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 achieved including both the low-frequency electric field applied along the helix axis and the optical field orthogonal to it.
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…
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…
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 …
We experimentally study how the cholesteric pitch, $P$, depends on the equilibrium one, $P_0$, in planar liquid crystal (LC) cells with both strong and semistrong anchoring conditions. The cholesteric phase was induced by dissolution in the nematic LC the right-handed chiral dopant 7-DHC (7-dehydrocholesterol, provitamin $D_3$) which transforms to left-handed tachysterol under the action of UV irradiation at the wavelength of 254 nm. By using the model of photoreaction kinetics we obtain dependencies of isomers concentrations and thus the equilibrium pitch on UV irradiation dose. The cholester…
A series of asymmetric dimers with an odd number of atoms in the spacer were found to form different types of twisted structures despite being achiral. The formation of a variety of helical structures is accompanied by a gradual freezing of molecular rotation. The tight pitch heliconical nematic (NTB) phase and heliconical tilted smectic C (SmCTB) phase are formed. In the lowest temperature smectic phase, HexI, the twist is expressed through the formation of hierarchical structure: nano-scale helices and mesoscopic helical filaments. The short pitch helical structure in smectic phases is confi…
Resonant x-ray scattering shows that the bulk structure of the twist-bend liquid crystal phase, recently discovered in bent molecular dimers, has spatial periodicity without electron density modulation, indicating a lattice-free heliconical nematic precession of orientation that has helical glide symmetry. In situ study of the bulk helix texture for the dimer CB7CB shows an elastically-confined temperature-dependent minimum helix pitch, but a remarkable elastic softness of pitch in response to dilative stresses. Scattering from the helix is not detectable in the higher temperature nematic phas…
Many nanoparticle-based chiral liquid crystals are composed of polydisperse rod-shaped particles with considerable spread in size or shape, affecting the mesoscale chiral properties in, as yet, unknown ways. Using an algebraic interpretation of Onsager-Straley theory for twisted nematics, we investigate the role of length polydispersity on the pitch of nanorod-based cholesterics with a continuous length polydispersity, and find that polydispersity enhances the twist elastic modulus, $K_{2}$, of the cholesteric material without affecting the effective helical amplitude, $K_{t}$. In addition, fo…
The nanostructure of two novel sulfur containing dimer materials has been investigated experimentally by hard and by resonant tender X-ray scattering techniques. On cooling the dimers through the nematic to twist-bend nematic (N-NTB) phase transition, the correlation length associated with short-range positional order drops, while the heliconical orientational order becomes more correlated. The heliconical pitch shows a stronger temperature dependence near the N-NTB transition than observed in previously studied dimers, such as the CBnCB series of compounds. We explain both this strong variati…
We present a microscopic analysis of the instability of the nematic phase to chirality when molecular chirality is introduced perturbatively. We show that previously neglected short-range biaxial correlations play a crucial role in determining the cholesteric pitch. We propose an order parameter which quantifies the chirality of a molecule.
We have written expressions for the free energy of a cholesteric liquid crystal in an approximation using the elasticity constants K_1, K_2, K_3 and the energy variation and the corresponding energy and energy gradient along the direction of the director vector n at each lattice point for the lattice model. A feature of this lattice model is the shift of the n components in space relative to each other. An assessment has been made of the error associated with the respective substitution. Such an approach can increase the accuracy of calculations of the energy and dynamics of localized states i…
Solids with spatially varying photonic structure offer gaps to light of a wider range of frequencies than do simple photonic systems. We solve numerically the field distribution in a solid cholesteric with a linearly varying inverse pitch (helical wavevector) using equations we derive for the general case. The simple idea that the position where the Bragg condition is locally satisfied is where reflection takes place is only true in part. Here, reflection is due to a region where the waves are forced to become evanescent, and the rate of variation of structure determines over which distance th…
We report measurements of the cholesteric pitch and twist elastic constant $(K_{22})$ in monodisperse suspensions of the rod-like virus filamentous bacteriophage {\it fd}. Measurements were taken for concentrations spanning the entire cholesteric region at several ionic strengths and temperatures. In the limit of high ionic strength the cholesteric pitch $(P_0)$ scales with concentration (c) as $P_0 \propto c^{-1.66}$. As the ionic strength decreases the scaling exponent systematically changes to lower values.
