The Twist Elastic Constant and Anchoring Energy of the Nematic Liquid Crystal 4-N-Octyl-4-Cyanobiphenyl

The twist elastic constant of the nematic liquid crystal 4-n-octyl-4'-cyano-biphenyl (8CB) and the azimuthal anchoring energy at the SiO-nematic interface have been measured by using the torsion pendulum technique. The twist elastic constant of 8CB is found to be systematically larger than that measured by the Freedericksz transition technique. The azimuthal anchoring energy is found to decrease rapidly as the nematic-isotropic transition temperature is approached. This behaviour is analogous to that already reported by us for the nematogen 5CB and can be interpreted by extending the Berreman model of the anchoring energy at a grooved interface.     

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.     

Elastic,dielectric and optical constants of 4'-pentyl-4-cyanobiphenyl

4'-n-Pentyl-4-cyanobiphenyl (5CB) is a room temperature nematic liquid crystal with a high positive dielectric anisotropy and a high chemical stability. Many experimental results concerning the elastic and dielectric constants of 5CB are available in the literature, although there is often no satisfactory agreement between the experimental data obtained by different groups, especially as far as the dielectric constants are concerned. Furthermore, no detailed investigation of the temperature dependence of the elastic and dielectric constants close to the nematic-isotropic transition temperature T _NI has yet been reported. In this paper, we report the measurement of the elastic and dielectric constants of 5CB, and the temperature behaviour close to T _NI has been investigated in detail. The experiment consists in the measurement of the director deformation induced by an electric field using simultaneously both a dielectric and an optical method. The simultaneous use of these two methods provides an indirect check on the reliability of the measurements. Special attention has been devoted to control possible sources of uncertainty. In particular, the effects of finite anchoring energy and of finite pretilt angle have been considered. The temperature dependence of the anisotropy of the refractive indices is also obtained in the experiment.     

Anchoring properties of a nematic liquid crystal on anisotropic hydroxypropylcellulose films

Thin solid films of hydroxypropylcellulose (∼15-30 µm) prepared from liquid crystalline and isotropic aqueous solutions are used as liquid crystal alignment layers. Using the standard nematic liquid crystal 5CB we measured the interface properties of these solid films as a function of the polymer concentration in the aqueous precursor solution, expressed in terms of zenithal and azimuthal anchoring orientations and extrapolation lengths. The hydroxypropylcellulose thin films are found to induce a planar orientation of 5CB independently of the polymer concentration, with the alignment along the polymer backbone. The zenithal anchoring strength is found to be strong and essentially independent of the temperature far from the nematic-isotropic transition, with an extrapolation length ξ_θ≈50 nm. The zenithal anchoring becomes weaker near the nematic-isotropic transition, as expected. The azimuthal anchoring strength is found to be intermediately weak and strongly dependent on the polymer concentration, with an extrapolation length varying from ξ_θ≈250 nm to ξ_ϕ≈500 nm. These films are particularly interesting since their surface topography and morphology may be tuned by varying a few parameters in the film preparation process, such as the polymer concentration in the aqueous solution.     

Director orientation of a ferroelectric liquid crystal on substrates with rubbing treatment: The effect of surface anchoring strength

Abstract

One of the most important problems with ferroelectric liquid crystals is obtaining homogeneous as well as bistable alignment, not only to study their physical characteristics but also for their application to optical devices. In this connection it was predicted that the formation of homogeneous alignment requires strong surface anchoring, whereas bistability requires weak anchoring. We have therefore developed a method to determine the surface anchoring strength, and have tried to clarify whether there is a suitable anchoring range. It was found that A/K ₂₂ (A is the surface anchoring and K ₂₂ is the twist elastic constant of liquid crystal) of 4 × 10^?2 to 2 μm^?1 satisfies the contradictory requirements for homogeneous as well as bistable alignments for the material studied, and the bookshelf structure is successfully formed with this condition.     

Experimental measurement of the azimuthal anchoring energy function at a SiO-nematic interface

The functional form of the azimuthal anchoring energy, i.e. the anisotropic part of the interfacial free energy, at the interface between the nematic liquid crystal 4-n-pentyl-4'-cyanobiphenyl and an obliquely evaporated SiO substrate is measured for the first time by using a reflectometric method. The anchoring energy function is obtained by measuring the director rotation on the interface caused by an external magnetic field ranging from 0 to 2·3 T. The dependence of the anchoring energy on the director azimuthal angle is found to be well fitted by the function W_a(ϕ) = W_asin² ϕ in agreement with the predictions of the Berreman model for the anchoring at a grooved interface.     

