Hidden traces of chirality in the fluctuations of a fully unwound cholesteric.

Confinement and hydrodynamic interactions often play an important role in the fluctuation dynamics of soft matter systems, which can typically be studied using light scattering techniques. With experimental and theoretical methodologies, I demonstrate here that chirality is an additional critical parameter that leads to diverging decay times and correlation lengths in chiral liquid crystal cells with a fully unwound cholesteric helix. This study combines light scattering measurements made in a tailored microscope geometry and theoretical calculations of the decay dynamics of chiral orientational fluctuations-including hydrodynamics-to establish the existence of two soft chiral modes of fluctuations driving the destabilization of the unwound cholesteric. Despite the achirality of the equilibrium state of unwound cholesterics, this study indicates that chirality hides itself in the orientational fluctuation modes and plays a major role in their dynamics, which can be exploited to locally measure the strength of chirality in frustrated chiral liquid crystal cells.

Structure and Lehmann rotation of drops in a surfactant-doped bent-core liquid crystal.

The structure of the nematic (cholesteric) drops that form at the clearing temperature of a mixture of the bent-core molecule CB7CB and the rodlike molecule 8CB doped with a surfactant is optically determined. Using experimental observations and numerical simulations, it is demonstrated that the director field inside these drops is not escaped concentric, as previously proposed, but twisted bipolar. The Lehmann rotation of these drops in the presence of a temperature gradient is described. Their rotation velocity is shown to be proportional to the temperature gradient and to the surface twist angle of the director field and inversely proportional to the drop radius, thus revealing a fundamental scaling law for the Lehmann effect of nematic and cholesteric twisted-bipolar droplets.

Chirality-Enhanced Periodic Self-Focusing of Light in Soft Birefringent Media.

We experimentally and numerically show that chirality can play a major role in the nonlinear optical response of soft birefringent materials, by studying the nonlinear propagation of laser beams in frustrated cholesteric liquid crystal samples. Such beams exhibit a periodic nonlinear response associated with a bouncing pattern for the optical fields, as well as a self-focusing effect enhanced by the chirality of the birefringent material. Our results open new possible designs of nonlinear optical devices with low power consumption and tunable interactions with localized topological solitons.

Physics-based multistep beam propagation in inhomogeneous birefringent media.

We present a unified theoretical framework for paraxial and wide-angle beam propagation methods in inhomogeneous birefringent media based on a minimal set of physical assumptions. The advantage of our schemes is that they are based on differential operators with a clear physical interpretation and easy numerical implementation based on sparse matrices. We demonstrate the validity of our schemes on three simple two-dimensional birefringent systems and introduce an example of application on complex three-dimensional systems by showing that topological solitons in frustrated cholesteric liquid-crystals can be used as light waveguides.

Ring-shaped liquid crystal structures through patterned planar photo-alignment.

Patterned liquid crystal (LC) configurations find widespread applications in functional devices such as lenses, gratings, displays and soft-robots. In combination with external stimuli such as an applied electric field, photo-alignment at the surfaces offers an attractive way to stabilize different LC structures in the bulk of a device. Herein, a planar LC cell is developed using a photo-alignment layer at the bottom substrate and a rubbed nylon film at the top substrate. Patterned planar photo-alignment is achieved by modulating the linear polarization with a spatial light modulator (SLM) and projecting the pattern onto the bottom substrate. A ring pattern is written into the photo-alignment layer with a continuous rotation between an inner radius and an outer radius. In the other regions the alignment is parallel to the rubbing direction at the top substrate. Four different LC configurations are observed: structure A in which a ring-shaped region is formed with an out of plane (vertical) orientation perpendicular to the substrate, structure B which has a single disclination loop and a 180° twist at the inner region of the photo-patterned ring (r < rin), structure C which has no discontinuities but a 360° twist in the inner region of the photo-patterned ring (r < rin) and structure D with 2 disclination loops. The LC director configuration for all 4 structures is simulated through finite element (FE) Q-tensor simulations and the optical transmission for each structure is simulated using a generalized beam propagation method.

Ray-based optical visualisation of complex birefringent structures including energy transport.

We propose an efficient method to simulate light propagation in lossless and non-scattering uniaxial birefringent media, based on a standard ray-tracing technique supplemented by a newly-derived transport equation for the electric field amplitude along a ray and a tailored interpolation algorithm for the reconstruction of the electromagnetic fields. We show that this algorithm is accurate in comparison to a full solution of Maxwell's equations when the permittivity tensor of the birefringent medium typically varies over a length much bigger than the wavelength. We demonstrate the usefulness of our code for soft matter by comparing experimental images of liquid crystal droplets with simulated bright-field optical micrographs, and conclude that our method is more general than the usual Jones method, which is only valid under polarised illumination conditions. We also point out other possible applications of our method, including liquid crystal based flat element design and diffraction pattern calculations for periodic liquid crystal samples.

Role of anchoring energy on the texture of cholesteric droplets: Finite-element simulations and experiments.

