Curso introductorio de cristales líquidos I: fases y propiedades estructurales
DOI:
https://doi.org/10.31349/RevMexFis.22.020217Keywords:
Soft Matter, Anisotropy, Self-assembly, Phase Transitions, Order Parameters, Tensor AlgebraAbstract
Los cristales líquidos son el prototipo de la llamada materia condensada suave. En términos simples, son “líquidos con estructura” que históricamente han recibido mucho interés tanto por ser fuente de nuevos conceptos y conocimientos en Física, como por tener aplicaciones electroópticas importantes, e. g. en las pantallas de computadoras portátiles y teléfonos celulares. Más recientemente, se ha descubierto que los cristales líquidos podrían aplicarse en la fabricación de metamateriales y en biomedicina, donde son potencialmente útiles en la identificación de tejidos, la repartición controlada de fármacos y la detección de bacterias y virus. No obstante, en México, los cursos sobre cristales líquidos se incluyen en muy pocos programas universitarios de Física y en la mayoría de los casos son optativos. Por ello, es escasa la literatura en español para la enseñanza sobre cristales líquidos. En este artículo discutiremos sobre la Física elemental de los cristales líquidos y las herramientas matemáticas que permiten analizarlos. Principalmente, explicaremos cómo caracterizar analíticamente la simetría y el orden de los cristales líquidos nemáticos uniaxiales estáticos, la fase de cristal líquido más sencilla de todas. Conduciremos esta explicación en términos básicos, apropiados para estudiantes de ciencias o ingenierías a un nivel intermedio de licenciatura, con conocimientos de álgebra lineal y cálculo vectorial, que deseen acercarse por primera vez a este tema. Nuestro objetivo es objetivo es apoyar a la comunidad científica mexicana en la formación de recursos humanos en este campo.
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 the 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 the elementary physics of liquid crystals and the mathematical tools that permit us to analyze them. We will explain, mainly, how to analytically characterize the symmetry and order of static uniaxial nematic liquid crystals, the simplest 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 to this subject for the first time. Our goal is to support the Mexican scientific community in preparing human resources in this field.
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