The Molecular Dynamics Of Liquid Crystals
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The Molecular Dynamics Of Liquid Crystals
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Author : G.R. Luckhurst
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Molecular Dynamics Of Liquid Crystals written by G.R. Luckhurst and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Liquid-crystalline phases are now known to be formed by an ever growing range of quite diverse materials, these include those of low molecular weight as well as the novel liquid-crystalline polymers, such phases can also be induced by the addition of a solvent to amphiphilic systems leading to lyotropic liquid crystals. Irrespective of the structure of the constituent molecules these numerous liquid-cl)'Stailine phases are characterised by their long range orientational order. In addition certain phases exhibit elements of long range positional order. Our understanding, both experimental and theoretical, at the molecular level of the static behaviour of these fascinating and important materials is now well advanced. In contrast the influence of the long range order; both orientational and positional, on the molecular dynamics in liquid Cl)'Stais is less well understood. In an attempt to address this situation a NATO Advanced Study Institute devoted to liquid ctystal dynamics was held at n Ciocco, Barga, Italy in September 1989. This brought together experimentalists and theoreticians concerned with the various dynamical processes occurring in all liquid crystals. The skills of the participants was impressively wide ranging; they spanned the experimental techniques used in the study of molecular dynamics, the nature of the systems investigated and the theoretical models employed to understand the results. While much was learnt it was also recognised that much more needed to be done in order to advance our understanding of molecular dynamics in liquid Cl)'Stais.
Nuclear Magnetic Resonance Of Liquid Crystals
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Author : Ronald Y. Dong
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nuclear Magnetic Resonance Of Liquid Crystals written by Ronald Y. Dong and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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, together 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 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 and includes new mathematical appendices.
Advances In The Computer Simulatons Of Liquid Crystals
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Author : Paolo Pasini
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Advances In The Computer Simulatons Of Liquid Crystals written by Paolo Pasini and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Science categories.
Computer simulations provide an essential set of tools for understanding the macroscopic properties of liquid crystals and of their phase transitions in terms of molecular models. While simulations of liquid crystals are based on the same general Monte Carlo and molecular dynamics techniques as are used for other fluids, they present a number of specific problems and peculiarities connected to the intrinsic properties of these mesophases. The field of computer simulations of anisotropic fluids is interdisciplinary and is evolving very rapidly. The present volume covers a variety of techniques and model systems, from lattices to hard particle and Gay-Berne to atomistic, for thermotropics, lyotropics, and some biologically interesting liquid crystals. Contributions are written by an excellent panel of international lecturers and provides a timely account of the techniques and problems in the field.
Nuclear Magnetic Resonance Spectroscopy Of Liquid Crystals
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Author : Ronald Y. Dong
language : en
Publisher: World Scientific
Release Date : 2010
Nuclear Magnetic Resonance Spectroscopy Of Liquid Crystals written by Ronald Y. Dong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Science categories.
