The book intends to give a state-of-the-art overview of flexoelectricity, a linear physical coupling between mechanical (orientational) deformations and electric polarization, which is specific to systems with orientational order, such as liquid crystals. Chapters written by experts in the field shed light on theoretical as well as experimental aspects of research carried out since the discovery of flexoelectricity. Besides a common macroscopic (continuum) description the microscopic theory of flexoelectricity is also addressed. Electro-optic effects due to or modified by flexoelectricity as well as various (direct and indirect) measurement methods are discussed. Special emphasis is given to the role of flexoelectricity in pattern-forming instabilities. While the main focus of the book lies in flexoelectricity in nematic liquid crystals, peculiarities of other mesophases (bent-core systems, cholesterics, and smectics) are also reviewed. Flexoelectricity has relevance to biological (living) systems and can also offer possibilities for technical applications. The basics of these two interdisciplinary fields are also summarized.
Liquid crystals are widely used in flat panel displays and smart windows. In flat panel display application, one way to improve the efficiency is to decrease the driving frequency when static images are displayed. As the driving frequency is decreased, the transmittance of the display may vary with time, a phenomenon known as flickering. We carried out both experimental and simulation studies to investigate the origins that cause the flickering problem. Our results show that flexoelectric effect and ions in the liquid crystal are the main factors responsible for the flickering. We quantitatively analyzed the flickering caused by the two factors. The ionic effect can be eliminated by using the fluorinated liquid crystals with high resistivity. The flexoelectric effect is attributed to the intrinsic flexoelectric coefficient of the liquid crystal and nonuniformity of the liquid crystal director configurations. We demonstrated that polymer stabilization can smooth the spatial variation of the liquid crystal orientation, while doping a liquid crystal dimer can reduce the flexoelectric coefficient of the liquid crystal. Using these methods we are able to reduce the flickering significantly. Radiant energy-flow control and privacy control are two important features for smart windows (or glass). Current smart window technologies can, however, only control one of them: radiant energy flow or privacy. Therefore, a dual-mode smart window is highly desirable. We developed a dual-mode switchable liquid-crystal window that can control both radiant energy flow and privacy. The switchable liquid-crystal window makes use of dielectric and flexoelectric effects. In the absence of an applied voltage, the window is clear and transparent, and radiant energy can flow through it and the scenery behind the window can be seen. When a low-frequency (50 Hz) voltage is applied, the window is switched to an optical scattering and absorbing state by a flexoelectric effect, and thus, privacy is protected. When a high-frequency (1 kHz) voltage is applied, the window is switched to an optical absorbing but nonscattering state through a dielectric effect, and thus, radiant energy flow is controlled. Smart windows can be categorized mainly into two types according to the operation principle: electrical switchable window and thermal switchable windows. In the electric switchable window, voltage must be applied to switch the window, which consumes energy and is not environmentally friendly. Therefore, a power-free smart window is highly demanded. We developed a thermal switchable smart window that is sensitive to ambient temperature. The window is based on a liquid crystal whose orientation imposed by an alignment layer varies with temperature. The liquid crystal layer is sandwiched between two parallel polarizers to make the window. At high temperature, the liquid crystal is aligned parallel to the cell substrate and rotates the polarization of the incident light after the first polarizer by 90o such that incident light is completely absorbed by the second polarizer, and the transmittance of the window is 0. When temperature is decreased, the liquid crystal is tilted toward the cell substrate normal and rotates the polarization of the incident light less so that some light can pass the second polarizer, and the transmittance of the window increases. When temperature is decreased below a critical value, the liquid crystal is aligned perpendicular to the cell substrate and does not rotate the polarization of the incident light such that all light passes the second polarizer, and the transmittance reaches a maximum.
Liquid Crystal Devices are crucial and ubiquitous components of an ever-increasing number of technologies. They are used in everything from cellular phones, eBook readers, GPS devices, computer monitors and automotive displays to projectors and TVs, to name but a few. This second edition continues to serve as an introductory guide to the fundamental properties of liquid crystals and their technical application, while explicating the recent advancements within LCD technology. This edition includes important new chapters on blue-phase display technology, advancements in LCD research significantly contributed to by the authors themselves. This title is of particular interest to engineers and researchers involved in display technology and graduate students involved in display technology research. Key features: Updated throughout to reflect the latest technical state-of-the-art in LCD research and development, including new chapters and material on topics such as the properties of blue-phase liquid crystal displays and 3D liquid crystal displays; Explains the link between the fundamental scientific principles behind liquid crystal technology and their application to photonic devices and displays, providing a thorough understanding of the physics, optics, electro-optics and material aspects of Liquid Crystal Devices; Revised material reflecting developments in LCD technology, including updates on optical modelling methods, transmissive LCDs and tunable liquid crystal photonic devices; Chapters conclude with detailed homework problems to further cement an understanding of the topic.
