Temperature dependence of bend elastic constant in oblique helicoidal cholesterics
Olena S. Iadlovska, Greta Babakhanova, Georg H. Mehl, Christopher Welch, Ewan Cruickshank, Grant J. Strachan, John M. D. Storey, Corrie T. Imrie, Sergij V. Shiy… 展开作者
Olena S. Iadlovska, Greta Babakhanova, Georg H. Mehl, Christopher Welch, Ewan Cruickshank, Grant J. Strachan, John M. D. Storey, Corrie T. Imrie, Sergij V. Shiyanovskii, Oleg D. Lavrentovich
Elastic moduli of liquid crystals, known as Frank constants, are of quintessential importance for understanding fundamental properties of these materials and for the design of their applications. Although there are many methods to measure the Frank constants in the nematic phase, little is known about the elastic constants of the chiral version of the nematic, the so-called cholesteric liquid crystal, since the helicoidal structure of the cholesteric renders these methods inadequate. Here we present a technique to measure the bend modulus $K_{33}$ of cholesterics that is based on the electrically tunable reflection of light at an oblique helicoidal $Ch_{OH}$ cholesteric structure. $K_{33}$ is typically smaller than 0.6 pN, showing a non-monotonous temperature dependence with a slight increase near the transition to the twist-bend phase. $K_{33}$ depends strongly on the molecular composition. In particular, chiral mixtures that contain the flexible dimer 1'',7''-bis(4-cyanobiphenyl-4'-yl) heptane (CB7CB) and rod-like molecules such as pentylcyanobiphenyl (5CB) show a $K_{33}$ value that is 5 times smaller than $K_{33}$ of pure CB7CB or of mixtures of CB7CB with chiral dopants. Furthermore, $K_{33}$ in CB11CB doped with a chiral agent is noticeably smaller than $K_{33}$ in a similarly doped CB7CB which is explained by the longer flexible link in CB11CB. The proposed technique allows a direct in-situ determination of how the molecular composition, molecular structure and molecular chirality affect the elastic properties of chiral liquid crystals.
Unique electro-optical properties of the oblique helicoidal cholesteric (ChOH) stem from its heliconical director structure. An applied electric field preserves the single harmonic modulation of the director while tuning the ChOH period and the corresponding Bragg peak wavelength within a broad spectral range. We use the response of ChOH to the electric field to measure the elastic constants of twist K22 and bend K33 directly in the cholesteric phase. The temperature dependencies of K22 and K33 allow us to determine the range of the electric tunability of the ChOH pitch and the heliconical ang…
Selective reflection of light by oblique helicoidal cholesteric (ChOH) can be tuned in a very broad spectral range by an applied electric field. In this work, we demonstrate that the peak wavelength of the selective reflection can be controlled by surface alignment of the director in sandwich cells. The peak wavelength is blue-shifted when the surface alignment is perpendicular to the bounding plates and red-shifted when it is planar. The effect is explained by the electric field redistribution within the cell caused by spatially varying heliconical ChOH structure. The observed phenomenon can …
Cholesteric liquid crystals with helicoidal molecular architecture are known for their ability to selectively reflect light with the wavelength that is determined by the periodicity of molecular orientations. Here we demonstrate that by using a cholesteric with oblique helicoidal(heliconical) structure, as opposed to the classic right-angle helicoid, one can vary the wavelength of selectively reflected light in a broad spectral range, from ultraviolet to visible and infrared (360-1520 nm for the same chemical composition) by simply adjusting the electric field applied parallel to the helicoida…
We investigate the pitch sensitivity of cholesteric phases of helicoidal patchy cylinders as a generic model for chiral (bio-)polymers and helix-shaped colloidal rods. The behaviour of the macroscopic cholesteric pitch is studied from microscopic principles by invoking a simple density functional theory generalised to accommodate weakly twisted director fields. Upon changing the degree of alignment along the local helicoidal director we find that cholesteric phases exhibit a sudden sense inversion whereby the cholesteric phase changes from left- to right-handed and vice versa. Since the local …
Electrically induced reorientation of liquid crystals (LCs) is a fundamental phenomenon widely used in modern technologies. We observe experimentally an electro-optic effect in a cholesteric LC with a distinct oblique-helicoidal director deformation. The oblique helicoid, predicted in late 1960-ies, is made possible by recently developed dimer materials with an anomalously small bend elastic constant. Theoretical, numerical, and experimental analysis establishes that both the pitch and the cone angle of the oblique helicoid increase as the electric field decreases. At low fields, the oblique h…
