferrocholesteric gels and elastomers in the local description using the director field as macroscopic variable. The magnetization is treated as a macroscopic dynamic degree of freedom and its coupling to all other macroscopic variables is examined in detail. We incorporate into our dynamic analysis terms that are linear in a magnetic field giving rise to a number of cross-coupling terms not possible otherwise. A number of properties that are unique to the class of systems studied arise. As an example for a static property we find a term in the generalized energy which is linear in the electric field and quadratic in the magnetic field. We find that applying a magnetic field to a ferrocholesteric can lead to reversible electric currents, heat currents and concentration currents, which change their sign with a sign change of macroscopic chirality. As an example of a rather intriguing dissipative dynamic contribution we point out that for ferrocholesterics and for ferrocholesteric gels and elastomers in a magnetic field extensional flow leads to electric and heat currents.

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References

  1. F. Reinitzer, Monatsh. Chemie 9, 421 (1888) english translation: F. Reinitzer, Liq. Cryst. 5.

    Article  Google Scholar 

  2. O. Lehmann, Ann. Phys. 2, 649 (1900).

    Article  Google Scholar 

  3. P.G. de Gennes, The Physics of Liquid Crystals (Clarendon Press, Oxford, 1975).

  4. S. Chandrasekhar, Liquid Crystals (Cambridge University Press, Cambridge, 1977).

  5. H. Finkelmann, H. Ringsdorf, J.H. Wendorff, Makromol. Chem. 179, 273 (1978).

    Article  Google Scholar 

  6. H. Finkelmann, H.J. Kock, G. Rehage, Makromol. Rapid Commun. 2, 317 (1981).

    Article  Google Scholar 

  7. J. Schätzle, H. Finkelmann, Mol. Cryst. Liq. Cryst. 142, 85 (1987).

    Article  Google Scholar 

  8. J. Schätzle, W. Kaufhold, H. Finkelmann, Makromol. Chem. 190, 3269 (1989).

    Article  Google Scholar 

  9. H.R. Brand Makromol. Rapid Commun.1057.

    Article  Google Scholar 

  10. W. Kaufhold, H. Finkelmann, H.R. Brand, Makromol. Chem. 192, 2555 (1991).

    Article  Google Scholar 

  11. J. Küpfer, H. Finkelmann, Makromol. Chem. Rapid Commun. 12, 717 (1991).

    Article  Google Scholar 

  12. H.R. Brand, H. Finkelmann, in Handbook of Liquid Crystals, edited by J.W. Goodby, Vol. 3 (Wiley, New York, 1998) p. 277.

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

    Article  ADS  Google Scholar 

  14. P.G. de Gennes, in Liquid Crystals of One- and Two-Dimensional Order, edited by W. Helfrich, G. Heppke (Springer, New York, 1980).

