Electroconvection in a Suspended Fluid Film: A Linear Stability Analysis

A suspended fluid film with two free surfaces convects when a sufficiently large voltage is applied across it. We present a linear stability analysis for this system. The forces driving convection are due to the interaction of the applied electric field with space charge which develops near the free surfaces. Our analysis is similar to that for the two-dimensional B\'enard problem, but with important differences due to coupling between the charge distribution and the field. We find the neutral stability boundary of a dimensionless control parameter ${\cal R}$ as a function of the dimensionless wave number ${\kappa}$. ${\cal R}$, which is proportional to the square of the applied voltage, is analogous to the Rayleigh number. The critical values ${{\cal R}_c}$ and ${\kappa_c}$ are found from the minimum of the stability boundary, and its curvature at the minimum gives the correlation length ${\xi_0}$. The characteristic time scale ${\tau_0}$, which depends on a second dimensionless parameter ${\cal P}$, analogous to the Prandtl number, is determined from the linear growth rate near onset. ${\xi_0}$ and ${\tau_0}$ are coefficients in the Ginzburg-Landau amplitude equation which describes the flow pattern near onset in this system. We compare our results to recent experiments.Comment: 36 pages, 7 included eps figures, submitted to Phys Rev E. For more info, see http://mobydick.physics.utoronto.ca

Where are the Hedgehogs in Nematics?

In experiments which take a liquid crystal rapidly from the isotropic to the nematic phase, a dense tangle of defects is formed. In nematics, there are in principle both line and point defects (``hedgehogs''), but no point defects are observed until the defect network has coarsened appreciably. In this letter the expected density of point defects is shown to be extremely low, approximately $10^{-8}$ per initially correlated domain, as result of the topology (specifically, the homology) of the order parameter space.Comment: 6 pages, latex, 1 figure (self-unpacking PostScript)

Surface alignment and anchoring transitions in nematic lyotropic chromonic liquid crystal

The surface alignment of lyotropic chromonic liquid crystals (LCLCs) can be not only planar (tangential) but also homeotropic, with self-assembled aggregates perpendicular to the substrate, as demonstrated by mapping optical retardation and by three-dimensional imaging of the director field. With time, the homeotropic nematic undergoes a transition into a tangential state. The anchoring transition is discontinuous and can be described by a double-well anchoring potential with two minima corresponding to tangential and homeotropic orientation.Comment: Accepted for publication in Phys. Rev. Lett. (Accepted Wednesday Jun 02, 2010

Weakly Nonlinear Analysis of Electroconvection in a Suspended Fluid Film

It has been experimentally observed that weakly conducting suspended films of smectic liquid crystals undergo electroconvection when subjected to a large enough potential difference. The resulting counter-rotating vortices form a very simple convection pattern and exhibit a variety of interesting nonlinear effects. The linear stability problem for this system has recently been solved. The convection mechanism, which involves charge separation at the free surfaces of the film, is applicable to any sufficiently two-dimensional fluid. In this paper, we derive an amplitude equation which describes the weakly nonlinear regime, by starting from the basic electrohydrodynamic equations. This regime has been the subject of several recent experimental studies. The lowest order amplitude equation we derive is of the Ginzburg-Landau form, and describes a forward bifurcation as is observed experimentally. The coefficients of the amplitude equation are calculated and compared with the values independently deduced from the linear stability calculation.Comment: 26 pages, 2 included eps figures, submitted to Phys Rev E. For more information, see http://mobydick.physics.utoronto.c

Orientational transitions in a nematic confined by competing surfaces

The effect of confinement on the orientational structure of a nematic liquid crystal model has been investigated by using a version of density-functional theory (DFT). We have focused on the case of a nematic confined by opposing flat surfaces, in slab geometry (slit pore), which favor planar molecular alignment (parallel to the surface) and homeotropic alignment (perpendicular to the surface), respectively. The spatial dependence of the tilt angle of the director with respect to the surface normal has been studied, as well as the tensorial order parameter describing the molecular order around the director. For a pore of given width, we find that, for weak surface fields, the alignment of the nematic director is perpendicular to the surface in a region next to the surface favoring homeotropic alignment, and parallel along the rest of the pore, with a interface separating these regions (S phase). For strong surface fields, the director is distorted uniformly, the tilt angle exhibiting a linear dependence with the distance normal to the surface (L phase). Our calculations reveal the existence of a first-order transition between the two director configurations, which is driven by changes in the surface field strength, and also by changes in the pore width. In the latter case the transition occurs, for a given surface field, between the S phase for narrow pores and the L phase for wider pores. A link between the L-S transition and the anchoring transition observed for the semi-infinite case is proposed. We also provide calculations with a phenomenological approach that yields the same main result that DFT in the scale length where this is valid.Comment: submitted to PR