We consider the interaction potential between two chiral rod-like colloids which consist of a thin cylindrical backbone decorated with a helical charge distribution on the cylinder surface. For sufficiently slender coiled rods a simple scaling expression is derived which links the chiral `twisting' potential to the intrinsic properties of the particles such as the coil pitch, charge density and electrostatic screening parameter. To predict the behavior of the macroscopic cholesteric pitch we invoke a simple second-virial theory generalized for weakly twisted director fields. While the handedne…
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…
We have investigated the relationship between the morphology of helical particles and the features of the cholesteric (N$^\ast $) phase that they form. Using an Onsager-like theory, applied to systems of hard helices, we show that the cholesteric handedness and pitch depend on both the pitch and the curliness of the particles. The theory leads to the definition of pseudoscalars that correlate the helical features of the phase to the chirality of the excluded volume of the constituent particles.
We present a generalized van der Waals theory for a lyotropic cholesteric system of chiral spherocylinders based on the classical Onsager theory for hard anisometric bodies. The rods consist of a hard spherocylindrical backbone surrounded with a square-well potential to account for attractive (or soft repulsive) interactions. Long-ranged chiral interactions are described by means of a simple pseudo-scalar potential which is appropriate for weak chiral forces of a predominant electrostatic origin. Based on the formalism proposed by Straley [Phys. Rev. A {\bf 14}, 1835 (1976)] we derive explicit…
The upper critical temperature Tc2 for the phase transition between the Cholesteric phase (N*) and the Twist Grain Boundary C phase with the layer inclination tilted to the pitch axis (TGBct) in thermotropic liquid crystals is determined by the mean field Chen-Lubensky approach. We show that the N*-TGBct phase transition is split in two with the appearance of either the TGBA or the TGB2q phase in a narrow temperature interval below Tc2. The latter phase is novel in being superposed from two degenerate TGBct phases with different (left and right) layers inclinations to the pitch axis.
Cholesteric liquid crystals (CLCs) have a characteristic length scale given by the pitch of the twisted stacking of their constituent rod-like molecules. Under homeotropic anchoring conditions where the molecules prefer to orient perpendicular to an interface, cholesteric interfaces exhibit striped phases with stripe widths commensurate with the pitch. Conversely, planar anchoring conditions have the molecules remain in the plane of the interface so that the CLC twists perpendicular to it. Recent work [L. Tran et al. Phys. Rev. X 7, 041029 (2017)] shows that varying the anchoring conditions dr…
The chiral, heliconical (twist-bend) nematic ground state is reported in an achiral, rigid, bent-core mesogen (UD68). Similar to the nematic twist-bend (NTB) phase observed in bent molecular dimers, the NTB phase of UD68 forms macroscopic, smectic-like focal-conic textures and exhibits nanoscale, periodic modulation with no associated modulation of the electron density, i.e., without a detectable lamellar x-ray reflection peak. The NTB helical pitch is pTB ~ 14 nm. When an electric field is applied normal to the helix axis, a weak electroclinic effect is observed, revealing 50 um-scale left- a…
Active elastomeric liquid crystal particles with initial cylindrical shapes are obtained by means of soft lithography and polymerization in a strong magnetic field. Gold nanocrystals infiltrated into these particles mediate energy transfer from laser light to heat, so that the inherent coupling between the temperature-dependent order and shape allows for dynamic morphing of these particles and well-controlled stable shapes. Continuous changes of particle shapes are followed by their spontaneous realignment and transformations of director structures in the surrounding cholesteric host, as well …
The application of a sufficiently strong strain perpendicular to the pitch axis of a monodomain cholesteric elastomer unwinds the cholesteric helix. Previous theoretical analyses of this transition ignored the effects of Frank elasticity which we include here. We find that the strain needed to unwind the helix is reduced because of the Frank penalty and the cholesteric state becomes metastable above the transition. We consider in detail a previously proposed mechanism by which the topologically stable helical texture is removed in the metastable state, namely by the nucleation of twist disclin…
General symmetry arguments, dating back to de Gennes dictate that at scales longer than the pitch, the low-energy elasticity of a chiral nematic liquid crystal (cholesteric) and of a Dzyaloshinskii-Morya (DM) spiral state in a helimagnet with negligible crystal symmetry fields (e.g., MnSi, FeGe) is identical to that of a smectic liquid crystal, thereby inheriting its rich phenomenology. Starting with a chiral Frank free-energy (exchange and DM interactions of a helimagnet) we present a transparent derivation of the fully nonlinear Goldstone mode elasticity, which involves an analog of the Ande…
When a chiral isotropic elastomer is brought to low temperature cholesteric phase, the nematic degree of freedom tends to order and form a helix. Due to the nemato-elastic coupling, this also leads to elastic deformation of the polymer network that is locally coaxial with the nematic order. However, the helical structure of nematic order is incompatible with the energetically preferred elastic deformation. The system is therefore frustrated and appropriate compromise has to be achieved between the nematic ordering and the elastic deformation. For a strongly chiral elastomer whose pitch is much…
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 …
We propose a construction of a cholesteric pitch axis for an arbitrary nematic director field as an eigenvalue problem. Our definition leads to a Frenet-Serret description of an orthonormal triad determined by this axis, the director, and the mutually perpendicular direction. With this tool we are able to compare defect structures in cholesterics, biaxial nematics, and smectics. Though they all have similar ground state manifolds, the defect structures are different and cannot be, in general, translated from one phase to the other.
