Laser light scattering technique for non-invasive in situ simultaneous measurements on elastic constants and viscosity coefficients of nematic liquid crystals

Theelasticconstantsandtheviscositycoefficientsarethekeyparametersforthephysicalpropertiesofnematicliquidcrystals(LCs)[1,2],fortheyarecorrespondingtothethresholdvoltageandtherespondingtimeofliquidcrystaldisplaydevices[3,4].Sofarnotechniquethatcansimultaneouslymeasurethetwoparametersinsituhasbeenreported.TheelasticconstantsandviscositycoefficientsofnematicLCsatthepresentaremeasuredusingdifferentmethodsindependently.TheviscositycoefficientsisgenerallymeasuredwithOstwaldviscosimeter,andtheelasti…     

Critical Elastic Coefficient of Liquid Crystals and Hysteresis

P. G. de Gennes predicted the analogies between the effect of the elastic coefficients to liquid crystals and the effect of applied magnetic fields to superconductors, and predicted that all elastic coefficients diverge to infinity at smectic-C to nematic transition. One would expect quantitative comparison in the analogies. In the case of equal elastic coefficients (K ₁ = K ₂ = K ₃ = K), we define the critical value K ^c of the elastic coefficients and make comparison of it with the upper critical magnetic field H _{C 3} for type II superconductors. We classify the smectic liquid crystals into subcritical, critical and supercritical cases according to the Ginzburg-Landau parameter κ, the wave number q and the boundary value of the director at the surface. We show that in the subcritical case the liquid crystal does not undergo phase transition; and in the supercritical case both phase transition and hysteresis occur. The prediction of de Gennes is true in the critical case where μ _π (u ₀, q) = κ ² and K ^c = + ∞.     

Rotational viscosity coefficients of nematic and smecticC liquid crystals: Statistical theory

Summary The rotational diffusion of a rodlike molecule in a nematic and smecticC liquid crystal is considered in the molecular-field approximation. The microscopic friction constant, which determines the molecular rotation drag, possesses an exponential temperature dependence with the activation energy determined by the isotropic part of the intermolecular interaction energy. The rotational viscous coefficients,γ ₁ andγ _⊥ are obtained by averaging of the corresponding microscopic stress tensor with the nonequilibrium distribution function. The additional activation energy, proportional to the corresponding order parameter, appears in the expressions for the rotational viscosity coefficients both in nematics andC smectics. Work presented at the second USSR-Italy Bilateral Meeting on Liquid Crystals held in Moscow, September 15–21, 1988.     

Investigations of twist elastic constant K<Subscript>22</Subscript> of new nematic liquid crystal materials using threshold IPS method

The liquid crystal technology is one of the most popular at the present time. To the most important parameters of liquid crystals belong optical anisotropy, viscosity, and twist elastic constants. One of the most difficult and problematic to measure parameters is a twist elastic constant K₂₂. For new liquid crystalline materials, we have to characterize their physical properties, also a twist elastic constant K₂₂.     

Hadron production near threshold

Final state interaction effects inpp→ pΛK ⁺ andpd →³Heη reactions are explored near threshold to study the sensitivity of the cross-sections to thepΛ potential and theηN scattering matrix. The final state scattering wave functions between Λ andp andη and³He are described rigorously. The Λ production is described by the exchange of one pion and aK-meson between two protons in the incident channel. Theη production is described by a two-step model, where in the first step a pion is produced. This pion then produces anη by interacting with another nucleon     

Structure,elasticity and phase transitions in liquid crystals with deformations

ABSTRACT

A molecular-statistical theory describing the nematic liquid crystals (LCs) with spherical inclusions (or point defects) is proposed. At given size of inclusions and nematic order parameters at the surfaces of inclusions (zero in the case of point defects) and far from inclusions (where the nematic LC is almost uniform), the distribution of nematic order parameters in the bulk of LC with inclusions was found to be fully determined by the elastic constants of LC. We have found and explained the two-step heat-driven transformation from the nematic phase into the isotropic phase, with the intermediate phase in between. The nematic order parameters and the elastic constants are evaluated in the framework of a unified approach based on the features of pair interaction potentials of the individual LC molecules. It is shown that, in the case of K₃₃ < K₁₁, the point defects should destroy the conventional nematic phase.     