This edited volume provides an extensive overview of how nuclear magnetic resonance can be an indispensable tool to investigate molecular ordering, phase structure, and dynamics in complex anisotropic phases formed by liquid crystalline materials. The chapters, written by prominent scientists in their field of expertise, provide a state-of-the-art scene of developments in liquid crystal research. The fantastic assortment of shape anisotropy in organic molecules leads to the discoveries of interesting new soft materials made at a rapid rate which not only inject impetus to address the fundamental physical and chemical phenomena, but also the potential applications in memory, sensor and display devices. The review volume also covers topics ranging from solute studies of molecules in nematics and biologically ordered fluids to theoretical approaches in treating elastic and viscous properties of liquid crystals. This volume is aimed at graduate students, novices and experts alike, and provides an excellent reference material for readers interested in the liquid crystal research. It is, indeed, a reference book for every science library to have. Sample Chapter(s). Chapter 1: Novel Strategies for Solving Highly Complex NMR Spectra of Solutes in Liquid Crystals (1,464 KB). Contents: Novel Strategies for Solving Highly Complex NMR Spectra of Solutes in Liquid Crystals (E E Burnell et al.); Analytical Potentials of Natural Abundance Deuterium NMR Spectroscopy in Achiral Thermotropics and Polypeptide Chiral Oriented Solvents (P Lesot & C Aroulande); Noble Gas Probes in NMR Studies of Liquid Crystals (J Jokisaari); Bicelles OCo A Much Needed Magic Wand to Study Membrane Proteins by NMR Spectroscopy (R Soong et al.); Advances in Proton NMR Relaxometry in Thermotropic Liquid Crystals (P J Sebastiuo et al.); Deuterium NMR Study of Magnetic Field Distortions in Ferroelectric Mesogens (R Y Dong); Deuteron NMR Study of the Effects of Random Quenched Disorder in 12CB Silica Dispersions (D Finotello & V Pandya); Dynamics of Liquid Crystals by Means of Deuterium NMR Relaxation (C A Veracini & V Domenici); Translational Self-Diffusion Measurements in Thermotropics by Means of Statistic Field Gradients NMR Diffusometry (M Cifelli); Deuterium NMR Studies of Static and Dynamic Director Alignment for Low Molar Mass Nematics (A Sugimura & G R Luckhurst); Viscoelastic Properties of Liquid Crystals: Statistical-Mechanical Approaches and Molecular Dynamics Simulations (A V Zakharov); Carbon-13 NMR Studies of Thermotropic Liquid Crystals (R Y Dong); A Combined DFT and Carbon-13 NMR Study of a Biaxial Bent-Core Mesogen (A Marini et al.). Readership: Chemists, physicists and material scientists. In particular, NMR spectroscopists.
Advances In Liquid Crystal Research And Applications
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Author : Lajos Bata
language : en
Publisher: Elsevier
Release Date : 2013-10-22
Advances In Liquid Crystal Research And Applications written by Lajos Bata and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Science categories.
Advances in Liquid Crystal Research and Applications, Volume 1 is a collection of papers presented at the Third Liquid Crystal Conference of the Socialist Countries, held in Budapest on August 27-31, 1979. This volume is comprised of three parts. The first part deals with the phases and structures of liquid crystals through methods employing synthesis, X-ray studies, electron diffraction, and calorimetric determination. The second part discusses molecular dynamics and dynamical methods where mostly dielectric investigations into liquid crystal properties are emphasized. This part includes the developments in the study of molecular dynamics in liquid crystals. Other topics presented in this part are the acousto-optical and ultrasonic relaxation methods. The third part covers the continual properties of liquid crystals: their properties and behavior when exposed to different testing methods and variables. For example, a correlation between viscosity coefficients of starting components and those of their mixtures is attempted, resulting when MBBA and EBBA in different percentages are mixed, that none of their coefficients is found to obey any pronounced law. However, the viscosity coefficients given in the table may serve as reference data for further studies. Physicists; process engineers; and graduate students in physics, chemistry, and materials science fields; and university professors and lecturers related to studies in the field of liquid crystals will find this collection of papers highly informative and rewarding.
Liquid Crystals And Their Computer Simulations
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Author : Claudio Zannoni
language : en
Publisher:
Release Date : 2022
Liquid Crystals And Their Computer Simulations written by Claudio Zannoni and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with SCIENCE categories.
"There are two main approaches to the theoretical study of liquid crystals: continuum and molecular. The first, well covered in various good books (e.g. those by Chandrasekhar [1992]; de Gennes and Prost [1993]; Virga [1994]; Kleman and Lavrentovich [2003]; Stewart [2004]; Oswald and Pieranski [2005, 2006]; Barbero and Evangelista [2006]) considers anisotropic systems at macroscopic level and typically deals with optical and elastic properties as well as with many practical electrooptical applications of liquid crystals. At continuum level, liquid crystals are assumed to exist and their properties (e.g. elastic constants and viscosities) to be known, insofar as they are needed to parameterize the relevant equations. Molecules, phase transitions and spectroscopic properties are not normally taken into consideration. In this line of work computer simulations typically refer to a determination of the preferred orientation (director) or of the ordering tensor field that minimize the elastic free energy under a variety of boundary conditions, while dynamics is normally related to the solution of hydrodynamics equations for anisotropic fluids. The other main line of investigation deals"--
Ionic Liquid Crystals
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Author : Giacomo Saielli
language : en
Publisher: MDPI
Release Date : 2019-06-24
Ionic Liquid Crystals written by Giacomo Saielli and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-24 with Technology & Engineering categories.