  15. H.R. Brand, H. Pleiner, Physica A 208, 359 (1994).

    Article  ADS  Google Scholar 

  16. A.M. Menzel, H. Pleiner, H.R. Brand, J. Chem. Phys. 126, 234901 (2007).

    Article  ADS  Google Scholar 

  17. A.M. Menzel, H. Pleiner, H.R. Brand, J. Appl. Phys. 105, 013593 (2009).

    Article  Google Scholar 

  18. A.M. Menzel, H. Pleiner, H.R. Brand, Eur. Phys. J. E 30, 371 (2009).

    Article  Google Scholar 

  19. K. Urayama, R. Mashita, I. Kobayashi, T. Takigawa, Macromolecules 40, 7665 (2007).

    Article  ADS  Google Scholar 

  20. D. Rogez, P. Martinoty, Eur. Phys. J. E 34, 69 (2011).

    Article  Google Scholar 

  21. R.E. Rosensweig, Ferrohydrodynamics (Cambridge University Press, Cambridge, 1985).

  22. H.-W. Müller, M. Liu, Phys. Rev. E 64, 061405 (2001).

    Article  ADS  Google Scholar 

  23. H.-W. Müller, M. Liu, Phys. Rev. E 67, 043202 (2003).

    Article  ADS  Google Scholar 

  24. H.-W. Müller, Y.M. Jiang, M. Liu, Phys. Rev. E 67, 031201 (2003).

    Article  ADS  Google Scholar 

  25. B. Huke, M. Lücke, Rep. Prog. Phys. 67, 1731 (2004).

    Article  ADS  Google Scholar 

  26. S. Odenbach, J. Phys.: Condens. Matter 16, R1135 (2004).

    ADS  Google Scholar 

  27. B. Fischer, B. Huke, M. Lücke, R. Hempelmann, J. Magn. & Magn. Mater. 289, 74 (2005).

    Article  ADS  Google Scholar 

  28. P. Ilg, M. Kröger, S. Hess, J. Magn. & Magn. Mater. 289, 325 (2005).

    Article  ADS  Google Scholar 

  29. S.H.L. Klapp, J. Phys.: Condens. Matter 17, R525 (2005).

    ADS  Google Scholar 

  30. P. Ilg, E. Coquelle, S. Hess, J. Phys.: Condens. Matter 18, S2756 (2006).

    Google Scholar 

  31. F. Brochard, P.G. de Gennes, J. Phys. (Paris) 31, 691 (1970).

    Article  Google Scholar 

  32. J. Rault, P.E. Cladis, J.P. Burger, Phys. Lett. A 32, 1410 (1970).

    Article  Google Scholar 

  33. C.F. Hayes, Mol. Cryst. Liq. Cryst. 36, 245 (1976).

    Article  Google Scholar 

  34. L. Liébert, A. Martinet, J. Phys. (Paris) 40, 363 (1979).

    Article  Google Scholar 

  35. S.-S. Chen, S.H. Chiang, Mol. Cryst. Liq. Cryst. 144, 359 (1987).

    Article  Google Scholar 

  36. J.C. Bacri, A.M.F. Neto, Phys. Rev. E 50, 3860 (1994).

    Article  ADS  Google Scholar 

  37. S.I. Burylov, Y.L. Raikher, Mol. Cryst. Liq. Cryst. 258, 123 (1995).

    Article  Google Scholar 

  38. M. Koneracká, V. Závičová, P. Kopčanský, J. Jadzyn, G. Czechowski, B. Zywucki, J. Magn. & Magn. Mater. 157/158, 589 (1996).

    Article  ADS  Google Scholar 

  39. Yu. Raikher, V.I. Stepanov, J. Magn. & Magn. Mater. 201, 182 (1999).

    Article  ADS  Google Scholar 

  40. I. Potočová, M. Koneracká, P. Kopčanský, M. Timko, L. Tomčo, J. Jadzyn, G. Czechowski, J. Magn. & Magn. Mater. 196, 578 (1999).

    Article  ADS  Google Scholar 

  41. E. Jarkova, H. Pleiner, H.-W. Müller, A. Fink, H.R. Brand, Eur. Phys. J. E 5, 583 (2001).

    Article  Google Scholar 

  42. E. Jarkova, H. Pleiner, H.-W. Müller, H.R. Brand, J. Chem. Phys. 118, 2422 (2003).

    Article  ADS  Google Scholar 

  43. A. Mertelj, D. Lisjak, M. Drofenik, M. Čopič, Nature 504, 237 (2013).

    Article  ADS  Google Scholar 

  44. A. Mertelj, N. Osterman, D. Lisjak, M. Čopič, Soft Matter 10, 9065 (2014).

    Article  ADS  Google Scholar 

  45. M. Zrínyi, L. Barsi, A. Büki, Europhys. Conf. Abstract 19, 40 (1995).

    Google Scholar 

  46. M. Zrínyi, L. Barsi, A. Büki, Polym. Gels Netw. 5, 415 (1997).

    Article  Google Scholar 

  47. L. Barsi, A. Büki, S. Szabó, M. Zrínyi, Progr. Colloid Polym. Sci. 102, 57 (1996).

    Article  Google Scholar 

  48. M. Zrínyi, Trends Polym. Sci. 5, 280 (1997).

    Google Scholar 

  49. D. Szabó, G. Szeghy, M. Zrínyi, Macromolecules 31, 6541 (1998).

    Article  ADS  Google Scholar 

  50. E. Jarkova, H. Pleiner, H.-W. Müller, H.R. Brand, Phys. Rev. E 68, 041706 (2003).

    Article  ADS  Google Scholar 

  51. G. Pessot, P. Kremer, D.Y. Borin, S. Odenbach, H. Löwen, A.M. Menzel, J. Chem. Phys. 141, 124904 (2014).

    Article  ADS  Google Scholar 

  52. D. Collin, G.K. Auernhammer, O. Gavat, P. Martinoty, H.R. Brand, Macromol. Rapid Commun. 24, 737 (2003).

    Article  Google Scholar 

  53. Z. Varga, J. Feher, G. Filipcsei, L. Zrinyi, Macromol. Symp. 200, 93 (2003).

    Article  Google Scholar 

  54. D. Günther, D.Y. Borin, S. Günter, S. Odenbach, Smart Mater. Struct. 21, 015005 (2012).

    Article  ADS  Google Scholar 

  55. S. Bohlius, H.R. Brand, H. Pleiner, Phys. Rev. E 70, 061411 (2004).

    Article  ADS  Google Scholar 

  56. A.M. Menzel, J. Chem. Phys. 141, 194907 (2014).

    Article  Google Scholar 

  57. T.C. Lubensky, Phys. Rev. A 6, 452 (1972).

    Article  ADS  Google Scholar 

  58. T.C. Lubensky, Mol. Cryst. Liq. Cryst. 23, 99 (1973).

    Article  Google Scholar 

  59. H. Pleiner, H.R. Brand, in Pattern Formation in Liquid Crystals, edited by A. Buka, L. Kramer (Springer, New York, 1996) p. 15.

