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.

Microscopic shear flow simulations of a biaxial smectic A liquid crystal based on the soft ellipsoid string-fluid.

We have studied the behaviour of a biaxial smectic A liquid crystal based on the soft ellipsoid string-fluid in shear flow by molecular dynamics simulation using the SLLOD equation of motion. This is facilitated by the fact that the biaxial symmetry allows linear relations between the pressure and the velocity gradient. This means that linear irreversible thermodynamics can be applied independently of the simulations to obtain the torques determining the orientations of the system and that the predictions of this theory can be cross-checked by the simulations. It turns out that there is a torque turning the smectic layers to the orientation parallel to the vorticity plane if the simulation is started in another orientation. In the orientation parallel to the vorticity plane where the director formed by the long axes of the molecules, nw, is perpendicular to the vorticity plane there is another torque keeping the director formed by the normals of the broadsides of the molecules, nu, parallel to this plane at a constant alignment angle, ψ relative to the streamlines independently of the strain rate. Moreover, this alignment angle seems to be the one where the irreversible energy dissipation rate, , is minimal. This is in agreement with a recently proven theorem according to which is minimal in the linear regime of a nonequilibrium steady state. Finally, we studied the orientation of nu when the smectic layers are parallel to the shear plane. In a simulation this orientation is stabilised by the periodic boundary conditions. Then we found that there was a nonlinear torque turning nu to the orientation perpendicular to the streamlines thus minimising the value of even though this value is larger than the value of in the orientation parallel to the vorticity plane. This means that is minimized given the external boundary conditions.

Microstructural and Dynamical Heterogeneities in Ionic Liquids.

Ionic liquids (ILs) are a special category of molten salts solely composed of ions with varied molecular symmetry and charge delocalization. The versatility in combining varied cation-anion moieties and in functionalizing ions with different atoms and molecular groups contributes to their peculiar interactions ranging from weak isotropic associations to strong, specific, and anisotropic forces. A delicate interplay among intra- and intermolecular interactions facilitates the formation of heterogeneous microstructures and liquid morphologies, which further contributes to their striking dynamical properties. Microstructural and dynamical heterogeneities of ILs lead to their multifaceted properties described by an inherent designer feature, which makes ILs important candidates for novel solvents, electrolytes, and functional materials in academia and industrial applications. Due to a massive number of combinations of ion pairs with ion species having distinct molecular structures and IL mixtures containing varied molecular solvents, a comprehensive understanding of their hierarchical structural and dynamical quantities is of great significance for a rational selection of ILs with appropriate properties and thereafter advancing their macroscopic functionalities in applications. In this review, we comprehensively trace recent advances in understanding delicate interplay of strong and weak interactions that underpin their complex phase behaviors with a particular emphasis on understanding heterogeneous microstructures and dynamics of ILs in bulk liquids, in mixtures with cosolvents, and in interfacial regions.

Shear flow simulations of smectic liquid crystals based on the Gay-Berne fluid and the soft sphere string-fluid.

We have studied the shear flow of the smectic A phase of three coarse grained liquid crystal model systems, namely two versions of the Gay-Berne fluid and the soft sphere string-fluid. At low shear rates, the orientation where the smectic layers are parallel to the shear plane and the orientation parallel to the vorticity plane are both stable in all the systems. In one of the Gay-Berne fluids, there is a transition from the orientation parallel to the shear plane to the orientation parallel to the vorticity plane. At higher shear rates, a nonequilibrium nematic phase is obtained in all the systems in the same way as in linear alkanes under shear. If the initial configuration is an equilibrium smectic A phase or a nematic phase with the molecules parallel to the streamlines, the orientation parallel to the shear plane is attained at low shear rates in the Gay-Berne fluids. In order to analyze the stability of the different orientations, the torque acting on the liquid crystal is calculated. It consists of an elastic torque caused by deformations due to the shape of the simulation cell and the periodic boundary conditions and a shear-induced torque. The elastic torque stabilizes both the orientation parallel to the shear plane and the orientation parallel to the vorticity plane because the liquid crystal is deformed if it is turned away from these orientations. The shear-induced torque, on the other hand, always turns the liquid crystal to the orientation parallel to the vorticity plane where the viscosity and the irreversible energy dissipation rate are minimal. Since the latter torque is proportional to the square of the shear rate, rather high shear rates are required for it to overwhelm the elastic torque. However, the elastic torque decreases with the system size so that it is likely that the shear-induced torque will dominate in large systems and that the orientation parallel to the vorticity plane will be attained at low or even zero shear rate.

