Abstract.
Tabe and Yokoyama found recently that the optical axis in a chiral monolayer of a ferronematic rotates when water evaporates from the bath: the chiral molecules act as propellers. When the axis is blocked at the lateral walls of the trough, the accumulated rotation inside creates huge splays and bends. We discuss the relaxation of these tensions, assuming that a single dust particle nucleates disclination pairs. For the simplest geometry, we then predict a long delay time followed by a non-periodic sequence of “bursts”. These ideas are checked by numerical simulations.
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References
Y. Tabe, H. Yokoyama, Nat. Mater. 2, 806 (2003).
For convenience, we define \(\Delta\mu\) for unit mass of the water rather than per water molecule.
P.-G. de Gennes, J. Prost, The Physics of Liquid Crystals, second edition (Oxford University Press, 1995).
Note that our anchoring energy depends on the cosine and not on cosine squared, because we are dealing with a ferronematic.
The periodicity is \(2\pi\) because we deal with a ferronematic where \(\phi=0\) and \(\phi=\pi\) are not equivalent.
One can obtain the solution to equation (4) with boundary conditions \(\phi(x=0)=0\) and \(\phi(x=\infty)=\Omega t\), by taking \(z(x,t)=\Omega-\partial\phi(x,t)/\partial t\). It then follows that \(z=\Omega[1- {\rm Erf} (\frac12 x/\sqrt{Dt})]\). At the origin we thus find that \(\partial\phi(0)/\partial x=\frac{2}{\sqrt{\pi}}\Omega \left(\frac{t}{D}\right)^{1/2}\).
J.S. Langer, V. Ambegaokar, Phys. Rev. 164, 498 (1967).
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PACS:
61.30.Hn Surface phenomena: alignment, anchoring, anchoring transitions, surface-induced layering, surface-induced ordering, wetting, prewetting transitions, and wetting transitions - 61.30.Jf Defects in liquid crystals
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Tsori, Y., Gennes, PG.d. Frustrated rotations in nematic monolayers. Eur. Phys. J. E 14, 91–96 (2004). https://doi.org/10.1140/epje/i2004-10010-8
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DOI: https://doi.org/10.1140/epje/i2004-10010-8