Legendre Polynomials and Angular Momentum

An introduction to Legendre polynomials as precursor to studying angular momentum in quantum chemistry,

Continued Fraction Solutions to Hermite's, Legendre's and Laguerre's Differential Equation

The continued fraction method for solving differential equations is illustrated using three famous differential equations used in quantum chemistry.

Aromic Units, Why We Need Them and How They Work

Quantum Chemistry is usually carried out using Atomic Units, so a careful discussion of these units is warranted.

Triatomic Molecular Orbitals

If elementary Quantum Chemistry stops at diatomic molecules, some students may be left with false impressions concerning how one builds polyatomic molecule's LCAO-MOs. This reading discusses building such molecular orbitals from atomic orbitals centered at different spatial coordinates.

Diseño y fabricación de dispositivos basados en cristal líquido polimérico

Esta tesis se centra en el estudio y desarrollo de dispositivos de aplicación basados en cristal líquido polimérico. Las propiedades de los cristales líquidos los hacen interesantes para su uso en el desarrollo de dispositivos de seguridad para autenticación de productos y marcas, y detección y prevención de falsificaciones. Asimismo, pueden ser muy útiles para fabricar dispositivos basados en CLs dispersos en polímero, los cuales tienen a su vez múltiples aplicaciones. La orientación de las moléculas de cristal líquido y la birrefringencia son las dos características principales que afectan a las propiedades de estos dispositivos. Un dispositivo de cristal líquido estándar consiste en un sándwich formado por dos sustratos de vidrio transparente, dotados con electrodo de ITO (Indium Tin Oxide) en su superficie interna, que confinan el cristal líquido en su interior. En la primera parte de esta tesis se describen las características más importantes que describen una célula de cristal líquido. Esta introducción básica en necesaria para la correcta comprensión de los capítulos posteriores en los que se detalla el desarrollo concreto de los dispositivos desarrollados en la investigación llevada a cabo. Por ejemplo, en el caso de los dispositivos de seguridad se han eliminado los sustratos de vidrio (en la última fase de su desarrollo) para conseguir dispositivos flexibles. En la segunda parte de la tesis se incluye la descripción completa de los dispositivos fabricados, así como de los protocolos de fabricación seguidos y diseñados específicamente para ello. También se detallan en esta parte los resultados obtenidos, así como las propiedades ópticas y electroópticas en cada caso, y el/los equipos de caracterización utilizados. Utilizando cristal líquido nemático y colorante dicroico, se han desarrollado dispositivos que contienen múltiples imágenes latentes en cada cara del mismo. Utilizando distintas técnicas de alineamiento se consigue crear cualquier tipo de motivo latente, ya sean símbolos sencillos, figuras, logotipos o incluso imágenes con escala de gris. Cuanto más complejo es el dispositivo, mayor es la dificultad para reproducirlo en una eventual falsificación. Para visualizar e identificar los motivos es necesario emplear luz polarizada, por ejemplo, con la ayuda de un sencillo polarizador lineal. Dependiendo de si el polarizador está colocado delante del dispositivo o detrás del él, se mostrarán las imágenes generadas en una u otra cara. Este efecto es posible gracias al colorante dicroico añadido al CL, a la orientación inducida sobre las moléculas, y a la estructura de twist utilizada en los dispositivos. En realidad, para ver el efecto de los dispositivos no es necesario el uso de un polarizador, basta con el reflejo de una superficie dielétrica (percialmente polarizado), o la luz emitida por la pantalla de dispositivos de consumo comunes como un televisor LCD, un monitor de ordenador o un “smartphone”. Por otro lado, utilizando una mezcla entre un CL nemático polimérico y un CL nemático no polimérico es posible fabricar dispositivos LCPC (Liquid Crystal Polymer Composite) con propiedades electroópticas muy interesantes, que funcionan a tensiones de conmutación bajas. El CL polimérico conforma una estructura de red en el interior del sándwich que mantiene confinado al CL nemático en pequeños microdominios. Se han fabricado dispositivos LCPC con conmutación inversa utilizando tanto alineamiento homogéneo como homeotrópico. Debido a que tanto la estructura de CL polimérico como el CL nemático que rellena los microdominios están orientados en una misma dirección de alineamiento preinducida, la luz dispersada por el dispositivo se encuentra polarizada. La dirección de polarización coincide con la dirección de alineamiento. La innovación aportada por esta investigación: un nuevo dispositivo LCPC inverso de respuesta ultrarápida y polarizada basado en la mezcla de dos CL nemáticos y, un dispositivo de seguridad y autenticación, patentado internacionalmente, basado en CL nemáticos dopados con colorante dicroico. Abstract This thesis is centered on the availability to use polymerizable liquid crystals to develop non-display application LC devices. Liquid crystal properties make them useful for the development of security devices in applications of authentication and detection of fakes, and also to achieve polymer dispersed LC devices to be used for different applications that will be studied here. Induced orientation of liquid crystal molecules and birefringence are the two main properties used in these devices. A standard liquid crystal device is a sandwich consisting of two parallel glass substrates carrying a thin transparent ITO (Indium‐Tin‐Oxide) electrode on their inner surfaces with the liquid crystal in the middle. The first part of this thesis will describe the most important parameters describing a liquid crystal cell. This basis is necessary for the understanding of later chapters where models of the liquid crystal devices will be discussed and developed. In the case of security devices the standard structure of an LC device has been modified by eliminating the glass substrates in order to achieve plastic and flexible devices. The second part of the thesis includes a detailed description of the devices achieved and the manufacturing protocols that have been developed ad-hoc. The optical and electrooptical properties and the characterization equipment are described here as well. Employing nematic liquid crystal and dichroic colorants, we have developed devices that show, with the aid of a polarizer, multiple images on each side of the device. By different alignment techniques it is possible to create any kind of symbols, drawings or motifs with a grayscale; the more complex the created device is, the more difficult is to fake it. To identify the motifs it is necessary to use polarized light. Depending on whether the polarizer is located in front of the LC cell or behind it, different motifs from one or the other substrate are shown. The effect arises from the dopant color dye added to the liquid crystal, the induced orientation and the twist structure. In practice, a grazing reflection on a dielectric surface is polarized enough to see the effect. Any LC flat panel display (LCD TV, computer, mobile phone) can obviously be used as backlight as well. On the other hand, by using a mixture of polymerizable and non-polymerizable nematics liquid crystals it is also possible to achieve LCPC (Liquid Crystal Polymer Composite) devices that show really interesting electrooptical characteristics using low switching voltages. Polymerizable LC creates a hollow structure inside the sandwich glass cell that keep nematics liquid crystal confined creating microdomains. Homogeneous and homeotropic alignments have been used to develop inverse switching mode LCPCs. Due to the double LC oriented structure, the outgoing scattered light from these devices is already polarized. The polarization axis coincides with LC molecules director, the alignment direction promoted. The novelties derived from the investigation presented here, new ultrafast inverse LCPC with polarized outgoing scattered light based on oriented nematic LC mixture, and an internationally patented security and authentication device based on nematics (doped with dichroic dye) oriented polymerizable LC.