Resonances inη-light nucleus systems

We locate resonances inη-light nucleus elastic scattering using the time delay method. We solve few-body equations within the finite rank approximation in order to calculate the t-matrices and hence the time delay for theη-³He andη-⁴He systems. We find a resonance very close to the threshold inη-³He elastic scattering, at about 0.5 MeV above threshold with a width of ∼2 MeV. The calculations also hint at the presence of sub-threshold states in both the cases     

Director dynamics near the nematic-smectic-A phase transition

The Landau-de Gennes model for the free energy of a nematic liquid crystal near the phase transition to the smectic A-phase is used to determine the frequency dependence of the fluctuation corrections to the Frank elastic constants. It is shown that the interaction of the fluctuations of the smectic order parameter and the director results in corrections to all the Frank elastic constants. In the low-frequency limit (ω→0), the corrections to the Frank elastic constants K ₂₂ and K ₃₃ are the largest, and decrease to zero in the infinite-frequency limit. The correction to K ₁₁ is negative, and vanishes in both limits. The absolute value of the correction to K ₁₁ is the largest at frequencies in the megahertz range. It is shown that in oriented nematics the interaction of the smectic fluctuations and the director limits deviations of the director from the direction of preferred orientation, as a result of which relaxation of both inhomogeneous and homogeneous distortions of the director field can be observed. It is also shown that this gives rise to a frequency interval in the megahertz range in which shear waves begin to propagate in the nematic. The propagation speed of these waves is roughly a hundred times smaller than that of sound and strongly depends on the direction of propagation. Zh. éksp. Teor. Fiz. 114, 2022–2033 (December 1998)     

Structures and autocorrelation functions of liquid Al and Mg modelled via Lennard-Jones potential from molecular dynamics simulation

The structures and autocorrelation functions of Al and Mg in the liquid state are investigated through the pair distribution functiong(r), the diffusion coefficients as well as the shear viscosity via the Green-Kubo and Einstein relations. From the structure and the Enskog relation we determined the frequency of collisions of atoms in the first shell ofg(r) in the systems. We also discovered that the packing fraction of Lennard-Jones liquids should be approximately half the reduced density value. This approximation is accurate to within 99%. The temperature dependence of the pair distribution function and the atomic mean square displacement are investigated by performing simulations at various experimental temperatures and corresponding densities. The structures of the systems are affected by temperature via movements of atoms in the first minimum ofg(r). The Lennard-Jones model shows that density dependence of the shear viscosity is in agreement with what is expected of simple liquids in the range of investigated temperatures and densities. In the gas limit, the Stoke-Einstein relationDη =K _BT /2πσ is grossly overestimated by Lennard-Jones model. This could not be attributed to deficiencies in the model, as other investigators using first principle method could not obtain the gas limit of the Stoke-Einstein relation.     

Interaction between disinclinations in nematic liquid crystals

The forces of interaction between disinclinations in nematic liquid crystals as well as between a disinclination and a wall are calculated on the basis of the elastic theory of Oseen and Frank under the assumption K₁₁ = K₃₃.     

Numerical investigation of influence of ionic space charge and flexoelectric polarization on measurements of elastic constants in nematic liquid crystals

Deformations of nematic layers caused by magnetic field allow determination of the elastic constants of liquid crystal. In this paper, we simulated numerically the deformations of planar and homeotropic nematic layers. The flexoelectric properties of the nematic and presence of ions were taken into account. Our aim was to show the influence of flexoelectricity on the results of the real measurement of the elastic constants k₃₃ and k₁₁. In these simulations, we calculated the optical phase difference ΔΦ between the ordinary and extraordinary rays of light passing through the layer placed between crossed polarizers as a function of the magnetic field induction B. One of the elastic constants can be calculated from the magnetic field threshold for deformation. The ratio k₃₃/k₁₁ can be found by means of fitting theoretical ΔΦ(B) dependence to the experimental results. The calculations reveal that the flexoelectric properties influence the deformations induced by the external magnetic field. In the case of highly pure samples, this may lead to false results of measurement of the elastic constants ratio k₃₃/k₁₁. This influence can be reduced if the nematic material contains ions of sufficiently high concentration. These results show that the flexoelectric properties may play an important role, especially in well purified samples.     