Certain nematic liquid crystals, e.g., those formed by banana-shaped molecules, can exhibit a low-temperature twist-bend nematic (Ntb) phase. Upon addition of chiral dopants, a chiral version of the twist-bend phase (N*tb) can be observed below the conventional chiral nematic (N*) phase, while under electric field the N* phase is transformed into a specific state known as "heliconical cholesteric". In this work, we have studied the well-known Ntb-forming system CB7CB:CB6OCB with addition of 5CB and chiral dopants (ChD) using optical microscopy, differential scanning calorimetry (DSC), and meas…
A novel light-sensitive chiral dopant ChD-3816 (an azo compound containing 4-hexanoyloxyphenyl and 2-isopropyl-5-methylcyclohexylbenzoate moieties) was used for inducing helical twisting in Ntb-forming mixtures of CB7CB/CB6OCB with 5CB added to decrease the phase transition temperatures. The effects of ChD-3816 upon phase transition temperatures, as well as effects of its concentration on the measured values of helical twisting were determined. Most of the measured parameters could be varied due to light-induced trans-cis isomerization of ChD-3816. Under electric field, selective reflection sp…
Handedness of the director twist in cholesteric liquid crystals is commonly assumed to be the same throughout the medium, determined solely by the chirality of constituent molecules or chiral additives, albeit distortions of the ground-state helicoidal configuration often arise due to the effects of confinement and external fields. We directly probe the twist directionality of liquid crystal director structures through experimental three-dimensional imaging and numerical minimization of the elastic free energy and show that spatially localized regions of handedness opposite to that of the chir…
Blue phases of cholesteric liquid crystals offer a spectacular example of naturally occurring disclination line networks. Here we numerically solve the hydrodynamic equations of motion to investigate the response of three types of blue phases to an imposed Poiseuille flow. We show that shear forces bend and twist and can unzip the disclination lines. Under gentle forcing the network opposes the flow and the apparent viscosity is significantly higher than that of an isotropic liquid. With increased forcing we find strong shear thinning corresponding to the disruption of the defect network. As t…
Most theoretical descriptions of lyotropic cholesteric liquid crystals to date focus on homogeneous systems in which the rod concentration, as opposed to the rod orientation, is uniform. In this work, we build upon the Onsager-Straley theory for twisted nematics and study the effect of weak concentration gradients, generated by some external potential, on the cholesteric twist. We apply our theory to chiral nematics of nanohelices in which the supramolecular helix sense is known to spontaneously change sign upon variation of particle concentration, passing through a so-called compensation poin…
We study elastic interactions between colloidal particles and deformation landscapes of undulations in a cholesteric liquid crystal under an electric field applied normal to cholesteric layers. The onset of undulation instability is influenced by the presence of colloidal inclusions and, in turn, layers' undulations mediate the spatial patterning of particle locations. We find that the bending of cholesteric layers around a colloidal particle surface prompts the local nucleation of an undulations lattice at electric fields below the well-defined threshold known for liquid crystals without incl…
We present an investigation of the phase diagram of cholesteric liquid crystals within the framework of Landau - de Gennes theory. The free energy is modified to incorporate all three Frank elastic constants and to allow for a temperature dependent pitch in the cholesteric phase. It is found that the region of stability of the cubic blue phases depends significantly on the value of the elastic constants, being reduced when the bend elastic constant is larger than splay and when twist is smaller than the other two. Most dramatically we find a large increase in the region of stability of blue ph…
Cholesteric Liquid Crystals (CLCs), subject to externally applied magnetic fields and confined between two parallel planar surfaces with strong homeotropic anchoring conditions, are found to undergo transitions to different types of helicoidal configurations with disclinations. Analytical and numerical studies are performed in order to characterise their properties. In particular, we produce a phase diagram for the transitions from the nematic state to the helicoidal phases in terms of the molecular chirality and the strength of the applied magnetic field.
