Asymmetric counterpropagating fronts without flow

Out-of-equilibrium systems exhibit domain walls between different states. These walls, depending on the type of connected states, can display rich spatiotemporal dynamics. In this Rapid Communication, we investigate the asymmetrical counterpropagation of fronts in an in-plane-switching cell filled with a nematic liquid crystal. Experimentally, we characterize the different front shapes and propagation speeds. These fronts present dissimilar elastic deformations that are responsible for their asymmetric speeds. Theoretically, using a phenomenological model, we describe the observed dynamics with fair agreement.

Figure 1

Asymmetric counter propagating fronts in an in-plane-switching cell filled with an $E7$ nematic liquid crystal, applying a tension of $V=20$ Vpp and $f=1$ kHz. Experimental snapshots at different times. Parallel polarizer and analyzer (following the $x$ axis) for $t<0$ and crossed polarizer (following the $y$ axis) and analyzer (following the $x$ axis) for $t>0$. The black disk in the center is a glass sphere and the dashed lines emphasize the speed with which each front propagates.

Figure 2

Sketch of the experimental setup, which represents an in-plane-switching cell connected to the functions generator and observed through a microscope (top) with white light (down). Thickness between the two glass plates, $d=8.8\pm 0.2\mu \mathrm{m}$. Thickness of a glass plate, $g=1$ mm. Active zone, $l\times l=1{\mathrm{cm}}^2$. Gap between two electrodes, $e=15\mu \mathrm{m}$. The polarizer $P$ and the analyzer $A$ can be either perpendicular or parallel to each other.

Figure 3

Front profiles. Counterpropagative fronts connecting two different molecular orientations, the $\alpha$ and $\beta$ states, (a) with a top glass bead perturbation, observed between crossed polarizers, and (b) with a bottom glass bead perturbation, observed between parallel polarizers. (c) Left and (d) right front core with sizes $e_1$ and $e_2$, respectively. (e) Stationary solution of model Eq. (1) for $\eta =0$ and $\nu >0$.

Figure 4

Counterpropagative fronts connecting two different molecular orientations for two different glass bead positions: [(a) and (b)] on an electrode and [(c) and (d)] on a gap. The electrodes and the gap are respectively represented by $\{e,g\}$.

Figure 5

Front solution in an in-plane-switching cell filled with nematic liquid crystal. (a) Left and right front velocity versus voltage amplitude at $f=1$ kHz; the right and left fronts are represented by gray and black curves, respectively. Experimental snapshots on the top of the sample, (b) without voltage, observed with parallel polarizers ($P//A$), and (c) with voltage, observed between crossed polarizers ($P\perp A$), grayscale image. Schematic molecules orientation in the liquid crystal sample with voltage in the bulk (d) and at the midplane $\mathrm{\Pi }$ (e). The different states that connect the fronts are emphasized in thicker symbols (red) in the bottom panels. $•$ Glass ball causing a local perturbation. Solid lines account for the different walls between domains in panel (e).