K-matrix analysis of the (IJ<Superscript>PC</Superscript> = 00<Superscript>+ +</Superscript>)-wave in the mass region below 1900 MeV

We present the results of the current analysis of the partial wave IJ ^PC = 00^{+ +} based on the available data for meson spectra ( ππ, KˉK,ηη,η,ππππ). In the framework of the K-matrix approach, the analytical amplitude has been reconstructed in the mass region 280 MeV < < 1900 MeV. The following scalar-isoscalar states are seen: comparatively narrow resonances f ₀(980), f ₀(1300), f ₀(1500), f ₀(1750) and the broad state f₀(1200-1600). The positions of the amplitude poles (masses and total widths of the resonances) are determined as well as pole residues (partial widths to meson channels ππ, KˉK,ηη,η,ππππ). The fitted amplitude gives us the positions of the K-matrix poles (bare states) and the values of bare-state couplings to meson channels thus allowing the quark-antiquark nonet classification of bare states. On the basis of the obtained partial widths to the channels ππ, KˉK,ηη,η, we estimate the quark/gluonium content of f ₀(980), f ₀(1300), f ₀(1500), f ₀(1750), f₀(1200-1600). For f ₀(980), f ₀(1300), f ₀(1500) and f ₀(1750), their partial widths testify the qˉq origin of these mesons though being unable to provide precise evaluation of the possible admixture of the gluonium component in these resonances. The ratios of the decay coupling constants for the f₀(1200-1600) support the idea about the gluonium nature of this broad state. Received: 14 May 2002 / Accepted: 20 August 2002 / Published online: 11 February 2003 RID="a" ID="a"e-mail: anisovic@thd.pnpi.spb.ru Communicated by A. Sch?fer     

Effect of electric field on the rheological and dielectric properties of a liquid crystal exhibiting nematic-to-smectic-A phase transition

We report simultaneous measurements of shear viscosity (η) and dielectric constant (ε) of octyloxy cyanobiphenyl (8OCB) in the nematic (N) and smectic-A (SmA) phases as functions of temperature and electric field. With increasing electric field η increases in the N phase whereas it decreases in the SmA phase and saturates beyond a particular field in both the phases. The flow curves in the intermediate-field range show two Newtonian regimes in the N phase. The temperature-dependent behavior of η and ε at zero or at small electric field suggests the occurrence of several structures that results from precessional motion of the director along the neutral direction as reported in similar other system. We show that the precessional motions are gradually suppressed with increasing electric field and the effective viscosity resembles with the Miesowicz viscosity η ₁ at high enough electric field. In the intermediate field range the temperature-dependent η exhibits anomalous behavior across the N-SmA phase transition which is attributed to the large contribution of Leslie coefficient α ₁.     

Flexoelastic properties of polar liquid crystals

Structural properties of liquid crystals, such as the order parameters and the orientational, radial, and direct correlation distribution functions of polar liquid crystals 4-n-heptyloxy-4′-n-cyanobiphenyl (7OCB) and 4-n-hexyloxy-benzylidene-4′-n-aminobenzonitrile (HBAB) have been calculated using a combination of numerical simulation and statistical mechanics methods. It has been shown that the calculated values of both the Frank elastic coefficients K _i (i = 1, 2, 3) corresponding to the splay, twist, and bend deformations and the flexoelectric coefficients e _i (i = 1, 3) agree with the experimental data for 7OCB. The calculated values of the same coefficients for HBAB have been published for the first time.     

The structure of the distortion free-energy density in nematics: Second-order elasticity and surface terms

Summary By means of a phenomenological approach, we demonstrate that the mixed splay-bend elastic constantK ₁₃ in the free energy density of nematic liquid crystals must be considered zero, unless the bulk contributions of the squares of the distortion second-order derivatives are taken into account, together with the squares of the first-order derivatives times the second-order derivatives, and with the fourth powers of the first-order derivatives. Such contributions just reduce to one in the presence of—and close to—a threshold. Furthermore, the saddle-splayK ₂₄-term instead is shown always to play an essential role, as the bulk first-order elasticity, in determining the distortion free energy of nematics with weak anchoring subjected to spatial deformations. Finally, the new surfacelike elastic constants are shown to have a nilpotent character: thus they behave as well asK ₂₄ from the point of view of the variational calculus. Work presented at the second USSR-Italy Bilateral Meeting on Liquid Crystals held in Moscow, September 15–21, 1988.     

