Twist Viscosity Research Articles

Diffusion-driven rotation in cholesteric liquid crystals studied using molecular dynamics simulation of a mixture of the Gay-Berne fluid and the Lennard-Jones fluid.

Diffusion-driven rotation in cholesteric liquid crystals has been studied using molecular dynamics simulation. Then a chemical potential gradient parallel to the cholesteric axis induces a torque that rotates the director at a constant rate around this axis, besides driving a mass current. An equimolar mixture of Gay-Berne ellipsoids and Lennard-Jones spheres was used as the molecular model. In order to keep the system homogeneous, the color conductivity algorithm was used to apply a color field instead of a chemical potential gradient to drive a mass current. Then the particles are given a color charge that interacts with a color field in the same way as with an electric field, but these charges do not interact with each other. This algorithm is often used to calculate the mutual diffusion coefficient. In the above liquid crystal model, it was found that the color field induces a torque that rotates the director at a constant rate around the cholesteric axis in addition to driving a mass current. The phenomenon was quantified by calculating the cross-coupling coefficient between the color field and the director angular velocity. The results were cross-checked by using a director rotation algorithm to exert a torque to rotate the director at a constant rate. Besides rotation of the director, this resulted in a mass current parallel to the cholesteric axis. The cross-coupling coefficient between the torque and the mass current was equal to the cross-coupling coefficient between the color field and the director rotation rate within a statistical uncertainty of 10 percent, thus fulfilling the Onsager reciprocity relations. As a further cross-check, these cross-coupling coupling coefficients, the color conductivity, and the twist viscosity were calculated by evaluating the corresponding Green-Kubo relations. Finally, it was noted that the orientation of the cholesteric axis parallel to the color field is the one that minimizes the irreversible energy dissipation rate. This is in accordance with a theorem stating that this quantity is minimal in the linear regime of a nonequilibrium steady state.

Recent progresses in lyotropic chromonic liquid crystal research: elasticity, viscosity, defect structures, and living liquid crystals

ABSTRACTLyotropic chromonic liquid crystals (LCLCs) are formed by linear stacks of disc-shaped molecular in water. Combined by weak, non-covalent forces, these aggregates are reversible, flexible and polydisperse. The self-assembly nature of the basic building units gives nematic LCLCs interesting physical properties, such as very small twist constant as compared with splay and bend constants, very large splay and twist viscosities, strong temperature dependence of , , and , diverse responses to different ionic additives, and large and azimuthally asymmetric disclination cores. We discuss our experimental studies on the viscoelastic properties and the fine structure of disclinations of LCLCs and attribute their unusual properties to the fact that LCLC aggregates are not fixed in size, but vary in response to changes of temperature, concentration and ionic content in the system. We further use these properties to explain intriguing phenomena in the ‘living liquid crystals’ composed of chromonic liquid crystal and motile bacteria Bacillus Subtilis.

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.

Twist viscosities and flow alignment of biaxial nematic liquid crystal phases of a soft ellipsoid-string fluid studied by molecular dynamics simulation

We have calculated the twist viscosity and the alignment angle between the director and the stream lines in shear flow of a liquid crystal model system, which forms biaxial nematic liquid crystals, as functions of the density, from the Green-Kubo relations by equilibrium molecular dynamics simulation and by a nonequilibrium molecular dynamics algorithm, where a torque conjugate to the director angular velocity is applied to rotate the director. The model system consists of a soft ellipsoid-string fluid where the ellipsoids interact according a repulsive version of the Gay-Berne potential. Four different length-to-width-to-breadth ratios have been studied. On compression, this system forms discotic or calamitic uniaxial nematic phases depending on the dimensions of the molecules, and on further compression a biaxial nematic phase is formed. In the uniaxial nematic phase there is one twist viscosity and one alignment angle. In the biaxial nematic phase there are three twist viscosities and three alignment angles corresponding to the rotation around the various directors and the different alignments of the directors relative to the stream lines, respectively. It is found that the smallest twist viscosity arises by rotation around the director formed by the long axes, the second smallest one arises by rotation around the director formed by the normals of the broadsides, and the largest one by rotation around the remaining director. The first twist viscosity is rather independent of the density whereas the last two ones increase strongly with density. One finds that there is one stable director alignment relative to the streamlines, namely where the director formed by the long axes is almost parallel to the stream lines and where the director formed by the normals of the broadsides is almost parallel to the shear plane. The relative magnitudes of the components of the twist viscosities span a fairly wide interval so this model should be useful for parameterisation experimental data.