In this book we have collected a series of state-of-the art papers written by specialists in the field of ionic liquid crystals (ILCs) to address key questions concerning the synthesis, properties, and applications of ILCs. New compounds exhibiting ionic liquid crystalline phases are presented, both of calamitic as well as discotic type. Their dynamic and structural properties have been investigated with a series of experimental techniques including differential scanning calorimetry, polarized optical spectroscopy, X-ray scattering, and nuclear magnetic resonance, impedance spectroscopy to mention but a few. Moreover, computer simulations using both fully atomistic and highly coarse-grained force fields have been presented, offering an invaluable microscopic view of the structure and dynamics of these fascinating materials.
Computer Simulations Of Liquid Crystals And Polymers
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Author : Paolo Pasini
language : en
Publisher: Springer Science & Business Media
Release Date : 2005
Computer Simulations Of Liquid Crystals And Polymers written by Paolo Pasini and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Liquid crystals categories.
Dielectric Properties Of Liquid Crystals
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Author : Zbigniew Galewski
language : en
Publisher:
Release Date : 2007-01-01
Dielectric Properties Of Liquid Crystals written by Zbigniew Galewski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Liquid crystals categories.
Introduction - This book, consisting of 10 chapters, should be treated as a complement that brings the reader up to date with the latest contributions to the rich literature on liquid crystals. A prominent place in this literature is occupied by the dielectric properties which are important in estimation of usefulness of these materials and in understanding the molecular processes determining various mesophases. In the field of dielectrics in general, and in connection with the structure and phase transitions the entries in references [1-14] can be recommended. With respect to general aspects of liquid-crystalline properties and molecular dynamics one can point out the references [15-36]. Most of them contain as well chapters on dielectric properties. In addition there is a number of books and monographs related strictly to the dielectric properties of liquid crystals, in particular references [37-45]. For the readers less familiar with this topic and interested in the basic knowledge of dielectric aspects of liquid crystals one can suggest the reviews [46-48]. Basic difference between properties of isotropic liquid and liquid crystal lies in the existence in the latter case of at least one degree of order. The ordering can be also considered with respect to a crystalline phase. Thus introducing at least one degree of disorder (rotational or translational) causes the occurrence of a mesophase which, however, is not identical with the liquid-crystalline phase. If the mesophase is to be liquid-crystalline, it should possess at least one translational degree of disorder. The disorder connected with further degrees of freedom leads to rich polymorphism. The most characteristic feature of liquid-crystalline phases is a precisely defined degree of disorder of molecules building these phases and their anisotropy which is exhibited in molecular structure and all measurable physical parameters such as polarizability. This is the reason why such phases are also called anisotropic liquids. The insertion into the molecules that form mesophases of fragments either chiral or influencing antagonistically already present fragments (e.g. by replacing one alkyl group by perfluorinated chain) leads to additional interactions which compete with interactions responsible for the stability of liquid-crystalline phases. This