Eur. Phys. J. E (2002) 8: 413-420
https://doi.org/10.1140/epje/i2002-10024-2

Smectic-A edge dislocations in a very thin cell

¹ Condensed Matter Physics Department, Jožef Stefan Institute, Jamova 39, 1000, Ljubljana, Slovenia
² Laboratory of Physics of Complex Systems, Faculty of Education, University of Maribor, Koroška 160, 2000, Maribor, Slovenia
³ Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia

^* e-mail: Milan.ambrozic@ijs.si

Received: 21 February 2002
Published online: 25 January 2014

Abstract

We study stable “bookshelf” smectic-A structures within a very thin plane-parallel cell of thickness L in which the mismatch between surface preferred (d _s) and intrinsic (d₀) smectic layer thicknesses occurs. The Landau-Ginzburg approach based on a complex smectic order parameter is used. For a weak enough smectic positional anchoring strength W smectic layers adopt the modified bookshelf profile. In a thick enough cell with increasing W a lattice of edge dislocations is continuously formed at the confining surfaces and then depinned from them. The structure with dislocations is formed when the condition d ₀/(ζ _s |d ₀/d _s − 1|) ∼ 2 is fulfilled, where ζ _s is the positional surface anchoring extrapolation length. If the cell is thin enough the dislocations formed at opposite cell plates annihilate and consequently the smectic layers adopt a locked bookshelf structure. This transition is discontinuous and takes place when d ₀/(L|d ₀/d _s − 1|) ∼ 5 is realized. To observe these transitions in a cell of thickness L∼ 1μm the conditions W∼ 10^-6 J/m ² and |d ₀/d _s − 1| ∼ 5 · 10⁻⁴ have to be fulfilled. All the three qualitatively different structures coexist at the triple point.