Abstract : A positive nematic liquid crystal (5CB) sample is confined in cylindrical cells under strong or weak axial anchoring boundary conditions when a radial nonuniform low-frequency electric field is applied and the flexoelectric effect is taken into account. Based on the Frank elastic free energy, the surface energy of the Rapini–Papoular approximation, the polarization free energy and the flexoelectric free energy caused by electric field, we obtain the free energy density of the nematic and solve the corresponding Euler–Lagrange equation numerically. We investigate the director distribution, the critical voltage and the critical exponent of nematic liquid crystal in cylindrical cells. It follows that the critical exponent is the classical one. It is also shown that the critical voltage in the system is affected by the flexoelectric effect, the geometric effect and radial weak anchoring effect on the cylindrical surfaces. A new type of director transition caused by the flexoelectric effect, the dielectric coupling effect and the radial weak anchoring effect is found.
Flexoelectricity in liquid crystals is thought to be due to a coupling between dielectric properties and shape anisotropy of the molecules and described by the fiexoelectric coefficients el and e3. Two experiments are needed to measure el and e3 and it is usual to measure the difference (el - e3) and the sum (el + e3) and then calculate el and e3· The first experiment to measure the difference (el - e3) uses a TN structure with an in-plane applied electric field. Due to the dielectric coupling, the director aligns with the electric field and due to the fiexoelectric effect, the director tilts out of plane. This tilt is measured optically using two laser beams at oblique incidence, e.g. 45°. Using a theoretical model the experimental data is fitted and the difference (el - e3) extracted. The second experiment to measure the sum (el + e3) uses a Pi cell. Applying an ac voltage the transmission through the device is a repeating oscillating signal which contains 1st and 2nd harmonics. The 1st harmonic corresponds to the fiexoelectric effect and the 2nd harmonic to the dielectric effect. Using a lock-in amplifier, the harmonics were measured and the sum (el + e3) extracted using a theoretical model to fit the experimental data. Unfortunately, the data proved the experiment to be unreliable and another method was developed, which uses a BAN cell. The third experiment uses simple pulses in a BAN cell and also measures the sum (el + e3). The big disadvantage of the BAN cell is an internal voltage, which is created by the homeotropic alignment layer and the fiexoelectric polarisation. The internal voltage has the same effect on the director profile as the fiexoelectric effect, which is a big problem in measuring fiexoelectricity. Using a material, which is non ionic and has no fiexoelectricity, the internal bias could be measured and taken into account. Applying short de pulses of opposite sign, the fiexoelectric effect can be observed by the optical response and can be measured. Using these experiments, a number of investigation are being carried out such as the correlation between fiexoelectricity and the molecular structure, ions, elastic properties, molecular orientation, dielectric anisotropy 6E, and order parameter S. The results showed that fiexoelectricity only depends on ions and dielectric properties which was very interesting and surprising at the same time.
This book presents a compilation of self-contained chapters covering a wide range of topics within the broad field of soft condensed matter. Each chapter starts with basic definitions to bring the reader up-to-date on the topic at hand, describing how to use fluid flows to generate soft materials of high value either for applications or for basic research. Coverage includes topics related to colloidal suspensions and soft materials and how they differ in behavior, along with a roadmap for researchers on how to use soft materials to study relevant physics questions related to geometrical frustration.
This book was written to enable physicists and engineers to learn, within a single course, some topics in variational calculus, theory of elasticity, molecular models, and surface properties of nematic materials. It prepares graduate students for studies that require a simple knowledge in the physics of nematic liquid crystals.With this consideration in mind, the authors have formulated the problems concerning the continuum theory of liquid crystals into a precise form. In working out the solutions, they have analyzed, systematically and naturally, the techniques and methods of variational calculus. Special attention is dedicated to the analysis of well-posed and ill-posed variational problems. The presence of sub-surface discontinuity in the nematic orientation is analyzed using different techniques. A full chapter is devoted to this aspect of the theory of elasticity of nematic media.
This book contains a comprehensive description of the mechanical equilibrium and deformation of membranes as a surface problem in differential geometry. Following the pioneering work by W Helfrich, the fluid membrane is seen as a nematic or smectic ? A liquid crystal film and its elastic energy form is deduced exactly from the curvature elastic theory of the liquid crystals. With surface variation the minimization of the energy at fixed osmotical pressure and surface tension gives a completely new surface equation in geometry that involves potential interest in mathematics. The investigations of the rigorous solution of the equation that have been carried out in recent years by the authors and their co-workers are presented here, among which the torus and the discocyte (the normal shape of the human red blood cell) may attract attention in cell biology. Within the framework of our mathematical model by analogy with cholesteric liquid crystals, an extensive investigation is made of the formation of the helical structures in a tilted chiral lipid bilayer, which has now become a hot topic in the fields of soft matter and biomembranes.
