Side group functionalized liquid crystalline polymers and blends VII. Phase behaviour and elastic constants K1 and K3 for hydrogen bonded blends of a functionalized LC copolymer with a low molecular mass non-mesogenic dopant

New hydrogen bonded blends of LC copolymers containing functional carboxyl groups with a low molecular mass pyridine-containing dopant were obtained and the orientational, optical and elastic properties of the blends were measured using the Fréedericksz method of threshold transitions in a magnetic field. The averaged order parameter S of the hydrogen bonded blends is found to be lower than that of the initial functionalized LC polymers. Furthermore, a considerable increase in the K₃/K₁ ratio is observed caused by an increment in the average 'effective' length of the hydrogen bonded mesogenic group. For the first time it is proven that LC blends with hydrogen bonded mesogenic groups obey the same main relationship of orientational elastic deformations as common nematic LC polymers with covalent bonding of mesogenic side groups.     

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.     

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.     

Dynamics of nematic point defects in a capillary with tilted boundary conditions

The motion of a single point defect in a cylindrical cavity filled with a nematic liquid crystal is described by solving numerically the simplified equations of nematodynamics. Perfect homeotropic anchoring for the director on the lateral boundary would result in the creation of domains with equal elastic energy, escaped upwards or downwards along the cavity axis and separated by point defects of strength ± 1. Defects do not move as long as they are sufficiently far apart. However, small deviations from homeotropic anchoring remove this degeneracy and the energetically favourable domains start to expand at the expense of the others, thus setting the defects in motion along the tube. We present a new numerical approach, which neglects the backflow, for studying the influence of both the pretilt and the elastic anisotropy (K ₃₃ ≠ K ₁₁) on the motion of a defect. We show how even very small pretilt angles (≈1°) result in speeds observed in experiments. For a moderate elastic anisotropy, the velocity of a +1 defect equals the velocity of a -1 defect, whereas for K ₃₃?K ₁₁ a + 1 defect moves faster than a -1 defect. For small pretilts we confirm a good qualitative agreement with an existing analytical approach, which proves inaccurate for large pretilts.     

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.     

At-edge minima in elastic photon scattering amplitudes for dilute aqueous ions

Elastic photon scattering and absorption in the vicinity of core atomic orbital energies give rise to resonances in the elastic photon scattering cross-section. Of interest is whether a dilute-ion aqueous system provides an environment suitable for testing independent particle approximation (IPA) predictions. Predictions of the energy of these resonances have been determined for a Dirac–Slater exchange potential with a Latter tail. At BM28 (ESRF), tuneable X-rays were obtained at eV resolution using a 1 1 1 Si monochromator. From target systems including Cu²⁺ and Zn²⁺, the X-rays were scattered through high angle from an aqueous medium contained in a thin Perspex cell provided with 8 μm kaplan windows. An energy resolution of ∼500 eV from the HPGe detector was adequate to separate the elastic scattering signal from K_α radiation but not from Compton or K_β contributions. The Compton contribution from the medium was removed assuming validity of the relativistic impulse approximation. The contribution due to K_β fluorescence and the resonant X-ray Raman scattering process were handled by assuming the branching ratio for K_α and K_β contributions to be constant and to be accurately described by fluorescent yields measured above edge. At ionic concentrations ranging from 0.01 to 0.1 mol/l, resonance structures accord with predictions of elastic scattering cross-sections calculated within IPA. Amplitudes calculated using modified form-factors and anomalous scatter factors computed from a Dirac–Slater exchange potential were convolved with a Lorentzian of several eV (FWHM).     

Calculations of the frequency dependences of viscosity coefficients and elastic moduli for solutions of electrolytes over broad ranges of thermodynamic parameter variations

The dynamic equations obtained earlier for the coefficients of bulk η_V(ω) and shear η_S(ω) viscosities and bulk K(ω) and shear μ(ω) elastic moduli were used to calculate these values for a certain model of solution structure in the approximation of the theory of osmotic solution properties. The interparticle interaction potential was written as the sum of the potential of hard spheres and Coulomb attraction. The corresponding thermodynamic parameter values for the density ρ, temperature, concentration C, and adiabatic bulk modulus K _S were taken from experimental works. The results of numerical calculations of the viscoelastic properties of solutions over broad ranges of thermodynamic parameter and frequency variations were plotted and tabulated. The calculation results are compared with the available experimental data. The theoretical viscoelastic properties of solutions of electrolytes were in satisfactory agreement with the published experimental data and the results of numerical experiments for classic liquids.     

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.     

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.     

The frequency dispersion of dynamic transfer coefficients and elastic moduli of magnetic liquids

The analytic equations for viscosity coefficients and the corresponding elastic moduli obtained in [3] were used to calculate these values over a wide range of reduced frequency values (ω* ≈ 10^?7?10). The volume η _v (ω) and shear η _s (ω) viscosity coefficients decreased as the frequency increased. The dispersions η _v (ω) and K _r (ω) were only caused by the contribution of structural relaxation, and the dispersions η _s (ω) and μ(ω), by translational and structural relaxation. The shear elastic modulus μ(ω) and relaxation volume elastic modulus K _r (ω) increased as the frequency grew. The results obtained were in satisfactory agreement with the conclusions from general relaxation theory.     