Rheology of phosphonium ionic liquids: a molecular dynamics and experimental study.

We have studied the rheological behavior of the ionic liquid trihexyl(tetradecyl)phosphonium bis(mandelato)borate, [P66614][BMB], and compared it with that of another ionic liquid, namely trihexyl(tetradecyl)phosphonium chloride, [P66614][Cl]. The non-halogenated [P66614][BMB] has been selected as it is known to provide enhanced lubrication performance and is, consequently, of technological importance. The ionic liquid [P66614][Cl], despite its relatively simple anion, exhibits viscosities very similar to those of [P66614][BMB], making it an excellent reference fluid for the modeling study. The viscosities of the ionic liquids have been obtained by equilibrium atomistic simulations using the Green-Kubo relation, and by performing nonequilibrium shear flow simulations. The influence of the simulation system size and a reduction of the atomic charges on the viscosities of the ionic liquids are systematically studied. The atomic charges are reduced to mimic the temperature dependent charge transfer and polarization effects. It has been found that scaling the point charges with factors between 0.60 and 0.80 from full ion charges can provide reliable viscosities of [P66614][BMB], consistent with the experimentally measured viscosities within the studied temperature interval from 373 to 463 K. The viscosities of [P66614][Cl] have been obtained with scaling factors between 0.80 and 1.0 reflecting the lower polarizability and charge transfer effects of the chloride anion.

Microstructures and dynamics of tetraalkylphosphonium chloride ionic liquids.

Atomistic simulations have been performed to investigate the effect of aliphatic chain length in tetraalkylphosphonium cations on liquid morphologies, microscopic ionic structures, and dynamical quantities of tetraalkylphosphonium chloride ionic liquids. The liquid morphologies are characterized by sponge-like interpenetrating polar and apolar networks in ionic liquids consisting of tetraalkylphosphonium cations with short aliphatic chains. The lengthening aliphatic chains in tetraalkylphosphonium cations lead to polar domains consisting of chloride anions and central polar groups in cations being partially or totally segregated in ionic liquid matrices due to a progressive expansion of apolar domains in between. Prominent polarity alternation peaks and adjacency correlation peaks are observed at low and high q range in total X-ray scattering structural functions, respectively, and their peak positions gradually shift to lower q values with lengthening aliphatic chains in tetraalkylphosphonium cations. The charge alternation peaks registered in the intermediate q range exhibit complicated tendencies due to a cancellation of peaks and anti-peaks in partial structural functions for ionic subcomponents. The particular microstructures and liquid morphologies in tetraalkylphosphonium chloride ionic liquids intrinsically contribute to distinct dynamics characterized by mean square displacements, van Hove correlation functions, and non-Gaussian parameters for ionic species in the heterogeneous ionic environment. Most tetraalkylphosphonium cations have higher translational mobilities than their partner anions due to strong coordination of chloride anions with central polar groups in tetraalkylphosphonium cations through strong Coulombic and hydrogen bonding interactions. The increase of aliphatic chain length in tetraalkylphosphonium cations leads to a concomitant shift of van Hove correlation functions and non-Gaussian parameters to larger radial distances and longer time scales, respectively, indicating the enhanced translational dynamical heterogeneities of tetraalkylphosphonium cations and the corresponding chloride anions.

Interfacial Structures of Trihexyltetradecylphosphonium-bis(mandelato)borate Ionic Liquid Confined between Gold Electrodes.