Opto-optical modulation in N-(p-methoxybenzylidene)-p-butylaniline

A method of opto-optical modulation in liquid crystals is reported. An Ar+-laser beam is employed to modulate a second He–Ne laser. The highest frequency achieved was 1.5 × 103 pulses per second with input modulating powers smaller than 10 mW. A homeotropic N-(p-methoxybenzylidene)-p-butylaniline liquid-crystal cell was employed as the nonlinear medium.

Electrohydrodynamic behavior in twisted-wedge nematic structures

A new type of domain for nematic liquid crystals with a twisted-wedge structure is presented. This new type of domain appears from the low frequency range to 10 kHz. This behavior was observed for square and pulsed excitations. The liquid crystal was N-(p-methoxybenzylidene)-p'-butylaniline) (MBBA) used at room temperature. These domains offer a higher degree of complexity than conventional Williams domains. The corresponding stability chart is presented.

New non-reorientational, non-thermal optical nonlinear effect in MBBA

It is widely known the anular-shaped beam divergence produced by the optical reorientation induced in nematics by a Gaussian beam. Recent works have found a new effect in colored liquid crystal (MBBA, Phase V,...) showing a similar spatial distribution. A new set of random-oscillating rings appears for light intensities over a certain threshold. The beam divergence due to that effect is greater than the molecular reorientation induced one.

Self-beating instabilities in bistable devices

Since the observation of optical bistability by Gibbs et al., optical bistability has been the field where researchers from many fields have found a common place to work. More recently, when Ikeda and co-workers discussed the effect of a delayed feedback on instability of a ring cavity containing a non linear dielectric medium, and pointed out that the transmitted light from the ring cavity can be periodic or chaotic in time under a certain condition, optical bistable devices have shown new possibilities to be applied in many different fields. The novel phenomenon has been predicted to be observed in the hybrid optical device and has been confirmed by Gibbs et al. Moreover, as we have shown, a similar effect can be obtained when liquid crystal cells are employed as non linear element.

Instabilities In hybrid optical bistable devices with nonlinear feedback

As we have shown,several output conditions can be obtained from a hybrid optical bistable device when twisted nematic liquid crystal cells are employed as nonlinear elements.

Optical behaviour of cholesteric blue phases in electric fields

The optical behaviour of cholesteric mixtures of negative dielectric anisotrony under electric fields is reported. A mixture of S 311~ (31.35 %) + N 5 was employed. AC voltages (f = 1000 Hz) betweeen 0 and 150 volts were applied. Cells 23 micron thick, with internal SnO2 electrodes, were used.

Aplicaciones de la biestabilidad óptica

The main application of hybrid Optical Bistable devices to optical Communication and Optical Computing are reported. The employed nonlinear has been liquid crystal that modelizes very well the general behaviour of OBD's.

Optical memory with TNLC devices (1982)

In this paper we describe a twisted nematic liquid crystal (TNLC) device structure with optical feedback capable of bistable operation and optical memory. Its structure is the conventional one as employed in hybrid optical bistability.

Electrodynamic tether applications and constraints

Propulsion and power generation by bare electrodynamic tethers are revisited in a unified way and issues and constraints are addressed. In comparing electrodynamic tethers, which do not use propellant, with other propellantconsuming systems, mission duration is a discriminator that defines crossover points for systems with equal initial masses. Bare tethers operating in low Earth orbit can be more competitive than optimum ion thrusters in missions exceeding two-three days for orbital deboost and three weeks for boosting operations. If the tether produces useful onboard power during deboost, the crossover point reaches to about 10 days. Power generation by means of a bare electrodynamic tether in combination with chemical propulsion to maintain orbital altitude of the system is more efficient than use of the same chemicals (liquid hydrogen and liquid oxygen) in a fuel cell to produce power for missions longer than one week. Issues associated with tether temperature, bowing, deployment, and arcing are also discussed. Heating/cooling rates reach about 4 K/s for a 0.05-mm-thick tape and a fraction of Kelvin/second for the ProSEDS (0.6-mm-radius) wire; under dominant ohmic effects, temperatures areover200K (night) and 380 K (day) for the tape and 320 and 415 K for that wire. Tether applications other than propulsion and power are briefly discussed.