Statistical properties of focal conic textures in smectic liquid crystals

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Abstract
In a smectic sample, the layers must be equidistant, but they may be curved. When the boundary conditions are not compatible with flat layers, one obtains a focal conic texture. We consider here the most familiar case where each unit in this texture fills a certain cone. The interstices between these cones are filled by smaller cones, etc. We discuss some features of this iterative filling of space, and show that it should persist down to a few molecular lengths. An estimate of the energy associated with the iterated structure indicates, that (in the absence of all external fields) focal conic textures are less expensive than grain boundaries, in agreement with the standard optical aspect of smectic samples. We discuss the scattering of light by an iterated focal conic texture, in terms of a simple scaling law ; the resulting angular dependence of the scattered intensity is anomalous and may allow for a direct determination of the « scaling index » n associated with the iterative process

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