Abstract.
Symmetry considerations yield the general form, up to second order terms, for the deformation elastic energy of a nematic monolayer, composed by symmetric achiral molecules, on a rigid planar substrate. The deformation energy contains an elastic contribution linear in the deformation tensor, whose elements are the spatial derivatives of the average molecular orientation. This linear Lifshitz-invariant-like term can be responsible for a ground state of the nematic monolayer periodically deformed if the relevant elastic constant is stiffer than a critical value. The wave-length of the modulation diverges at the transition threshold. We show that only large variations of the tilt angle form stable states. The effect of a destabilizing electric or magnetic field on the layer is to induce (i) the transition towards the tilt-modulated phase, while (ii) for higher enough values of the field the modulation is destroyed.
Similar content being viewed by others
References
V.M. Kaganer, H. Möhwald, P. Duta, Rev. Mod. Phys. 71, 779 (1999)
S.A. Langer, J.P. Sethna, Phys. Rev. A 34, 5035 (1986)
G.A. Hinshaw Jr., R.G. Petschek, R.A. Pelcovits, Phys. Rev. Lett. 60, 1864 (1988)
J.V. Selinger, Z.-G. Wang, R.F. Bruinsma, C.M. Knobler, Phys. Rev. Lett. 70, 1139 (1993)
T. Ohyama, A.E. Jacob, D. Mukamel, Phys. Rev. E 53, 2595 (1996)
J. Maclennan, M. Seul, Phys. Rev. Lett. 69, 2082 (1992)
J. Pang, N.A. Clark, Phys. Rev. Lett. 73, 2332 (1994)
P.G. de Gennes, J. Prost, The Physics of Liquid Crystals (Clarendon Press, Oxford 1994)
A. Rapini, M. Papoular, J. Phys. Colloq. (France) 30, C4 (1969)
P.I.C. Texeira, T.J. Sluckin, J. Chem. Phys. 97, 1498 (1992)
I. Lelidis, G. Barbero, Phys. Rev. E 71, 22701 (2005)
G. Barbero, L.R. Evangelista, An Elementary Course on the Continuum Theory for Nematic Liquid Crystals (World Scientific, Singapore, 2001)
A.L. Alexe-Ionescu, G. Barbero, A. Th. Ionescu, A.K. Zvezdin, Liq. Cryst. 20, 9 (1996)
A.L. Alexe-Ionescu, G. Barbero, A. Th. Ionescu, Phys. Lett. A 204, 71 (1995)
S.T. Lagewall, I. Dhal, Mol. Cryst. Liq. Cryst. 114, 151 (1984)
G. Barbero, G. Durand, J. Phys. 47, 2129 (1986)
H. Yokoyama, H.A. van Sprang, J. Appl. Phys. 57, 4520 (1985)
R.B. Meyer, Phy. Rev. Lett. 22, 918 (1969)
I. Lelidis, G. Barbero, Phys. Lett. A 311, 242 (2003)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lelidis, I., Barbero, G. Substrate induced 1D tilt-modulated state in nematic monolayers. Eur. Phys. J. E 19, 119–128 (2006). https://doi.org/10.1140/epje/e2006-00016-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epje/e2006-00016-5