Recent numerical simulations of hard helical particle systems unveiled the existence of a novel chiral nematic phase, termed screw-like, characterised by the helical organization of the particle C$_2$ symmetry axes round the nematic director with periodicity equal to the particle pitch. This phase forms at high density and can follow a less dense uniform nematic phase, with relative occurrence of the two phases depending on the helix morphology. Since these numerical simulations were conducted under three-dimensional periodic boundary conditions, two questions could remain open. Firstly, the r…
The extended Frank elastic energy density is used to investigate the existence of a stable periodically modulate structure that appears as a ground state exhibiting a twist-bend molecular arrangement. For an unbounded sample, we show that the twist-bend nematic phase $N_{TB}$ is characterized by a heliconical structure with a pitch in the nano-metric range, in agreement with experimental results. For a sample of finite thickness, we show that the wave vector of the stable periodic structure depends not only on the elastic parameters but also on the anchoring energy, easy axis direction, and th…
We study cholesteric order in liquid crystal shells with planar degenerate anchoring. We observe that the bipolar and radial configurations intensively reported for bulk droplets have a higher degree of complexity when the liquid crystal is confined to a spherical shell. The bipolar configuration is replaced by a structure where the boojums are linked to a stack of disclination rings that spans the shell, while the radial configuration exhibits a double helix structure where two disclinations wind around each other. Our results confirm recent numerical simulations and highlight the complexity …
We study the problem of a cholesteric liquid crystal confined to an elliptical channel. The system is geometrically frustrated because the cholesteric prefers to adopt a uniform rate of twist deformation, but the elliptical domain precludes this. The frustration is resolved by deformation of the layers or introduction of defects, leading to a particularly rich family of equilibrium configurations. To identify the solution set, we adapt and apply a new family of algorithms, known as deflation methods, that iteratively modify the free energy extremisation problem by removing previously known sol…
Cholesteric elastomers possess a macroscopic ``phase chirality'' as the director n rotates in a helical fashion along an optical axis $z$ and can be described by a chiral order parameter. This parameter can be tuned by changing the helix pitch p and/or the elastic properties of the network. The cholesterics also possess a local nematic order, changing with temperature or during solvent swelling. In this paper, by measuring the power of optical rotation, we discover how these two parameters vary as functions of temperature or solvent adsorbed by the network. The main result is a finding of pron…
We study the phase diagram of director structures in cholesteric liquid crystals of negative dielectric anisotropy in homeotropic cells of thickness d which is smaller than the cholesteric pitch p. The basic control parameters are the frustration ratio d/p and the applied voltage U. Fluorescence Confocal Polarising Microscopy allows us to directly and unambiguously determine the 3-D director structures. The results are of importance for potential applications of the cholesteric structures, such as switchable gratings and eyewear with tunable transparency based.
