Leslie Coefficient Research Articles

Thermomechanical coupling in coarse grained cholesteric liquid crystal model systems with pitches of realistic length.

Thermomechanical coupling in cholesteric liquid crystals, i.e. when a temperature gradient parallel to the cholesteric axis rotates the director, has been studied in a model system of soft ellipsoids where the interaction potential has been augmented by a chiral potential. More specifically, the cross coupling coefficient between the temperature gradient and the director angular velocity, or Leslie coefficient, has been obtained as a function of the pitch by evaluating the corresponding Green-Kubo relation by molecular dynamics simulation. The product of the Leslie coefficient and the pitch has been found to be constant within the statistical uncertainty. This is in accordance with a symmetry condition originally proposed by de Gennes and it means that the Leslie coefficient of systems with longer pitches can be obtained from systems with shorter pitches. Since the pitches of realistic systems are usually very long, it becomes possible to study thermomechanical coupling in these systems which otherwise would have required prohibitively long simulations. Since we also have obtained rather accurate data on the cross correlation function between the director angular velocity and the heat current density, it becomes possible to analyse the mechanism of thermomechanical coupling to some extent.

Thermomechanical coupling, heat conduction and director rotation in cholesteric liquid crystals studied by molecular dynamics simulation

The lack of a centre of inversion in a cholesteric liquid crystal allows linear cross couplings between thermodynamic forces and fluxes that are polar vectors and pseudovectors, respectively. This makes it possible for a temperature gradient parallel to the cholesteric axis to induce a torque that rotates the director, a phenomenon known as the Lehmann effect or thermomechanical coupling. The converse is also possible: a torque applied parallel to the cholesteric axis rotates the director and drives a heat flow. In order to study this phenomenon, nonequilibrium molecular dynamics simulation algorithms and Green-Kubo relations evaluated by equilibrium molecular dynamics simulation have been used to calculate the Leslie coefficient, i.e. the cross coupling coefficient between the temperature gradient and the director angular velocity, for a model system composed of soft prolate ellipsoids of revolution interacting via the Gay-Berne potential augmented by a chiral interaction potential causing the formation of a cholesteric phase. It is found that the Leslie coefficient is two orders of magnitudes smaller than other transport coefficients such as the heat conductivity and the twist viscosity, so that very long simulations are required to evaluate it. The Leslie coefficient decreases with the pitch but it has not been possible to determine the exact functional dependence of this coefficient on the pitch. Since very long simulations have been performed to evaluate the Leslie coefficient, very accurate values have been obtained for the twist viscosity and the heat conductivity as a by-product and it is found that they are very similar to the values of the corresponding quantities in the achiral nematic phase that arises when the pitch goes to infinity.

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 η1 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 α1.

Geometrical content of Leslie coefficients

In this work, we will study how the effective geometry acquired by nematic molecules under thermal vibration contribute to the determination of the Leslie coefficients. To do this, we will divide this work in two sections. In the first section, we present the geometrical fundamentals of the so-called Hess-Baalss (HB) approach [D. Baalss and S. Hess, Phys. Rev. Lett. 57, 86 (1986)] where we show that its basic assumptions can be understood as a geometrical interpretation of de Gennes' passage from the microscopic to the macroscopic order parameter. In the second section, we use an extended version of the HB approach [M. Simões, K. Yamaguti, and A. J. Palangana, Phys. Rev. E 80, 061701 (2009)] to obtain the geometrical contribution to each Leslie coefficient. Our results will be compared with experimental data, and we will show that the Miesowicz's coefficients are connected as long as the ratio α(3)/α(4) between these Leslie coefficients can be considered small.

Nematic liquid crystal viscosity: inadequacies of microscopic theories

Recently Janik et al. reported measurements of the Miesowicz viscosity coefficients of the nematic liquid crystal and confronted them with the results of the available theoretical models. They found that none of them can be successfully applied for the purpose of the Miesowicz-type experiment. In this paper I present an explanation why the microscopic theories seem inadequate. In particular, I analyze the applicability and conclusions of the Osipov-Terentjev model, whose final predictions are highlighted to be the same as those of the Kuzuu-Doi theory. It has been shown that the microscopic theories can perfectly explain the behavior of the Miesowicz coefficients difference eta(3)-eta(2) but are inadequate to study their ratio eta(3)/eta(2), which is contributed by the Leslie coefficient alpha(4). A disagreement between experimental data and the theoretical results for alpha(4) is attributed to the fact that the isotropic contribution to alpha(4) in the nematic phase is beyond the scope of the theories that are based on the anisotropic orientational distributions.

Static External Field Effects on the Hydrodynamic Instability of Liquid Crystals Subject to Simple Shear Flow

External field effects on the hydrodynamic instability of a nematic liquid crystal (LC) monodomain are analyzed using the two-dimensional Ericksen−Leslie continuum theory neglecting the Frank elasticity. It is found that in a static magnetic field, the so-called aligning−type LC with the third Leslie coefficient α3 0 can show aligning in a strong magnetic field. The aligning−tumbling and tumbling−aligning transition points are calculated. Corresponding state diagrams for director tumbling and shear aligning are presented, and the tumbling loop is found. The aligning angles in the stable state and the tumbling periods in the unstable state are described analytically, along with the necessary and sufficient conditions for director tumbling. It is especially noteworthy that the direction of the external field plays a crucial role in controlling the hydrodynamic...

