Elasticity-driven partial demixing in cholesteric liquid crystal films

We discuss the partial demixing of a chiral nematic mixture of a chiral and an achiral compound, induced by inhomogeneous confinement between substrates. While the effect is tiny in low molar mass mixtures, it is predicted to be noticeable in polymeric systems. The potential of the effect for improving performance of liquid crystal based photonic devices is discussed.

Figure 1

Sketch of a CLC confined between tilted substrates, with surface alignment along the figure normal. Dashed lines indicate domain boundaries, where a discontinuous jump of the helical pitch occurs. Arrows in the bottom indicate the partial demixing of chiral and achiral compounds induced by the lateral pitch gradient.

Figure 2

Spatial dependence of the reduced concentration variation $\delta /C$ along the cross section of the Cano wedge. At positions $x/L=N\left(N=1,2,\dots \right)$, the wedge accommodates $N$ director turns with bulk equilibrium pitch. The discontinuity of the helical pitch at domain boundaries results in a damped saw-tooth-like concentration profile. Also included are the envelopes of the concentration variation (dashed curves, $\sim 1/x$).

Figure 3

Demixing strength $C$ of an athermal mixture $\left(\chi =0\right)$ as a function of volume fraction ${\overline{\varphi }}_1$ of the chiral compound. Curves are plotted for various volumes of the constituents ($n_{\text{p}}v=1,\dots ,{10}^4{\text{nm}}^3$, as indicated in the figure), and assuming $\tilde{q}=2\times {10}^7{\text{m}}^{-1}$, $K_2={10}^{-11}\text{J}/\text{m}$, and $T=300\text{K}$.

Figure 4

(Color online) Structure of a polymeric CLC mixture. Mixture of a chiral nematic random copolymer (a) with chiral (C) and achiral $\left({\text{A}}_1\right)$ side groups and a nematic homopolymer (b) with achiral side groups $\left({\text{A}}_2\right)$.

Figure 5

Photonic properties of a CLC film: (a) reflectivity for circularly polarized illumination; (b) photonic density of states for the light mode showing a stop band (normalized with respect to the DOS of a homogeneous medium with the same average refractive index). Graphs are plotted assuming index matching of the surrounding medium and using parameters $\alpha =0.1$ and $N=20$. The vertical dashed lines indicate the location of the band edges.

Figure 6

Location of the long-wavelength band-edge resonance as a function of film thickness. The distance between the long-wavelength band-edge resonance and the band edge is plotted as a function of film thickness (in terms of total number of director turns along the film normal, $N$) for various values of the relative dielectric anisotropy $\left(\alpha =0.025,0.5,\dots ,0.2\right)$. The inset shows the parameter $s$ of the approximate power law ${\lambda }_{\text{R}}-{\lambda }_{\text{R}}^{\left(\infty \right)}=s\left(\alpha \right)N^{-2}$ as a function of $\alpha$.

Figure 7

(Color online) Effect of tilted substrates on the photonic properties in the absence of any demixing effects: (a) reflectivity and (b) photonic density of states (normalized with respect to the DOS in an isotropic medium) in a Cano wedge, assuming a relative dielectric anisotropy $\alpha =0.05$. The reduced wavelength ${\overline{\lambda }}^{\prime }=\lambda /\left(⟨\overline{n}⟩\overline{p}\right)$ is used. The reduced coordinate $x/L$ is defined in the same way as in Fig. 2.

Figure 8

Spatial dependence of the long-wavelength band-edge resonance in a Cano wedge: (a) without any demixing effects; [(b) and (c)] including demixing effects—material parameters optimized for constant resonance wavelength in each domain (b) and optimized for continuous spatial dependence in the wavelength region around $x/L=45$ (c).