causes the frustration phenomena, i.e. the mutual overlapping of interactions frequently responsible for opposite effects. These induced phenomena conduce to unexpected structures (banana-type or columnar-type mesophases) and properties such as helicity, ferroelectricity or antiferroelectricity. Of particular interest seem to be ferroelectric liquid crystals (chiral tilted smectics such as SmC*, SmI* and others) showing collective modes: tilt fluctuations (soft modes) and phase fluctuations (Goldstone mode). Unusual progress observed in the last half-century has occurred due to use of some additional interacting fragments and structural details. Liquid crystalline polymers and metalomesogens present rapidly growing branches of knowledge of liquid crystal. Ferromagnetism and superconductivity of liquid crystals still pose a challenge. In this monograph we present different aspects of dielectric properties of mesogens. Chapter 1 presented by Otowski is dedicated to general problems of the molecular dipole s motion in electric field. Based on the broadband dielectric studies results of a few liquid-crystalline substances, their dielectric behavior is discussed by means of Nordio-Rigatti-Segre theory. The pretransitional anomalies observed in isotropic phase close to the phase transitions by means of dielectric measurements are described by Drozd-Rzoska, Rzoska and Janik in Chapter 2. An extended part of this book is devoted to chiral liquid crystals, the importance of which for applications and expectations for them are continuously increasing. The principles of the dielectric behavior of chiral liquid-crystalline compounds based on general considerations applying for other dipolar systems as well is presented by Hoffmann in Chapter 3. In general considerations based on the example of 12 selected substances showing extremely rich polymorphism Marzec, Mikulko, Wróbel and Haase analyze impressive behaviors of collective modes (Chapter 4). The problem of non-linear dielectric effects constitutes an important part of this book. A general introduction to the non-linear dielectric spectroscopy is contained in Chapter 5 elaborated by Kedziora, who concentrates himself on the isotropic phase, solutions and precritical phenomena. The problem of molecular properties of smectic materials and relaxation in ferroelectric liquid crystals with particular attention paid to electrooptic phenomena are discussed by Kuczynski in Chapter 6. Advantages of electrooptic methods applied to chiral tilted smectic liquid crystals with either ferroelectric or antiferroelectric dipole order are known. However, less popular problem of so called organic glass formers presented by Massalska-Arodz, Sciesinska, Sciesinski, Krawczyk, Inoba and Zielinski in Chapter 7 deserved attentions. Properties of these materials are discussed by using the results of complementary methods such as INS, QENS, adiabatic calorimetry and far-infrared spectra. Chapter 8, presented by Rózanski, is devoted to the dielectric properties of liquid crystals confined in porous matrices or dispersed throughout solid matrices. Such systems seem to be fascinating not only from the point of view of surface interactions but also due to attractive properties of dispersed systems in nanoscale. Of great value is also Chapter 9 by Kocot, Merkel, Sufin, Vij and Mehl describing dendrimeric liquid crystals built of molecules containing siloxane or carbosilazane cores. The problems of dynamics and ordering are discussed in terms of IR and dielectric spectroscopy results. Chapter 10, written by Urban, is committed to the relaxation processes in calamitic liquid crystals with emphasis on pressure and temperature effects. Finally let us direct readers attention to general references relating to the new liquid crystalline compounds [49] and IUPAC classification of these systems [50]. 