Chiral Incommensurate Helical Phase in a Smectic of Achiral Bent-Core Mesogens

An achiral, bent-core mesogen forms several tilted smectic liquid crystal phases, including a nonpolar, achiral de Vries smectic $A$ which transitions to a chiral, ferroelectric state in applied electric fields above a threshold. At lower temperature, a chiral, ferrielectric phase with a periodic, supermolecular modulation of the tilt azimuth, indicated by a Bragg peak in carbon-edge resonant soft x-ray scattering, is observed. The absence of a corresponding resonant umklapp peak identifies the superlayer structure as a twist-bend-like helix that is only weakly modulated by the smectic layering.

Figure 1

Experimental characterization of PAL30. (a) The PAL30 molecule, showing the all-trans length calculated using the program spartan. (b)–(d) Phase properties vs temperature. The solid vertical lines denote phase boundaries and the crosshatching phase coexistence. (b) SAXS shows the smectic layer spacing in all phases to be $d_0\approx 48\AA$. Resonant carbon $K$-edge reflections are from superlayer modulations of the molecular orientation about the layer normal $z$, the peak at $d_H\approx 150\AA$ corresponding to the pitch of the incommensurate, helical precession in the Sm2 phase, and at $d_B=2d_0$ to the bilayer ordering of the Sm3 and Sm4 phases. (c) Birefringence of planar-aligned cells with layers normal to the plates, with and without applied electric field ($E=20\mathrm{V}/\mu \mathrm{m}$). (d) Polarization current (in nA) in response to a triangle-wave applied electric field: a single-peak, Langevin-like response at lower temperatures in the Sm1 phase; a triple peak in the Sm2 phase, associated with ferrielectric switching [25] and indicative of helical unwinding [8], coalescing into a double peak in the Sm3, indicating a nonpolar ground state at $E=0$; and a single current peak in the Sm4 phase caused by the block polarization switching of the ferroelectric ${\mathrm{SmC}}_A{P}_F$ ground state. (e)–(m) Characteristic optical textures in a planar cell, viewed between crossed polarizers. The $E=0$ textures are focal conics typical of a fluid smectic with an optic axis along $z$. Field application induces chiral, tilted conglomerate domains (of opposite handedness) in the Sm1–Sm3 phases, but only a change in birefringence in the Sm4. (n)–(q) Proposed superlayer structure of PAL30 phases, with and without applied electric field: (n) Sm1: achiral de Vries–like $\mathrm{SmA}\to \text{chiral}$ ${\mathrm{SmC}}_S{P}_F$; Sm2: superlayer chiral helix $\to$ chiral ${\mathrm{SmC}}_S{P}_F$; Sm3: superlayer chiral bilayer ${\mathrm{SmC}}_A{P}_A\to \text{chiral}$ ${\mathrm{SmC}}_S{P}_F$; Sm4: ${\mathrm{SmC}}_A{P}_F$ with $\mathbf{P}$ parallel to the $\text{glass}\to {\mathrm{SmC}}_A{P}_F$ with $\mathbf{P}$ normal to the glass.

Figure 2

X-ray scattering from PAL30. (a) SAXS gives a peak from the smectic layer ordering at $q=q_0$. The RSXS peak at $q_H$ indicates that there is superlayer orientational ordering with periodicity $d_H$ in the Sm2 phase. In general, superlayer orientational modulation in a smectic generates RSXS peaks at wave vectors along the layer normal at $q(l,m)=l(2\pi /d_0)\pm m(2\pi /d_H)$ [10]. The observation of an RSXS reflection at $q=q(0,1)$ and the absence of an umklapp peak at $q=q(1,-1)$ in the Sm2 confirms a superlayer helix with a scattering amplitude modulation due to the smectic layering that is undetectably weak. (b) Temperature dependence of resonant scattering. The helix peak at $q_H\approx 1/(2.8d_0)$ becomes diffuse in the Sm3 phase. Splitting of the bilayer peak at $q_B$, which would indicate helical precession of the bilayer structure, is not observed.

Figure 3

Optical tilt of PAL30 vs applied field. The Sm1 phase shows no electro-optic response in weak fields $E<E_{\mathrm{th}}$. Fields $E>E_{\mathrm{th}}$ induce an electroclinic tilt and result in the formation of chiral domains. $E_{\mathrm{th}}$, which becomes smaller with decreasing $T$ (inset), matches closely $E_{\text{sat}}$, the field at which the induced polarization saturates, extracted from Fig. 1. The Sm2 phase exhibits a chiral electroclinic effect near $E=0$ and hysteresis in the field-induced helix unwinding to the ${\mathrm{SmC}}_S{P}_F$ state.