The elastic distortion and stability of biaxial nematic liquid crystal on the surface grooves

Fukuda et al. reexamined the Berreman's model which attributes the surface anchoring to the elastic distortion of the uniaxial nematic liquid crystal induced by the grooves of a surface. They showed that at the variance with the assumption made in the original approach of Berreman, the azimuthal distortion of the director cannot be considered as negligibly small. Now this method is generalized to the biaxial nematic liquid crystals, with some approximations for the elastic constants. We obtain an additional term in the elastic distortion energy per unit area which depends on the second power of the cosine of the angle made between the main director n at infinity and the direction of the surface grooves. This additional term describes the distortion energy of the minor director m induced by the surface grooves when the n director is anchored exactly along the grooves. We have studied the stability of the n director around the grooves, and in one-constant model for each director the stability condition is that the elastic constant of the n director is the maximum.     

Low-frequency dilational elasticity of the nematic 4'-pentyl-4-biphenylcarbonitrile (5CB)/water interface

Axisymmetric oscillating pendant drop shape analysis has been used to study the interfacial rheology of the liquid crystal 4'-pentyl-4-biphenylcarbonitrile (5CB) in water with homeotropic anchoring. Nearly spherical 5CB droplets were subjected to low frequency (1-5 mHz) volume oscillations, and the increase in tension with surface dilation was used to calculate the complex modulus. The droplet interface response is completely elastic, with no relaxations occurring on the experimental time scale. This surprising result is attributed to droplet storage of elastic energy in the form of distorted orientational distributions within the bulk (Frank elasticity) and on the surface (anchoring elasticity).     

Simultaneous photoacoustic measurements of specific heat and thermal conductivity critical behaviour at a smectic A–nematic phase transition

Abstract

Simultaneous measurements of the thermal conductivity and specific heat at the smectic A-nematic phase transition in 4-n-octyl-4′-cyanobiphenyl (8CB) have been carried out with the photoacoustic technique. A critical increase in the thermal conductivity is reported. A critical decrease in the thermal diffusivity data confirms that the transition in 8CB is fluctuation dominated as also shown by the critical behaviour of the specific heat.     

Saddle-splay and mechanical instability in nematics confined to a cylindrical annular geometry

Abstract

The occurrence of a mechanical instability is predicted for a nematic liquid crystal confined to a cylindrical annular geometry. The surfaces impose either a bend distortion (azimuthal configuration) or a splay distortion (radial configuration) in the plane of the cylinders′ cross-section. Remarkably, the instability appears also with strong anchoring, and, when the torsional anchoring is weak, then the saddle-splay elastic constant K24 deeply influences the critical radii.     

Polar anchoring strengths of nematic liquid crystal on high-density polymer brush surfaces

ABSTRACT

Herein, the polar anchoring energy coefficient (A_θ) of nematic liquid crystal (NLC) was examined for high-density polymer brushes via capacitance measurements. The A_θ is 10^?4 J m^?2 for the brushes of poly(methyl methacrylate), poly(ethyl methacrylate) and poly(styrene). The value decreases to 10^?5 J m^?2 for poly(n-butyl methacrylate) and poly(hexyl methacrylate) with lower glass transition temperatures. However, each polymer brush displays a constant A_θ value over a temperature range of ?15°C to 90°C, which is hardly affected by the graft density and brush thickness. At 25°C, A_θ is 10 times greater than the corresponding azimuthal anchoring energy coefficient (A_φ); therefore, NLCs on polymer brushes can be preferentially aligned along the in-plane component of the applied field.     

Light scattering from a nematic monodomain in an electric field Twist elastic constant and viscosity coefficient of nematic polymer–solvent mixtures

Abstract

The light scattering technique was used to investigate the viscoelastic parameters characterizing director twist distortions in miscible nematic mixtures of 5CB (pentacyanobiphenyl) with two side chain liquid crystal polymers and a main chain liquid crystal polymer. By applying an AC electric field to homeotropically-aligned nematic monodomains of the mixtures, the field-dependent scattering intensities and director orientation fluctuation relaxation rates yield, respectively, the twist elastic constant K ₂₂ and viscosity coefficient γ₁. The results directly demonstrate that the addition of liquid crystal polymers causes substantial decreases of the relaxation rates for dynamic light scattering from the twist mode and these changes are due to small decreases in K ₂₂ coupled with large increases in γ₁. The decrements in K ₂₂ are comparable for both side chain and main chain liquid crystal polymers. The relative increase in the twist viscosity for the side chain liquid crystal polymers is much smaller than those of main chain polymers. A theoretical model is used to qualitatively interpret the difference between the viscous behaviour of the twist mode for both side chain and main chain liquid crystal polymers in a nematic solvent.     

