Partially Ordered Systems – serie

In the last 20 years the study of nonlinear nonequilibrium phenomena in spa­ tially extended systems, with particular emphasis on pattern-forming phenomena, has been one of the very active areas in physics, exhibiting interesting ramifi­ cations into other sciences. During this time the study of the "classic" systems, like Rayleigh-Benard convection and Taylor vortex flow in simple fluids, has also been supplemented by the study of more complex systems. Here liquid crystals have played, and are still playing, a major role. One might say that liquid crystals provide just the right amount and right kind of complexity. They are full of non­ linearities and give rise to new symmetry classes, which are sometimes actually simpler to deal with qualitatively, but they still allow a quantitative description of experiments in many cases. In fact one of the attractions of the field is the close contact between experimentalists and theorists. Hydrodynamic instabilities in liquid crystals had already experienced a period of intense study in the late 1960s and early 1970s, but at that time neither the ex­ perimental and theoretical tools nor the concepts had been developed sufficiently far to address the questions that have since been found to be of particular interest. The renewed interest is also evidenced by the fact that a new series of workshops has evolved. The first one took place in 1989 in Bayreuth and united participants from almost all groups working in pattern formation in liquid crystals.

Electrooptic effects provide the basis for much liquid-crystal display technology. This book, by two of the leaders in liquid-crystal research in Russia, presents a complete and accessible treatment of virtually all known phenomena occurring in liquid crystals under the influence of electric fields.

Spatio-temporal patterns appear almost everywhere in nature, and their description and understanding still raise important and basic questions. However, if one looks back 20 or 30 years, definite progress has been made in the modeling of insta­ bilities, analysis of the dynamics in their vicinity, pattern formation and stability, quantitative experimental and numerical analysis of patterns, and so on. Universal behaviors of complex systems close to instabilities have been determined, leading to the wide interdisciplinarity of a field that is now referred to as nonlinear science or science of complexity, and in which initial concepts of dissipative structures or synergetics are deeply rooted. In pioneering domains related to hydrodynamics or chemical instabilities, the interactions between experimentalists and theoreticians, sometimes on a daily basis, have been a key to progress. Everyone in the field praises the role played by the interactions and permanent feedbacks between ex­ perimental, numerical, and analytical studies in the achievements obtained during these years. Many aspects of convective patterns in normal fluids, binary mixtures or liquid crystals are now understood and described in this framework. The generic pres­ ence of defects in extended systems is now well established and has induced new developments in the physics of laser with large Fresnel numbers. Last but not least, almost 40 years after his celebrated paper, Turing structures have finally been ob­ tained in real-life chemical reactors, triggering anew intense activity in the field of reaction-diffusion systems.

Introductions to solid state physics have, ever since the initial book by F. Seitz in 1940, concentrated on simple crystals, with few atoms per cell, bonded together by strong ionic, covalent, or metallic bonds. References to weaker bonds, such as van der Waals forces in rare gases, or to geometric or chemical disorder (e.g., alloys or glasses) have been limited. The physical understanding of this ?eld started well before Seitz’s book and led to a number of Nobel prizes after the last war. Applications cover classical metallurgy, el- tronics, geology and building materials, as well as electrical and ionic transport, chemical reactivity, ferroelectricity and magnetism. But in parallel with this general and well publicized trend, and sometimes earlier as far as physical concepts were concerned, an exploration and increasingly systematic study of softer matter has developed through the twentieth century. More often in the hands of physical chemists and crystallographers than those of pure physicists, the ?eld had for a long time a reputation of complexity. If progress in polymers was steady but slow, interest in liquid crystals had lain dormant for forty years, after a bright start lasting through 1925, to be revived in the late 1960s based on their possible use in imaging techniques. The optoelectronic properties of the ?eld in general are even more recent.

Solitons are a well-known and intriguing aspect of nonlinear behavior in a continuous system such as a fluid: a wave propagates through the medium without distortion. Liquid crystals are highly ordered systems without a rigid, long-range structure. Solitons in liquid crystals (sometimes referred to as "walls") have a wide variety of remarkable properties that are becoming important for practical applications such as electroluminescent display. This book, the first review of the subject to be published, contains not only surveys of the existing literature, but presents new results as well.