Formation of disclination lines near a free nematic interface

We have studied the nucleation and the physical properties of a -1/2 wedge disclination line near the free surface of a confined nematic liquid crystal. The position of the disclination line has been related to the material parameters (elastic constants, anchoring energy and favored anchoring angle of the molecules at the free surface). The use of a planar model for the structure of the director field (whose predictions have been contrasted to those of a fully three-dimensional model) has allowed us to relate the experimentally observed position of the disclination line to the relevant properties of the liquid crystals. In particular, we have been able to observe the collapse of the disclination line due to a temperature-induced anchoring angle transition, which has allowed us to rule out the presence of a real disclination line near the nematic/isotropic front in directional growth experiments. 61.30.Jf,61.30.G

The Cone Phase of Liquid Crystals: Triangular Lattice of Double-Tilt Cylinders

We predict the existence of a new defect-lattice phase near the nematic - smectic-C (NC) transition. This tilt- analogue of the blue phase is a lattice of double-tilt cylinders. We discuss the structure and stability of the cone phase. We suggest that many `nematics' exhibiting short range layering and tilt order may in fact be in the molten cone phase, which is a line liquid.Comment: 4 Pages, 3 Figure

Geometrically-controlled twist transitions in nematic cells

We study geometrically-controlled twist transitions of a nematic confined between a sinusoidal grating and a flat substrate. In these cells the transition to the twisted state is driven by surface effects. We have identified the mechanisms responsible for the transition analytically and used exact numerical calculations to study the range of surface parameters where the twist instability occurs. Close to these values the cell operates under minimal external fields or temperature variations

Bifurcations in annular electroconvection with an imposed shear

We report an experimental study of the primary bifurcation in electrically-driven convection in a freely suspended film. A weakly conducting, submicron thick smectic liquid crystal film was supported by concentric circular electrodes. It electroconvected when a sufficiently large voltage $V$ was applied between its inner and outer edges. The film could sustain rapid flows and yet remain strictly two-dimensional. By rotation of the inner electrode, a circular Couette shear could be independently imposed. The control parameters were a dimensionless number ${\cal R}$, analogous to the Rayleigh number, which is $\propto V^2$ and the Reynolds number ${\cal R}e$ of the azimuthal shear flow. The geometrical and material properties of the film were characterized by the radius ratio $\alpha$, and a Prandtl-like number ${\cal P}$. Using measurements of current-voltage characteristics of a large number of films, we examined the onset of electroconvection over a broad range of $\alpha$, ${\cal P}$ and ${\cal R}e$. We compared this data quantitatively to the results of linear stability theory. This could be done with essentially no adjustable parameters. The current-voltage data above onset were then used to infer the amplitude of electroconvection in the weakly nonlinear regime by fitting them to a steady-state amplitude equation of the Landau form. We show how the primary bifurcation can be tuned between supercritical and subcritical by changing $\alpha$ and ${\cal R}e$.Comment: 17 pages, 12 figures. Submitted to Phys. Rev. E. Minor changes after refereeing. See also http://mobydick.physics.utoronto.c

Optically guided mode study of nematic liquid crystal alignment on a zero-order grating

B. T. Hallam and J. Roy Sambles, Physical Review E, Vol. 61, pp. 6699-6704 (2000). "Copyright © 2000 by the American Physical Society."The characterization of a liquid crystal cell, which comprises one zero-order (that is, at the wavelength of study it is nondiffractive) diffraction grating and one rubbed polyimide-coated substrate, has been performed using an optically guided mode technique. The cell is filled with nematic liquid crystal E7 (manufactured and sold by Merck, Poole, U.K.). The excitation of fully leaky guided modes within the liquid crystal layer has allowed the optical director profile to be quantified under the application of weak in-plane electric fields. The fitting of angle-dependent optical data to multilayer optical theory yields the accurate twist profile of the liquid crystal for different field strengths. Comparisons with profiles predicted from elastic continuum theory, assuming a Rapini-Papoular-type anchoring at the surfaces, allow both the azimuthal anchoring strength at each surface and the twist elastic constant of the bulk to be accurately determined. Repeating these measurements as a function of temperature allows the surface and bulk order parameters of the grating-aligned liquid crystal to be deduced