Fluctuation shift of the nematic–isotropic phase transition temperature

A macroscopic counterpart to the microscopic mechanism of the straightening dimer mesogens conformations, proposed recently by S.M. Saliti, M.G. Tamba, S.N. Sprunt, C. Welch, G.H. Mehl, A. Jakli, and J.T. Gleeson [Phys. Rev. Lett. 116, 217801 (2016)] to explain their experimental observation of the unprecedentedly large shift of the nematic–isotropic transition temperature is discussed. The proposed interpretation is based on singular longitudinal fluctuations of the nematic order parameter. Since these fluctuations are governed by the Goldstone director fluctuations, they exist only in the nematic state. External magnetic field suppresses the singular longitudinal fluctuations of the order parameter (similarly as is the case for the transverse director fluctuations, although with a different scaling over the magnetic field). The reduction of the fluctuations changes the equilibrium value of the magnitude of the order parameter in the nematic state. Therefore, it leads to additional (with respect to the mean field contribution) fluctuation shift of the nematic–isotropic transition temperature. Our mechanism works for any nematic liquid crystals, however the magnitude of the fluctuation shift increases with decrease in the Frank elastic moduli. Since some of these moduli supposed to be anomalously small for so-called bent-core or dimer nematic liquid crystals, just these liquid crystals are promising candidates for the observation of the predicted fluctuation shift of the phase transition temperature.     

Effect of high electric fields on the nematic to isotropic transition in a material exhibiting large negative dielectric anisotropy

We report the experimental high electric field phase diagram of a nematic liquid crystal which exhibits a large negative dielectric anisotropy. We measure simultaneously the birefringence (Δn) and the dielectric constant (epsilon_⊥) at various applied fields as functions of the local temperature of an aligned sample. We also measure the higher harmonics of the electrical response of the medium. The following experimental results are noted: (i) enhancement of orientational order parameter S in the nematic phase due to both the Kerr effect and quenching of director fluctuations; (ii) enhancement in the paranematic to nematic transition temperature (T_PN) with field; (iii) divergence of the order parameter susceptibility beyond the tricritical point as measured by third harmonic electrical signal; (iv) a small second harmonic electrical signal which also diverges near T_PN, indicating the presence of polarised domains. Our measurements show that ΔT_PN(= T_PN(E)-T_NI(0)) varies linearly with |E| whereas the Landau de Gennes theory predicts a dependence on E². It is argued that the quenching of director fluctuations by the field makes the dominant contribution to all the observations, including the thermodynamics of the transition.     

Fluctuations of orientational order in a uniaxial nematic liquid crystal with biaxial molecules and its response to an external field

Homogeneous thermal fluctuations of the orientational order parameters S and G of biaxial molecules in a uniaxial nematic liquid crystal are investigated in the framework of the molecular-statistical theory. It is demonstrated that the molecular biaxiality significantly affects the order parameters S and G, their temperature dependences in the nematic phase, the amplitude and the temperature dependence of the order parameter fluctuations in the nematic and isotropic phases, and the character of the transition from the nematic phase to the isotropic liquid phase. It is established that the fluctuations of the parameters S and G in the nematic phase are related to the temperature dependences of S and G and the susceptibilities χ_S and χ_G of the nematic liquid crystal to external fields, which leads to a change in the parameters S and G at a fixed director orientation. Explanations are offered for the known experimental data on the orientational ordering of biaxial molecules under the action of external fields in the isotropic phase of nematic liquid crystals.     

Isotropic to nematic transition of aerosil-disordered liquid crystals

We present a high-resolution study of the isotropic to nematic phase transition of a low birefringence liquid-crystal compound incorporating an aerosil gel. Calorimetry, light scattering, and microscopy data coherently combine to allow for an accurate determination of the temperature dependence of the onset of the nematic state. The nematic order develops on cooling through two distinct processes while the nematic correlation length mildly decreases. We understand the doubling of the phase transition as due to a crossover from a random-dilution regime, where the silica gel couples to the scalar part of the nematic order parameter, to a low-T random-field regime, where the coupling induces distortions in the director field.     

