Geometry, focal conic domains

Y.H. Kim, D.K. Yoon, M.C. Choi, H.S. Jeong, M.W. Kim, O.D. Lavrentovich, H.-T. Jung, Confined self-assembly of toric focal conic domains (The effects of confined geometry on the feature size of toric focal conic domains). Langmuir 25, 1685-1691 (2009)... 

This paper is written as an introductory review for the unlearnt. It is constructed as follows. The first part deals with some generalities of the geometry of Focal Conic Domains (FCD s). The second one is devoted to an analytical description of the sheets which constitute the domains. This is the starting point of the calculation of the energy of different types of FCD s, which is made in the third part. We complete the discussion with some experimental observations in lyotropic systems (fourth part). The fifth part is devoted to the problem of space filling we are considering it in the case of FCD of the first and second species. The last part is devoted to the question of the nucleation and growth of FCD s. 

It is possible to produce extended areas of homeotropically-aligned smectic phases, but when the mesophase is formed by cooling from the melt on an unprepared surface, a disordered pattern of distinct domains is usually formed. Textures of this kind are known as focal conics because of the geometry of the basic structural units. These are formed by stacking concentric, curved, cooling-tower shaped layers inside each other like Russian dolls (Fig. 1.21). The reason why such an apparently complex structure of this kind arises spontaneously is not immediately obvious, but... 

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