Masao Doi, Onsager principle as a tool for approximation, Chinese. Xianmin Xu, Yana Di, and Masao Doi, Variational method for contact line problems in sliding liquids, Phys.
Xingkun Man and Masao Doi, Ring to mountain transition in deposition pattern of drying droplets, Phys. Masao Doi, A principle in dynamic coarse graining - Onsager principle and its applications -, DOI 10.1140/epjst/e2016-60128-5, EPJE (2016) Yana Di, Xianmin Xu and Masao Doi, Theoretical analysis for meniscus rise of a liquid contained between a flexible film and a solid wall, EPL 113 36001 1-4 (2016)Ĩ. Nematic liquid crystals (NLCs) of achiral molecules or racemic mixtures form flat films and show uniform textures between circular polarizers when suspended in TEM grids and merged under water. On addition of chiral dopants to the liquid crystal the films exhibit concentric ring patterns and radial variation of the birefringence color. We show this is related to a biconvex shape of the chiral liquid crystal film and the rings are due to interference. Our analysis show the films have a spherical lens shape and they can be used for optical imaging similar to the microlens arrays of the compound eye of insects. The curvature radii of the biconvex lens array are in the range of few millimeters. We propose that the unwinding of the helical structure at the grid walls drives the lensing. The relation between the lens curvature and the helical pitch, the twist elastic constant, and the interfacial tension of the material is derived. We argue that these spontaneously forming microlenses can be used for various sensors. The first liquid crystal shells were produced in the Weitz lab, using a microfluidic technique, one decade ago.
Since then a number of groups around the world have adapted the production technology, and shells of nematic, cholesteric, smectic-A, and smectic-C types have been explored, with varying combinations of boundary conditions, and experiments have been complemented with computer simulations and theory. A major driving force for these studies is the spontaneous appearance of defects on shells with (partial) tangential alignment, arising due to the spherical topology. Another fascinating effect is the photonic cross communication arising between multiple shells of short-pitch cholesteric liquid crystal, where the curvature and the internal periodic structure interplay to generate regular but surprisingly complex multi-colored patterns.
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