  60. H.R. Brand, H. Pleiner, Eur. Phys. J. E 37, 122 (2014).

    Article  Google Scholar 

  61. A.M.F. Neto, L. Liébert, A.M. Levelut, J. Phys. (Paris) 45, 1505 (1984).

    Article  Google Scholar 

  62. A.M.F. Neto, Y. Galerne, L. Liébert, J. Phys. Chem. 89, 3939 (1985).

    Article  Google Scholar 

  63. A.M.F. Neto, A.M. Levelut, Y. Galerne, L. Liébert, J. Phys. (Paris) 49, 1301 (1988).

    Article  Google Scholar 

  64. T. Kroin, A.M.F. Neto, L. Liébert, Y. Galerne, Phys. Rev. A 40, 4647 (1989).

    Article  ADS  Google Scholar 

  65. A.N. Zakhlevnykh, P.A. Sosnin, Int. J. Polym. Mater. 27, 89 (1994).

    Article  Google Scholar 

  66. A.N. Zakhlevnykh, V. Shavkunov, J. Magn. & Magn. Mater. 210, 279 (2000).

    Article  ADS  Google Scholar 

  67. D. Reis, E. Akpinar, A.M. Figueiredo Neto, J. Phys. Chem. B 117, 942 (2013).

    Article  Google Scholar 

  68. A.M.F. Neto, Liq. Cryst. Rev. 2, 47 (2014).

    Article  Google Scholar 

  69. H.R. Brand, Makromol. Chem. Rapid Commun. 10, 441 (1989).

    Article  Google Scholar 

  70. A.M. Menzel, H.R. Brand, J. Chem. Phys. 125, 194704 (2006).

    Article  ADS  Google Scholar 

  71. S.T. Kim, H. Finkelmann, Makromol. Chem. Rapid Commun. 22, 429 (2001).

    Article  Google Scholar 

  72. A. Komp, J. Rühe, H. Finkelmann, Makromol. Chem. Rapid Commun. 26, 813 (2005).

    Article  Google Scholar 

  73. H.R. Brand, H. Pleiner, D. Svenšek, Phys. Rev. E 88, 024501 (2013).

    Article  ADS  Google Scholar 

  74. P.E. Cladis, H.R. Brand, H. Pleiner, Liq. Cryst. Today 9, 4024501 (1999).

    Google Scholar 

  75. H.R. Brand, H. Pleiner, P.E. Cladis, Physica A 351, 189 (2005).

    Article  ADS  Google Scholar 

  76. S.R. de Groot, P. Mazur, Nonequilibrium Thermodynamics (North Holland, Amsterdam, 1962).

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

    Article  ADS  Google Scholar 

  78. D. Forster, Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions (W.A. Benjamin, Reading, Mass., 1975).

  79. H.R. Brand, H. Pleiner, Phys. Rev. A 37, 2736 (1988).

    Article  ADS  Google Scholar 

  80. D. Svenšek, H. Pleiner, H.R. Brand, Phys. Rev. E 78, 021703 (2008).

    Article  ADS  Google Scholar 

  81. H. Pleiner H.R. Brand, EPL 89, 26003 (2010).

    Article  ADS  Google Scholar 

  82. H. Pleiner, M. Liu, H.R. Brand, Rheol. Acta 39, 560 (2000).

    Article  Google Scholar 

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Authors and Affiliations

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

    Helmut R. Brand & Alexander Fink

  2. Max-Planck-Institute for Polymer Research, POBox 3148, 55021, Mainz, Germany

    Helmut R. Brand & Harald Pleiner

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  1. Helmut R. Brand
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  2. Alexander Fink
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Correspondence to Helmut R. Brand.

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Brand, H.R., Fink, A. & Pleiner, H. Macroscopic behavior of ferrocholesteric liquid crystals and ferrocholesteric gels and elastomers. Eur. Phys. J. E 38, 65 (2015). https://doi.org/10.1140/epje/i2015-15065-8

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  • DOI: https://doi.org/10.1140/epje/i2015-15065-8

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