Probing matter with beams of photons, neutrons and electrons provides the main source of information about both the microscopic and macroscopic structure of materials. This is particularly true of media, such as crystals and liquid crystals, that have a periodic structure. This book discusses the interaction of waves (which may represent x-rays, gamma rays, electrons, or neutrons) with various kinds of ordered media. After two chapters dealing with exact and approximate solutions to the scattering problem in periodic media in general, the author discusses: the diffraction of Mobbauer radiation in magnetically ordered crystals; the optics of chiral liquid crystals; the radiation of fast particles in regular media (Cherenkov radiation); nonlinear optics of periodic media; neutron scattering in magnetically ordered media; polarization phenomena in x-ray optics; magnetic x-ray scattering; and Mobbauer filtration of synchrotron radiation.

Liquid crystals, widely used in displays for electronic equipment and other applications, have highly unusual properties arising from the anisotropy of their molecules. It appears that some aspects of the fluid dynamics of liquid crystals, such as their viscosity, can be understood only by considering the role played by thermal fluctuations. In order to provide a theoretical framework for understanding the experimental results, the authors devote a large part of the book to a derivation of the nonlinear dynamic equations and to a discussion of linearized equations for the various types of liquid crystals. The diagrammatic and other techniques they use are of general use in condensed matter physics, and this exposition should thus be of interest to all condensed-matter theorists.

Intended for researchers and students in physics, chemistry and materials science, this work aims to provide the necessary background information and sufficient mathematical and physical detail to study research literature in nuclear magnetic resonance studies of liquid crystals. This second edition, updated throughout, incorporates many new references, corrects typographical errors, and includes new mathematical appendices.

Granular materials can be found in an enormous variety of places: from the powders used to make vitamin pills to the rings of Saturn, from beaches to grain elevators, and from pottery clay to interstellar dust. This text covers the basic properties of uniform granular materials, the mixing and segregation of heterogeneous materials (the famous "brazil-nut problem"), and numerical models.

Objects that differ from their mirror images, such as the left and right hands, play an important role in physics at all lengths scales, from elementary particles to macroscopic systems. The handedness, or chirality, of molecules in liquid crystals has a remarkable influence on the macroscopic physical properties of these systems, including the appearance of new phases. Indeed, the majority of optical applications of liquid crystals is due to chiral structures, namely the thermochromic effect of cholesteric liquid crystals, the optical activity in twisted nematic liquid crystal displays, and the ferroelectric and antiferroelectric switching of smectic liquid crystals.This book describes the main aspects of chirality in liquid crystals, and points out some of the open questions of current research. The chapters, each by an expert in the field, review the highlights of the important topics and representative questions in the field of chiral liquid crystals.

Introductions to solid state physics have, ever since the initial book by F. Seitz in 1940, concentrated on simple crystals, with few atoms per cell, bonded together by strong ionic, covalent, or metallic bonds. References to weaker bonds, such as van der Waals forces in rare gases, or to geometric or chemical disorder (e.g., alloys or glasses) have been limited. The physical understanding of this ?eld started well before Seitz’s book and led to a number of Nobel prizes after the last war. Applications cover classical metallurgy, el- tronics, geology and building materials, as well as electrical and ionic transport, chemical reactivity, ferroelectricity and magnetism. But in parallel with this general and well publicized trend, and sometimes earlier as far as physical concepts were concerned, an exploration and increasingly systematic study of softer matter has developed through the twentieth century. More often in the hands of physical chemists and crystallographers than those of pure physicists, the ?eld had for a long time a reputation of complexity. If progress in polymers was steady but slow, interest in liquid crystals had lain dormant for forty years, after a bright start lasting through 1925, to be revived in the late 1960s based on their possible use in imaging techniques. The optoelectronic properties of the ?eld in general are even more recent.

Relaxation and diffusion are general and common phenomena in many branches of condensed matter physics, chemistry and materials sciences. In disordered and partially ordered systems the classes of materials include liquids, colloids, polymers, rubbers, plastic crystals, biomolecules, ceramics, electrolytes, fuel cell materials, molten salts, glasses, and etc. Each class is further subdivided into many different types of materials. For example, glasses vary from metallic glasses, oxide glasses, chalcogenide glasses, polymeric and organic glasses, and each form a separate discipline. In past years research has suffered from undue fragmentation in terms of individual classes of materials. Dr. Ngai was one of the few who recognized the existence of a remarkable universality of relaxation and diffusion properties across the diverse classes of materials, and he suggested that some yet undiscovered fundamental physics is behind this universalityBeginning in 1979 with the publication of two articles in Comment Solid State Physics, Dr. Ngai launched an interdisciplinary study of relaxation and diffusion that has continued to the present. At this time, experimental evidence of universal behavior are plentiful and well substantiated. Dr. Ngai has also created a theoretical framework to characterize, correlate and interpret these universal properties. This book will be of interest to a large number of researchers across many disciplines.

