Diffraction of light by topological defects in liquid crystals

We study light scattering by a hedgehog-like and linear disclination topological defects in a nematic liquid crystal by a metric approach. Light propagating near such defects feels an effective metric equivalent to the spatial part of the global monopole and cosmic string geometries. We obtain the scattering amplitude and the differential and total scattering cross section for the case of the hedgehog defect, in terms of the characteristic parameters of the liquid crystal. Studying the disclination case, a cylindrical partial wave method is developed. As an application of the previous developments, we also examine the temperature influence on the localization of the diffraction patterns.Comment: Correcting some typos,15 pages, 3 figures, accepted for publication in Liquid Crystal

Shear instabilities of freely standing thermotropic smectic-A films

In this Letter we discuss theoretically the instabilities of thermotropic freely standing smectic-A films under shear flow\cite{re:wu}. We show that, in Couette geometry, the centrifugal force pushes the liquid crystal toward the outer boundary and induces smectic layer dilation close to the outer boundary. Under strong shear, this effect induces a layer buckling instability. The critical shear rate is proportional to $1/\sqrt{d}$, where $d$ is the thickness of the film.Comment: 12 pages, 2 figure

Phase-ordering dynamics of the Gay-Berne nematic liquid crystal

Phase-ordering dynamics in nematic liquid crystals has been the subject of much active investigation in recent years in theory, experiments and simulations. With a rapid quench from the isotropic to nematic phase a large number of topological defects are formed and dominate the subsequent equilibration process. We present here the results of a molecular dynamics simulation of the Gay-Berne model of liquid crystals after such a quench in a system with 65536 molecules. Twist disclination lines as well as type-1 lines and monopoles were observed. Evidence of dynamical scaling was found in the behavior of the spatial correlation function and the density of disclination lines. However, the behavior of the structure factor provides a more sensitive measure of scaling, and we observed a crossover from a defect dominated regime at small values of the wavevector to a thermal fluctuation dominated regime at large wavevector.Comment: 18 pages, 16 figures, animations available at http://www.physics.brown.edu/Users/faculty/pelcovits/lc/coarsening.htm

Columnar Liquid Crystals in Cylindrical Nanoconfinement

Axial orientation of discotic columnar liquid crystals in nanopores of inorganic templates, with the columns parallel to the axis of the nanochannels, is considered desirable for applications such as production of molecular wires. Here, we evaluate experimentally the role of the rigidity of the LC columns in achieving such orientation in nanopores where the planar anchoring (i.e., columns parallel to wall surface) is enforced. We studied the columnar phase of several discotic compounds with increasing column rigidity in the following order: dendronized carbazole, hexakis(hexyloxy)triphenylene (HAT6), a 1:1 HAT6-trinitrofluorenone (TNF) complex, and a helicene derivative. Using 2-D X-ray diffraction, AFM, grazing incidence diffraction, and polarized microscopy, we observed that the orientation of the columns changes from circular concentric to axial with increasing column rigidity. Additionally, when the rigidity is borderline, increasing pore diameter can change the configuration from axial back to circular. We derive expressions for distortion free energy that suggest that the orientation is determined by the competition between, on the one hand, the distortion energy of the 2-d lattice and the mismatch of its crystallographic facets with the curved pore wall in the axial orientation and, on the other hand, the bend energy of the columns in the circular configuration. Furthermore, the highly detailed AFM images of the core of the disclinations of strength +1 and +1/2 in the center of the pore reveal that the columns spiral down to the very center of the disclination and that there is no amorphous or misaligned region at the core, as suggested previously