Edge profiles at lamellar phase/melt interfaces

We study in the framework of the continuum theory of dislocations the structure of the interface between an AB diblock copolymer lamellar film deposited on a solid substrate and an A-homopolymer melt. The dislocation inside the lamellar phase induces steps at the interface. The shape of the profile at the edge of a step (edge profile) depends on the distance of the dislocation from the interface. The profile and the equilibrium location of the dislocations are both studied as a function of the film thickness, D. For large D, the dislocation is stabilized at a finite distance, h_eq, from the interface, due to the small surface tension and large surface bending elastic constant, K_s. For zero surface tension, h_eq ≈ K_s/(2K), where K is the bulk bending elastic constant. For small D, h_eq is mainly determined by the proximity of the solid substrate. The edge profile along the interface is a monotonic function of the distance along the interface for large D of the film and becomes nonmonotonic for small D. Also the dislocation energy strongly depends on D for small D. The theory is discussed in connection to recent experimental studies of diblock copolymer films deposited on a solid substrate.     

Evaluation of high-frequency elastic moduli and shear relaxation time of the Lennard-Jones fluid using three known analytical expressions for radial distribution function

High-frequency elastic moduli (G_∞ and K_∞) for a Lennard-Jones (LJ) fluid have been calculated using three known analytical expressions for radial distribution function (RDF) at different temperatures and densities and compared with the corresponding values of these properties obtained from molecular dynamics (MD).     

A simple method to measure the twist elastic constant of a nematic liquid crystal

We demonstrate a simple method for measuring the twist elastic constant (K₂₂) of a nematic liquid crystal (LC). By adding some chiral dopant to an LC host, the LC directors rotate 180° in a homogeneous cell, which is known as 180° super-twisted nematic (STN) cell. By preparing two such STN cells with different chiral concentrations and measuring their Fréedericksz threshold voltages, we can obtain the K₂₂ and helical twisting power simultaneously. In the whole process, there is no need to measure the pitch length. Our obtained K₂₂ values agree well with those reported by using other methods.     

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.     

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.     

Stress–strain relations of crosslinked rubbers under different types of strain

Experimental data for the stresses and the deformations for crosslinked rubbers at uniaxial and symmetrical and asymmetrical biaxial extension and pure shear are given. Stressed states up to 100% extension are described by a single parameter, the highly elastic potential of Bartenev and Khazanovich. The classical statistical potential of Kuhn-James-Guth-Treloar is not in agreement with experimental data, as shear modulus G has different values for different types of stressed states.     

K3ReH6 – Synthese,Struktur und magnetische Eigenschaften

K₃ReH₆ – Synthesis, Structure, and Magnetic Properties K₃ReH₆ and K₃ReD₆ were synthesized by the reaction of potassium hydride (deuteride) with rhenium powder under a hydrogen pressure between 3000–3500 bar at 850 K. X-ray investigations on powdered samples and elastic neutron diffraction experiments on the deuterated compound at the triple axis spectrometer TAS 1 in the temperature range 5–600 K led to the atomic arrangement, which corresponds to that of the cryolite with [ReH₆]^3–-octahedra as characteristic units. Magnetic susceptibility measurements in the temperature range from 3.5 K and room temperature revealed a weak temperature independent paramagnetism. Quantum mechanical calculations confirm these facts and show in detail that the large value of the spin-orbit coupling parameter is essential for the magnetic behaviour.     

A ductile-brittle zone in polyimides depending on the reaction temperature

The mechanical and optical properties of polyimides were studied in this paper and the influence of the variation of the reaction temperature on the physico-chemical properties of the polymers was evaluated. From this the dependence of the stress-strain diagrams on the reaction temperature, as well as the stresses and strains at fracture were experimentally determined. Moreover, the elastic moduli and Poisson's ratios, as well as the refractive index of the polymers were evaluated for different temperatures of imidization. In order to define also the behaviour of the polymers as thin membranes at fracture, simple tension tests with edge-cracked thin strips were executed up to fracture. The method of caustics was used, with the specimens loaded inK _I mode of deformation at different stress-levels to evaluate the stress intensity factors of the materials in the non-linear zone of loading. TheK _I -factor was evaluated by applying the simple Dugdale-Barenblatt model for the ductile materials, whereas for brittle samples the elastic theory was used. Interesting results concerning the physico-mechanical properties of the polyimides were derived.     

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.     

“Electrocapillary” curve on solid metal obtained by holographic interferometry

A new very sensitive method was developed for obtaining the “electrocapillary” curve of a solid metal. The method is based on the measurement of small elastic deformations of a strip caused by the changes of the surface tension forces. For the precise measurement of the strip bending (the radius of curvature) holographic interferometry was applied. It is shown that a change of the surface tension ±0.1 mN m^?1 can be registered. The “electrocapillary” curve of platinum in 0.05 M H₂SO₄ solution was obtained. It was found that the zero charge potential is +0.25 V versus normal hydrogen electrode. The double layer capacity was evaluated. The method is not very sensitive to temperature changes and can be applied in any case when the working electrode (metal strip) is mounted in a transparent glass cell.