Granular materials can be found in an enormous variety of places: from the powders used to make vitamin pills to the rings of Saturn, from beaches to grain elevators, and from pottery clay to interstellar dust. This text covers the basic properties of uniform granular materials, the mixing and segregation of heterogeneous materials (the famous "brazil-nut problem"), and numerical models.

Solitons are a well-known and intriguing aspect of nonlinear behavior in a continuous system such as a fluid: a wave propagates through the medium without distortion. Liquid crystals are highly ordered systems without a rigid, long-range structure. Solitons in liquid crystals (sometimes referred to as "walls") have a wide variety of remarkable properties that are becoming important for practical applications such as electroluminescent display. This book, the first review of the subject to be published, contains not only surveys of the existing literature, but presents new results as well.

Spatio-temporal patterns appear almost everywhere in nature, and their description and understanding still raise important and basic questions. However, if one looks back 20 or 30 years, definite progress has been made in the modeling of insta­ bilities, analysis of the dynamics in their vicinity, pattern formation and stability, quantitative experimental and numerical analysis of patterns, and so on. Universal behaviors of complex systems close to instabilities have been determined, leading to the wide interdisciplinarity of a field that is now referred to as nonlinear science or science of complexity, and in which initial concepts of dissipative structures or synergetics are deeply rooted. In pioneering domains related to hydrodynamics or chemical instabilities, the interactions between experimentalists and theoreticians, sometimes on a daily basis, have been a key to progress. Everyone in the field praises the role played by the interactions and permanent feedbacks between ex­ perimental, numerical, and analytical studies in the achievements obtained during these years. Many aspects of convective patterns in normal fluids, binary mixtures or liquid crystals are now understood and described in this framework. The generic pres­ ence of defects in extended systems is now well established and has induced new developments in the physics of laser with large Fresnel numbers. Last but not least, almost 40 years after his celebrated paper, Turing structures have finally been ob­ tained in real-life chemical reactors, triggering anew intense activity in the field of reaction-diffusion systems.

Liquid crystals have become ubiquitous in the displays for electronic devices, ranging from wrist watches to laptop computers. Nuclear magnetic resonance has become one of the important techniques for determining their structures and properties. Intended for researchers and students in physics, chemistry and materials science, this book provides the necessary background information and sufficient mathematical and physical detail to study the current research literature. The book begins with a survey of liquid crystal phases and field effects and with an introduction to the basic physics of nuclear magnetic resonance; it then discusses orientational ordering and molecular field theories for various liquid crystal molecules and NMR studies of uniaxial and biaxial phases. Subsequent chapters consider spin relaxation processes (using a semiclassical approach) and rotational, translational, and internal molecular dynamics of liquid crystals. The final chapter discusses two-dimensional and multiple-quantum NMR spectroscopies and their application in elucidating liquid crystal properties. This second edition, updated throughout, incorporates many new references, corrects typographical errors, and includes new mathematical appendices.

One of the most important aspects of solid materials is the regularity of the arrangement of the constituent molecules, that is, the long-range order. The focus of this book is on the contribution made by the ordering of bond orientations (as distinguished from the orientations of the molecules themselves) on the behavior of condensed systems, particularly their phase transitions. Examples in which bond-orientational effects play an important role are liquid crystals, quasicrystals, and two-dimensional crystals. This book contains contributions by many of the foremost researchers in the field. The chapters are tutorial reviews of the subject, written both for the active researcher looking for a review of a topic and for the graduate student investigating an exciting area of research. The contributions include an overview by J.D. Brock, Cornell; a discussion of computer simulation studies by K.J. Strandburg, Argonne; chapters on phase transition in hexatic liquid crystals by C.C. Huang, Minnesota and C.A. Murray, Texas A&M; and chapters on quasicrystals by S. Sachdev, Yale, M.V. Jaric, A.I. Goldman, Iowa State, and T.-L. Ho, Ohio State.

