Bend Elastic Constants Research Articles

Measurement of elastic constants of nematic liquid crystals with use of hybrid in-plane-switched cell

AbstractA new method for quick and pretty accurate measurements of splay, twist and bend elastic constants of nematic liquid crystals is experimentally verified. The main concept relies on exploiting only the electric field and determining magnitudes of nematic elastic constants from threshold fields for Freedericksz transitions in only one hybrid in-plane-switched cell. In such cell the deformations of an investigated liquid crystal are controlled by three separated pairs of electrodes confining measurement domains. In two of them inter-digital electrodes are mounted on one cell cover. Splay, twist and bend elastic constants can be measured by a proper choice of electrodes’ configuration together with orienting cover coatings (without applying magnetic fields). In this paper, we describe layout of our cells and results of experimental tests by using different liquid crystals: 5CB and 6CHBT (with positive dielectric anisotropy), Demus’ esters (with negative dielectric anisotropy) and new liquid crystals mixtures produced in our university.

Structure–property correlation of a hockey stick-shaped compound exhibiting N-SmA-SmCa phase transitions

We report the measurement of birefringence, dielectric constant, splay, bend elastic constants and rotational viscosity in the nematic phase (N) of a hockey stick-shaped compound exhibiting smectic-A (SmA) and anticlinic smectic-C (SmCa) phase transitions at lower temperature. It is found that the physical properties are significantly different than calamitics and partially similar to the bent-core liquid crystals. It exhibits the positive dielectric and the negative elastic anisotropy. The optical and the thermal measurements show that all the transitions are first order. The rotational viscosity is comparatively higher than calamitic liquid crystals and exhibits weak pre-transitional divergence. The temperature dependent static dielectric measurements indicate antiparallel correlation of both the longitudinal and the transverse components of dipole moments in both the smectic phases. The parallel component of the dielectric constant exhibits a single Debye type relaxation in all the phases. The activation energy in the N, SmA and SmCa phases are comparatively larger than that of the respective phases of calamitic liquid crystals and can partially be attributed to the higher rotational viscosity of the hockey stick-shaped compound.

Methylene-linked liquid crystal dimers and the twist-bend nematic phase

The transitional properties of three methylene-linked liquid crystal dimers are reported, namely, 1,5-bis(4-cyanoanilinebenzylidene-4′-yl)pentane (CN-5-CN), 1,5-bis(4-methoxyanilinebenzylidene-4′-yl)pentane (1O-5-O1), and 1,5-bis(4-ethoxyanilinebenzylidene-4′-yl)pentane (2O-5-O2). Each dimer exhibits two monotropic mesophases. The higher temperature mesophase is a normal nematic phase while the lower temperature phase is assigned as a twist-bend nematic phase. The assignment of the twist-bend nematic phase was based on the strong similarities in the optical textures observed to those reported recently for a structurally similar dimer. The complete miscibility of the mesophases exhibited by CN-5-CN and 1O-5-O1 has been established. The analogous hexamethylene-linked dimers exhibit only the normal nematic phase as do the corresponding ether-linked dimers. A review of the literature reveals another five methylene-linked odd-membered dimers that exhibit a nematic–nematic transition and, in each, the lower temperature nematic phase exhibits similar properties to those reported for the twist-bend nematic phase. The formation of this new nematic phase has been attributed to a negative bend elastic constant which results from the bent geometry of methylene-linked odd-membered dimers.

Nematic viscosity estimation using director kickback dynamics

The coupling between director rotation and bulk flow of a liquid crystal can cause many interesting, and often unwanted, effects. The associated ‘backflow’ and director ‘kickback’ have been observed and modelled over a number of years and have been used in the determination of nematic elastic constants and viscosities, usually through complicated fitting procedures. In this paper we develop a simple model of the flow and director dynamics during switch-off in a standard Freedericksz cell which, together with the classical switch-on dynamics, can be used to develop a relatively accurate, computationally inexpensive, two-mode fitting procedure capable of estimating splay and bend elastic constants, cell thickness and two combinations of the nematic viscosities. We do this by using an eigenfunction expansion for the director dynamics equation together with an analytical expression for the coefficients of the relaxing modes. This allows a simple estimation for the maximum director angle during kickback and the time after which the director has recovered to its initial state, which are comparable with a full numerical simulation, and leads to confidence in the accuracy of a two-mode eigenfunction expansion.