1. Boettcher C. J. F., van Belle O.C., Bordewijk P. and Rip A., 1973, Theory of Electric Polarization, Vol.I: Dielectrics in Static Fields, 2nd revised edition, Elsevier Science Ltd, Amsterdam. 2. Boettcher C.J.F. and Bordewijk, 1978, Theory of Electric Polarization, Vol.II. Dielectrics in Time-dependent Fields, 2nd revised edition, Elsevier Science Ltd, Amsterdam. 3. Hill N., Vaughan W.E., Price A.H. and Davies M., 1969, Dielectric Properties and Molecular Behaviour, van Nostrand, London. 4. Froehlich H., 1958, Theory of Dielectrics, Oxford University Press, London. 5. von Hippel A.R., 1995, Dielectric Materials and Applications, Artech House Publishers. 6. Davies M., 1965, Some Electrical and Optical Aspects of Molecular Behaviour, Pergamon Press, Oxford. 7. Scaife B.K.P., 1998, Principle of Dielectrics, Revised edition, Oxford University Press, Clarendon, Oxford. 8. Riande E. and Diaz-Calleja R., 2004, Electrical Properties of Polymers, Marcel Dekker, NY. 9. Jonscher A.K., 1996, Universal Relaxation Law, Chelsea Dielectric Press Ltd, London. 10. Grigas J., 1996, Microwave Dielectric Spectroscopy of Ferroelectrics and Related Materials, Series: Ferroelectricity and Related Phenomena, Volume 9, Gordon and Breach Science Publishers, Philadelphia. 11. Runt J.P. and Fitzgerald J.J.(Eds.), 1997, Dielectric Spectroscopy of Polymeric Materials, American Chemical Society, Washington, DC. 12. Havriliak S. and Havriliak S.J., 1996, Dielectric and Mechanical Relaxation in Materials, Hanser Verlag, München. 13. Gaiduk V.I. and McConnel J.R., 1999, Dielectric Relaxation and Dynamics of Polar Molecules, World Scientific Pub. Co.Inc., Singapore. 14. Kremer F. and Schönhals A. (Eds) 2002, Broadband Dielectric Spectroscopy, Springer, NY. 15. Demus D., Goodby J., Gray G.W., Spiess H.W. and Vill V. (Eds.), 1998, Handbook of Liquid Crystals, 4-Volume Set, Wiley-VCH, Veinheim. 16. Demus D., Goodby J., Gray G.W., Spiess H.W. and Vill V (Eds.), 1999, Physical Properties of Liquid Crystals, Wiley-VCH, Veinheim. 17. Stegemeyer H. (Ed.), 1994, Liquid Crystals, Steinkopff, Darmstadt and Springer, NY. 18. Buka A. (Ed.), 1993, Modern Topics in Liquid Crystals. From Neutron Scattering to Ferroelectricity, World Scientific, Singapore. 19. Dierking I., 2003. Texture of Liquid Crystals, Wiley-VCH, Weinheim. 20. Luckhurst G.R. and Gray G.W. (Eds.), 1979, The Molecular Physics of Liquid Crystals, Academic Press, London. 21. de Gennes P.G. and Prost J., 1993, The Physics of Liquid Crystals, 2nd edition, Clarendon Press, Oxford. 22. Gray G.W. and Goodby J.W., 1984, Smectic Liquid Crystals. Textures and Structures, Leonard Hill, Glasgow. 23. Martellucci S. and Chester A.N. (Eds.), 1992, Phase Transitions in Liquid Crystals, NATO ASI Series, Vol.B290, Plenum Press, NY. 24. Luckhurst G.R. and Veracini C.A. (Eds.), 1994. The Molecular Dynamics of Liquid Crystals, NATO ASI Series, Vol.C431, Kluwer, Dordrecht. 25. Priestley E.B., Wojtowicz P.J. and Sheng P. (Eds.), 1975, Introduction to Liquid Crystals, Plenum Press, NY. 26. Lagerwall S.T., 1999, Ferroelectric and Antiferroelectric Liquid Crystals, Wiley-VCH, Weinheim. 27. Baus M., Rull L.F. and Ryckaert J.P. (Eds.), 1995, Observation, Prediction and Simulation of Phase Traansitions in Complex Fluids, Kluwer, Dordrecht. 28. Anisimov M.A., 1991, Critical Phenomena in Liquids and Liquid Crystals, Gordon & Breach, Philadelphia 29. Vertogen G. and de Jeu W.H., 1986, Thermotropic Liquid Crystals, Fundamentals, Springer, Berlin 30. de Jeu W.H., 1980, Physical Properties of Liquid Crystalline Materials, Gordon & Breach, NY 31. Helfrich W. and Heppke G., (Eds.), 1980, Liquid Crystals of One and Two Dimensional Order, Springer, Berlin. 32. Goodby J.W., Blinc R., Clark N.A., Lagerwall S.T., Osipov M.A., Pikin S.A., Sakurai T., Yoshino K. and }eka B., 1991, Ferroelectric Liquid Crystals. Principles, Properties and Applications, Series: Ferroelectricity and Related Phenomena, Volume 7. Gordon and Breach, Philadelphia. 