Topological Defects

Abstract

As was seen in Chap.8 many bulk states of matter exhibit a, partial or full, orientational and/or translational order. Until now this order has always been considered to be perfect although, in practice, many bulk phases exhibit defects, i.e., domains where this order departs from the one originally postulated. Such defects are usually very stable, because the free energy cost to remove them easily exceeds the thermal energy, and prevent the system to reach its true defect-free equilibrium state. In some cases they are induced by the system’s boundary conditions and are, hence, unavoidable, i.e., they correspond to the true equilibrium state given the applied boundary conditions.

In most cases these defects correspond to an elastic deformation of the ideal structure. In the context of soft matter, where by definition of “soft ” the elastic constants are weak, the number of observable defect-structures is extremely large.Defects are usually classified according to their topological nature: point defects,line defects, etc. Whereas point defects are easily visualized, this is not the case of the line defects because the latter are spatially extended structures. Point defects are often encountered in crystalline structures under the form of vacancies (a crystal node without particle) or interstitials (a particle not attached to a crystal node). The study of point defects is presently well understood and requires no new concepts. On the contrary, the study of line defects, which are very frequent in liquid crystals,is much more difficult and not yet fully understood. Line defects produce a texture in many liquid crystals and the optical observation of this texture, which is typical of a particular type of liquid crystal, is often used as a means to identify the liquid crystal type. By “texture” one should understand here the spatial organization of the different line defects. Many different liquid crystal textures have been observed but, for simplicity, only the study of line defects, and their texture, in nematic liquid crystals will be considered here.