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 the pitch of the $\rm N_{tb}$ phase. For a material with positive magnetic susceptibility anisotropy, when the magnetic field $\bf{H}$ is parallel to the helical axis, $\bf{t}$, the field modifies the coupling parameter between the director and the helical axis, thus shifting the interval of values for which this coupling results in the $\rm N_{tb}$ phase. If $\bf{H}$ is perpendicular to $\bf{t}$, it is shown that the pitch of the nematic director $\bf n$ precession increases with $\bf{H}$, and at a critical value of $H_c$ it becomes infinite as in a cholesteric liquid crystal, that is, one gets a uniform orientation of n. Our results include the behaviour of a cholesteric under field as a limiting case.
We apply the minimum energy paths (MEPs) approach to study the helix unwinding transition in chiral nematic liquid crystals. A mechanism of the transition is determined by a MEP passing through a first order saddle point on the free energy surface. The energy difference between the saddle point and the initial state gives the energy barrier of the transition. Two starting approximations for the paths are used to find the MEPs representing different transition scenarios: (a) the director slippage approximation with in-plane helical structures; and (b) the anchoring breaking approximation that i…
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…
Mesogenic dimers in the twist-bend nematic phase exhibit much higher flexoelectric polarization than in their uniform nematic phase. In order to theoretically investigate this data, we extend the symmetry based linear elastic theory of the twist-bend nematic phase developed in Phys. Rev. E 92, 030501(R) 2015, by including flexoelectricity under the action of an external electric field perpendicular to the helical axis. We show that at the nematic towards twist-bend nematic transition, a new flexoelectric mode becomes active. Consequently, the present model predicts the increase of the effectiv…
While twist-bend nematic phases have been extensively studied, the experimental observation of two dimensional, oscillating splay-bend phases is recent. We consider two theoretical models that have been used to explain the formation of twist-bend phases -- flexoelectricity and bond orientational order -- as mechanisms to induce splay-bend phases. Flexoelectricity is a viable mechanism, and splay and bend flexoelectric couplings can lead to splay-bend phases with different modulations. We show that while bond orientational order circumvents the need for higher order terms in the free energy, th…
The critical behavior at the transition from uniform nematic to twist-bend modulated nematic phase is revealed and shown to be well explained by the mean field approximation. The study was performed on a group of materials that exhibit an unusually broad temperature range of the nematic phase above the twist-bend modulated nematic phase, so the critical range in which the order parameter fluctuations are strong and can be experimentally observed is wide. The formation of instantaneous helices is observed already several degrees above the transition temperature, strongly influencing the birefri…
We describe the geometry of bend distortions in twist-bend nematic liquid crystals in terms of their fundamental degeneracies, which we call $β$ lines. These represent a new class of line-like topological defect. We use them to construct and characterise novel structures, including grain boundary and focal conic smectic-like defects, Skyrmions, and knotted merons. We analyse their local geometry and global structure, showing that their intersection with any surface is twice the Skyrmion number. Finally, we demonstrate how arbitrary knots and links can be created and describe them in terms of m…
The twist-bend nematic phase (NTB) is characterized by a conically twisting director and by a dramatic softening of the bend elastic constant before the transition to NTB phase. In the recently found splay nematic phase (NS) the splay elastic constant tends to zero, resulting in a splay modulation perpendicular to the director. We model both phases with a single Q-tensor free energy including a term that breaks the degeneracy between the splay and bend elastic constant, and a flexoelectric term coupling the divergence of the Q-tensor with polarization. NTB or NS phase is obtained by a change o…
Nematic twist--bend is the fifth nematic phase recognized in nature. This phase exhibits spiral orientational order, thus it is a chiral structure and it can be stabilized in systems composed of achiral molecules. The microscopic origin of this spontaneous chiral symmetry breaking is to a large extent unknown but phenomenologically it appears stabilized by assuming coupling between steric polar and orientational orderings. Understanding of how external fields affect the stability of this phase is of great intellectual interest and of relevance to potential applications. Within mesoscopic Landa…