Flow alignment phenomena in liquid crystals studied by molecular dynamics simulation

The flow alignment of a nematic liquid crystal has been studied as a function of temperature, beginning at high temperature in the nematic phase and down to the nematic-smectic A phase transition. The alignment angle is obtained by estimating the twist viscosities by nonequilibrium molecular dynamics (NEMD) methods. These estimates are cross-checked by evaluating the corresponding equilibrium fluctuation relations. As a further comparison, shear flow simulations are carried out by application of the SLLOD equations of motion (so named because of their close relationship to the Doll's equation of motion, which can be derived from the Doll's tensor Hamiltonian), whereby the alignment angle is obtained directly. All these methods give consistent results for the alignment angle. At low temperatures near the nematic-smectic A transition the system becomes flow unstable. In this region the alignment angle has been calculated as a function of time.

Twist viscoelastic coefficient of novel thiol terminated alkoxy-cyanobiphenyl nematic liquid crystals

We report our studies on the refractive indices and twist viscoelastic coefficient of novel thiol terminated alkoxy-cyanobiphenyl nematic liquid crystals. Dynamic light scattering (DLS) was employed to measure the twist viscoelastic coefficient as a function of temperature and the length of alkoxy chain. Our studies show that the twist viscoelastic coefficient is about three times smaller than that of the ordinary alkoxy-cyanobiphenyl nematic liquid crystals. DLS experiments carried out on this system with applied electric field show that the director relaxation frequency increases. These measurements yield the ratio of dielectric anisotropy to twist viscosity. We have also estimated the activation energy corresponding to twist viscosity.

Investigation of the Visco-Elastic Properties of Mixtures with Different Birefringence

The STN switching mechanism is governed by elastic constant ratios K33/K11 and K22/K11 (K11,K22 and K33 are respectively the splay, twist and bend elastic constants). This work explores the limitation of K22/K11 and how this can be translated into material/mixture design. The visco-elastic parameters K11, K22, ηsplay and γ1, were measured by dynamic light scattering (DLS) for three mixtures, based respectively on cyanobiphenyls, phenylbenzoates and dicyclohexyls with birefringence Δn ranging from 0.05 to 0.2. This study confirms that K22 and K11 only show slight variation for these mixtures; therefore, the ratio of K22/K11 remains remarkably constant and cannot be exploited in material design. In contrast, the twist and splay viscosities are directly related to the composition of the mixtures. Strongly polar nematic liquid crystals, such as the cyanobiphenyls, exhibit higher rotational viscosity coefficients. This work also outlines the dependence of the measurement accuracy of the visco-elastic parameters on the birefringence of the material investigated.

Viscous Properties of Nematic Mixture at Variation of PVT-State Parameters

The results of acoustic investigations of the viscous properties of a nematic liquid crystal mixture with wide temperature range at varying PVT-state parameters are presented. The original ultrasonic set-up was elaborated to provide the determination of some dissipative parameters including the ratio of twist viscosity γ1 to magnetic susceptibility anisotropy Δχ as a function of pressure (P) and temperature (T) at constant volume (V). It is found that the ratio γ1/Δχ exponentially decreases with increasing temperature or with decreasing pressure. This agrees with the free volume theory. According to our calculation free volume increases with temperature or decreasing pressure. The energies of activation (Ev, Ep) of the twist viscosity at constant volume and pressure are calculated. The dependence of Leslie viscosity coefficient α1 on temperature is determined too.

