Flow dynamics of focal conic domains in smectic-A liquid crystals

(supplemental material for Visualization, coarsening, and flow dynamics of focal conic domains in simulated smectic-A liquid crystals", Danilo B. Liarte, Matthew Bierbaum, Muxin Zhang, Brian D. Leahy, Itai Cohen, and James P. Sethna, submitted 2014.

Smectic-A liquid crystals are formed of molecules that arrange themselves into layers. Like crystals, which have rows and columns and layers of atoms in a regular array, smectic-A materials have layers -- but in each layer the order is random, like a liquid. These smectic layers have a strong preference to be equally spaced. (If we distort the smectic, the layers prefer to bend than to deviate from equal layer spacing.)

This leads to defects that form focal conics -- ellipses and hyperbolas.

In this set of animations, we show simulation results for the dynamical evolution of smectic-A liquid crystals. Experiments are often performed by putting the smectic between two microscope slides. The slides can have different anchoring conditions. Planar boundary conditions are treatments which align the smectic molecules parallel to the glass slides, meaning the layers are perpendicular to the slide. Homeotropic boundary conditions align the layers parallel to the slide (and hence flat). Planar boundary conditions naturally attach one of the two confocal conics in each domain to the microscope slide, so imaging the top and bottom is the natural thing to do. For homeotropic boundary conditions, the top and bottom are flat and boring, so experimentalists (and simulators) examine instead an intermediate height in the sample. In each case, the images are taken with light (simulated or real) transmitted through crossed polarizers on either side: the dark and light regions show the defect structures.

Focal conic formation and growth

The first and second simulations show the nucleation and growth of focal conic defects starting from random initial conditions.
Top boundary of the simulated coarsening sample with planar anchoring (layers perpendicular to the glass slides). Coarsening viewed on an intermediate plane within the bulk of a sample, with homeotropic boundary conditions (layers parallel to the top and bottom boundaries).

Periodic shear

In this set of animations, we show simulation and experimental results for the flow dynamics of smectic-A liquid crystals subject to shear strain, with one of the glass slides oscillating sideways with respect to the other. In the first three simulations, we initialize our movie by evolving from a random initial configuration for a time T where clear focal conics are formed. We then apply the shear dynamical equations of motion for an amplitude of oscillation equals twice the gap size, and a frequency of 2 \pi / T. The animations show three periods of oscillation.

Shear, planar boundary conditions

First we compare theory with experiment for sheared planar boundary conditions, where the smectic layers are perpendicular to the upper and lower glass slides. (The long axis of the smectic molecules, which point normal to the layers, are hence parallel to the glass slides.)

Bottom boundary of a simulated sample with planar anchoring (layers perpendicular to the glass slides). Top boundary of the same simulated sample with planar anchoring (layers perpendicular to the glass slides). Experimental movie of 8CB with planar anchoring, under oscillatory shear with an amplitude of 0.73 at 0.1 Hz, with plates separated by a gap of 21 microns (sped up for viewing).

For planar anchoring under external shear, the focal conics in the experiments and simulations seem qualitatively similar.

Shear, homeotropic boundary conditions

Second, we compare theory with experiment for sheared homeotropic boundary conditions (where the long axis of the smectic molecules are perpendicular to the glass slides, and hence the layers are parallel).

An intermediate plane within the bulk of a sample, with homeotropic boundary conditions (layers parallel to the top and bottom boundaries). An isolated defect in a homeotropically aligned sample; strain amplitude 0.4 sheared at 0.4 Hz with a gap size of 15 microns. Experimental movie of 8CB with initially homeotropic anchoring with lots of defects, under oscillatory shear with an amplitude of 0.42 at 1.0 Hz, with plates separated by a gap of 15 microns (sped up for viewing; the movie is ~20 minutes of shearing).

Here the simulation differs from the experiment in at least two important ways. First, the simulation has large 'bands' separating the cross-hatched circles (representing a vertical focal conic defect representing the dimple near the stem of the 'apple-shaped' focal conic layers. Second, the experiment under shear destroys the original focal conic defects, and develops a new pattern of domains with eccentricity perpendicular to the direction of shear. Whether this represents differences in the parameters of the simulation and the experiment (relative elastic or viscous constants or rates), or important new physics (dislocations omitted from the simulation) remains to be discovered.

Last modified: January 14, 2015

James P. Sethna, sethna@lassp.cornell.edu; This work supported by the Basic Energy Sciences division of the Department of Energy, through grant DE-FG02-07ER46393, and by the National Science Foundation CBET-PMP 1232666 and DMR-1056662.

Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).