Spontaneous formation of polarization gratings by liquid crystals made of bent dimeric molecules is reported. The grating is formed within the temperature range of the twist bend modulated nematic phase, NTB, without the necessity to pattern the cell surfaces, therefore the modulated nematic phase is a promising candidate for low-cost modulators and beam steering devices, the polarization properties of which can be tuned by temperature. In addition, the study of the diffracted light properties turns out to be a sensitive measuring technique for determination of the 3D spatial variation of the …
We review the physics underlying Meyer's conjecture of how macroscopic-scale twist and bend conspire within the Frank-Oseen elasticity theory of nematics to create a heliconical arrangement of the uniaxial, apolar nematic director, the so-called "twist bend nematic" $\rm N_{TB}$. We show that since 2011 a second, lower-temperature nematic phase observed in odd methylene-linked cyanobiphenyl dimers discovered by Toriumi and called $\rm N_X$, has been incorrectly identified as $\rm N_{TB}$. Moreover, as more quantitative data on the $\rm N_X$ emerged, Meyer's simple prediction has been distorted…
Recently, Tavarone et al. (J. Chem. Phys. 143, 114505 (2015)) discussed phase behavior of zig-zag and bow-shaped particles composed of three needles. The authors presented very interesting results of extensive Monte Carlo simulations with periodic boundary conditions in the constant-NVT and the constant-NPT ensembles. In addition to isotropic, nematic, and smectic phases, they identified a modulated nematic, which is actually the nematic splay-bend phase ($N_{SB}$), long-anticipated for bent-core systems (Europhys. Lett. 56, 247 (2001)). They also described isotropic-nematic and nematic-smecti…
Confinement Reveals Hidden Splay-Bend Order in Twist-Bend Nematics
Institute of Theoretical Physics and Mark Kac Center for Complex Systems Research, Jagiellonian University（雅盖隆大学理论物理研究所与马克·卡克复杂系统研究中心）；International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SKCM²), Hiroshima University（广岛大学缠绕手性超物质可持续发展国际研究所）
In this paper, the two-dimensional pure bending of a hyperelastic substrate coated by a nematic liquid crystal elastomer (abbreviated as NLCE) is studied within the framework of nonlinear elasticity. The governing system, arising from the deformational momentum balance, the orientational momentum balance and the mechanical constraint, is formulated, and the corresponding exact solution is derived for a given constitutive model. It is found that there exist two different bending solutions. In order to determine which the preferred one is, we compare the total potential energy for both solutions…
The nonlinear elastic properties of nematic liquid crystals have acquired new interest with the recent experimental observation of bulk modulated nematic phases which are composed by achiral molecules. We extend the Oseen-Zocher-Frank's elastic theory for nematic liquid crystals by including gradients of the nematic strain tensor in the elastic deformation energy. The invariants of the elastic tensor fields, up to the fourth order in the nematic director spatial derivatives, are calculated. An alternative approach that consists in the extension of the linear elastic energy to higher powers of …
We study the flow behaviour of a twist-bend nematic $(N_{TB})$ liquid crystal. It shows three distinct shear stress ($σ$) responses in a certain range of temperatures and shear rates ($\dotγ$). In Region-I, $σ\sim\sqrt{\dotγ}$, in region-II, the stress shows a plateau, characterised by a power law $σ\sim{\dotγ}^α$, where $α\sim0.1-0.4$ and in region-III, $σ\sim\dotγ$. With increasing shear rate, $σ$ changes continuously from region-I to II, whereas it changes discontinuously with a hysteresis from region-II to III. In the plateau (region-II), we observe a dynamic stress fluctuations, exhibitin…
We propose an extension of Frank-Oseen's elastic energy for bulk nematic liquid crystals which is based on the hypothesis that the fundamental deformations allowed in nematic liquid crystals are splay, twist and bend. The extended elastic energy is a fourth order form in the fundamental deformations. The existence of bulk spontaneous modulated or deformed nematic liquid crystal ground states is investigated. The analysis is limited to bulk nematic liquid crystals in the absence of limiting surfaces and/or external fields. The non deformed ground state is stable only when Frank-Oseen's elastic …