Rapid viscous flow of a nematic liquid crystal in the vicinity of the nematic-smectic <Emphasis Type="Italic">A</Emphasis> transition

The resistance to shear flow is investigated theoretically for polar liquid crystals, such as 4-n-octyl-4′-and 4-n-octyloxy-4′-cyanobiphenyls. It is established that the lowest resistance to shear flow at temperatures in the vicinity of the nematic-smectic A phase transition point T _NA is observed when the nematic director is oriented perpendicular to both the flow velocity vector and the flow velocity gradient. The three Miesowicz shear viscosity coefficients η_i (i=1–3) at temperatures close to the phase transition temperature (tens of millikelvins from T _NA ) and far from this transition are calculated in the framework of the Ericksen-Leslie theory. The decrease in the viscosity coefficients in the order η₂>η₁>η ₃ is explained by the fact that fluctuations of the local smectic order in the nematic phase lead to a singular behavior of the viscosity coefficient η₂, whereas the other two viscosity coefficients η₁ and η₃ are not affected by order parameter fluctuations.     

Critical exponents for Fréedericskz transition in nematics between concentric cylinders

The equilibrium tilt angle profile in a cell limited by two concentric cylinders filled with nematic liquid crystals is determined for strong homeotropic anchoring at the surfaces. The anchoring condition is such that the nematic director is perpendicular to the cylinder axes and a radial nonuniform electric field is applied to investigate a Fréedericksz transition. The distortions induced by the field remain in the plane perpendicular to the cylinder axes, and a threshold field is analytically determined indicating a transition from a pure splay to a splay-bend conformation of the director. It is shown that this transition can be induced by the thickness of the region between the two cylinders, and can be detected even in the absence of an external field. If the maximum value of the tilt angle is assumed as an order parameter, its behavior near to the transition can be used to obtain the critical exponent, which is the same as the one obtained in the mean field approximation. These results are indications that nontrivial consequences may occur when complex fluids are subject to non-planar geometries.     

Computer simulation study of the two-dimensional nematic lattice model based on the modified Gruhn–Hess pair potential model

A modified Gruhn–Hess pair potential model, where the potential parameters related to the elastic constants are different from the original model, was investigated with the aid of Monte Carlo (MC) simulation and Mean Field (MF) theory based upon a two-dimensional nematic lattice model. The model produces a ground state in perfect nematic order, where particles are aligned in the lattice plane. Both the MF predictions and the simulation results for the second-rank ordering tensor show that the system is biaxial in the low-temperature region, with a positive primary order parameter and the main director aligned along the lattice axis. A transition to uniaxial order takes place at higher temperatures with a negative primary order parameter and the director is orthogonal to the lattice plane. This orientational order survives up to temperatures higher than the transition temperature of the three-dimensional lattice model, possibly at all finite temperatures. MF predictions agree qualitatively with simulation but, in quantitative terms, the transition temperature is overestimated by 52%.     

表面极化对弱锚定向列液晶盒饱和特性的影响

以修正后的Rapini-Papoular锚定能公式为基础, 用理论分析和数值计算相结合的方法, 详细研究表面极化对液晶盒饱和特性的影响. 得出了求解指向矢分布的数学方程, 推导出了计算正常二级转变饱和电压的解析式, 同时结合最新报道, 给出了异常一级转变饱和电压的数值计算方法. 此外, 本文引入了反映指向矢分布特征的参量, 讨论了表面极化对此参量的影响. 结果表明, 指向矢最大倾角的位置随表面极化的增大将远离中央平面向基板移动. 一级转变饱和电压随弱锚定基板表面极化的增大而减小, 随强锚定基板表面极化的增大而增大. 而对二级转变, 饱和电压随表面极化的变化与一级转变恰恰相反. 本文所得结论对液晶表面物理的理解及液晶实际应用都具有重要的指导意义.     