In the last 20 years the study of nonlinear nonequilibrium phenomena in spa­ tially extended systems, with particular emphasis on pattern-forming phenomena, has been one of the very active areas in physics, exhibiting interesting ramifi­ cations into other sciences. During this time the study of the "classic" systems, like Rayleigh-Benard convection and Taylor vortex flow in simple fluids, has also been supplemented by the study of more complex systems. Here liquid crystals have played, and are still playing, a major role. One might say that liquid crystals provide just the right amount and right kind of complexity. They are full of non­ linearities and give rise to new symmetry classes, which are sometimes actually simpler to deal with qualitatively, but they still allow a quantitative description of experiments in many cases. In fact one of the attractions of the field is the close contact between experimentalists and theorists. Hydrodynamic instabilities in liquid crystals had already experienced a period of intense study in the late 1960s and early 1970s, but at that time neither the ex­ perimental and theoretical tools nor the concepts had been developed sufficiently far to address the questions that have since been found to be of particular interest. The renewed interest is also evidenced by the fact that a new series of workshops has evolved. The first one took place in 1989 in Bayreuth and united participants from almost all groups working in pattern formation in liquid crystals.

Liquid crystals, widely used in displays for electronic equipment and other applications, have highly unusual properties arising from the anisotropy of their molecules. It appears that some aspects of the fluid dynamics of liquid crystals, such as their viscosity, can be understood only by considering the role played by thermal fluctuations. In order to provide a theoretical framework for understanding the experimental results, the authors devote a large part of the book to a derivation of the nonlinear dynamic equations and to a discussion of linearized equations for the various types of liquid crystals. The diagrammatic and other techniques they use are of general use in condensed matter physics, and this exposition should thus be of interest to all condensed-matter theorists.

Probing matter with beams of photons, neutrons and electrons provides the main source of information about both the microscopic and macroscopic structure of materials. This is particularly true of media, such as crystals and liquid crystals, that have a periodic structure. This book discusses the interaction of waves (which may represent x-rays, gamma rays, electrons, or neutrons) with various kinds of ordered media. After two chapters dealing with exact and approximate solutions to the scattering problem in periodic media in general, the author discusses: the diffraction of Mößbauer radiation in magnetically ordered crystals; the optics of chiral liquid crystals; the radiation of fast particles in regular media (Cherenkov radiation); nonlinear optics of periodic media; neutron scattering in magnetically ordered media; polarization phenomena in x-ray optics; magnetic x-ray scattering; and Mößbauer filtration of synchrotron radiation.

Among the various new directions in modern polymer science, the design and investigation of liquid crystal (LC) polymers have been the ones growing most actively and fruitfully. In spite of that, the possible formation of an anisotropic LC phase was only demonstrated theoretically for the first time in the 1950s by Onsager [1] and Flory [2], and then experimentally verified in the studies with polypeptides solutions. In essence, the studies of these LC lyotropic systems did not deviate from the theme of purely academic interest. It was at the beginning of the 1970s that the experimental "explosion" occurred, when aromatic polyamides were synthesized and their ability to form LC solutions in certain very aggressive solvents was discovered. The search for practical applications of such LC systems was crowned with the successful creation of the new generation of ultrastrong high-modulus ther­ mostable fibers, such as the Kevlar, due to the high degree of order of the macromolecules in the anisotropic LC state. In fact, these investigations coincided with the swift emergence on the practical "scene" of thermotropic low-molar-mass liquid crystals, with the use of these materials in microelectronics and electro optics (figures and let­ ters indicators, displays in personal computers, and flat TV, etc.). Polymer scientists also began to develop methods of synthesizing thermotropic LC polymers by incorporating mesogenic fragments in the main (main-chain LC polymers) or side branchings of the macromolecules (side-chain or comb­ shaped polymers).

Over the last decades, the study of surfactants (detergents, for example) has been profoundly changed by ideas and techniques from physics, chemistry, and materials science. Among these are: self assembly; critical phenomena, scaling, and renormalization; high-resolution scattering, and magnetic resonance spectroscopy. This book represents the first systematic account of these new developments, providing both a general introduction to the subject as well as a review of recent developments. The book will be a very useful tool for the biophysist, biochemist or physical chemist working in the field of surfactants.

Objects that differ from their mirror images, such as the left and right hands, play an important role in physics at all lengths scales, from elementary particles to macroscopic systems. The handedness, or chirality, of molecules in liquid crystals has a remarkable influence on the macroscopic physical properties of these systems, including the appearance of new phases. Indeed, the majority of optical applications of liquid crystals is due to chiral structures, namely the thermochromic effect of cholesteric liquid crystals, the optical activity in twisted nematic liquid crystal displays, and the ferroelectric and antiferroelectric switching of smectic liquid crystals.This book describes the main aspects of chirality in liquid crystals, and points out some of the open questions of current research. The chapters, each by an expert in the field, review the highlights of the important topics and representative questions in the field of chiral liquid crystals.