Complex fluids in condensed matter: The liquid crystals

Liquid crystals are intermediate states in which matter can present itself, between the crystalline solid and the isotropic liquid. Materials that can present this type of state are made up of molecules, or aggregates of molecules, which present significant shape anisotropy. The liquid crystalline states present complex spatial structures, which pose fundamental questions in the study of the structure of matter. They are characterized by presenting some degree of order: long-range orientational and short-range positional. Its technological applications are diverse, in particular, the electro-optics (displays) with low energy consumption. In this article we present a review of this area, emphasizing lyotropic liquid crystals (formed by mixtures of amphiphilic molecules and solvent) that have a great interface with biological systems. We also discuss the theoretical models that describe phase diagrams of lyotropic nematic structures.