Invited Lecture. Experimental studies of the anchoring energy of nematic liquid crystals

An analysis is given of experimental techniques for measuring the anchoring energy, W, of nematic liquid crystals with solid surfaces. Two novel methods for measuring W in homeotropically oriented samples are discussed. The first is based on the stabilization of the flexoelectric distortion by a magnetic field. In the second the thickness dependence of the phase delay for the light beam transmitted through a wedge-form cell with the hybrid orientation of a nematic should be measured. New experimental data on thickness and temperature dependences of the anchoring energy for homogeneously oriented 5CB are also presented. The anchoring energy was even measured for thin interface layers in the isotropic phase and its critical behaviour near the N-I transition is also discussed. New data were also obtained for the anchoring energy of nematics at crystalline surfaces.     

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.     

Measurement of the orientational elastic constants and the twist viscosity of nematic side chain polymers

Abstract

The temperature dependence of the three elastic constants k _ii (i = 1, 2, 3) and the twist viscosity γ₁ of two nematic side chain polyacrylates and one comparable low molecular weight compound have been measured by means of the Freedericksz effect. The change from the low to the high molecular liquid crystal causes a change of the ratio k ₃₃/k ₁₁ from greater to less than unity, but the order of magnitude of the elastic constants remains the same. In contrast, the twist viscosity of the polymeric liquid crystal is about 1000 times greater in magnitude than that of a comparable low molecular weight liquid crystal. The activation energy for the viscosity of the polymer differs by a factor 3–4 from that of the low molecular weight liquid crystal. The elastic constants as well as the twist viscosity show a quadratic dependence on the order parameter S over a wide temperature range.     

Investigation of the viscoelastic properties of 4-propoxy-biphenyl-4-carbonitrile

ABSTRACT

We report on the temperature-dependent measurements of dielectric permittivity, birefringence, elastic constants and rotational viscosity for 4-propoxy-biphenyl-4-carbonitrile in the nematic region. The temperature dependence of the three elastic constants was determined from studies of the Freédericksz transition. The thermal dependence of elastic constants shows features similar to the literature (bend > splay > twist). Elastic constants are proportional to the square of the order parameter. Temperature-dependent dielectric characterisation was carried out at a frequency of 10 kHz. The compound shows positive dielectric anisotropy in the nematic phase. The rotational viscosity is found to be relatively low. Temperature dependence of order parameter is estimated using Haller’s method. The figure of merit was also calculated as a function of temperature.     

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.     

A numerical technique for predicting microstructure in liquid crystalline polymers

A numerical technique has been developed to model texture in nematic liquid crystals. The technique differentiates between splay, twist and bend distortions and includes splay-splay compensation. The technique is tested by the simulation of the Freedericksz transition and by the determination of minimum energy director fields for specific boundary conditions. To model the bulk, periodic boundary conditions are imposed. The effect of elastic anisotropy on disclination character has been investigated by terminating simulations before all the defects have been annihilated. With a low twist constant, twist disclinations are observed; with a high twist constant, wedge disclinations are observed. With a low twist constant and high splay constant, realistic for polymeric liquid crystals, features observed experimentally are simulated.     

The formula of anchoring energy for a nematic liquid crystal

The interface energy for a nematic liquid crystal (NLC) is considered as the sum of potential energy between LC molecules and molecules of the substrate surface, and a formula for anchoring energy is derived by elementary principles. The anchoring energy for a NLC should have two terms, the first term is the same as the Rapini–Papoular expression, the second is related to the normal of interface and resultes from the biaxial property of a NLC induced by interface. Hence there are two anchoring coefficients, W ₁ and W ₂. We demonstrate that W ₁ is equal to the tilt angle strength A_θ , and W ₂ corresponds to the difference between A_θ and the azimuthal strength A_? . Thus A_θ –A_? is due to the biaxial property of the NLC near the interface. Applying this formula to the twisted NLC cell, we discuss the threshold and saturation field, as well as the maximal tilt angel θ _m with respect to A_θ /A_? . Previously proposed formulae are discussed from our point view.     

Temperature dependence of pitch and twist elastic constant in a cholesteric to smectic A phase transition

To understand chirality in cholesteric (Ch) liquid crystals, we performed an experimental study on the Ch-smetic A (SmA) transition of a cholesteric liquid crystal. By studying the reflection spectrum at zero field and at the critical electric field used to unwind the helical structure, we were able to measure the helical pitch P and the twist elastic constant K ²² in the Ch phase. As the temperature was lowered toward the Ch-TGB phase transition, the helical pitch and twist elastic constant diverged. The results support the model that short range SmA forms in the Ch phase. When the results were fitted by power-law temperature dependence, the exponent for P was 0.78 and the exponent for K ²² was 1.36.