Orientation of mesophase pitch in capillary and channel flows

Abstract Analytical solutions to the Leslie-Ericksen equations are discussed for flow through a circular capillary and a rectangular channel. The analysis allows for a director component out of the flow-gradient plane. The resulting orientation profiles match the commonly observed textures of mesophase pitch-based carbon fibres, specifically the radial and line-origin textures. Thus, this formulation would appear to be correct for the flow of discotic mesophase pitches. Furthermore, the velocity profile for capillary flow suggests the possibility of measuring the Leslie coefficient α4 for a mesophase pitch using a capillary rheometer.

Influence of a temperature gradient on the simple shear now of a nematic liquid crystal

The influence of a temperature gradient across the channel on the steady-state simple shear flow of a nematic liquid crystal is investigated. The in-plane mean molecular orientation, velocity field and temperature profile are calculated on the basis of the Leslie-Ericksen theory. The dependence of the elasticity and viscosity on the temperature and the anisotropy of the heat conduction are taken into account. Results are obtained for a flow-aligning and a tumbling nematic. By shifting the temperature across the height of the channel so that the Leslie coefficient α 3 changes sign at some point between the two bounding plates, the combination of flow-alignment and tumbling in a simply sheared liquid crystal is evaluated.

Theory of orientational modes at a nematic-solid interface When do surface modes appear?

Abstract Orientational modes at a solid-nematic interface with Rapini-Papoular boundary conditions are analysed in the framework of continuum nematodynamics, including the coupling of the director and fluid velocity. In the case of planar orientation, a surface mode appears in addition to the ordinary bulk modes, if the coupling between the director and fluid velocity, governed by the Leslie coefficient μ2, is large enough. The dispersion relation for the surface mode exhibits two distinctive regimes as μ2 increases. In a realistic situation, the relaxation rate of the surface mode is several times slower than that of the corresponding bulk mode.

Transient shear flow of a unidomain liquid-crystalline polymer

The transient shear stress response of a unidomain liquid crystalline polymer has been analyzed using a two-dimensional approximation of the linear theory of Ericksen, Leslie, and Parodi. Under constant shear rate deformation, polymers with a negative Leslie coefficient α 3 , which adopt a stable steady-state flow alignment angle, are predicted to exhibit a single strew minimum at a strain less than unity, while a tumbling nematic with α 3 >0 is predicted to exhibit the initial stress maximum at a strain greater than unity. The Leslie coefficients α 1 , α 2 and α 3 as well as the Miesowicz viscosities η c and η b were estimated from shear startup experiments for a unidomain solution of poly(n-hexyl isocyanate) in p-xylene and were compared with predictions from Doi's molecular theory of liquid crystalline polymers

Axisymmetrical Flow of a Nematic Liquid Crystal around a Sphere

Abstract The axisymmetrical steady flow of an incompressible nematic liquid crystal around a sphere is studied on the basis of the Leslie-Ericksen equations. We assume low Reynolds numbers and a fixed director orientation parallel to the moving sphere (or the moving liquid crystal at infinite distance). The influence of the Leslie coefficient a, is neglected. We find a series representation for the streamfunction and the pressure. The force on the sphere, which only depends on the viscosity coefficients η1, and η2 but not on η3, can be represented by a simple formula. Stream line patterns and the pressure distribution on the sphere are presented for several viscosity coefficient ratios. The determination of viscosity coefficients on the basis of the measurement of the force on the sphere is discussed.

Flow of a Nematic Liquid Crystal Around a Cylinder

Abstract The differential equations for the flow of an incompressible nematic liquid crystal perpendicular to an infinite long cylinder are developed for low Reynolds numbers and a fixed director orientation on the basis of the Leslie-Ericksen theory. Some general results are discussed. The velocities and the force on the cylinder only depend on the shear viscosity coefficients n1, n2, and α1, whereas the pressure additionally depends on the Leslie coefficient α5. In a “falling cylinder experiment”, the cylinder will not fall vertically if the director is neither parallel nor perpendicular to the gravitational field. Numerical calculations are performed with the aid of the artificial compressibility method. Stream line patterns as well as results on pressure and force on the cylinder are presented.

Ultrasonic shear and 'capillary viscosity study of 4-cyano-4'-n-heptylbiphenyl in the nematic and the isotropic state

Using capillary viscometry and ultrasonic shear at frequencies between 50 and 70 MHz, we have measured viscous properties of 4-cyano-4'-n-biphenyl (7-CB) in the nematic and the isotropic state. The data in the nematic state, when compared with results from low frequency shear experiments, raise important questions on the behaviour of the Leslie coefficient α3 [1, 2].