Unwinding of the uniform lying helix structure in cholesteric liquid crystals next to a spatially uniform aligning surface

The symmetry of the cholesteric uniform lying helix (ULH) structure, where the helix axis is aligned in a single direction parallel to the device substrates, is not compatible with a uniform surface alignment and an unwinding of the helical structure is expected at the interface. Fluorescence confocal polarizing microscopy experiments are performed on the interface between a bulk ULH and a uniform aligning surface (for both planar and homeotropic alignments). The results are analyzed in the framework of a finite difference numerical simulation based on the Frank elastic distortion, to determine relevant director structures. An optical model is introduced to predict three-dimensional fluorescence profiles for the structures. Comparison of experimental and theoretical results shows that the equilibrium structure of the system involves a continuous unwinding of the helix close to the surface.

Figure 1

Director plots for two possible transitions from a bulk ULH structure to a planar substrate. (a) The unwinding of the helix is facilitated by a ${\tau }^{-1/2}{\lambda }^{+1/2}$ disclination pair close to the substrate every half pitch [1]. The singular ${\tau }^{-1/2}$ disclinations are denoted by circles while the nonsingular ${\lambda }^{+1/2}$ disclinations are marked with squares. (b) An alternative situation is a smooth transition from the bulk helix to the planar substrate periodic over a full cholesteric pitch. This configuration avoids disclination formation but does require a region of twist in the opposite sense to the helix, which is ringed.

Figure 2

(Color online) Schematic of the arrangement of optical components in a fluorescence confocal polarizing microscopy system. The polarizer ensures that only fluorescence light with the same polarization as the excitation beam passes through the setup to the photomultiplier tube, while the pinhole guarantees that the measured fluorescence originates only from the focal region of the excitation beam.

Figure 3

FCPM images of the interface between a ULH bulk and a uniform planar substrate at $z=d$, with $10{\text{V}}_{\text{RMS}}$ applied perpendicular to the surface and a chiral pitch of $20\mu \text{m}$. The ULH structure was formed by cooling from the isotropic to cholesteric phase with the field applied and the in-plane orientation of the helix is dictated by the surface alignment, for which the easy axis is in the $y$ direction. The incident polarization of the laser is designated by $\mathbf{P}$ in each image, which is in (a) the $y$ direction (perpendicular to the helix axis) and (b) the $x$ direction (parallel to the helix).

Figure 4

FCPM images revealing the ULH structure near a uniform planar substrate at $z=d$, with the easy axis in the $y$ direction. The polarization of the incident laser beam $\mathbf{P}$ is along the $y$ direction (perpendicular to the helix axis) in each image. Image (a) shows the $20\mu \text{m}$ pitch material in a ULH structure that was aligned by inducing flow within the device, with a voltage of $13.1{\text{V}}_{\text{RMS}}$ applied perpendicular to the substrates. Image (b) shows the $10\mu \text{m}$ pitch material in a ULH structure that was aligned by cooling from the isotropic with an applied voltage $20{\text{V}}_{\text{RMS}}$.

Figure 5

FCPM images of the ULH structure near a uniform homeotropic substrate at $z=d$, when the incident polarization $\mathbf{P}$ of the laser is (a) perpendicular and (b) parallel to the helix axis. The material used had a pitch of $\sim 10\mu \text{m}$ and there is $20{\text{V}}_{\text{RMS}}$ applied between the substrates.

Figure 6

(Color online) Calculated director structures for a continuous unwinding of the bulk ULH structure next to a substrate promoting uniform (a) planar and (b) homeotropic alignment. An electric field of $0.15\text{V}/\mu \text{m}$ is applied perpendicular to the substrates. Lower electric fields result in an expansion of the unwinding region next to the substrate in the negative $z$ direction. In (a) the helix axis is perpendicular to the substrate alignment direction, displaying a lesser degree of elastic distortion than the structure presented in Fig. 1b.

Figure 7

Theoretical prediction of the FCPM images for the ULH unwinding continuously next to a substrate promoting uniform planar alignment with easy axis in the $y$ direction. The images are calculated for the polarization state of the excitation beam $\mathbf{P}$ perpendicular (a) and parallel (b) to the helix axis.

Figure 8

Theoretical prediction of the FCPM images for the ULH unwinding continuously next to a substrate promoting uniform homeotropic alignment. The images are calculated for the polarization state of the excitation beam $\mathbf{P}$ perpendicular (a) and parallel (b) to the helix axis.