A New Generation Process and Matrix Representation of Disclinations in Nematic and Cholesteric Liquid Crystals

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Abstract
Disclinations in nematic liquid crystals are described as transitions between two different states of quantized bulk deformations in a layer. The quantized states of deformation are due to well defined uniform boundary conditions, which allow only discrete solutions of the partial Euler differential equations governing the deformation. A new continuous generation process for the non-singular disclinations of integer strength is discussed. The local turns of the director field, involved in this process, can be used for an algebraic description of the topological properties of the disclinations. This formalism can also be applied to disclinations of half integer strength and to disclinations in cholesteric liquid crystals. From this theory, the existence of stable disclinations of the strength s = 0 can be predicted. Disclinations of integer strength are created by an experimental process analogous to the new theoretical generation process. Experimental evidence for the existence of disclinations of the strength O is given.