33. Pikin S.A., 1991, Structural Transformations in Liquid Crystals, Gordon and Breach, NY. 34. Haberlandt R., Michel D., Poppel A. and Stannarius R., 2005, Molecules in interaction with surfaces and interfaces, Springer NY. 35. Crawford G.P. and }umer S., (Eds), Liquid Crystals in Complex Geometries, 1996, Taylor & Francis, London. 36. Muaevic I., Blinc R. and }eka B., 2000, The Physics of Ferroelectric and Antiferroelectric Liquid Crystals, World Scientific, Singapore. 37. Haase W. and Wróbel S. (Eds.), 2003, Relaxation Phenomena. Liquid Crystals, Magnetic Systems, Polymers, High-TC Superconductors, Metallic Glasses., Springer, NY. 38. Kresse H., 1983, in: Advances in Liquid Crystals, Vol.6, Brown G.H. (ed.), Academic Press, NY. 39. Coffey W.T. and Kalmykov Y.P. 2000, Adv.Chem.Phys. 111, 487. 40. de Jeu W.H., 1978, in: Solid State Physics, Supplement 14. Liebert L. (ed.), Academic Press. 41. Rzoska S.J. and Zhelezny V.P., (Eds), 2004, Nonlinear Dielectric Phenomena in Complex Liquids, Kluwer, Dordrecht. 42. Urban S. and Wuerflinger A., 1979, Adv.Chem.Phys., 98, 143. 43. Kresse H., 1982, Fortschrifte der Physik, 80, 507. 44. Urban S., 2001, in: Physical Properties of Liquid Crystals: Nematics, Dunmur D., Fukuda A. and Luckhurst G. (Eds.), Inspec, London, p.267. 45. Blinov L.M. and Chigrinov V.G., 1994, Electrooptic Effects in Liquid Crystal Materials, Springer, NY. 46. Meier G. and Saupe A., 1966, in: Liquid Crystals, Brown G.H., Dines G.J. and Labes M.M. (Eds.), Gordon and Breach, Philadelphia. 47. Kresse H., 1998, in: Handbook of Liquid Crystals, Demus D., Goodby J., Gray G.W., Spiess H.W. and Vill V. (Eds.), Vol.2, Wiley-VCH, Veinheim. 48. Dunmur D and Toriyama K., 1998, in: Handbook of Liquid Crystals, Demus D., Goodby J., Gray G.W., Spiess H.W. and Vill V. (Eds.), Vol. 1, Wiley-VCH, Veinheim. 49. Vill V., 2006, LiqCryst 4.6. Data Base, Fujitsu. 50. Byron M. et al. 2001, Pure Appl.Chem., 73, 845.
Liquid Crystals I
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Author : D.M.P. Mingos
language : en
Publisher: Springer
Release Date : 2003-09-04
Liquid Crystals I written by D.M.P. Mingos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-04 with Technology & Engineering categories.
The liquid crystalline state may be identified as a distinct and unique state of matter which is characterised by properties which resemble those of both solids and liquids. It was first recognised in the middle of the last century through the study of nerve myelin and derivatives of cholesterol. The research in the area really gathered momentum, however, when as a result of the pioneering work of Gray in the early 1970's organic compounds exhibiting liquid crystalline properties were shown to be suitable to form the basis of display devices in the electronic products. The study of liquid crystals is truly multidisciplinary and has attached the attention of physicists, biologists, chemists, mathematicians and electronics engineers. It is therefore impossible to cover all these aspects fully in two small volumes and therefore it was decided in view of the overall title of the series to concentrate on the structural and bonding aspects of the subject. The Chapters presented in these two volumes have been organised to cover the following fundamental aspects of the subiect. The calculation of the structures of liquid crystals, an account of their dynamical properties and a discussion of computer simulations of liquid crystalline phases formed by Gay Berne mesogens. The relationships between molecular conformation and packing are analysed in some detail. The crystal structures of liquid crystal mesogens and the importance of their X ray scattering properties for characterisational purposes are discussed.