Fluctuation-Driven 1st-Order Isotropic-to-Tetrahedratic Phase Transition

Motivated in part by recent experiments on liquid crystals with bent-core molecules, which are observed to display a spontaneous chiral symmetry breaking, we introduce a field theory of a 3rd-rank tensor order parameter T^{ijk} to describe the isotropic-to-tetrahedratic phase transition that we predict to take place in these materials. We study the critical properties of the corresponding phase transition and find that this transition, continuous at the mean-field level, is generically driven 1st-order by thermal fluctuations.Comment: 4 pgs. RevTex, 2 eps figures, submitted to Europhysics Letter

Stability of Texture and Shape of Circular Domains of Langmuir Monolayers

Finite domains of a Langmuir monolayer in a phase with tilted molecules can be modeled by a simple elastic free energy of an XY order parameter with isotropic and anisotropic line tension terms. The domains can and often do contain nontrivial textures, which in turn influence the shape of the domains. Herein we investigate the properties of a simplified isotropic model with a single elastic constant. For circular domains a first-order phase transition is found between two distinct textures: an exterior defect (or ``virtual boojum'') texture, and an interior defect texture. Starting with a circular domain and either of these two textures as a ground state, we find shape instabilities develop that depend on the elastic constants and line tensions in the simplified model. In both cases a necessary but not sufficient condition for the onset of shape instabilities is the possibility for a local negative effective line tension to develop from the anisotropic line tension term.Comment: 14 double column RevTex pages, 8 eps figure

Dynamics of smectic elastomers

We study the low-frequency, long-wavelength dynamics of liquid crystal elastomers, crosslinked in the smectic-$A$ phase, in their smectic-$A$, biaxial smectic and smectic-$C$ phases. Two different yet related formulations are employed. One formulation describes the pure hydrodynamics and does not explicitly involve the Frank director, which relaxes to its local equilibrium value in a non-hydrodynamic time. The other formulation explicitly treats the director and applies beyond the hydrodynamic limit. We compare the low-frequency, long-wavelength dynamics of smectic-$A$ elastomers to that of nematics and show that the two are closely related. For the biaxial smectic and the smectic-$C$ phases, we calculate sound velocities and the mode structure in certain symmetry directions. For the smectic-$C$ elastomers, in addition, we discuss in some detail their possible behavior in rheology experiments.Comment: 19 pages, 3 figure

Chiral Lyotropic Liquid Crystals: TGB Phases and Helicoidal Structures

The molecules in lyotropic membranes are typically aligned with the surface normal. When these molecules are chiral, there is a tendency for the molecular direction to twist. These competing effects can reach a compromise by producing helicoidal defects in the membranes. Unlike thermotropic smectics, the centers of these defects are hollow and thus their energy cost comes from the line energy of an exposed lamellar surface. We describe both the twist-grain-boundary phase of chiral lamellar phases as well as the isolated helicoidal defects.Comment: 10 pages, plain TeX, two included figures, revision corrects figures onl