Molecular dynamics simulations of a ferroelectric nematic liquid under shear flow

We perform nonequilibrium molecular dynamics simulations to examine the change in orientational order of a ferroelectric nematic liquid crystal under shear flow, specifically planar Couette flow. The orientational order is found to decrease with increasing shear rate. This drop in orientational order is not due to structural changes but is rather a result of the director dynamics being flow unstable. Employing both nonequilibrium and equilibrium molecular dynamics with the director orientation fixed, we determine the shear and twist viscosities which relate the pressure tensor to the shear or strain rate tensor in a nematic liquid crystal under flow. The Miesowicz viscosities are then obtained from linear combinations of the shear and twist viscosities. The short-range spatial structure of the ferroelectric nematic liquid crystal is similar to that of a ferroelectric tetragonal I lattice. The relative magnitudes of the Miesowicz viscosities can be understood by examining the shear stress response of this lattice to a shear deformation.

Transport properties of cholesteric liquid crystals studied by molecular dynamics simulation

We have studied the transport properties of a cholesteric liquid crystal by molecular dynamics simulation. The molecules consist of six soft ellipsoids of revolution, the axes of which are perpendicular to the line connecting their centres of symmetry. The angle between the symmetry axes of two adjacent ellipsoids is 7.5°, so the molecules are twisted. At high densities they form a cholesteric phase where their twist axes are oriented around the cholesteric axis and the symmetry axes of the ellipsoids are approximately parallel to the local director. We have been particularly interested in thermomechanical coupling or the Lehmann effect, which arises when a temperature gradient parallel to the cholesteric axis induces a torque that rotates the director. The converse is also possible: rotation of the director can drive a heat current. The thermal conductivity, the twist viscosity, the cross-coupling coefficient between the temperature gradient and the torque, and the cross-coupling coefficient between the director angular velocity and the heat current have been calculated by non-equilibrium molecular dynamics simulation methods (NEMD) and by evaluation of the Green-Kubo relations from equilibrium simulations. Two ensembles have been utilized: the ordinary canonical ensemble and another ensemble where the director angular velocity is constrained to be a constant of motion. All the methods give consistent results for the twist viscosity and the thermal conductivity. The NEMD estimates of the cross-coupling coefficients agree within a relative error of 20%. This is consistent with the Onsager reciprocity relations that state that the two cross-coupling coefficients should be equal. The relative error of the Green-Kubo estimates is about 100% even though the order of magnitude is the same as that of the NEMD estimates.

Twist viscosity of mixtures of low molar mass nematics

Measurements of the twist viscosity, γ1(DLS) and twist elastic coefficient, K22(DLS) by electric-field-dependent dynamic light scattering (EFDLS) are reported for low molar mass nematics (LMMNs) 4′-heptyl-4-cyanobiphenyl (7CB) and 4′-octyl-4-cyanobiphenyl (8CB), and their binary mixtures at several temperatures in the nematic state. The results are compared with values (γ1(Rheol)=α3–α2) computed from rheological measurements of the Leslie viscosities α2 and α3. For the binary mixtures, at each temperature, the measured twist viscosity γ1(DLS) and corresponding twist elastic constant K22(DLS) show approximately a linear additive dependence on concentration. The calculated twist viscosity, γ1(Rheol), agrees with γ1(DLS) for the pure components, but is significantly smaller for the binary mixtures. Our observations appear to be consistent with a recent report of a discrepancy between values of the tumbling parameter λ, determined using a small-strain oscillatory optical technique, vs those measured by a rheological method. These results suggest that, in the rheological measurements at large strains, the rate of director rotation for mixtures may be affected by a flow-induced change in structure, e.g., shear-induced biaxiality.