In a nematic gel, the appearance of nematic order is accompanied by a spontaneous elongation of the gel parallel to the nematic director. If such a gel is made chiral, it has a tendency to form a cholesteric helical texture, in which local elongation of the gel parallel to the nematic director is suppressed due to the requirement of elastic compatibility. We show that a conical helix in which the director makes an oblique angle with respect to the helix axis serves as an energy minimizing compromise between the competing tendencies for elongation and twisting. We find the dependence of the hel…
We describe the basic properties and consequences of introducing active stresses, with principal direction along the local director, in cholesteric liquid crystals. The helical ground state is found to be linearly unstable to extensile stresses, without threshold in the limit of infinite system size, whereas contractile stresses are hydrodynamically screened by the cholesteric elasticity to give a finite threshold. This is confirmed numerically and the non-linear consequences of instability, in both extensile and contractile cases, are studied. We also consider the stresses associated to defec…
The confinement of liquid crystals inside curved geometries leads to exotic structures, with applications ranging from bio-sensors to optical switches and privacy windows. Here we study how curvature affects the alignment of a cholesteric liquid crystal. We model the system on the mesoscale using the Landau-de Gennes model. Our study was performed in three stages, analysing different curved geometries from cylindrical walls and pores, to toroidal domains, in order to isolate the curvature effects. Our results show that the stresses introduced by the curvature influence the orientation of the l…
We investigate the statistical mechanics of chirality and biaxiality in liquid crystals through a variety of theoretical approaches, including Monte Carlo simulations, lattice mean-field theory, and Landau theory. All of these calculations show that there is an important interaction between cholesteric twist and biaxial order: The twist acts as a field on the biaxial order, and conversely, the biaxial order increases the twist, i.e. reduces the pitch. We model the behavior of chiral biaxial liquid crystals as a function of temperature, and discuss how the predictions can be tested in experimen…
Stiff, elongated biomolecules such as filamentous viruses, DNA or cellulose nanocrystals are known to form liquid crystals often exhibiting a helical supramolecular organization. Little is known about the microscopic origin, size and handedness of the helical pitch in these, so-called cholesteric phases. Experimental observations in chiral lyotropics suggest that long-ranged chiral forces of electrostatic origin acting between the mesogens are responsible for such organization. Using large-scale computer simulation we study the sensitivity of the pitch imparted by soft microscopic helices and …
We examine the influence of bidirectional anchoring on the unwinding of a planar cholesteric liquid crystal induced by the application of a magnetic field. We consider a liquid crystal layer confined between two plates with the helical axis perpendicular to the substrates. We fixed the director twist on one boundary and allow for bidirectional anchoring on the other by introducing a high-order surface potential. By minimizing the total free energy for the system, we investigate the untwisting of the cholesteric helix as the liquid crystal attempts to align with the magnetic field. The transiti…
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 …
Periodic structures of phases with orientational order of molecules, but homogenous electron density distribution: a short pitch cholesteric, blue phase and twist-bend nematic phase, were probed by a resonant soft x-ray scattering (RSoXS) at the carbon K-edge. The theoretical model shows that in case of a simple heliconical nematic structure two resonant signals corresponding to the full and half pitch band should be present, while only the full pitch band is observed in experiment. This suggests that the twist-bend nematic phase has complex structure with a double-helix, built of two interloc…
We consider a Lebwohl-Lasher model of chiral particles confined in a planar cell (slit pore) with different boundary conditions, and solve it using mean-field theory. The phase behaviour of the system with respect to temperature and pore width is studied. Two phenomena are observed: (i) an isotropic-cholesteric transition which exhibits an oscillatory structure with respect to pore width, and (ii) an infinite set of winding transitions caused by commensuration effects between cholesteric pitch and pore width. The latter transitions have been predicted and analysed by other authors for choleste…
We consider a one-dimensional variational problem arising in connection with a model for cholesteric liquid crystals. The principal feature of our study is the assumption that the twist deformation of the nematic director incurs much higher energy penalty than other modes of deformation. The appropriate ratio of the elastic constants then gives a small parameter $\varepsilon$ entering an Allen-Cahn-type energy functional augmented by a twist term. We consider the behavior of the energy as $\varepsilon$ tends to zero. We demonstrate existence of the local energy minimizers classified by their o…