Temperature and orientation dependence of surface relief gratings based on dye-doped polymer film with the interface of nematic liquid crystals

The formation of surface relief grating on dye-doped polymer film with the interface of nematic liquid crystals has been investigated by means of the holographic technique. The first-order diffraction efficiency of surface relief grating depends on the temperature and the orientation of molecular director in the interface of nematic liquid crystals. The diffraction efficiency is roughly independent of thermal fluctuations of molecular director in the most part of nematic temperature range and apparently drops near the transition temperature. The morphology of surface relief grating demonstrates that the surface modulation is larger for molecular director parallel to the groove direction. The experimental result also shows that the first-order diffraction efficiency is dependent on the surface modulation of surface relief grating.     

Surface driven transition in a nematic liquid crystal cell

Surface driven reorientation effects in a nematic liquid crystal cell caused by light-induced changes of the anchoring parameters were studied. Theoretical consideration of one-dimensional flat distributions of the director has shown that the director can undergo threshold reorientation between hybrid, homeotropic, and planar alignments as the anchoring energy varies continuously. The threshold reorientation takes place when the reference and light-induced easy axes are perpendicular. In the one-elastic-constant approximation the light-induced transition was found to be of second order as shown by a critical increase of the director thermal fluctuations in the vicinity of the transition point. These effects were experimentally studied in the cells containing 5CB liquid crystal aligned by the photosensitive azo-containing polymer layer. Zh. éksp. Teor. Fiz. 112, 2045–2055 (December 1997) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

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)     

Order parameter and its critical exponent for some binary mixtures showing induced nematic phase

Refractive index measurements as a function of temperature have been performed for an induced nematic binary system by means of thin prism technique. The temperature dependence of the birefringence (Δn) has been assessed from the measured refractive index data. A direct extrapolation method has been employed to determine the orientational order parameter for the investigated mixtures and the order parameter so obtained has also been compared with the mean field values. The Haller type fitting expression results in a relatively lower value of the order parameter critical exponent (β) compared to the theoretically predicted values. Therefore, a four-parameter power law expression, consistent with the mean field theory as well as the first-order character of the nematic–isotropic (N-I) phase transition have been used to explore the critical behavior of the order parameter near the N-I transition.     

The elastic anisotropy of nematic elastomers

We examine the robustness of order in nematic elastomers under mechanical strains imposed along and perpendicularly to the director when director rotation is prohibited. In contrast to electric and magnetic fields applied to conventional nematics, mechanical fields are shown theoretically and experimentally to greatly affect the degree of nematic order and related quantities. Unlike in liquid nematics, one can impose fields perpendicular to the director, thereby inducing biaxial order which should be susceptible to experimental detection. Nematic elastomers with unchanging director and degree of order should theoretically have the same elastic moduli for longitudinal and transverse extensions. This is violated when nematic order is permitted to relax in response to strains. Near the transition we predict the longitudinal modulus to be smaller than the transverse modulus; at lower temperatures the converse is true, with a crossover a few degrees below the transition. The differences are ascribed to the different temperature dependence of the stiffness of uniaxial and biaxial order. We synthesised side chain single-crystal nematic polymer networks, performed DSC, X-ray, birefringence, and thermo-mechanical characterisations, and then obtained linear moduli from stress-strain measurements. Received 29 September 2000     

Fluctuations in liquid crystals in the presence of a flexoelectric effect

We examine director fluctuations in nematic liquid crystals in an electric field in the presence of a flexoelectric effect. For the planar and homeotropic orientations we calculate the correlation functions and analyze these functions near the Freedericksz transition and the flexoelectric instability threshold. For both geometries we calculate the angular dependence of the intensity of light scattered by director fluctuations and examine its behavior at electric field strengths close to critical. Zh. éksp. Teor. Fiz. 112, 1675–1693 (November 1997)     

PMRD investigations of molecular dynamics and phase transitions in the liquid crystal 6CHBT