The understanding of self-organization in the twist-bend nematic $(N_\text{TB})$ phase, identified in 2011 in liquid crystal dimers, is at the forefront of soft matter research worldwide. This new nematic phase develops structural chirality in the isotropic $(I)$ and the uniaxial nematic $(N_\text{U})$ phases, despite the fact that the molecules forming the structure are chemically achiral. Molecular, shape-induced flexopolarization provides a viable mechanism for a qualitative understanding of $N_\text{TB}$ and the related phase transitions. The key question that remains is whether with this …
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…
The twist-bend nematic (Ntb) phase is a recent addition to the nematic (N) phases of liquid crystals (LCs). A net polar order in the Ntb phase under an external electric field was predicted in several recent theoretical studies but yet to be experimentally realized. We investigated the polar nature, dielectric properties, electro-optical switching and optical transmission properties of a bent LC dimer CB7CB. The LC showed a relatively high-temperature nematic (N) phase and a lower-temperature nematic (NX) phase (also called Ntb in literature). A threshold-dependent polarization current respons…
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…
Infrared spectroscopy (IR) and quantum chemistry calculations, based on density functional theory (DFT) were used to study the structure and the molecular interactions in the nematic (N) and twist-bend (NTB) phases of thioether-linked dimers. Infrared absorbance measurements were conducted in a polarized beam for homogeneously aligned samples to measure and understand the orientation of the vibrational transition dipole moments in the liquid crystal states. Revealing temperature-dependent changes in the mean IR absorbance in the twist-bend nematic phase were observed. In the transition from th…
In twist-bend nematic (N\textsubscript{TB}) liquid crystals (LCs), the mean molecular orientation exhibits heliconical structure with nanoscale periodicity. On the mesoscopic scale, N\textsubscript{TB} resembles layered systems (like smectics), where the helical pitch is equivalent to "pseudo-layers" without a true mass density wave. We study rheological properties of a N\textsubscript{TB} phase and compare the results with those of an usual SmA phase. Analysing the shear response and adapting a simplified physical model for rheology of defect mediated lamellar systems we measure the pseudo-la…
The dielectric spectra of the twist bend nematic phase of the bent shaped achiral liquid crystal dimer are studied for the determination of the different relaxation modes. The two molecular processes were assigned one to the precessional rotation of the longitudinal components of the cyanobiphenyl groups and the second to the spinning rotation of the transverse component of the dimer. The low frequency peak shows a peculiar temperature behavior at the twist bend nematic to nematic transition. This peak can be assigned to a collective fluctuation of the tilt angle of the coarse grained director…
In this work we present a simple qualitative model to describe shear rheological behavior of the twist-bend nematic liquid crystals. We find that at relatively low shear rate the effective viscosity decreases with the shear rate manifesting so-called shear-thinning phenomenon. At intermediate shear rate the stress is almost independent of the shear rate (a sort of plateau), and at large shear rate Newtonian rheology takes place. Within our theory we estimate the critical values of the shear rate in terms of coarse grained shear viscosity coefficients of the effective smectics equivalent to the…
We demonstrate that nature has produced a close-packed helical twisted filamentous material in the biomineralization of the mollusc. In liquid crystals, twist-bend nematics have been predicted and observed. We present and analyse evidence that the helical biomineral microstructure of mollusc shells may be formed from such a liquid-crystal precursor.
Characterization of the sub-micrometer hierarchy levels in the twist-bend nematic phase with nanometric helices via photopolymerization. Explanation for the sign reversal in the polar response
We have numerically studied a liquid composed of achiral, bent-shaped molecules built of tangent spheres. The system is known to spontaneously break mirror symmetry, as it forms a macroscopically chiral, twist-bend nematic phase [Phys. Rev. Lett. 115, 147801 (2015)]. Here, we have examined the full phase diagram of such liquid and observed several phases characterized by orientational and/or translational ordering of molecules. Apart from conventional nematic, smectic A, and the above-mentioned twist-bend nematic phase, we have identified antiferroelectric smectic A phase. For large densities …
