Abstract.
We present the derivation of the macroscopic equations for uniaxial ferronematic gels and elastomers. We deal with the superparamagnetic case, where no permanent magnetization is present and the anisotropy is provided by the nematic director. We include the magnetization as an independent dynamic degree of freedom. As a consequence special emphasis is laid on possible static and dynamic cross-couplings between magnetization and the non-magnetic degrees of freedom, as director reorientations, flow, elastic strains and relative rotations between director and the elastic network. In particular, we find reversible dynamic cross-couplings among rotations of the magnetization, the director, relative rotations, and deformational flow that allow for new possibilities to manipulate such materials. Application of simple (oscillatory) shear induces, in general, a finite magnetization normal to the shear plane and a relative rotation in the shear plane, whose amplitudes are linear in the shear rate. Induced magnetization, induced relative rotation and the director are mutually orthogonal, with the director aligned obliquely to the flow direction. This orientation is independent of the shear rate and is a material property.
Graphical abstract
Similar content being viewed by others
References
R.E. Rosensweig, Ferrohydrodynamics (Cambridge University Press, Cambridge, 1985)
H.-W. Müller, M. Liu, Phys. Rev. E 64, 061405 (2001)
H.-W. Müller, M. Liu, Phys. Rev. E 67, 043202 (2003)
H.-W. Müller, Y.M. Jiang, M. Liu, Phys. Rev. E 67, 031201 (2003)
B. Huke, M. Lücke, Rep. Prog. Phys. 67, 1731 (2004)
S. Odenbach, J. Phys.: Condens. Matter 16, R1135 (2004)
B. Fischer, B. Huke, M. Lücke, R. Hempelmann, J. Magn. & Magn. Mater. 289, 74 (2005)
P. Ilg, M. Kröger, S. Hess, J. Magn. & Magn. Mater. 289, 325 (2005)
S.H.L. Klapp, J. Phys.: Condens. Matter 17, R525 (2005)
P. Ilg, E. Coquelle, S. Hess, J. Phys.: Condens. Matter 18, S2756 (2006)
F. Brochard, P.G. de Gennes, J. Phys. (Paris) 31, 691 (1970)
J. Rault, P.E. Cladis, J.P. Burger, Phys. Lett. A 32, 1410 (1970)
C.F. Hayes, Mol. Cryst. Liq. Cryst. 36, 245 (1976)
L. Liébert, A. Martinet, J. Phys. (Paris) 40, 363 (1979)
S.-S. Chen, S.H. Chiang, Mol. Cryst. Liq. Cryst. 144, 359 (1987)
J.C. Bacri, A.M.F. Neto, Phys. Rev. E 50, 3860 (1994)
S.I. Burylov, Y.L. Raikher, Mol. Cryst. Liq. Cryst. 258, 123 (1995)
M. Koneracká, V. Závičová, P. Kopčanský, J. Jadzyn, G. Czechowski, B. Zywucki, J. Magn. & Magn. Mater. 157/158, 589 (1996)
S. Fontanini, A.L. Alexe-Ionescu, G. Barbero, A.M.F. Neto, J. Chem. Phys. 106, 6187 (1997)
Yu. Raikher, V.I. Stepanov, J. Magn. & Magn. Mater. 201, 182 (1999)
I. Potočová, M. Koneracká, P. Kopčanský, M. Timko, L. Tomčo, J. Jadzyn, G. Czechowski, J. Magn. & Magn. Mater. 196, 578 (1999)
C.Y. Matuoa, A.M. Figueiredo Neto, Phys. Rev. E 60, 1815 (1999)
E. Jarkova, H. Pleiner, H.-W. Müller, A. Fink, H.R. Brand, Eur. Phys. J. E 5, 583 (2001)
E. Jarkova, H. Pleiner, H.-W. Müller, H.R. Brand, J. Chem. Phys. 118, 2422 (2003)
A. Mertelj, D. Lisjak, M. Drofenik, M. Čopič, Nature 504, 237 (2013)
M. Zrínyi, L. Barsi, A. Büki, Europhys. Conf. Abstract 19, 40 (1995)
M. Zrínyi, L. Barsi, A. Büki, Polym. Gels Netw. 5, 415 (1997)
L. Barsi, A. Büki, S. Szabó, M. Zrínyi, Progr. Colloid Polym. Sci. 102, 57 (1996)
M. Zrínyi, L. Barsi, A. Büki, J. Chem. Phys. 104, 8750 (1996)
M. Zrínyi, L. Barsi, D. Szabó, H.G. Kilian, J. Chem. Phys. 106, 5685 (1997)
M. Zrínyi, Trends Polym. Sci. 5, 280 (1997)
