In situ measurements of twist and bend elastic constants in the oblique helicoidal cholesteric

Unique electro-optical properties of the oblique helicoidal cholesteric (${\mathrm{Ch}}_{\mathrm{OH}}$) stem from its heliconical director structure. An applied electric field preserves the single-harmonic modulation of the director while tuning the ${\mathrm{Ch}}_{\mathrm{OH}}$ period and the corresponding Bragg-peak wavelength within a broad spectral range. We use the response of ${\mathrm{Ch}}_{\mathrm{OH}}$ to the electric field to measure the elastic constants of twist $K_{22}$ and bend $K_{33}$ directly in the cholesteric phase. The temperature dependencies of $K_{22}$ and $K_{33}$ allow us to determine the range of the electric tunability of the ${\mathrm{Ch}}_{\mathrm{OH}}$ pitch and the heliconical angle. The data are important for understanding how molecular composition and chirality influence macroscopic elastic properties of the chiral liquid crystals and for the development of ${\mathrm{Ch}}_{\mathrm{OH}}$-based optical devices.

Figure 1

The oblique helicoidal cholesteric structure ${\mathrm{Ch}}_{\mathrm{OH}}$ in an applied electric field: the ${\mathrm{Ch}}_{\mathrm{OH}}$ pitch $P$ and the conical angle θ both decrease when the electric field E increases.

Figure 2

(a) Reflection and transmission modes of the oblique incidence setup (top view). The $xz$ plane of incidence is parallel to the goniometer stage, and the angle of incidence β is measured from the normal to the ${\mathrm{Ch}}_{\mathrm{OH}}$ cell. The polarizations of the incident and reflected rays are set by the polarizer ($\mathrm{P}$) and analyzer ($\mathrm{A}$), respectively. (b) ${\mathrm{Ch}}_{\mathrm{OH}}$ cell geometry.

Figure 3

Temperature dependencies of dielectric permittivities ${\varepsilon }_{\parallel },{\varepsilon }_{\perp }$, and $\mathrm{\Delta }\varepsilon$ measured in the N and Ch mixtures (filled and empty symbols, respectively).

Figure 4

(a) MicroImager map of the optical retardance of the ${\mathrm{Ch}}_{\mathrm{OH}}$ cell subject to a high in-plane electric field $E>E_{NC}$. (b) Temperature dependence of the birefringence measured in $N$ (empty symbols) and Ch (filled symbols) mixtures. The size of all data symbols exceeds the error of measurement.

Figure 5

(a) Temperature dependence of the pitch $P_0$ ($T$) measured in the wedge cell and (b) Bragg reflections corresponding to $P_0$/4 and $P_0$/6; oblique incidence of light, ${\mathrm{Ch}}_{\mathrm{OH}}$ cell thickness $d=16\mu \mathrm{m}$.

Figure 6

(a) Capacitance and (b) interference maxima vs electric field; homeotropic ${\mathrm{Ch}}_{\mathrm{OH}}$ cell, $d=3.3\mu \mathrm{m}$, in the capacitance measurements and the planar ${\mathrm{Ch}}_{\mathrm{OH}}$ cell, $d=22.7\mu \mathrm{m}$, in the spectral measurements. The kinks correspond to the critical field $E_{NC}$. (c) Temperature dependence of the critical fields $E_{NC}$ and $E_{N*C}$; $E_{N*C}$ is measured experimentally and deduced from Eq. (1).

Figure 7

Polarizing optical microscopy of the ${\mathrm{Ch}}_{\mathrm{OH}}$ to Ch transition at $T=20{}^{\circ }\mathrm{C}$: (a) ${\mathrm{Ch}}_{\mathrm{OH}}$ texture at $E=0.58\mathrm{V}/\mu \mathrm{m}$; (b) nucleation of Ch texture, 30 s after the field is reduced to $E_{N*C}=0.52\mathrm{V}/\mu \mathrm{m}$; (c) expansion of the Ch texture at the same temperature and the applied field, 8 min after the start of nucleation.

Figure 8

The field dependence of Bragg reflection wavelength used to calculate $K_{33}$.

Figure 9

(a) Temperature dependencies of $K_{33}$ and $K_{22}$, and (b) chiral parameter $K_C$.

Figure 10

Temperature dependencies of (a) the elastic ratios κ and κ/(1−κ), (b) maximum $P_{N*C}$ and minimum $P_{NC} {\mathrm{Ch}}_{\mathrm{OH}}$ pitches, (c) ratio of the pitches $P_{N*C}/P_{NC}$, and (d) maximum opening cone angle ${\theta }_{N*C}$.