Atomistic molecular dynamics simulations have been performed to study microscopic the interfacial ionic structures, molecular arrangements, and orientational preferences of trihexyltetradecylphosphonium-bis(mandelato)borate ([P6,6,6,14][BMB]) ionic liquid confined between neutral and charged gold electrodes. It was found that both [P6,6,6,14] cations and [BMB] anions are coabsorbed onto neutral electrodes at different temperatures. The hexyl and tetradecyl chains in [P6,6,6,14] cations lie preferentially flat on neutral electrodes. The oxalato and phenyl rings in [BMB] anions are characterized by alternative parallel-perpendicular orientations in the mixed innermost ionic layer adjacent to neutral electrodes. An increase in temperature has a marginal effect on the interfacial ionic structures and molecular orientations of [P6,6,6,14][BMB] ionic species in a confined environment. Electrifying gold electrodes leads to peculiar changes in the interfacial ionic structures and molecular orientational arrangements of [P6,6,6,14] cations and [BMB] anions in negatively and positively charged gold electrodes, respectively. As surface charge density increases (but lower than 20 µC/cm2), the layer thickness of the mixed innermost interfacial layer gradually increases due to a consecutive accumulation of [P6,6,6,14] cations and [BMB] anions at negatively and positively charged electrodes, respectively, before the formation of distinct cationic and anionic innermost layers. Meanwhile, the molecular orientations of two oxalato rings in the same [BMB] anions change gradually from a parallel-perpendicular feature to being partially characterized by a tilted arrangement at an angle of 45° from the electrodes and finally to a dominant parallel coordination pattern along positively charged electrodes. Distinctive interfacial distribution patterns are also observed accordingly for phenyl rings that are directly connected to neighboring oxalato rings in [BMB] anions.

Atomistic Insight into Tetraalkylphosphonium Bis(oxalato)borate Ionic Liquid/Water Mixtures. 2. Volumetric and Dynamic Properties.

Atomistic molecular dynamics simulations have been performed to investigate volumetric quantities and dynamic properties of binary trihexyltetradecylphosphonium bis(oxalato)borate ([P6,6,6,14][BOB]) ionic liquid (IL)/water mixtures with different water concentrations. The predicted liquid densities for typical [P6,6,6,14][BOB] IL/water mixtures are consistent with available experimental data with a relative discrepancy of less than 3%. The liquid densities and excess molar volumes of all studied [P6,6,6,14][BOB] IL/water mixtures are characterized by concave and convex features, respectively, within full water concentration range. The dynamic properties of [P6,6,6,14] cations, [BOB] anions, and water molecules are particularly analyzed through calculation of velocity autocorrelation functions, diffusion coefficients, and reorientational autocorrelation functions and correlation times. The translational and reorientational mobilities of three species become faster upon increasing water concentration in [P6,6,6,14][BOB] IL/water mixtures and present complex dynamical characteristics arising from three distinct microscopic diffusion features within the full water concentration range. The obtained striking volumetric quantities and particular dynamic properties are well correlated to microscopic liquid structural organization and distinct local ionic environment of all studied [P6,6,6,14][BOB] IL/water mixtures.

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.

Self-diffusion in the non-Newtonian regime of shearing liquid crystal model systems based on the Gay-Berne potential.

The self-diffusion coefficients of nematic phases of various model systems consisting of regular convex calamitic and discotic ellipsoids and non-convex bodies such as bent-core molecules and soft ellipsoid strings have been obtained as functions of the shear rate in a shear flow. Then the self-diffusion coefficient is a second rank tensor with three different diagonal components and two off-diagonal components. These coefficients were found to be determined by a combination of two mechanisms, which previously have been found to govern the self-diffusion of shearing isotropic liquids, namely, (i) shear alignment enhancing the diffusion in the direction parallel to the streamlines and hindering the diffusion in the perpendicular directions and (ii) the distortion of the shell structure in the liquid whereby a molecule more readily can escape from a surrounding shell of nearest neighbors, so that the mobility increases in every direction. Thus, the diffusion parallel to the streamlines always increases with the shear rate since these mechanisms cooperate in this direction. In the perpendicular directions, these mechanisms counteract each other so that the behaviour becomes less regular. In the case of the nematic phases of the calamitic and discotic ellipsoids and of the bent core molecules, mechanism (ii) prevails so that the diffusion coefficients increase. However, the diffusion coefficients of the soft ellipsoid strings decrease in the direction of the velocity gradient because the broadsides of these molecules are oriented perpendicularly to this direction due the shear alignment (i). The cross coupling coefficient relating a gradient of tracer particles in the direction of the velocity gradient and their flow in the direction of the streamlines is negative and rather large, whereas the other coupling coefficient relating a gradient in the direction of the streamlines and a flow in the direction of the velocity gradient is very small.

Multiscale modeling of the trihexyltetradecylphosphonium chloride ionic liquid.