The base for this manuscript was laid down by the studies carried out in the article by Senyuk B, et. al. Proceedings of SPIE. 2005; 5936: 59360W-1-9. In the present manuscript, a planar layer of the photosensitive cholesteric, based on the chiral dopant 2-(4'-phenylbenzylidene)-p-menthane-3-one dissolved in the nematic E7, under the alternating electric field was explored. In particular, the influence of UV exposure and the value of the azimuthal anchoring energy on electro- and photoswitching of undulation instabilities was considered. Due to the decrease in a ratio between the LC cell thick…
We study the effects of chirality at the segment scale on the thermodynamics of block copolymer melts using self consistent field theory. In linear diblock melts where segments of one block prefer a twisted, or cholesteric, texture, we show that melt assembly is critically sensitive to the ratio of random coil size to the preferred pitch of cholesteric twist. For weakly-chiral melts (large pitch), mesophases remain achiral, while below a critical value of pitch, two mesocopically chiral phases are stable: an undulated lamellar phase; and a phase of hexagonally-ordered helices. We show that the…
Molecular chirality controls droplet division and helical fiber formation in liquid crystal emulsions
Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学与物理学院）；Condensed Matter Physics Department, Jožef Stefan Institute（约热·斯蒂芬研究所凝聚态物理系）；Dynamics of Complex Fluids, Max Planck Institute for Dynamics and Self-Organization（马克斯·普朗克动力学与自组织研究所复杂流体动力学）；Department of Chemistry, Faculty of Science, Tokyo University of Science（东京理科大学理学部化学系）
We introduce a comprehensive numerical framework to generically infer the emergent macroscopic properties of uniaxial nematic and cholesteric phases from that of their microscopic constituent mesogens. This approach, based on the full numerical resolution of the Poniewierski-Stecki equations in the weak chirality limit, may expediently handle a wide range of particle models through the use of Monte-Carlo sampling for all virial-type integrals. Its predictions in terms of equilibrium cholesteric structures are found to be in excellent agreement with previous full-functional descriptions, thereb…
Telephone-cord patterns have been recently observed in smectic liquid crystal capillaries. In this paper we analyse the effects that may induce them. As long as the capillary keeps its linear shape, we show that a nonzero chiral cholesteric pitch favors the SmA*-SmC* transition. However, neither the cholesteric pitch nor the presence of an intrinsic bending stress are able to give rise to a curved capillary shape. The key ingredient for the telephone-cord instability is spontaneous polarization. The free energy minimizer of a spontaneously polarized SmA* is attained on a planar capillary, char…
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…
We consider helical configurations of a cholesteric liquid crystal (CLC) sandwiched between two substrates with homogeneous director orientation favored at both confining plates. We study the CLC twist wavenumber $q$ characterizing the helical structures in relation to the free twisting number $q_0$ which determines the equilibrium value of CLC pitch, $P_0=2π/q_0$. We investigate the instability mechanism underlying transitions between helical structures with different spiral half-turn numbers. Stability analysis shows that for equal finite anchoring strengths this mechanism can be dominated b…
Liquid crystalline (LC) mixtures of cholesteryl oleyl carbonate (COC) and 4-pentyl-4'-cyanobiphenyl (5CB), as well as dispersions of single-walled carbon nanotubes (NTs) in these mixtures, were studied by means of selective reflection measurements, differential scanning calorimetry (DSC) and optical microscopy. The relative mass of COC in a mixture X was varied between 0.4 and 1.0, the temperature range of measurements was between 284 K and 314 K, and concentration of NTs was fixed at 0.1 %. Two important anomalies were noted: (1) the cholesteric to smectic-A transition temperature increased o…
It is shown that curved and flat helical double twisted liquid crystal (DTLC) in blue phase, can be unstable (stable) depending of the sign, negative (positive) of sectional curvature, depending on the pitch of the helix of the nematic crystal. In both cases Cartan torsion is presented. It is also shown that the instability or stability depends on the value of the pitch of the helix in nematic crystals. Frank energy stability A similar result using the method of Frank energy stability in the twist of cholesteric liquid crystal was given by Kiselev and Sluckin [PRE 71(2005)], where the free twi…
The nematic twist-bend ($\mathrm{N_{TB}}$) phase, exhibited by certain thermotropic liquid crystalline (LC) dimers, represents a new orientationally ordered mesophase -- the first distinct nematic variant discovered in many years. The $\mathrm{N_{TB}}$ phase is distinguished by a heliconical winding of the average molecular long axis (director) with a remarkably short (nanoscale) pitch and, in systems of achiral dimers, with an equal probability to form right- and left-handed domains. The $\mathrm{N_{TB}}$ structure thus provides another fascinating example of spontaneous chiral symmetry break…
The recently discovered twist-bend nematic phase, $\rm N_{tb}$, is a non-uniform equilibrium nematic phase that presents a spontaneous bend with a precession of the nematic director, $\textbf{n}$, on a conical helix with a tilt angle $θ$ and helical pitch $P$. The stability of the $\rm N_{tb}$ phase has been recently demonstrated from the elastic point of view by extending the Frank elastic energy density of the nematic phase to include the symmetry element of helical axis, $\bf t$. In the present communication, we investigate the influence of an external bulk field (magnetic or electric) on t…