Ensemble-Averaged Dynamic Light Scattering from Polymer-Stabilized Liquid Crystals

We report measurements of the viscoelastic parameters associated with the twist distortion of polymer-stabilized liquid crystal materials (PSLC), made by polymerizing 4,4′-bis-(acryloyloxy)-1,1′-biphenylene (BAB) and 4-butoxybenzyl 4-[6-(methacryloyloxyl-hexyloxy]benzoate (BMB6) to form fibrous networks in a nematic liquid crystal solvent (4′-phenyl-4-cyanobiphenyl, 5CB). By varying the BAB/BMB6 ratio, the twist elastic constant, K22, and viscosity, γ1, were investigated over a range of crosslink densities using electric-field-dependent dynamic light scattering (EFDLS). In PSLC samples, the formation of a highly-crosslinked, phase-separated polymer network can lead to optically heterogeneous behavior of the EFDLS data. Thus, it is necessary to evaluate the ensemble-averaged EFDLS relaxation function through spatial averaging. The results show that the polymer network causes a change in the twist relaxation rate, depending on the cross-link density of the specimens. The twist viscosity was found to increase with decrease in cross-link density, which appears to occur because higher cross-link density causes collapse of the gel fibers and less interaction between the fibers and nematic medium.

Twist Viscosity of a Side-Chain Liquid-Crystalline Polysiloxane Dissolved in a Tumbling Nematic Solvent

The dynamics of the twist distortion was characterized by electric-field-dependent dynamic light scattering (EFDLS) for a dilute solution of a side-chain liquid crystalline polysiloxane (SCLCP) dissolved in the tumbling nematic solvent, 4‘-octyl-4-cyanobiphenyl (8CB). The results show a decrease in twist relaxation rate on dissolution of the SCLCP due to a large increase in twist viscosity δγ1 with negligible change in twist elastic constant K22. By comparing the twist viscosity values, γ1 = α3 − α2, with previous measurements of the strain periodicity of oscillations in the shear stress transients due to director tumbling, γp = (π/δp)(1 + δp2), where δp = (−α3/α2)1/2, we further investigate the corresponding changes in Leslie viscosities, δα2 and δα3. The results indicate that δα2 and δα3 have opposite signs. These observations, together with literature data on the electrorheological behavior of these solutions, can be self-consistently described by a hydrodynamic model of the viscous dissipation by Brochard, modified through inclusion of an additional dissipation process which derives from an elastic torque between director rotation and LCP orientation.

Electrorheological determination of the Leslie viscosity coefficient (α 2 ) of a main-chain liquid crystal polymer in a nematic solvent

Analysis of the electrorheological response of thermotropic solutions of a main-chain liquid crystal polymer (MCLCP) in a low molar mass nematic solvent is performed at a fixed shear rate as a function of the applied field strength. The Leslie viscosity coefficient α2 can be obtained by least squares fits to an equation describing the balance between the viscous and electric torques, formulated via the two dimensional Leslie-Ericksen-Parodi theory. We find that the increment Δα2 on dissolving the MCLCP increases linearly with molecular weight, consistent with earlier light scattering measurements of the increment in the twist viscosity, Δγ1, and also with previous electrorheological measurements of the increment in the Miesowicz viscosity Δηc.

Twist Viscosity of Side-Chain Liquid-Crystalline Polysiloxanes in a Nematic Solvent

Electric-field-dependent dynamic light scattering (EFDLS) was used to determine the twist elastic constant and twist viscosity of miscible nematic solutions of side-chain liquid crystal polysiloxan...

Shear flow simulations of biaxial nematic liquid crystals

We have calculated the viscosities of a biaxial nematic liquid crystal phase of a variant of the Gay–Berne fluid [J. G. Gay and B. J. Berne, J. Chem. Phys. 74, 3316 (1981)] by performing molecular dynamics simulations. The equations of motion have been augmented by a director constraint torque that fixes the orientation of the directors. This makes it possible to fix them at different angles relative to the stream lines in shear flow simulations. In equilibrium simulations the constraints generate a new ensemble. One finds that the Green–Kubo relations for the viscosities become linear combinations of time correlation function integrals in this ensemble whereas they are complicated rational functions in the conventional canonical ensemble. We have evaluated these Green–Kubo relations for all the shear viscosities and all the twist viscosities. We have also calculated the alignment angles, which are functions of the viscosity coefficients. We find that there are three real alignment angles but a linear stability analysis shows that only one of them corresponds to a stable director orientation. The Green–Kubo results have been cross checked by nonequilibrium shear flow simulations. The results from the different methods agree very well. Finally, we have evaluated the Miesowicz viscosities [D. Baalss, Z. Naturforsch. Teil A 45, 7 (1990)]. They vary by more than 2 orders of magnitude. The viscosity is consequently highly orientation dependent.