We present a numerical method to compute defect-free textures inside cholesteric domains of arbitrary shape. This method has two interesting properties, namely a robust and fast quadratic convergence to a local minimum of the Frank free energy, thanks to a trust region strategy. We apply this algorithm to study the texture of cholesteric droplets in coexistence with their isotropic liquid in two cases: when the anchoring is planar and when it is tilted. In the first case, we show how to determine the anchoring energy at the cholesteric-isotropic interface from a study of the optical properties of droplets of different sizes oriented with an electric field. This method is applied to the case of the liquid crystal CCN-37. In the second case, we come back to the issue of the textural transition as a function of the droplet radius between the double-twist droplets and the banded droplets, observed for instance in cyanobiphenyl liquid crystals. We show that, even if this transition is dominated by the saddle-splay Gauss constant K_{4}, as was recently recognized by Yoshioka et al. [Soft Matter 12, 2400 (2016)1744-683X10.1039/C5SM02838H], the anchoring energy does also play an important role that cannot be neglected.

Generalized drift velocity of a cholesteric texture in a temperature gradient.

We propose a general method to calculate the drift velocity of cholesteric textures subjected to a temperature gradient when the backflow effects are negligible. The textures may be Translationally Invariant Configurations (TICs) or localized structures such as cholesteric droplets or cholesteric fingers. For the TICs and for the droplets, the drift is rotational while for the fingers, the drift is translational. We show that for the TICs, the drift is only due to the thermomechanical coupling terms of Leslie (classical term) and of Akopyan and Zel'dovich (which are additional texture-dependent terms). For the localized structures, we show that another mechanism involving the temperature variations of the elastic constants and the existence of a transverse temperature gradient can lead to a drift which adds to the one due the classical thermomechanical effects.

Continuous Rotation of Achiral Nematic Liquid Crystal Droplets Driven by Heat Flux.

Suspended droplets of cholesteric (chiral nematic) liquid crystals spontaneously rotate in the presence of a heat flux due to a temperature gradient, a phenomenon known as the Lehmann effect. So far, it is not clear whether this effect is due to the chirality of the phase and the molecules or only to the chirality of the director field. Here, we report the continuous rotation in a temperature gradient of nematic droplets of a lyotropic chromonic liquid crystal featuring a twisted bipolar configuration. The achiral nature of the molecular components leads to a random handedness of the spontaneous twist, resulting in the coexistence of droplets rotating in the two senses, with speeds proportional to the temperature gradient and inversely proportional to the droplet radius. This result shows that a macroscopic twist of the director field is sufficient to induce a rotation of the droplets, and that the phase and the molecules do not need to be chiral. This suggests that one can also explain the Lehmann rotation in cholesteric liquid crystals without introducing the Leslie thermomechanical coupling-only present in chiral mesophases. An explanation based on the Akopyan and Zeldovich theory of thermomechanical effects in nematics is proposed and discussed.

Do Lehmann cholesteric droplets subjected to a temperature gradient rotate as rigid bodies?

We performed a Fluorescence Recovery After Photobleaching (FRAP) experiment during the Lehmann rotation of cholesteric droplets in thermodynamic coexistence with the isotropic liquid and subjected to a temperature gradient. By creating and tracking bleached spots near the surface of banded droplets (in which the cholesteric helix is perpendicular to the gradient) and concentric circle droplets oriented by an electric field (in which the helix is parallel to the gradient), we found that neither type of droplet rotates as a solid. This result shows that the texture rotation is mainly due to the local director rotation.

Lehmann rotation of cholesteric droplets: Role of the sample thickness and of the concentration of chiral molecules.

We study the role of the sample thickness d and of the concentration C of chiral molecules during the Lehmann rotation of cholesteric droplets of radius R subjected to a temperature gradient G→. Two configurations are studied depending on how the helix is oriented with respect to G→. The first result is that, at fixed C and R, the rotation velocity ω increases with d when the helix is parallel to G→, whereas it is independent of d when the helix is perpendicular to G→. The second result is that, for a given C,ω0=limR→0ω(R) is the same for the two types of droplets independently of d. This suggests that the, as yet unknown, physical mechanism responsible for the droplet rotation is the same in the two types of droplets. The third result is that the Lehmann coefficient ν[over ¯] defined from the Leslie-like relation ω0= G¯G/γ1 (with γ_1 the rotational viscosity) is proportional to the equilibrium twist q. Last, but not least, the ratio R¯=ν ¯/q depends on the liquid crystal chosen but is independent of the chiral molecule used to dope the liquid crystal.

Droplet relaxation in Hele-Shaw geometry: Application to the measurement of the nematic-isotropic surface tension.

Shape measurements after the coalescence of isotropic droplets embedded in a thin sample of a homeotropic nematic phase provides a tool to measure the nematic-isotropic surface tension. In addition, this experiment allows us to check the scaling laws recently given by Brun et al. [P.-T. Brun, M. Nagel, and F. Gallaire, Phys. Rev. E 88, 043009 (2013)] to explain the relaxation of ellipsoidal droplets in a Hele-Shaw cell.