Polar interactions between bent–core molecules as a stabilising factor for inhomogeneous nematic phases with spontaneous bend deformations

ABSTRACT

It is generally accepted that the transition into the twist–bend nematic phase (N_TB) is driven by an elastic instability related to the reduction of the bend elastic constant. Here we use a molecular–statistical theory to show that sufficiently strong polar interactions between bent-shaped molecules may lead to experimentally observed reduction of the bend elastic constant in the nematic phase even if electrostatic dipole–dipole interactions are not taken into account. We propose a simple model of bent–core particles and derive explicit analytical expressions which enable one to understand how polar molecular shape affects the elastic constants, and, in particular, the important role of the bend angle. Numerical graphs showing temperature variations of all elastic constants are also presented including the variation of the bend and splay elastic constants before and after the renormalisation determined by local polar order of molecular steric dipoles and the corresponding polar correction to the one-particle distribution function.     

Elastic constants,viscosity and dielectric properties of bent-core nematic liquid crystals doped with single-walled carbon nanotubes

Single-walled carbon nanotubes (SWCNTs) are dispersed in (4’-fluoro phenyl azo) phenyl-4-yl 3-[N-(4’-n-hecyloxy 2-hydroxybenzylidene)amino]-2-methylbenzoate (6–2M-F) a bent-core nematic (BCN) liquid crystalline medium composed of bent-shaped molecules with short core, reduced bend angle possessing polar fluoro substituent in longitudinal direction and methyl group in bent direction. Such molecules are at the borderline of typical bent-core and rod-like molecules resembling hockey stick shape with intermediate properties. The elastic anisotropy is negative for 6–2M-F (bend elastic constant K₃₃ < splay elastic constant K₁₁); similar to other BCNs reported earlier with smectic-like clusters; but turns to high positive (K₃₃ > K₁₁) value by insertion of SWCNT (concentration ≥0.05 wt.%) in 6–2 M-F. The ratio of K₃₃/K₁₁ becomes comparable to the calamitic liquid crystals (LCs) in doped system. Dielectric anisotropy increases in the nanocomposite implying enhanced nematic ordering due to π–π electron interaction between CNTs and the LC molecules. Threshold voltage at first increases and then decreases with increasing CNT concentration owing to the respective variations in splay viscosity of the system. The present study demonstrated the interaction of SWCNTs with BCN molecules and reveals significant modifications in viscoelastic, dielectric and ionic properties of the host.     

Monte Carlo lattice simulations of the elastic behaviour of nematic liquid crystals

A pairwise additive potential, which approximately reproduces the free energy density for the elastic deformations of a nematic liquid crystal, originally proposed by Gruhn and Hess, has been investigated by simulating the three Freedericksz transitions as well as that of the Schadt-Helfrich cell. The pair potential depends on the three elastic constants K₁, K₂ and K₃ for the splay, twist and bend deformations, respectively. The results of the simulations are compared with the analytical solutions obtained from continuum theory in order to test the accuracy of the model potential at a quantitative level. This comparison is also made for different temperatures to explore the influence of director fluctuations on the elastic behaviour.     

Elastic,dielectric and optical constants of the nematic mixture E49

The Merck nematic mixture E49 exhibits a large nematic interval (0–100 °C) and a large dielectric anisotropy. Both of these features make E49 interesting for applications and basic physics. Unfortunately, no systematic measurements of the material constants of this mixture and their temperature dependence have been reported in the literature. In this paper we report experimental measurements of the splay and bend elastic constants (K ₁₁ and K ₃₃) of the ordinary and the extraordinary refractive indices (n _ort and n _par) at the wavelength λ?=?632.8 nm and of the two elastic constants parallel and orthogonal to the director (ε_par and ε_ort) at the frequency ν?=?5?kHz. The temperature dependence of all of these parameters is found in the temperature range 25–99 °C. The measurements of the elastic constants are performed using both a dielectric and an optical method simultaneously on the same nematic sample. The results obtained using the two methods are in a satisfactory agreement between them within the estimated experimental uncertainty. The ordinary and the extraordinary indices are measured using the prism method.     