Composite Method for Measurement of Splay, Twist and Bend Nematic Elastic Constants by Use of Single Special In-Plane-Switched Cell

A method for quick and pretty accurate measurements of splay, twist and bend elastic constants of nematic liquid crystals is proposed. The main concept relies on exploiting only electric field in a plane-parallel liquid crystal cell of special configuration with thin transparent comb-like electrodes on one cover and usual transparent plane electrode on the other. Rubbing in direction parallel to comb electrode stripes enforces homogeneous planar or homeotropic orientation of nematic molecules. Fréedericksz’ transition of pure splay, twist or bend form is initialised by applying voltage between the electrodes appropriately. The method was tested with three different comb-like electrode configurations and three nematics: 4-pentyl-4′-cyanobiphenyl, 4-trans-4′-n-hexyl-cyclohexyl-isothiocyanatobenzene and Demus’ esters.

Splay-bend elasticity and rotational viscosity of liquid crystal mixtures of rod-like and bent-core molecules

We report temperature dependent measurements of birefringence (Δn), splay (K11), bend (K33) elastic constants and rotational viscosity (γ1) of mixtures of rod-like and bent-core molecules. K11 and Δn remain almost constant for all the mixtures whereas K33 is always lower than K11 and further decreases with increasing concentration of bent-core molecules in the mixtures. Apart from the large jump in Δn at the nematic-isotropic transition (NI) a significant jump in Δn at the nematic-smectic transition (NS) is also observed that increases with increasing mol% of the bent-core compound in the mixtures. Rotational viscosity increases by a factor of four when the concentration of the bent-core compound increased from 0 to 10 mol%. The results are discussed on the basis of their structural similarity and mutual alignment in the nematic phase.

Crucial role of molecular curvature for the bend elastic and flexoelectric properties of liquid crystals: mesogenic dimers as a case study

Using a molecular field theory with atomistic modelling, we provide a complete description of the elastic and flexoelectric properties of the nematic phase formed by liquid crystal dimers which, depending on the parity of the number of atoms in the spacer, have either a bent (odd) or a straight (even) average shape. We can then estimate the flexoelastic ratio and make a direct comparison with the outcome of flexoelectro-optic measurements. Our results demonstrate the extreme sensitivity of the bend elasticity and flexoelectricity to the molecular structure, with dramatic differences between even and odd dimers. An unusually low bend elastic constant is predicted for the latter; we discuss the implications of this result for the high flexoelastic response and the existence of Blue Phases stable over a wide temperature range, which were both recently claimed for odd liquid crystal dimers.

Splay and bend elastic constants in the nematic phase of some disulfide bridged dimeric compounds

We report measurements of the temperature dependences of the splay (K11) and bend (K33) elastic constants of several homologues and a binary mixture of disulfide bridged symmetric dimers made of alkoxy cyanobiphenyl monomeric units. All of them have an even number m of carbon and sulfur atoms in the linking chain and expected to have linear conformations. Both K(11) and K(33) alternate depending on the parity of x which is the number of carbon atoms in the alkyl chain of a monomer. We will refer to this as 'odd-even' effect. This effect, occurs near the nematic-isotropic transition temperature. T(NI), but monotonically decrease with m at lower temperatures. We argue that these results imply large rotational fluctuations of the two halves of the dimers about the S-S bond giving rise to average bent conformations near T(NI). At lower temperatures those conformations which can adapt better to the given curvature deformation in the medium are favored.

Splay-bend elasticity of a nematic liquid crystal with T-shaped molecules

We measured the splay (K11) and bend (K33) elastic constants in the nematic phase of a liquid crystal with T-shaped molecules. We find that the ratio, K33/K11 ≃1 in the entire nematic range except very close to the nematic to Sm-A (SN) transition. Both K33 and K11 show pretransitional divergence as the SN transition is approached from higher temperature. The ratio, K33/K11 suggests that the length (L) to effective width (D) ratio (i.e., L/D ) is significantly smaller due to the presence of long and flexible lateral group, compared to that of rigid rodlike molecules. It is argued that apart from the extra contribution to the elasticity the long and flexible lateral group also has a significant contribution to the suppression of the splay fluctuations in the onset of smectic short-range fluctuation. The structure of the Sm-A phase is investigated by using small angle x-ray diffraction, and a possible arrangement of the molecules in the Sm-A layer is proposed.

Nematic Order in Small Systems: Measuring the Elastic and Wall-Anchoring Constants in Vibrofluidized Granular Rods

We investigate nematic order in vibrated granular rods confined to a small quasi-2D container less than 10 rod lengths in diameter. As rod density ρ increases, patterning shifts from bipolar to uniform alignment. We find that a continuum liquid crystal free energy functional captures key patterning features down to almost the particle size. By fitting theory to experiments, we estimate the relative values of bend and splay elastic constants and wall anchoring. We find that splay is softer than bend for all ρ and rod lengths tested, while the ratio of the average elastic constant to wall anchoring increases with ρ.