A multiscale modeling protocol was sketched for the trihexyltetradecylphosphonium chloride ([P6,6,6,14]Cl) ionic liquid (IL). The optimized molecular geometries of an isolated [P6,6,6,14] cation and a tightly bound [P6,6,6,14]Cl ion pair structure were obtained from quantum chemistry ab initio calculations. A cost-effective united-atom model was proposed for the [P6,6,6,14] cation based on the corresponding atomistic model. Atomistic and coarse-grained molecular dynamics simulations were performed over a wide temperature range to validate the proposed united-atom [P6,6,6,14] model against the available experimental data. Through a systemic analysis of volumetric quantities, microscopic structures, and transport properties of the bulk [P6,6,6,14]Cl IL under varied thermodynamic conditions, it was identified that the proposed united-atom [P6,6,6,14] cationic model could essentially capture the local intermolecular structures and the nonlocal experimental thermodynamics, including liquid density, volume expansivity and isothermal compressibility, and transport properties, such as zero-shear viscosity, of the bulk [P6,6,6,14]Cl IL within a wide temperature range.

Non-Newtonian rheological properties of shearing nematic liquid crystal model systems based on the Gay-Berne potential.

The viscosities and normal stress differences of various liquid crystal model systems based on the Gay-Berne potential have been obtained as functions of the shear rate in the non-Newtonian regime. Various molecular shapes such as regular convex calamitic and discotic ellipsoids and non-convex shapes such as bent core molecules and soft ellipsoid strings have been examined. The isotropic phases were found to be shear thinning with the shear rate dependence of the viscosity following a power law in the same way as alkanes and other non-spherical molecules. The nematic phases turned out to be shear thinning but the logarithm of the viscosity proved to be an approximately linear function of the square root of the shear rate. The normal stress differences were found to display a more or less parabolic dependence on the shear rate in the isotropic phase whereas this dependence was linear at low to intermediate shear rates in the nematic phase.

Formation of a columnar liquid crystal in a simple one-component system of particles.

We report a molecular dynamics simulation demonstrating that a columnar liquid crystal, commonly formed by disc-shaped molecules, can be formed by identical particles interacting via a spherically symmetric potential. Upon isochoric cooling from a low-density isotropic liquid state the simulated system underwent a weak first order phase transition which produced a liquid crystal phase composed of parallel particle columns arranged in a hexagonal pattern in the plane perpendicular to the column axis. The particles within columns formed a liquid structure and demonstrated a significant intracolumn diffusion. Further cooling resulted in another first-order transition whereby the column structure became periodically ordered in three dimensions transforming the liquid-crystal phase into a crystal. This result is the first observation of a columnar liquid crystal formation in a simple one-component system of particles. Its conceptual significance is in that it demonstrated that liquid crystals that have so far only been produced in systems of anisometric molecules can also be formed by mesoscopic soft-matter and colloidal systems of spherical particles with appropriately tuned interatomic potential.

Atomistic Insight into Tetraalkylphosphonium-Bis(oxalato)borate Ionic Liquid/Water Mixtures. I. Local Microscopic Structure.

Atomistic simulations have been performed to investigate the microscopic structural organization of aqueous solutions of trihexyltetradecylphosphonium bis(oxalato)borate ([P6,6,6,14][BOB]) ionic liquid (IL). The evolution of the microscopic liquid structure and the local ionic organization of IL/water mixtures as a function of the water concentration is visualized and systematically analyzed via radial and spatial distribution functions, coordination numbers, hydrogen bond network, and water clustering analysis. The microscopic liquid structure in neat IL is characterized by a connected apolar network composed of the alkyl chains of [P6,6,6,14] cations and isolated polar domains consisting of the central segments of [P6,6,6,14] cations and [BOB] anions, and the corresponding local ionic environment is described by direct contact ion pairs. In IL/water mixtures with lower water mole fractions, the added water molecules are dispersed and embedded in cavities between neighboring ionic species and the local ionic structure is characterized by solvent-shared ion pairs through cation-water-anion triple complexes. With a gradual increase in the water concentration in IL/water mixtures, the added water molecules tend to aggregate and form small clusters, intermediate chain-like structures, large aggregates, and eventually a water network in water concentrated simulation systems. A further progressive dilution of IL/water mixtures leads to the formation of self-organized micelle-like aggregates characterized by a hydrophobic core and hydrophilic shell consisting of the central polar segments in [P6,6,6,14] cations and [BOB] anions in a highly branched water network. The striking structural evolution of the [P6,6,6,14][BOB] IL/water mixtures is rationalized by the competition between favorable hydrogen bonded interactions and strong electrostatic interactions between the polar segments in ionic species and the dispersion interactions between the hydrophobic alkyl chains in [P6,6,6,14] cations.

