International Journal of Modern Physics B

Critical behavior at the transition from the nematic phase to the smectic A phase in liquid crystals has been of interest for over two decades. Discussions about the nature of the transition, its analogy to the superconducting transition, and the degree of anisotropy present in the critical exponents have been extensive during this time. This review article concentrates on the question of anisotropy at the nematic-smectic A transition. The experimental and theoretical work related to this question is summarized and compared. While progress has been made, there are many interesting questions related to this transition that remain for investigators to answer.

This article contains an overview of numerical simulations of phase transitions and critical phenomena in liquid crystals. After a brief description of the models studied in simulations and an elementary introduction to commonly used numerical methods, results obtained from existing numerical studies of phase transitions and critial phenomena in liquid crystals are reviewed and some directions for future work are suggested.

We review results of a high resolution systematic study of the specific heat for alkyl-cyanobiphenyl liquid crystals confined to the 0.2µm diameter cylindrical pores Anopore membranes. The nematic director alignment at the pore wall is varied from homeotropic to tangential by pore surface treatment. Several phenomena are uncovered by these studies which probed the weakly first order nematic to isotropic, the continuous smectic-A to nematic and the first order smectic-A to isotropic phase transitions. The specific heat is strongly dependent on the nematic director configuration, and confinement effects are remarkably distinct according to the order of the phase transition. The influence of elastic distortions and surface ordering and disordering effects are evident. Despite considerable departures from bulk behavior with regards to specific heat peaks size, rounding and width, and transition temperature shifts, a bulk-like critical behavior appears to be retained. The formation of smectic translational order within the pores is hindered for those liquid crystals that also possess a nematic phase. The average scalar order parameter temperature dependence is extracted from the specific heat results using a simplified Landau-de Gennes type of model, and is shown to be consistent with nuclear magnetic resonance results.

Free-standing liquid-crystal films constitute a unique and phenomenally rich system in which a number of physical phenomena may be carefully studied. In particular, they provide an ideal system in which the novel theories of defect-mediated melting in two-dimensions (2D) may be tested. Calorimetric data is presented that indicate that such theories cannot adequately account for phase transitions in effectively 2D free-standing liquid-crystal films only two molecular layers in thickness. Extensive Monte Carlo simulation studies have therefore been performed on a trial Hamiltonian that couples herringbone order to the hexatic order. In a relatively large region of parameter space, the simulation yields heat-capacity consistent with our calorimetric data. These results are discussed in the context of existing data on the structural, optical, and mechanical properties of free-standing films.

In the presence of external fields or in restricted geometries, the originally continuous helical symmetry of the Sm C* phase is broken by the appearence of field- or geometry-induced soliton-like domain walls. As a result of this symmetry breaking, a crossover between the plane-wave-like and soliton-like regime occurs in both static and dynamic properties which is responsible for some remarkable phenomena such as field-induced optical biaxiality or a field-induced band structure of collective excitations. Whereas we find in the plane-wave-like regime a degenerate soft mode which splits below the Sm A→Sm C* transition into a symmetry recovering Goldstone-phason-mode and an amplitudon mode, we find in the soliton regime a splitting of the phason mode into acoustic and optic-like branches separated by a band gap. Within the same framework we also discuss other remarkable and extraordinary properties such as reentrant phases, Lifshitz points, one dimensional photonic band gaps and thickness dependent phase diagrams.

In recent times, optical diffraction and reflection from periodically twisted liquid crystalline media have attracted a lot of attention. The important developments in this area have been considered here.

Thin submicron and micron films of liquid crystals placed between two isotropic media represent a particular example of confined systems. Such films can be prepared on the surface of glycerin or other liquids, In comparison with Langmuir monolayers, these films are macroscopically thick to involve the liquid crystalline order in the interplay between molecular structure and macroscopic organization. At the same time, the films are thin enough for such a strong competition between surface and bulk properties that transitional in-plane symmetry is spontaneously violated and a number of patterns appear: stripe domains, square lattices, strings, high strength defects and so on. We show that these structures are governed by the divergence (or “sufacelike”) K₁₃ and K₂₄ terms in the nematic free energy which have been ignored for decades. We also show that both terms can be included in the standard elasiticty theory without contradictions with the basic idea of the nematic phase. The one-dimensional confinement makes the films a unique object of investigation: although the phenomena observed are attributed to the vertical confinement, their manifestation is detected in a non-restricted film plane.

In a magnetic field, a liquid crystal exhibits many interesting defect configurations arising due to the diamagnetic anisotropy of the molecules. In this article the structure and properties of some defect states, in the presence of a magnetic field, will be reviewed.

The effect of the saddle-splay elastic constant K₂₄ on nematic director-fields is a topic of fundamental interest for the elastic theory of liquid crystals and plays a vital role in device applications where nematic liquid crystals are confined to a curved geometry. The first measurement of K₂₄ came more than sixty years after the pioneering work of Oseen, who made first steps toward the elastic theory of liquid crystals. Today the study of saddle-splay elasticity has become an important topic in liquid crystal physics. In this review we summarize the various methods used to measure K₂₄ in curved geometries and present the detailed theory behind the measurements.

The rheological and rheo-optical properties of nematic solutions of rodlike polymers are discussed. Magnetic field induced instability in the twist geometry is discussed in terms of the flow properties of these solutions. The rheological properties of these nematic solutions are compared to isotropic solutions of the same polymer. The behavior in shear flow of nematic solutions is discussed in terms of the Ericksen-Leslie equations. Deviations from those solutions are also discussed in context to polymeric nematics.

Recent interests in NMR spectroscopy of molecules oriented in liquid crystal solvents predominantly revolve around the developments of methods for (1) spectral simplification, (2) novel applications and (3) understanding of the solvent effects on molecular structure and function. A number of such results and their critical evaluations are presented, with emphasis on mixed liquid crystals of opposite diamagnetic susceptibility anisotropies, metal ion-ligand and weak molecular interactions and the discovery of novel liquid crystalline phase. Future directions of research, such as the use of ultra high magnetic fields, partially and perdeuterated samples and near magic angle spinning experiments, are highlighted.

A liquid crystal electro-optical effect with an optically “self-compensating” director configuration is proposed to provide a device that has a wide angle of view at all gray levels. Calculations and data are presented to show the beneficial results of coupling a tunable birefringence L.C. device that has reverse pretilt alignment with a negative birefringence compensator plate.