D. Szabó, G. Szeghy, M. Zrínyi, Macromolecules 31, 6541 (1998)
M. Zrínyi, D. Szabó, H.G. Kilian, Polym. Gels Netw. 6, 441 (1998)
T. Mitsumata, K, Ikeda, J. Ping Gong, Y. Osada, D. Szabó, M. Zrínyi, J. Appl. Phys. 85, 8451 (1999)
E. Jarkova, H. Pleiner, H.-W. Müller, H.R. Brand, Phys. Rev. E 68, 041706 (2003)
G. Pessot, P. Kremer, D.Y. Borin, S. Odenbach, H. Löwen, A.M. Menzel, J. Chem. Phys. 141, 124904 (2014)
D. Collin, G.K. Auernhammer, O. Gavat, P. Martinoty, H.R. Brand, Macromol. Rapid Commun. 24, 737 (2003)
Z. Varga, J. Feher, G. Filipcsei, L. Zrinyi, Macromol. Symp. 200, 93 (2003)
D. Günther, D.Y. Borin, S. Günter, S. Odenbach, Smart Mater. Struct. 21, 015005 (2012)
S. Bohlius, H.R. Brand, H. Pleiner, Phys. Rev. E 70, 061411 (2004)
H. Finkelmann, H. Ringsdorf, J.H. Wendorff, Makromol. Chem. 179, 273 (1978)
H. Finkelmann, H.J. Kock, G. Rehage, Makromol. Rapid Commun. 2, 317 (1981)
J. Schätzle, H. Finkelmann, Mol. Cryst. Liq. Cryst. 142, 85 (1987)
J. Schätzle, W. Kaufhold, H. Finkelmann, Makromol. Chem. 190, 3269 (1989)
H.R. Brand, Makromol. Rapid Commun. 10, 57 (1989)
H.R. Brand, Makromol. Rapid Commun. 10, 317 (1989)
W. Kaufhold, H. Finkelmann, H.R. Brand, Makromol. Chem. 192, 2555 (1991)
J. Küpfer, H. Finkelmann, Makromol. Chem. Rapid Commun. 12, 717 (1991)
J. Küpfer, H. Finkelmann, Macromol. Chem. Phys. 195, 1353 (1994)
H.R. Brand, H. Finkelmann, Physical Properties of Liquid Crystalline Elastomers, in Handbook of Liquid Crystals, edited by J.W. Goodby, Vol. 3 (Wiley, New York, 1998) p. 277
H.R. Brand, H. Pleiner, P. Martinoty, Soft Matter 2, 182 (2006)
P.G. de Gennes, in Liquid Crystals of One- and Two-Dimensional Order, edited by W. Helfrich, G. Heppke (Springer, New York, 1980)
H.R. Brand, H. Pleiner, Physica A 208, 359 (1994)
A.M. Menzel, H. Pleiner, H.R. Brand, J. Chem. Phys. 126, 234901 (2007)
A.M. Menzel, H. Pleiner, H.R. Brand, J. Appl. Phys. 105, 013593 (2009)
A.M. Menzel, H. Pleiner, H.R. Brand, Eur. Phys. J. E 30, 371 (2009)
K. Urayama, R. Mashita, I. Kobayashi, T. Takigawa, Macromolecules 40, 7665 (2007)
D. Rogez, P. Martinoty, Eur. Phys. J. E 34, 69 (2011)
S.R. de Groot, P. Mazur, Nonequilibrium Thermodynamics (North Holland, Amsterdam, 1962)
P.C. Martin, O. Parodi, P.S. Pershan, Phys. Rev. A 6, 2401 (1972)
D. Forster, Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions (W.A. Benjamin, Reading, Mass., 1975)
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) p. 15
V. Berejnov, J.-C. Bacri, V. Cabuil, R. Perzynski, Y.L. Raikher, Europhys. Lett. 41, 507 (1998)
S.-H. Chen, N.M. Amer, Phys. Rev. Lett. 51, 2298 (1983)
W.P. Mason, Physical Acoustics and the Properties of Solids (van Nostrand Company, New York, 1958)
H.R. Brand, H. Pleiner, Macromol. Rapid Commun. 11, 607 (1990)
P.G. de Gennes, The Physics of Liquid Crystals (Clarendon Press, Oxford, 1975)
H. Pleiner, M. Liu, H.R. Brand, Rheol. Acta 39, 560 (2000)
H. Löwen, J. Phys.: Condens. Matter 22, 364105 (2010)
R. Wittkowski, H. Löwen, H.R. Brand, Phys. Rev. E 82, 031708 (2010)
R. Wittkowski, H. Löwen, H.R. Brand, Phys. Rev. E 83, 061706 (2011)
R. Wittkowski, H. Löwen, H.R. Brand, Phys. Rev. E 84, 041708 (2011)
H. Pleiner, H. Brand, J. Phys. (Paris) Lett. 41, 491 (1980)
H.R. Brand, H. Pleiner, Phys. Rev. A 35, 3122 (1987)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Brand, H., Pleiner, H. Macroscopic behavior of ferronematic gels and elastomers. Eur. Phys. J. E 37, 122 (2014). https://doi.org/10.1140/epje/i2014-14122-2
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1140/epje/i2014-14122-2