Rotation in a magnetic field of nematic liquid crystalline samples with a negative anisotropy of their magnetic susceptibility

The behaviour of the mesophase directors when a sample with a negative anisotropy Deltachi in the magnetic susceptibility is rotated at a speed omega in a magnetic field B0 about an axis inclined at an angle beta is investigated by deuterium NMR spectroscopy. There are combinations of beta and omega which lead to the directors aligning along the spinning axis (stable region), and other combinations where the directors are either unaffected by the rotation, or have a timedependent distribution (unstable region). These two regions are separated by a line (the q line) whose position depends on beta and omegac DeltachiB02/2mu0gamma1, where gamma1 is a twist viscosity coefficient. Experiments on 4-n-propyl-4-cyanobicyclohexane (CCH3) are used to demonstrate how the q line, and hence omegac may be determined. Combining this result with a measurement of the anisotropy in the magnetic susceptibility, Deltachi, yields a value for gamma1.

Studies on the texture of nematic solutions of a rod-like polymer 1. Distortion of the director field in a magnetic field

The growth of the distortion of the director in an external field, and its relaxation on removal of the field are studied for nematic solutions of the rod-like poly(1,4-phenylene-2,6-benzobisthiazole), PBZT, over a range of concentration, polymer molecular weight and temperature. The twist viscosity and the order parameter are more weakly dependent on concentration than predicted for charged rod-like chains. This behaviour implies a short-range translational order in a direction orthogonal to the chain axis, induced by electrostatic interactions among the polycations on protonated PBZT. The relaxation gives a normal temperature dependence for the splay curvature elasticity, but that for the twist curvature is unexpectedly strong. This behaviour is interpreted as a weakening of the surface anchoring with increased temperature.

Green–Kubo relations for the viscosity of biaxial nematic liquid crystals

We derive Green–Kubo relations for the viscosities of a biaxial nematic liquid crystal. In this system there are seven shear viscosities, three twist viscosities, and three cross coupling coefficients between the antisymmetric strain rate and the symmetric traceless pressure tensor. According to the Onsager reciprocity relations these couplings are equal to the cross couplings between the symmetric traceless strain rate and the antisymmetric pressure. Our method is based on a comparison of the microscopic linear response generated by the SLLOD equations of motion for planar Couette flow (so named because of their close connection to the Doll’s tensor Hamiltonian) and the macroscopic linear phenomenological relations between the pressure tensor and the strain rate. In order to obtain simple Green–Kubo relations we employ an equilibrium ensemble where the angular velocities of the directors are identically zero. This is achieved by adding constraint torques to the equations for the molecular angular accelerations. One finds that all the viscosity coefficients can be expressed as linear combinations of time correlation function integrals (TCFIs). This is much simpler compared to the expressions in the conventional canonical ensemble, where the viscosities are complicated rational functions of the TCFIs. The reason for this is, that in the constrained angular velocity ensemble, the thermodynamic forces are given external parameters whereas the thermodynamic fluxes are ensemble averages of phase functions. This is not the case in the canonical ensemble. The simplest way of obtaining numerical estimates of viscosity coefficients of a particular molecular model system is to evaluate these fluctuation relations by equilibrium molecular dynamics simulations.

Dynamic Light Scattering Study of Polymer-Stabilized Liquid Crystal Monodomain

Abstract Dynamic light scattering (DLS) analysis is performed on a polymer-stabilized liquid crystal (PSLC) monodomain in the presence of an AC electric field. The twist elasticity and viscosity of the PSLC are determined. Compared with the nematic solvent (5CB), both the elasticity and the viscosity of the PSLC show substantial increases, reflecting the anchoring effect of the polymeric gel network. Time-resolved DLS measurements during the cure reaction yield information on the kinetics of network formation.