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

Twisted Line Liquids

We propose a model of directed lines where the average direction has the nature of a cholesteric liquid crystal. This model, for instance, would describe the liquid of screw dislocations in the twist-grain-boundary (TGB) phase of liquid crystals. We show that the presence of lines does not alter the long wavelength elasticity of a cholesteric and, therefore, does not stabilize Landau-Peierls instability of the cholesteric phase. We discuss other possible mechanisms for stabilizing the twist-grain-boundary phase.Comment: 10 pages, tex file (macros included), IASSNS-HEP-93/2

Elasticity Theory of a Twisted Stack of Plates

We present an elastic model of B-form DNA as a stack of thin, rigid plates or base pairs that are not permitted to deform. The symmetry of DNA and the constraint of plate rigidity limit the number of bulk elastic constants contributing to a macroscopic elasticity theory of DNA to four. We derive an effective twist-stretch energy in terms of the macroscopic stretch epsilon along and relative excess twist sigma about the DNA molecular axis. In addition to the bulk stretch and twist moduli found previously, we obtain a twist-stretch modulus with the following remarkable properties: 1) it vanishes when the radius of the helical curve following the geometric center of each plate is zero, 2) it vanishes with the elastic constant K_{23} that couples compression normal to the plates to a shear strain, if the plates are perpendicular to the molecular axis, and 3) it is nonzero if the plates are tilted relative to the molecular axis. This implies that a laminated helical structure carved out of an isotropic elastic medium will not twist in response to a stretching force, but an isotropic material will twist if it is bent into the shape of a helix.Comment: 19 pages, plain LaTeX, 1 included eps figur

Attitude control for spacecraft Patent

Attitude control system for spacecraft based on conversion of incident solar radiation on movable control surfaces into mechanical torque

Chirality in Liquid Crystals: from Microscopic Origins to Macroscopic Structure

Molecular chirality leads to a wonderful variety of equilibrium structures, from the simple cholesteric phase to the twist-grain-boundary phases, and it is responsible for interesting and technologically important materials like ferroelectric liquid crystals. This paper will review some recent advances in our understanding of the connection between the chiral geometry of individual molecules and the important phenomenological parameters that determine macroscopic chiral structure. It will then consider chiral structure in columnar systems and propose a new equilibrium phase consisting of a regular lattice of twisted ropes.Comment: 20 pages with 6 epsf figure