Critical Phenomena In Liquids And Liquid Crystals

Phase transitions and critical phenomena in liquids and liquid crystals have been the subject of intensive research since the 1960s. However, books on this fascinating subject have tended to be written by theorists for theorists. Professor Anisimov offers us a new approach: he aims to introduce experimentalists to the modern theories and their applications. After introducing the thermodynamics of phase transitions, he presents the modern theory of critical phenomena. He then concludes by illustrating the utility of this theory in the analysis of experimental measurements in classical fluids and binary mixtures, superfluid mixtures of helium isotopes and liquid crystals. Not only will this book be enjoyed by experimental physicists, chemists and material scientists, it will also offer the theorist an insight into the interpretation of the experimentalist's work.

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.

Derived from lectures at the University of Freiburg, this textbook introduces solid-state physics as well as the physics of liquids, liquid crystals and polymers. The five chapters deal with the key characteristics of condensed matter: structures, susceptibilities, molecular fields, currents, and dynamics. The author strives to present and explain coherently the terms and concepts associated with the main properties and characteristics of condensed matter, while minimizing attention to extraneous details. As a result, this text provides the firm and broad basis of understanding that readers require for further study and research.

This textbook provides an exposition of equilibrium thermodynamics and its applications to several areas of physics with particular attention to phase transitions and critical phenomena. The applications include several areas of condensed matter physics and include also a chapter on thermochemistry. Phase transitions and critical phenomena are treated according to the modern development of the field, based on the ideas of universality and on the Widom scaling theory. For each topic, a mean-field or Landau theory is presented to describe qualitatively the phase transitions. These theories include the van der Waals theory of the liquid-vapor transition, the Hildebrand-Heitler theory of regular mixtures, the Griffiths-Landau theory for multicritical points in multicomponent systems, the Bragg-Williams theory of order-disorder in alloys, the Weiss theory of ferromagnetism, the Néel theory of antiferromagnetism, the Devonshire theory for ferroelectrics and Landau-de Gennes theory of liquid crystals. This textbook is intended for students in physics and chemistry and provides a unique combination of thorough theoretical explanation and presentation of applications in both areas. Chapter summaries, highlighted essentials and problems with solutions enable a self sustained approach and deepen the knowledge.

This IMA Volume in Mathematics and its Applications AMORPHOUS POLYMERS AND NON-NEWTONIAN FLUIDS is in part the proceedings of a workshop which was an integral part of the 1984-85 IMA program on CONTINUUM PHYSICS AND PARTIAL DIFFERENTIAL EQUATIONS We are grateful to the Scientific Committee: Haim Brezis Constantine Dafermos Jerry Eri cksen David Kinderlehrer for planning and implementing an exciting and stimulating year-long program. We espe cially thank the Program Organizers, Jerry Ericksen, David Kinderlehrer, Stephen Prager and Matthew Tirrell for organizing a workshop which brought together scientists and mathematicians in a variety of areas for a fruitful exchange of ideas. George R. Sell Hans Weinberger Preface The diversity of experimental phenomena and the range of applications of liquid crystals present timely and challenging questions for experimentalists, mechanists, and mathematicians. The scope of this workshop was to bring together research workers and practitioners in these areas from laboratories, industry, and universities to explore common issues. The contents of this volume vary from descriptions of experimental phenomena, of which our understanding is insufficient, to questions of a mathematical nature and of efficient computation.

Now in paperback, this book provides an overview of the physics of condensed matter systems. Assuming a familiarity with the basics of quantum mechanics and statistical mechanics, the book establishes a general framework for describing condensed phases of matter, based on symmetries and conservation laws. It explores the role of spatial dimensionality and microscopic interactions in determining the nature of phase transitions, as well as discussing the structure and properties of materials with different symmetries. Particular attention is given to critical phenomena and renormalization group methods. The properties of liquids, liquid crystals, quasicrystals, crystalline solids, magnetically ordered systems and amorphous solids are investigated in terms of their symmetry, generalised rigidity, hydrodynamics and topological defect structure. In addition to serving as a course text, this book is an essential reference for students and researchers in physics, applied physics, chemistry, materials science and engineering, who are interested in modern condensed matter physics.

The sophistication of modern tools used in the study of statistical mechanics and field theory is often an obstacle to the easy understanding of new important current results reported in journals. The main purpose of this book is to introduce the reader to the methods of the fluctuation (field) theory of phase transitions and critical phenomena so as to provide a good source for research. The introductory contents are concerned with ideas of description, thermodynamic stability theory related to phase transitions, major experimental facts, basic models and their relationships. Special attention is paid to the mean field approximation and to the Landau expansion for simple and complex models of critical and multicritical phenomena. An instructive representation of the modern perturbation theory and the method of the renormalization group is developed for field models of phase transitions. The essential influence of the fluctuations on the critical behaviour is established together with the theory of correlation functions, Gaussian approximation, the Ginzburg criterion, ?- and 1/n- expansions as practical realizations of the renormalization group ideas. Applications of the theory to concrete aspects of condensed matter physics are considered: quantum effects, Bose condensation, crystal anisotropy, superconductors and liquid crystals, effects of disorder of type randomly distributed quenched impurities and random fields. This volume can be used as an advanced University course book for students with a basic knowledge of statistical physics and quantum mechanics. It could be considered as a complementary text to a standard University course on statistical physics.