An introductory review of the central ideas in the modern theory of dynamic critical phenomena is followed by a more detailed account of recent developments in the field. The concepts of the conventional theory, mode-coupling, scaling, universality, and the renormalization group are introduced and are illustrated in the context of a simple example---the phase separation of a symmetric binary fluid. The renormalization group is then developed in some detail, and applied to a variety of systems. The main dynamic universality classes are identified and characterized. It is found that the mode-coupling and renormalization group theories successfully explain available experimental data at the critical point of pure fluids, and binary mixtures, and at many magnetic phase transitions, but that a number of discrepancies exist with data at the superfluid transition of $^{4}\mathrm{He}$.

Theory of Dynamic Critical Phenomena

A broad review of recent research work on the preparation and the remarkable properties of intercalation compounds of graphite, covering a wide range of topics from the basic chemistry, physics and materials science to engineering applications.

Intercalation compounds of graphite

Most associate liquid crystals with their everyday use in laptop computers, mobile phones, digital cameras, and other electronic devices. However, in contrast to their rodlike (calamitic) counterparts, first described in 1907 by Vorlander, disklike (discotic, columnar) liquid crystals, which were discovered in 1977 by Chandrasekhar et al., offer further applications as a result of their orientation in the columnar mesophase, making them ideal candidates for molecular wires in various optical and electronic devices such as photocopiers, laser printers, photovoltaic cells, light-emitting diodes, field-effect transistors, and holographic data storage. Beginning with an overview of the various mesophases and characterization methods, this Review will focus on the major classes of columnar mesogens rather than presenting a library of columnar liquid crystals. Emphasis will be given to efficient synthetic procedures, and relevant mesomorphic and physical properties. Finally, some applications and perspectives in materials science and molecular electronics will be discussed.

Discotic Liquid Crystals: From Tailor-Made Synthesis to Plastic Electronics

Structure of the inverted hexagonal (HII) phase, and non-lamellar phase transitions of lipids.

This review discusses the physical properties of nematic, cholesteric, and smectic liquid crystals. Molecular theories of the liquid crystal phases are discussed and the molecular field theories of the phase transitions between the various liquid crystal phases are presented. The elastic theory and hydrodynamics of liquid crystals is developed. A wide variety of phenomena in liquid crystals, including elastic distortions, disclinations, flow properties, fluctuations, light scattering, wave propagation, nuclear magnetic resonance, effects of magnetic and electric fields, electrohydrodynamics, and optical properties, is discussed.

Physics of liquid crystals

A simple model for an interacting liquid of particles lacking an axis of rotational symmetry is proposed. The four order parameters necessary to describe an ordered phase are identified. An ensemble of such particles is described by a mean field theory. A phase diagram showing both uniaxial and biaxial phases results. The model predicts a phase diagram similar to that of the phenomenological model of Alben.

Ordered phases of a liquid of biaxial particles

The elastic constants of a hard-rod liquid crystal are calculated using the Onsager theory, with results similar to those given by Priest.

Frank Elastic Constants of the Hard-Rod Liquid Crystal

The Onsager theory for the liquid crystal phase transition of a gas of hard rods is known to be accurate if the rods are long enough. In order to quantify the necessary length, the first correction term (the third virial coefficient) to the Onsager theory is estimated numerically. On the basis of a study of the behavior of this function (for the cases L/D = 10, 20, 40, and 100), a model function which approximates its angular dependence is proposed. This is used to estimate the corrections to the predictions of the Onsager theory arising from the finite length of the rods, in both isotropic and ordered phases. It is concluded that the Onsager approximation is not quantitatively accurate for L/D < 100.

Joseph P. Straley

Papers

Physics of liquid crystals

Ordered phases of a liquid of biaxial particles

Frank Elastic Constants of the Hard-Rod Liquid Crystal

Third Virial Coefficient for the Gas of Long Rods