Character of the N D -D h (0, d) phase transition in diskotic liquid crystals

The first experimental data on the orientational ordering of a diskotic reentrant nematic N _D are presented. The data show that the phase transition N _D -D _h (0, d) is a strong first-order transition with a large jump ΔS≃0.2 in the orientational order parameter S of the molecules. This indicates an anomalously strong coupling between the columnar and orientational ordering of the molecules and explains the absence of fluctuational divergence of the elastic moduli K ₁₁ and K ₂₂ in the nematic phase near this transition. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 1, 29–32 (10 January 1996)     

Relation between orientational order parameters of matrix and probe in nematic liquid crystals

Summary The phenomenological relation between the orientational order parameters of matrix (S) and probe (S _p) has been obtained and confirmed for a large number of impure nematic liquid cyrstals. The temperature-dependent parts of the parametersS andS _p are proportional to one another and have the same critical behaviour over the whole mesophase range, although the absolute values ofS andS _p as well as their temperature dependencesS(T) andS _p(T) may be sufficiently different. The relation observed is not the consequence of the known molecular-statistical theories of impure nematic liquid crystals. Work presented at the second USSR-Italy Bilateral Meeting on Liquid Crystals held in Moscow, September 15–21, 1988.     

Photoproduction of η -mesons on the deuteron above S<Subscript>11</Subscript>(1535) in the presence of a narrow P<Subscript>11</Subscript>(1670) -resonance

Incoherent photoproduction of η -mesons on the deuteron is considered. The main attention is paid to the region above the S ₁₁(1535) -resonance where a rather narrow resonance-like structure in the total cross-section extracted for γn → ηn has been reported. The corresponding experimental results are analyzed from the phenomenological standpoint within the model containing a baryon P₁₁ with a mass of about 1670MeV and a width less than 30MeV. This resonance was suggested in some recent works as a nonstrange member of the pentaquark antidecuplet with J ^P = 1/2⁺ . The calculation is also performed for the polarized and unpolarized angular distributions of η -mesons. In addition, we present our predictions for the cross-sections of the neutral kaons and double pion photoproduction, where the same narrow P ₁₁(1670) -resonance is assumed to contribute through the decay into K ⁰Λ and πΔ configuration.     

Light-scattering experiments in dye-doped liquid crystals both to determine crystal parameters and to construct consistent neural network empirical physical formulas for scattering amplitudes

The aim of this paper is two-fold. Firstly, static laser light-scattering amplitude measurements in azo-dye doped nematic liquid crystals (NLCs) were made versus scattering angle, temperature and applied bias voltage. Three NLC parameters were determined: the elastic constant ratios K₁₁/K₂₂ by regression, phase transition temperatures, and Freedericksz voltages from the graphs. They were all doping ratio dependent. Secondly, as a novel approach, by a nonlinear universal function approximator layered feedforward neural network (LFNN) we constructed an explicit form of empirical physical formulas (EPFs) for theoretically unknown nonlinear azo-dye doped NLC scattering amplitude functions. Excellent LFNN test set (i.e. yet-to-be measured experimental data) predictions prove that the constructed LFNN-EPPs estimate unknown amplitude functions consistently. The LFFN-EPFs, too, confirmed the doping-ratio dependency. Also, comparing LFNN and regression amplitude fits, the LFNN fits were significantly better. In conclusion, physical laws embedded in the physical data can be consistently extracted by LFNN. One major potential application in the nonlinear optics domain is that these LFNN-EPFs, by differentiation, integration, minimization, etc., can be used to obtain further NLC scattering amplitude related molecular structural physical quantities. This could in turn help us to develop new nonlinear optical materials.     

Light scattering studies of crossover to a liquid crystal tricritical point

We have used light scattering to study nematic elastic constantsK ₂ andK ₃ in the alkyl-cyanobiphenyl (n CB) system. As the average alkyl chain lengthn increases, the temperature range of the nematic phase decreases and the system approaches a tricritical point. Our data are analyzed to determine the parallel and perpendicular correlation lengths and critical exponents for smectic short-range order. We find a continuous decrease in the critical exponentsv andv as the tricritical point, which occurs at 9.1 CB, is approached. There is also a significant decrease in the magnitude of the parallel correlation length at a fixed reduced temperature.