Second-harmonic generation and the influence of flexoelectricity in the nematic phases of bent-core oxadiazoles

Second-harmonic generation (SHG) in the nematic phase of bent-core oxadiazole-based liquid crystals (LCs) was studied and compared to that for the rod-like compound 4-cyano-4?-n-octylbiphenyl (8CB). Weak, isotropically scattered second-harmonic (SH) light was observed for all materials, consistent with SHG by nematic director fluctuations. The SH intensity produced by the bent-core materials was found to be up to ~ 3.4 times that of 8CB. We discuss this result in terms of the dependence of SH intensity on temperature, elastic constants and flexoelectric coefficients. We have calculated the latter by using a molecular field approach with atomistic modelling, thus demonstrating how molecular parameters contribute to the flexoelectric coefficients and illustrating the potential of this method for predicting the flexoelectric behaviour of bent-core LCs. We show that the increased SH signal in the bent-core compounds is partly due to their nematic phases being at a much higher temperature, and also potentially due to them having greater flexoelectric coefficients, up to ~1.5 times those of 8CB. These estimates are consistent with reports of increased flexoelectric coefficients in bent-core compounds in comparison to rod-like compounds.     

Determination of elastic constants of a binary system (7CPB+9.CN) showing nematic,induced smectic Ad and re-entrant nematic phases

The temperature variation of the splay and bend elastic constants of a binary system exhibiting nematic-induced smectic A_d and re-entrant nematic phases measured by electric field-induced Freedericksz transition method has been reported. As bend deformation is not permitted in the smectic A phase, bend elastic constant (K₃₃) could only be determined in the nematic and re-entrant nematic phases. In both the nematic phases, the splay elastic constant has the same order of magnitude and does not show any pretransitional effect. However, in the induced smectic A_d phase, the value of K₁₁ is about one to two orders higher than that in the nematic phases. The bend elastic constant shows a strong pretransitional effect near the nematic–smectic and smectic–re-entrant nematic phase transitions. The influence of the presence of the induced smectic phase is observed even in those mixtures which have no induced smectic phases. As the smectic phase is approached, the ratio K₃₃/K₁₁ increases rapidly and diverges to infinity.     

Tunable backflow in chiral nematic liquid crystals via twist-bend nematogens and surface-localised in-situ polymer protrusions

Dynamic electro-optic response of the liquid crystal (LC) director shows a backflow effect that is manifested as an optical bounce in chiral nematic LCs (N*LC) during field-induced homeotropic-twisted transition. The bend elastic constant (K₃₃) strongly influences the dynamics of backflow at the N*LC in homeotropic-twisted transition. The cyanobiphenyl LC dimers – CB7CB, CB9CB and CB11CB – possess a unique characteristic of inherent bend molecular configuration that lowers K₃₃. With the modulation of the effective K₃₃ in dimer-doped N*LCs, we report the tunability of the optical bounce that decreases with the increase in the length of flexible spacers in LC dimers. The doped LC dimers with short spacer lengths not only generate a strong backflow with an enhanced twist degeneracy of the LC director across the cell, but also prolong the time of disappearance of the optical bounce. Furthermore, we demonstrate the suppression of the optical bounce with surface localised polymer protrusions having 50–100 nm diameters, which allow faster dynamic relaxation process and reduced backflow. We envision a novel design of a tunable microfluidic device for precise flow control of organic or inorganic matter in LC medium that exploits the tunable backflow in LC dimer-doped N*LCs.     

Saddle–splay elasticity induced chiral structures in achiral liquid crystals within cylindrical geometry

ABSTRACT

On the basis of Landau–de Gennes theory and the finite-difference iterative method, spontaneous chiral structures in cylinders with degenerate planar boundary conditions are investigated. A double-twist director configuration can be achieved by the saddle–splay contribution, corresponding to the L₂₄ term in Landau–de Gennes theory. The twist angle increases as the radius R of the cylinder is reduced because the curvature of the cylindrical surface becomes larger. Moreover, we find fine structures of the domain walls and point defects between opposite-handed domains. An energy comparison shows that domain walls are the stable state for K₂₄/K> 0.6 (K₁₁ = K₃₃ = K, K₁₁, K₃₃ and K₂₄ are the splay, bend, saddle–splay elastic constants in Frank theory), whereas point defects are the stable state for K₂₄/K< 0.6.     

A Liquid Crystalline Oligomer Exhibiting Nematic and Twist‐Bend Nematic Mesophases

The twist‐bend nematic phase (N_TB) has been described as the structural link between the untilted uniaxial nematic phase (N) and the helical chiral nematic phase (N*). The N_TB phase exhibits phenomena of fundamental importance to science, that is, 1) the spontaneous formation of a helical pitch on the nanometer scale in a fluid and 2) the spontaneous breaking of mirror symmetry, leading to the emergence of chiral domains in an achiral system. In this Communication, we present a study on T4₉ [bis(4‐(9‐(4‐((4‐cyanobenzoyl)oxy)phenyl)nonyl)phenyl) 4,4′‐(nonane‐1,9‐diyl)dibenzoate], a liquid‐crystalline oligomer exhibiting the twist‐bend nematic phase, which has a molecular length that is of comparable dimensions to the sub‐10 nm pitch determined for CB9CB, and provide new insights into the differentiation between the nano‐ and macro‐science for self‐assembling supermolecular systems.     

