The blue phases of cholesteric liquid crystals are liquids that exhibit orientational order characterized by crystallographic space-group symmetries. We present here a pedagogical introduction to the current understanding of the equilibrium structure of these phases accompanied by a general overview of major experimental results. Using the Ginzburg-Landau free energy appropriate to the system, we first discuss in detail the character and stability of the usual helical phase of cholesterics, showing that for certain parameter ranges the helical phase is unstable to the appearance of one or more blue phases. The two principal models for the blue phases are two limiting cases of the Ginzburg-Landau theory. We explore each limit and conclude with some general considerations of defects in both models and an exact minimization of the free energy in a curved three-dimensional space.

Crystalline liquids: the blue phases

Landau theory of the nematic-isotropic phase transition

The optical and d.c. pulsed field Kerr Effects have been used to study the pretransitional behaviour in the isotropic phase for the alkyl cyano-biphenyl homologues (CN φ.φ CnH2n+1) for n = 5–8. From the dynamic and static measurements both the relaxation time (τ) and the Kerr Constant B have been found to be proportional to (T-T*)−1. These results are interpreted in terms of the Landau - de Gennes model and the characteristic parameters of this formalism have been given. The results are discussed in terms of the changing chemical structure.

Laser and Electric Field Induced Birefringence Studies on the Cyanobiphenyl Homologues

The out‐of‐plane anchoring strength at the interface between 4‐n‐pentyl‐4’‐cyanobiphenyl (5CB) and an obliquely evaporated SiO was measured as a function of temperature by applying the ‘‘high‐electric‐field technique’’ recently developed by Yokoyama and van Sprang [J. Appl. Phys. 57, 4520 (1985)]. The orientational ‘‘extrapolation length’’de for the interface was found to remain virtually constant at about 30 nm up to nearly 1 K below the clearing temperature Tc=308.4 K. At temperatures closer to Tc, however, it was observed to show an apparently critical increase, which approximately follows de∝[(Tc−T)/Tc]−0.45. At 0.043 K below Tc, de=183±3 nm, yielding the anchoring energy of (1.13±0.03)×10−5 J/m2. The implications of the observed temperature dependence are first investigated by extending Gibbs’ surface thermodynamics to a nematic‐wall interface, deriving a general relationship between the temperature variation of de and the surface excess entropy. In particular, it is concluded on thermodynamic grounds that the exponent of −0.45 can never be associated with a real critical behavior, but is indicative of the occurrence of crossover to a more singular or noncritical behavior. To draw specific connections between the temperature dependence of de and the orientational order near the interface,we develop a simple statistical mechanical theory of the anchoring strength, based on a van der Waals picture of the nematic‐wall interface. We show that the extrapolation length consists of two essentially distinct contributions: one is from the anisotropic interactions at the interface and the other is unconventionally from the interfacial inhomogeneity of the order parameter itself. For the most relevant cases, the van der Waals theory states that a reduction of the anchoring strength should always be accompanied by a depression of the surface order parameter. By comparing the theory with the experiment, the surface order parameters just below and above Tc are found to be 0.04 and 0.01, respectively, in agreement with the estimates from the contact angle and the pretransitional birefringence experiments. It is also argued, based on the present model, that the order parameter inhomogeneity is predominantly responsible for the quasicritical behavior of the anchoring strength.

Temperature dependence of the anchoring strength at a nematic liquid crystal‐evaporated SiO interface

An attempt is made to describe the kinetics of diffusionless first order phase transformations in terms of the time‐dependent Landau–Ginzburg equation. A steady‐state solution to the equation is presented such that an interface may propagate with a shape‐preserving profile under constant supercooling. The laws of growth and dissolution are derived and their condition of validity is discussed. The results provide a plausible basis for the interpretation of the kinetics of displacive transformations in solids and of certain first order transformations in liquid crystals.

Steady‐state kinetics of diffusionless first order phase transformations

The Landau approximation is known to give a good description of the pretransitional phenomena in the isotropic phase of nematic liquid crystals. We prove that, in the nematic phase too, just below the nematic-isotropic transition, the variations with temperature of the order parameter Q are well described by the theory based on the Landau expansion of the free energy F. The coefficients of the expansion of F are determined and the variations of F with Q are given for two nematic liquid crystals. The calculated values of Tc - T∗ and of the latent heats are in good agreement with the values obtained by independent way.

J. C. Filippini

Papers

Validity of the Landau Approximation in the Nematic Phase