Molecular dynamics simulation of planar elongational flow in a nematic liquid crystal based on the Gay-Berne potential.

Molecular dynamics simulations of planar elongational flow in a nematic liquid crystal model system based on the Gay-Berne fluid were undertaken by applying the SLLOD equations of motion with an elongational velocity field or strain rate. In order to facilitate the simulation, Kraynik-Reinelt periodic boundary conditions allowing arbitrarily long simulations were used. A Lagrangian constraint algorithm was utilized to fix the director at different angles relative to the elongation direction, so that the various pressure tensor elements could be calculated as a function of this angle. This made it possible to obtain accurate values of the shear viscosities which were found to agree with results previously obtained by shear flow simulations. The torque needed to fix the director at various angles relative to the elongation direction was evaluated in order to determine the stable orientation of the director, where this torque is equal to zero. This orientation was found to be parallel to the elongation direction. It was also noted that the irreversible entropy production was minimal when the director attained this orientation. Since the simulated system was rather large and fairly long simulation runs were undertaken it was also possible to study the cross coupling between the strain rate and the order tensor. It turned out to be very weak at low strain rates but at higher strain rates it could lead to break down of the liquid crystalline order.

Packing frustration in dense confined fluids.

Packing frustration for confined fluids, i.e., the incompatibility between the preferred packing of the fluid particles and the packing constraints imposed by the confining surfaces, is studied for a dense hard-sphere fluid confined between planar hard surfaces at short separations. The detailed mechanism for the frustration is investigated via an analysis of the anisotropic pair distributions of the confined fluid, as obtained from integral equation theory for inhomogeneous fluids at pair correlation level within the anisotropic Percus-Yevick approximation. By examining the mean forces that arise from interparticle collisions around the periphery of each particle in the slit, we calculate the principal components of the mean force for the density profile--each component being the sum of collisional forces on a particle's hemisphere facing either surface. The variations of these components with the slit width give rise to rather intricate changes in the layer structure between the surfaces, but, as shown in this paper, the basis of these variations can be easily understood qualitatively and often also semi-quantitatively. It is found that the ordering of the fluid is in essence governed locally by the packing constraints at each single solid-fluid interface. A simple superposition of forces due to the presence of each surface gives surprisingly good estimates of the density profiles, but there remain nontrivial confinement effects that cannot be explained by superposition, most notably the magnitude of the excess adsorption of particles in the slit relative to bulk.

Director alignment relative to the temperature gradient in nematic liquid crystals studied by molecular dynamics simulation.

The director alignment relative to the temperature gradient in nematic liquid crystal model systems consisting of soft oblate or prolate ellipsoids of revolution has been studied by molecular dynamics simulation. The temperature gradient is maintained by thermostating different parts of the system at different temperatures by using a Gaussian thermostat. It is found that the director of the prolate ellipsoids aligns perpendicularly to the temperature gradient whereas the director of the oblate ellipsoids aligns parallel to this gradient. When the director is oriented in between the parallel and perpendicular orientations a torque is exerted forcing the director to the parallel or perpendicular orientation. Because of symmetry restrictions there is no linear dependence of the torque being a pseudovector on the temperature gradient being a polar vector in an axially symmetric system such as a nematic liquid crystal. The lowest possible order of this dependence is quadratic. Thus the torque is very weak when the temperature gradient is small, which may explain why this orientation phenomenon is hard to observe experimentally. In both cases the director attains the orientation that minimises the irreversible entropy production.

Local order variations in confined hard-sphere fluids.

Pair distributions of fluids confined between two surfaces at close distance are of fundamental importance for a variety of physical, chemical, and biological phenomena, such as interactions between macromolecules in solution, surface forces, and diffusion in narrow pores. However, in contrast to bulk fluids, properties of inhomogeneous fluids are seldom studied at the pair-distribution level. Motivated by recent experimental advances in determining anisotropic structure factors of confined fluids, we analyze theoretically the underlying anisotropic pair distributions of the archetypical hard-sphere fluid confined between two parallel hard surfaces using first-principles statistical mechanics of inhomogeneous fluids. For this purpose, we introduce an experimentally accessible ensemble-averaged local density correlation function and study its behavior as a function of confining slit width. Upon increasing the distance between the confining surfaces, we observe an alternating sequence of strongly anisotropic versus more isotropic local order. The latter is due to packing frustration of the spherical particles. This observation highlights the importance of studying inhomogeneous fluids at the pair-distribution level.

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.