Direct visualization and measurement of the extrapolation length on cooling toward the nematic–smectic-Aphase transition temperature

A herringbone "easy axis" pattern is scribed into a polyimide alignment layer for liquid-crystal orientation using the stylus of an atomic force microscope. Owing to the liquid crystal's bend elasticity K33 , the nematic director is unable to follow the sharp turn in the scribed easy axis, but instead relaxes over an extrapolation length L=K33/W2φ, where W2φ is the quadratic azimuthal anchoring strength coefficient. By immersing a tapered optical fiber into the liquid crystal, illuminating the fiber with polarized light, and scanning the fiber close to the substrate, a visualization and direct measurement of L are obtained on approaching the nematic-smectic- A phase transition temperature T NA from above. L is found to exhibit a sharp pretransitional increase near T NA, consistent with a diverging bend elastic constant.

Temperature dependence of the electro‐optic characteristics in the liquid crystal display switching modes

As the physical properties of nematic liquid crystals vary with respect to temperature, the performances of liquid crystal displays (LCDs) are highly dependent on temperature. Additionally, it is well known that the electro‐optic characteristics of LCDs, such as transmittance and threshold voltage, also rely on the LCD switching modes. The temperature dependence of the electro‐optic characteristics of the wide‐viewing‐angle LCD modes, such as in‐plane switching (IPS), multidomain vertical alignment by patterned electrode (PVA), and fringe‐field switching (FFS), have been studied, and the results showed that the FFS mode has lower temperature dependence compared to the IPS and PVA modes. Since the liquid crystal (LC) reorients in different ways in each mode, this result is associated with the temperature dependence of LC's bend and twist elastic constants, and also with the position of the main reorientation, either in the middle or on the surface of the LC layer.

Elastic property of organized lipid assembly — Effect of water incorporation and chain melting

The effect of electric field on the capacitance of lipid–water dispersion properly aligned on polyvinyl alcohol coated glass electrodes, shows a transition pattern where a rapid change in orientation of the organized lipid assembly takes place for an electric field above a threshold value ( V th), similar to that of Freedericksz’s transition as observed in the case of thermotropic liquid crystals. The splay elastic constant, k 11 and the bend elastic constant, k 33 have been calculated from the measured values of capacitance of the cell below and above V th. These values change by several orders of magnitude depending upon the presence of water as well as temperature of chain melting of the lipid moiety.

Experimental Study of Anchoring Characteristics and Splay-Bend Surface-Like Elasticity of Nematics with Using Non-Twisted Nematic Cells

Question of second-order terms in bulk elastic free energy functional for nematics is discussed and investigated experimentally. Under assumption that these surface-like terms contribute only to surface free energy functional, they were firstly substituted by boundary conditions. Several flat-parallel cells (of thickness from 1.9 µm to 31.2 µm) filled with 5CB nematics of planar initial orientation (induced by substrates covered with rubbed SE130 polyimide) were investigated in static electric fields by measurement of their optical transmittance influenced by planar deformation states. The splay and bend elastic constants and anchoring characteristics were determined from these experimental data. The polar anchoring for this nematics-substrate system can not be qualified uniquely as strong or weak. Simulated optical transmittance characteristics computed with using these parameters imitate results of experiment with good accuracy within measurement errors. It is demonstrated that precise determining of nematics-substrate coupling and nematics material parameters is sufficient for quantitative description of nematics deformations. Afterwards the values of components of the free energy of nematics layer corresponding to the bulk elastic deformation, bulk interaction with electric field, nematics interaction with boundary and splay-bend surface contribution are computed from experimental data in two cases which can be interpreted as weak and strong anchoring. The following comparison of them leads to conclusions on the negligible magnitude order of the splay-bend elastic constant.

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 (εpar and εort) 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.

Curvature elasticity of nematic liquid crystals: simply a matter of molecular shape? Insights from atomistic modeling

The elastic moduli of low-molar-mass thermotropic liquid crystals (LCs) exhibit an intriguing dependence on the molecular structure of the constituents, which can be very important for applications. We have recently developed a molecular field theory, wherein the elastic constants of nematics are expressed in terms of integrals over the molecular surface. This theory, combined with molecular geometry optimization, allows us to connect mesoscale deformations in liquid crystals to atomic-scale details. Here we investigate typical mesogenic systems, i.e.para-azoxyanisole (PAA) and 4-n-alkyl,-4′-cyanobiphenyls (nCBs), whose elastic properties exhibit clear differences. We show that these can be traced back to differences in molecular shape. Our calculations also highlight the importance of the flexibility of mesogens, which was generally ignored by previous theories: in view of their different shape, conformers are shown to give different contributions to the elastic constants. The key role of deviations from a rod-like shape, which is generally assumed by models of mesogens, emerges from our calculations. The bend elastic constant is shown to be particularly sensitive to this feature; for a given compound, rod-like conformers give a high contribution to the bending stiffness, whereas the contribution of bent conformers is low or even negative. The possible implications of these findings are discussed, with special reference to the behavior of bent-core mesogens. Finally, we predict the temperature dependence of the surface-like elastic constants, whose experimental determination is still controversial; we find that these are generally smaller than the bulk moduli and even more sensitive to changes in the molecular shape.