Proton Magnetic Relaxation Dispersion (PMRD) measurements were carried out over a wide Larmor frequency range near the isotropic-nematic transition temperature (T _NI) and in the mid nematic phase of a low viscous liquid crystal 4-(trans-4′-hexylcyclohexyl)-isothiocyanatobenzene (6CHBT), with a view to examining the pre-transitional effects just above isotropic-nematic transition (T > T _NI) and the role of director fluctuations (DF) on the nematic phase stability of this system. The results near the transition indicate critical slowing down of the short-range nematic order modes just above T _NI with a mean field critical exponent characterizing the coherence length (ξ). The observed temperature independence of the correlation time associated with the reorientations (τ_R) and the extension of DF mode spectrum, in the mid-nematic phase, to relatively higher resonance frequencies seem to suggest fairly low hindering barriers for the tumbling of the molecules about their short axes.     

Self-assembly and nonlinear dynamics of dimeric colloidal rotors in cholesterics

We study by simulation the physics of two colloidal particles in a cholesteric liquid crystal with tangential order parameter alignment at the particle surface. The effective force between the pair is attractive at short range and favors assembly of colloid dimers at specific orientations relative to the local director field. When pulled through the fluid by a constant force along the helical axis, we find that such a dimer rotates, either continuously or stepwise with phase-slip events. These cases are separated by a sharp dynamical transition and lead, respectively, to a constant or an ever-increasing phase lag between the dimer orientation and the local nematic director.     

Reorientation effect on the current-voltage characteristics of a nematic cell

Possible mechanisms explaining the character of the relation I=I(V) for a nematic cell subjected to a large electric field are discussed, taking into account the reorientation effect of the nematic director induced by the external electric field. The analysis is performed in the quasi-static regime where the nematic orientation follows the time variation of the external field without delay. The time variation of the equivalent capacitance of the cell is equivalent to a pure resistance, and is responsible for a current peak when the applied voltage overcomes the threshold voltage for the transition of Fréedericksz.     

Molecular field theory for nematic liquid crystal film with finite layers

The nematic liquid crystal film composed of n molecular layers is studied based upon a spatially anisotropic pair potential, which reproduces approximately the elastic free energy density. On condition that the system has perfect nematic order, as in the Lebwohl—Lasher model, the director in the film is isotropic. The effect of the temperature is investigated by means of molecular field theory. Some new results are obtained. Firstly, symmetry breaking takes place when taking account of the temperature, and the state with the director along the normal of the film has the lowest free energy. Secondly, the N—I phase transition temperature increases as an effect of finite sizes instead of decreasing as in the Lebwohl—Lasher model. Thirdly, the nematic order is induced in the layers near the surface in the isotropic phase.     

Tricritical-like behavior of the nonlinear optical refraction at the nematic-isotropic transition in the E7 thermotropic liquid crystal

We use Z-scan technique to investigate the nonlinear optical response of the thermotropic liquid crystal E7 in the neighborhood of the nematic-isotropic phase transition. The analysis of the data for the nonlinear optical birefringence is compatible with an effective critical exponent of the order parameter, β = 0.28 ± 0.03, which is close to the classical value, β = 0.25 , for a tricritical point. The nonlinear optical absorption in the nematic range depends on the geometrical configuration of the nematic director with respect to the polarization beam, and vanishes in the isotropic phase.     

Flexoelectric polarization and second order elasticity for nematic liquid crystals

The flexoelectric properties of nematic liquid crystals are analysed. It is shown that in the frame of the usual elasticity two coefficients characterize completely the flexoelectric properties of the liquid crystal. These coefficients, in the limit of small scalar order parameter, i.e. near the clearing point, are approximately equal. More precisely they have the same linear term in the scalar order parameter, and differ for terms quadratic in this parameter. Their difference behaves, hence, as the usual nematic liquid crystal elastic constants, whereas their sum depends on the temperature, like the mixed splay-bend elastic constant. It is shown furthermore that in the frame of a second order elastic theory in the flexoelectric polarization there are no terms from the second order spatial derivatives of the nematic director, or the nematic tensor order parameter. Consequently also in the frame of the second order elasticity the flexoelectric polarization is given by the usual expression. This conclusion is important in connection with the surface polarization recently discovered in pretilted nematic liquid crystal samples.