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.     

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.     

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.     

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.     

Anomalies in the twist elastic behaviour of mixtures of calamitic and bent-core liquid crystals

ABSTRACT

The splay, twist and bend elastic constants (K₁₁, K₂₂ and K₃₃) have been measured as a function of temperature in bent-core/calamitic mixtures based on three different calamitic materials (5CB, 8CB and ZLI1132) and two bent-core dopants. The behaviour of the splay and bend constants are as expected; a reduction in K₃₃ of ~20%, in line with predictions from mixing rules and other observations. Interestingly, no change is seen in the splay constant, K₁₁ of the calamitic hosts. Surprisingly though, the twist elastic constant exhibits a reduction of 30 – 40% in all mixtures across the nematic range, an effect not previously reported and much larger than mixing rules can explain. The elastic behaviour is universal in our mixtures. We explain part of the reduction in the twist deformation by considering the influence of the chiral conformer fluctuations of the bent-core molecules on the twist elastic constants of the mixtures. However, the dramatic reduction can only be fully explained by also including contributions from chiral conformer fluctuations of the calamitic host, a form of chiral amplification.     

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.     

Elastic properties of a nematic in a tetrapalladium organyl-pentadecane system

The temperature dependences of birefringence Δn, anisotropy of permittivity ?_a, and elastic constants K ₁₁ and K ₃₃ in the nematic phase of a tetrapalladium organyl-pentadecane system with a pentadecane content of 55 wt % have been investigated experimentally. It has been shown that, as temperature is elevated, ?_a, K ₁₁, and K ₃₃ values decrease and Δn remains unchanged. Elastic constants K ₁₁ and K ₃₃ have been established to vary from 3.4 × 10^?7 to 5.6 × 10^?6 dyn and from 1.3 × 10^?6 to 27.4 × 10^?5 dyn, respectively. The value of ?_a has been revealed to vary over the range 0.2–0.5. It has been found that, at temperatures above the N₂ → Cr phase transition by 6°C, an imposed electric field induces the growth of tetrapalladium organyl crystals.     

Phase transition and elastic constants of 4-n-octyl-4′-cyanobiphenyl (8CB) obtained using the light-scattering anisotropy of turbidity

Abstract

A light-scattering technique was used to study the anisotropy of turbidity and the three elastic constants K ₁, K ₂ and K ₃ of 8CB as a function of temperature and sample thickness. The turbidity was measured in the nematic and schematic A phases at sample thicknesses l of 0.02, 0.04, 0.1 and 0.2 cm. The effect of the smectic-like (cybotactic nematic) order was observed near the smectic A-nematic phase transition. Owing to the surface-enhanced cybotactic order, evaluation of the elastic constants and order parameter was possible only from the turbidity data at l = 0.2 cm. From the divergence of both K ₂ and K ₃ near T_{S A N} we estimated an average critical exponent value v of 0.65, suggesting that S_A-N in 8CB is a second-order phase transition. The magnetic-field quenching of director fluctuations showed observed effects on the order of magnitude of the temperature dependence of the turbidities, elastic constants and order parameter.     

Side group functionalized liquid crystalline polymers and blends VIII. Nematic and SmAre phase formation in hydrogen-bonded blends of smectic side group LC polymers and a low molar mass dopant

Hydrogen-bonded blends based on smectic side group functionalized LC copolymers containing 4-alkyloxybenzoic acid fragments (proton donor) and a non-mesogenic low molecular mass dopant 4-cyanophenyl pyridine-4-carboxylate or 4-methoxyphenyl-d₄ pyridine-4-carboxylate (proton acceptor) were obtained. The blends containing 10-35 mol % of low molecular weight dopant form nematic (I-N-SmA) or re-entrant SmA phases (I-SmA-N-SmAre). The temperature dependence of the order parameter S, the birefringence Δn, and the splay K ₁ and bend K ₃ elastic constants of the nematic phase were studied by ²H NMR spectroscopy and the Fréedericksz method of threshold transitions in a magnetic field. A mechanism for the destruction of the SmA phase and the formation of the nematic phase in the hydrogen-bonded blends is suggested.     

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.     

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.     

Accurate measurement of the twist elastic constant of liquid crystal by using capacitance method

In this study, the twist elastic constant (k₂₂) of liquid crystals (LCs) was accurately measured using capacitance method. The constant can be obtained on the basis of accurate measurement of other LC parameters, such as parallel and vertical dielectric constants (ε_// and ε_⊥), splay and bend elastic constants (k₁₁ and k₃₃), and rotational viscosity coefficient (γ₁). First, by using dual-cell capacitance method and an LC cell capacitance model to measure ε_// and ε_⊥, k₁₁ and k₃₃ can be obtained from the threshold voltage determined from the voltage–capacitance curve of the parallel-aligned nematic LC layer and the comparison between the experimental and theoretical results based on the Frank elastic theory, respectively. In addition, γ₁ can be obtained from the measurement of the dynamic response in the parallel-aligned nematic cell. Finally, k₂₂ can be accurately determined using the threshold voltage of the twisted nematic LC cell. By adopting the above method, the measured k₂₂ for LC E7 was 6.7 × 10^?12 N. The proposed method is more rigorous and yields a more accurate measurement result than the other methods reported in the literature.     

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.     

Liquid-crystalline reference compounds

Abstract

A polar (PCH-5) and a non-polar (152) compound are introduced as liquid-crystalline bench-mark compounds. The materials chosen are affordable, stable, easy to handle and possess nematic mesophases between 30–54·9 and 24–103·4°C. All relevant macroscopic physical properties, such as refractive indices n _o n _e, dielectric permittivities ∥_?, elastic constants K ₁₁, K ₂₂ and K ₃₃, and bulk and rotational viscosities are given as a function of temperature, wavelength and frequency, when applicable. The reference compounds are available from E. Merck, Darmstadt.     

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%.     

Photoresponsive Stripe Pattern in Achiral Azobenzene Liquid Crystals

A periodic stripe pattern is found in the nematic phase close to the smectic phase of photoresponsive achiral liquid‐crystalline compounds. The origin of the stripe patterns can be ascribed to an extremely large bent elastic constant K₃₃. In addition, we succeeded in controlling the pattern by the following two methods: 1) the stripe disappears by a trans–cis photoisomerization upon UV light irradiation and reappears upon light termination, and 2) the stripe pattern is stabilized over the whole nematic phase, at approximately 10 °C, by polymerization of the compounds.     

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.     

Blue phase stability of n-OCB homologue chiral nematic liquid crystal mixtures

Blue phase (BP) stability of a chiral nematic liquid crystal (LC) mixture is dependent upon chemical structure as well as physical properties. In this study, the blue phase temperature range dependent on alkyl chain length was investigated in order to evaluate the relationship between blue phase stability and the molecular structures of four kinds of 4-n-alkyloxy-4'-cyanobiphenyl (n-OCB) homologue chiral nematic LC mixtures composed of rod-like nematic LCs. It was confirmed that the blue phase temperature range was strongly dependent upon the molecular parity, K ₃₃/K ₁₁ and the helical twist power of the n-OCB homologues chiral nematic LC mixtures.     

Critical behavior of the bend elastic constant of a liquid crystalline comblike polymer near the nematic–smectic A phase transition

The temperature dependence of the bending elastic constant of a combined comblike side- and main-chain liquid crystalline polymer near the nematic–smectic A phase transition was investigated. The bending constant K₃ diverges at the transition, but the critical exponent ν = 1.4 does not agree with the theoretical prediction. The large value of the exponent ν may be explained by the polydispersity of the polymer investigated.