Sten Sarman

Statistical mechanics of viscous flow in nematic fluids

We derive Green–Kubo (GK) relations for the viscosity coefficients of nematic liquid crystals. These GK relations are similar to, but considerably more complicated than, those of an isotropic fluid. In addition to shear viscosities there are also twist viscosities and cross couplings between the symmetric strain rate and the antisymmetric pressure tensor and vice versa. We show that the twist viscosity is inversely proportional to the mean square displacement of the director. Using the so‐called SLLOD equations of motion we construct nonequilibrium molecular dynamics (NEMD) algorithms that can be used to efficiently calculate the viscosity coefficients of nematic liquid crystals from atomistic computer simulations. We also devise an additional NEMD algorithm for controlling the angular velocity of the director in a nematic fluid. We derive a fluctuation relation for the alignment angle between the director and the streamlines in planar Couette flow and also for the shear induced molecular angular velocity...

The chemical potential of simple fluids in a common class of integral equation closures

An explicit formula for the chemical potential (μ) of simple fluids is derived for a whole class of integral equation theories, including the Percus–Yevick approximation and some other, more recently proposed closures. This formula only requires the pair correlation functions for one single state of the system, and applies to both homogeneous and inhomogeneous fluids. The coupling parameter integration method to calculate the chemical potential—where one particle is gradually coupled to the rest—is also investigated. It is shown that the μ value obtained in the approximate theories is not unique, but depends on the integration path. This behavior is due to inconsistencies of the approximation, which are discussed in some detail. For a certain choice of integration path the μ values obtained using the latter method agree with those from the explicit formula. Numerical results for the different closures are presented for a hard sphere fluid. The accuracy of μ depends strongly on the quality of the bridge function inside the hard core diameter.

On the statistical mechanics of inhomogeneous fluids in narrow slits. An application to a hard-sphere fluid between hard walls

Abstract A general method is suggested for the treatment of the equilibrium condition for inhomogeneous fluids in narrow slits in contact with the corresponding bulk fluid. The method is based on an exact equation for the variation in density distribution with the slit width, and relies upon accurate calculations of the anisotropic pair correlation functions for the fluid. As an example, we present results for a hard-sphere fluid between hard walls in the anisotropic Percus-Yevick approximation. The density profile and the pressure between the walls as functions of the slit width practically coincide with the corresponding grand canonical Monte Carlo simulation results.

A study of anisotropic pair distribution theories for Lennard-Jones fluids in narrow slits

Density profiles for inhomogeneous dense Lennard-Jones fluids in narrow planar slits are calculated using various integral-equation closures for the anisotropic pair distribution functions. Very good agreement with simulation studies is obtained for the Zerah-Hansen (ZH) closure and a variant of the modified hypernetted chain (MHNC) closure suggested here while the Percus-Yevick (PY), the soft-core mean spherical approximation (SMSA) and, in particular, the hypernetted chain (HNC) closures give inferior results. Various properties of the fluid as functions of the slit width are calculated in the ZH approximation, using closure parameters optimized for the bulk phase. The mean particle number per unit area virtually coincides with the values from grand canonical ensemble simulations. The net pressure between the walls, which is more difficult to calculate accurately, agrees well with the simulation result. The agreement can probably be further improved by fully optimizing the ZH closure for the inhomogeneo...

Self‐diffusion and heat flow in isotropic and liquid crystal phases of the Gay–Berne fluid

We use the so‐called Evans heat flow algorithm and the color conductivity algorithm to calculate the thermal conductivity, λ, and self‐diffusion, D, tensors of a model liquid crystal forming fluid, the Gay–Berne fluid. We compared the conductivities of the isotropic phase, the nematic liquid crystal phase, and the smectic B phase and found that the transverse components of λ and D in the nematic phase are about the same as λ and D for the isotropic phase at the same temperature and slightly lower density. The parallel components of λ and D are about two and four times as large as the respective transverse components. In the smectic B phase the parallel thermal conductivity ratio increases to about three, whereas the diffusion coefficient is virtually zero because of the solid like nature of this phase. We cross checked the results by deriving and evaluating the Green–Kubo relations for λ and D using conventional equilibrium molecular dynamics. We also discovered that in the presence of a temperature gradi...

Molecular dynamics of biaxial nematic liquid crystals

We devise a constraint algorithm that makes the angular velocity of the director of a liquid crystal a constant of motion. When the angular velocity is set equal to zero, a director based coordinate system becomes an inertial frame. This is a great advantage because most thermodynamic properties and time correlation functions of a liquid crystal are best expressed relative to a director based coordinate system. One also prevents the director reorientation from interfering with the tails of the time correlation functions. When the angular velocity is forced to be zero the constraints do not do any work on the system. This makes it possible to prove that ensemble averages of phase functions and time correlation functions are unaffected by the director constraint torques. The constraint algorithm also facilitates generalization of nonequilibrium molecular dynamics algorithms to liquid crystal phases. In order to test the algorithm numerically we have simulated a biaxial nematic phase of a variant of the Gay–...

MOLECULAR DYNAMICS OF LIQUID CRYSTALS

We derive Green-Kubo relations for the viscosities of a nematic liquid crystal. The derivation is based on the application of a Gaussian constraint algorithm that makes the director angular velocity of a liquid crystal a constant of motion. Setting this velocity equal to zero means that a director-based coordinate system becomes an inertial frame and that the constraint torques do not do any work on the system. The system consequently remains in equilibrium. However, one generates a different equilibrium ensemble. The great advantage of this ensemble is that the Green-Kubo relations for the viscosities become linear combinations of time correlation function integrals, whereas they are complicated rational functions in the conventional canonical ensemble. This facilitates the numerical evaluation of the viscosities by molecular dynamics simulations.

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 thermomechanical coupling in cholesteric liquid crystals

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 pseudo vectors respectively. This makes it possible for a temperature gradient parallel to the cholesteric axis to induce a torque which rotates the director. This phenomenon is known as the Lehmann effect. The converse is also possible: one can drive a heat current by rotating the director. In this work a recently developed non-equilibrium molecular dynamics simulation algorithm is applied to calculate the cross-coupling coefficient between the temperature gradient and the torque for a molecular model system based on the Gay-Berne fluid. According to the Onsager reciprocity relations this cross-coupling coefficient is equal to the coupling between the director angular velocity and the heat current. The cross-coupling coefficients are found to be very small but non-zero and the Onsager reciprocity relations are satisfied within the statistical uncertainty.

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 sta...