Curso introductorio de cristales líquidos I: fases y propiedades estructurales (Introductory Course on Liquid Crystals I: Phases and Structural Properties)

Liquid crystals are the prototype of the so-called soft condensed matter. In simple terms they are "structured liquids" that historically have received a lot of interest because they help to generate new concepts and knowledge in Physics, and possess important electro–optical applications, e. g., in displays of mobile computers and telephones. More recently, it has been discovered that liquid crystals could be applied in fabrication of metamaterials and in biomedicine where they are potentially useful for tissue identification, controlled drug delivery and detection of bacteria and viruses. However, in Mexico, liquid crystals courses are included only in a few undergraduate programs on Physics being elective in most of the cases. Therefore, literature for teaching about liquid crystals in Spanish is scarce. In this paper we will discuss about elementary Physics of liquid crystals and the mathematical tools that permit to analyze them. We will explain, mainly, how to analytically characterize the symmetry and order of static uniaxial nematic liquid crystals, the most simple of all liquid crystal phases. We will conduct this explanation in basic terms, suitable for science and engineering students at intermediate undergraduate level, with knowledge about linear algebra and vector calculus, willing to approach for the first time to this subject. Our goal is to support the Latin American scientific community in preparing human resources in this field. The article is written in Spanish to contribute to the establishment and communication of concepts that only exist in other languages in the specialized literature.