Physical characterisation of 4′-butyl-4-heptyl- bicyclohexyl-4-carbonitrile

We report measurements of birefringence, bend elastic constant, principal dielectric constants and conductivities as functions of temperature in the nematic phase of 4′-butyl-4-heptyl-bicyclohexyl-4-carbonitrile (CCN-47). The compound exhibits a small birefringence and a large negative dielectric anisotropy. Surprisingly, it shows a negative conductivity anisotropy, which probably owes its origin to the structural details of the molecules. The orientational order parameters (S) are estimated from both birefringence and dielectric anisotropy, and they agree well in the entire nematic range. The experimental results are compared with those on CCH7, which has a similar core structure but with a longitudinal dipole moment, in place of the transverse one of CCN-47.

Influence of a magnetic field on the nematic phase of hard colloidal platelets

We report on a study of the influence of a magnetic field on the nematic phase and the isotropic-to-nematic (IN) phase transition of hard colloidal gibbsite platelets. We find direct visual evidence of a shift of the IN transition to lower concentrations due to the magnetic field. The nematic phase readily aligns when contained between two parallel flat glass walls, with homeotropic orientation. This well-defined surface anchoring enables a measurement of the bend Frederiks transition, yielding the bend elastic constant of a nematic phase of hard disks as K(3) = 7 x 10(-14) N . By applying a rotating magnetic field on the nematic phase, we observe the bend-splay Frederiks transition, visible as a spatially periodic transient pattern with a wavelength that depends on sample thickness and field strength. Following a linear stability analysis we are able to account for this dependence in a qualitative way. Moreover, the rotating magnetic field enables us to render the nematic phase single domain, with well-defined director orientation.

Theory of anchoring on a two-dimensionally grooved surface

We investigate analytically the anchoring of a nematic liquid crystal on a two-dimensionally grooved surface of arbitrary shape, induced by the elastic distortions of a liquid crystal adjacent to the surface. Our theoretical framework applied to a surface with square grooves reveals that such a surface can exhibit bistable anchoring, while a direct extension of a well-known theory of Berreman [Phys. Rev. Lett. 28, 1683 (1972)] results in no azimuthal anchoring in the so-called one-constant case (K1=K2=K3, with K1, K2, and K3 being the splay, twist, and bend elastic constants, respectively). We show under the assumption of K1=K2=K that the direction of the bistable easy axes and the anchoring strength crucially depend on the ratios K3/K and K24/K, where K24 is the saddle-splay surface elastic constant. To demonstrate the applicability of our theory to general cases and to elucidate the effect of surface shape and the elastic constants on the properties of surface anchoring, we also consider several specific cases of interest; one-dimensional grooves of arbitrary shape, rhombic grooves, and surfaces possessing 2N -fold symmetry, including hexagonal grooves, and show the following: (i) The rescaled anchoring energy f(phi)/f(pi/2) of one-dimensional grooves, with phi being the angle between the director n and the groove direction, is independent of the groove shape. (ii) Whether two diagonal axes of rhombic grooves can become easy axes depends sensitively on K3/K, K24/K and the angle alpha between the grooves. The angle alpha yielding the maximum anchoring strength for given groove pitch and amplitude depends again on K3/K and K24/K; in some cases alpha=0 (one-dimensional grooves), and in other cases alpha not equal 0, gives the maximum anchoring strength. Square grooves (alpha=pi/2) do not necessarily exhibit the largest anchoring strength. (iii) A surface possessing 2N -fold symmetry can yield N -stable azimuthal anchoring. However, when K1=K2=K3 and N>or=3, azimuthal anchoring is totally absent irrespective of the value of K24. The direction of the easy axes depends on K3/K, K24/K, and whether N is even or odd.

Spontaneous bend patterns in homochiral ferroelectric SmCP films: evidence for a negative effective bend constant

We describe the spontaneous formation of striped and labyrinthine textures of the c-director in freely suspended polar smectic SmCPF films of a bent-core mesogen. Those films develop an instability of the uniform director field. The texture decomposes into local domains of alternating bend. Both right- and left-handed bends of the director occur with equal probability, independently of the overall chirality defined by the local structure of the SmCPF phase. Thus, despite the overall chirality, the system prefers a ground state with bend deformations of both handedness (ambidextrous) of the director. In this paper we suggest a theoretical explanation of this spontaneous bend of the c-director. We assume a negative effective bend elastic constant, in order to explain the formation and optical appearance of the observed stripe and labyrinthine patterns.