Building a general theoretical framework to describe the microscopic origin of macroscopic chirality in (colloidal) liquid crystals is a long-standing challenge. Here, we combine classical density functional theory with Monte Carlo calculations of virial-type coefficients, to obtain the equilibrium cholesteric pitch as a function of thermodynamic state and microscopic details. Applying the theory to hard helices, we observe both right- and left-handed cholesteric phases that depend on a subtle combination of particle geometry and system density. In particular, we find that entropy alone can ev…
Heliconical cholesteric liquid crystals are expected to be more sensitive to torque induced by light field since their structure allows both bend and twist in molecular orientations, differently from the conventional cholesterics in which only twist deformation is involved, requiring much higher fields. We report here a demonstration of tuning the helical pitch in heliconical cholesterics induced by an optical torque. Experimental observations are in agreement with expectations of the classical theory extended to include the effect of the optical field. A dual control of the helical pitch is a…
We describe the occurence and properties of liquid crystal phases showing two dimensional splay and bend distortions which are stabilised by flexoelectric interactions. These phases are characterised by regions of locally double splayed order separated by topological defects and are thus highly analogous to the blue phases of cholesteric liquid crystals. We present a mean field analysis based upon the Landau--de Gennes Q-tensor theory and construct a phase diagram for flexoelectric structures using analytic and numerical results. We stress the similarities and discrepancies between the cholest…
Dielectric spectroscopy of a twist bend nematic phase of an achiral bent core liquid crystalline compound under DC bias is used to investigate its response to electric field. Two collective relaxation processes are revealed, these are assigned to distortions of helicoidal structure by the external bias field. Frequency of the mode depends primarily on the helicoidal angle and has anomalous, softening- like behaviour at the nematic to the twist bend nematic transition. A coupling of dielectric anisotropy with electric field gives rise to a new equilibrium periodic structure in the time scale in…
We theoretically investigate the pitch of lyotropic cholesteric phases composed of slender rods with steric chirality transmitted via a weak helical deformation of the backbone. In this limit, the model is amenable to analytical treatment within Onsager theory and a closed expression for the pitch versus concentration and helical shape can be derived. Within the same framework we also briefly review the possibility of alternative types of chiral order, such as twist-bend or screw-like nematic phases, finding that cholesteric order dominates for weakly helical distortions. While long-ranged or …
This article re-examines a classic question in liquid-crystal physics: What are the elastic modes of a nematic liquid crystal? The analysis uses a recent mathematical construction, which breaks the director gradient tensor into four distinct types of mathematical objects, representing splay, twist, bend, and a fourth deformation mode. With this construction, the Oseen-Frank free energy can be written as the sum of squares of the four modes, and saddle-splay can be regarded as bulk rather than surface elasticity. This interpretation leads to an alternative way to think about several previous re…
We present a comprehensive set of measurements of optical, dielectric, diamagnetic, elastic and viscous properties in the nematic (N) phase formed by a liquid crystalline dimer. The studied dimer, 1,7-bis-4-(4-cyanobiphenyl) heptane (CB7CB), is composed of two rigid rod-like cyanobiphenyl segments connected by a flexible aliphatic link with seven methyl groups. CB7CB and other nematic dimers are of interest due to their tendency to adopt bent configurations and to form two states possessing a modulated nematic director structure, namely, the twist bend nematic, NTB, and the oblique helicoidal …