Effect of a rigid,non-polar solute on the dielectric anisotropy,the splay and bend elastic constants,and on the rotational viscosity coefficient of 4-4′-n-heptylcyanobiphenyl

The effect of mixing a rigid, non-polar, non-mesogenic solute, biphenyl (C₆H₅-C₆H₅), in the nematic solvent 7CB (4,4′-n-heptylcyanobiphenyl) is investigated. The solute is found to reduce the nematic order and a two-phase region appears. We report measurements of the transition temperatures, dielectric anisotropy, and splay and bend elastic constants, as well as the rotational viscosity coefficient by the method of electric field-induced Fréedericksz transition for biphenyl concentrations up to 8.0%.     

Fourth-order nematic elasticity and modulated nematic phases: a poor man’s approach

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 constants are positive. In case where at least one of them is negative, the ground state becomes deformed. The analysis of the stability of the deformed states in the space of the elastic parameters allows to characterise different types of deformed nematic phases. Some of them are new nematic phases, for instance a twist – splay nematic phase is predicted. Inequalities between second-order elastic constants which govern the stability of the twist–bend, splay–bend, and splay–twist states are obtained. Their stability in respect to triple splay–bend–twist deformations is investigated.     

The Chiral Twist-Bend Nematic Phase (N*TB)

The twist-bend nematic, N_TB, phase has been observed for chiral materials in which chirality is introduced through a branched 2-methylbutyl terminal tail. The chiral twist-bend nematic phase, N*_TB, is completely miscible with the N_TB phase of the standard achiral material, CB6OCB. The N*_TB phase exhibits optical textures with lower birefringence than those observed for the achiral N_TB phase, suggesting an additional mechanism of averaging molecular orientations. The N*−N*_TB transition temperatures for the chiral materials are higher than the N_TB−N transition temperatures seen for the corresponding racemic materials. This suggests the double degeneracy of helical twist sense in the phase is removed by the intrinsic molecular chirality. A square lattice pattern is observed in the N* phase over a temperature range of several degrees above the N*_TB–N phase transition, which may be attributed to a non-monotonic dependence of the bend elastic constant.     

Elastic properties of bimesogenic liquid crystals

The second nematic phase found in some bimesogenic liquid crystals with an odd flexible spacer has aroused considerable interest due to many unusual properties exhibited by them. However, the reason for such molecules to exhibit transitions to the modulated phase is still unclear. Dozov [Europhys Lett. 2001;56:247] predicted that negative K ₃₃ can lead to a modulated phase where the director has either splay-bend or twist-bend distribution. Though various theoretical studies have suggested that this scenario may be valid, no experimental evidence has so far been given. In order to study the influence of the elastic constants, we measured the splay and bend elastic constants in the ordinary nematic phase of a dimer material, CBC11CB, for temperatures down to 0.6°C above the Nx–Nu transition. Our results show that the bend constant is reduced by a factor of 2 compared with that closer to the I-Nu transition but is positive and the trend does not seem that K ₃₃ will extrapolate to zero or fall below it for the temperature range investigated. Compared to K ₁₁, K ₃₃ is reduced by a factor of 3, close to the Nu–Nx transition temperature.     

Elastic properties of bent-core nematic liquid crystals: the role of the bend angle

ABSTRACT

The nematic phase formed from bent-core liquid crystals has been the focus of intensive research for more than a decade. With the potential of biaxial nematic phase and other interesting features, such as high Kerr constants, large flexoelectric coefficients and anomalous elastic constants, these bent-core materials have been in the limelight of research. This paper presents a mini-review of the interesting elastic behaviour reported in various bent-core compounds. The review further focusses on two different types of bent-core compounds as exemplars: one derived from an oxadiazole and other a thiadiazole, highlighting the importance of bend angle in bent-core compounds. The universality of the unique behaviour of bend elastic constants via molecular field theory and atomistic modelling has also been summarised.     

Dielectric investigation of the diamagnetic anisotropy and elasticity of 4-trans-4′-n-hexyl-cyclohexyl-isothiocyanatobenzene (6CHBT)

Abstract

We have measured the dielectric constants of 6CHBT. The results from studies of various alignments and thicknesses measured under different electric and magnetic fields are presented. We discuss how the dielectric properties depend on boundary conditions, sample thickness and the magnitudes of electric and magnetic fields. Experimental results and discussion in the terms of continuum theory make it possible to compute the diamagnetic anisotropy (Δχ), as well as the splay and bend elastic constants (K ₁₁, K ₃₃) of 6CHBT.     

Simulation of texture evolution for nematic liquid crystalline polymers under shear flow

The development of microstructure in nematic liquid crystalline polymers under shear flow is investigated through computational simulation. By using a tensorial expression for the elastic torque, the nemato-dynamic equation is numerically resolved. The simulation shows that elastic anisotropy has a strong influence on the evolution of the director and that the ‘log-rolling’ orientation of the directors emerges for tumbling nematics if the twist constant is smaller than the splay and the bend constants, even though one starts from a structure in which the directors are aligned within the velocity and velocity gradient plane. The interaction of wedge disclination pairs subject to a shear flow field is also simulated. The generation, multiplication and interaction of inversion wall defects during shearing have been revealed. In general the wall moves to the boundaries and is absorbed by the boundaries. When two walls of opposite orientation meet, a loop may form, then shrink, and finally collapse. Correspondingly, if they have the same orientation, commutation will occur.     

Phase transitions,optical, dielectric and viscoelastic properties of colloidal suspensions of BaTiO3 nanoparticles and cyanobiphenyl liquid crystals

We report experimental studies on the phase transitions and physical properties of colloidal suspensions of BaTiO₃ nanoparticles and two cyanobiphenyl liquid crystals (4-pentyl-4?-cyanobiphenyl and 4-octyl-4?-cyanobiphenyl). From the differential scanning calorimetric measurements, we show that the nanoparticles have antagonistic effect on the isotropic to nematic and nematic to smectic-A phase transitions. The birefringence, dielectric anisotropy and splay elastic constant remain almost unchanged, whereas the bend elastic constant and rotational viscosity decrease considerably. The experimental results are discussed based on the possible contribution of BaTiO₃ nanoparticles and free surfactant molecules in the suspensions.     

Dielectric and elastic properties of a nematic phase induced by charge transfer interaction in a binary system containing disc-shaped molecules

Abstract

The dielectric constants and the elastic coefficients for splay (K ₁) and bend (K ₃) of the charge transfer induced nematic (N_c) phase of tridecyl pentakis(phenylethynyl)phenyl ether (1) doped with different amounts of 2,4,7-trinitrofluorenone (2) were determined by studying the electric field induced bend deformation using the capacitance method. A negative dielectric anisotropy was observed. For the bend elastic constant K ₃ values up to 22 × 10^?12 N are found which are one order of magnitude higher than the respective values of discotic nematic (N_D) phases. Values of 0·6–0·8 are obtained for the ratio K ₁/K ₃; these show a minimum for the equimolar complex.     

Lehmann rotatory power: a new concept in cholesteric liquid crystals

By doping a nematic phase with a chiral molecule one obtains a cholesteric phase. Each chiral molecule is characterised by its helical twisting power (HTP) which is defined as HTP?=?q/(2πC) where q is the equilibrium pitch of the cholesteric phase and C the concentration (in wt%) of chiral molecules. In a similar way, we define the Lehmann rotatory power (LRP) as LRP?=?v/(2πC) where v is the thermomechanical Lehmann coefficient. By making compensated mixtures, we measured the HTP and the LRP of five chiral molecules (R811, S2011, CC, CB15 and CE4) dissolved in an eutectic mixture 8CB/8OCB. We found that, although these quantities were different, their ratio R?=?LRP/HTP changed little from one molecule to another. This result shows that the Lehmann effect is closely, but not completely, related to the twist of the phase.     

Experimental studies on the phase diagram and physical properties of mixture of calamitic and discotic nematic liquid crystals

Physical studies on mixture of calamitic and discotic nematic liquid crystals are meagre although they are potential for optimising physical properties. Here, we report experimental studies on the phase diagram and physical properties of mixtures of ambient temperature discotic and calamitic nematic liquid crystals. A substantial decrease in several physical properties such as birefringence, dielectric anisotropy and elastic constants are observed with increasing wt% of discotic compound. On the other hand a large increase in the rotational viscosity is observed. Based on the experimental results a simple model of mutual orientation of the rod-like and disc-like molecules is proposed.