Pseudo-molecular approach for the elastic constants of nematic liquid crystals interacting via anisotropic dispersion forces

The bulk and the surface-like elastic constants of a nematic liquid crystal are calculated for an ensemble of particles interacting via anisotropic dispersion forces using the pseudo-molecular method. The geometrical anisotropy of the molecules is also taken into account in the calculations by choosing a molecular volume of ellipsoidal shape. Analytical expressions for the elastic constants are obtained as a function of the eccentricity in the molecular volume shape. The method allows one to explore the dependence on the molecular orientation with respect to the intermolecular vector by analyzing the magnitude and the behaviour of macroscopic elastic parameters defining the nematic phase.     

Theory of inelastic neutron scattering from molecular fluids

The time-dependent angular pair correlation function is discussed and its use in the analysis of inelastic neutron scattering experiments from polyatomic fluids is described, including both the coherent and incoherent spectra. The set of formal results given here permits a systematic interpretation of neutron inelastic scattering spectra on simple molecular liquids. Neutron spectra second moments are reviewed, and a new result for the fourth moment is given for the incoherent spectrum. Numerical results for the moments are obtained. The fourth moment depends on the mean squared torque and the mean squared force acting on a molecule in the fluid, and may provide a means for studying intermolecular forces in dense fluids. In addition, a method of calculating the correlation function for weak anisotropic forces is outlined.     

Direct calculation of bubble points for alkane mixtures by molecular simulation

This paper extends to flexible molecules an algorithm proposed earlier for the calculation of bubble points of simple fluids by Monte Carlo simulation (Ungerer, P., Boutin, A., and Fuchs, A. H., 1999, Molec. Phys., 97, 523). This algorithm is based on a pseudo-ensemble in which global volume, temperature and liquid phase mole numbers are fixed. A configurational bias method is used to treat flexible molecules, and the underlying assumptions regarding the molecular partition function for flexible chains are discussed. Molecular interactions are determined with an anisotropic united atoms intermolecular potential, recently optimized to represent vapour-liquid phase equilibria of n-alkanes. Two applications examples are given, concerning a binary mixture (methane + n-pentane) and a ternary system (methane + propane + n-decane) for which experimental data are available. Satisfactory convergence is obtained, except in the vicinity of critical conditions. Densities and vapour phase compositions are well represented. Bubble pressures appear significantly underestimated, however. The origin of this discrepancy and remedial methods are discussed.     

Emergent biaxiality in nematic microflows illuminated by a laser beam

Anisotropic fluids (e.g. liquid crystals) offer a remarkable promise as optofluidic materials owing to the directional, tunable, and coupled interactions between the material, flow, and the optical fields. Here we present a comprehensive in silico treatment of this anisotropic interaction by performing nonequilibrium molecular dynamics simulations. We quantify the response of a nematic liquid crystal (NLC) undergoing a Poiseuille flow in the Stokes regime, while being illuminated by a laser beam incident perpendicular to the flow direction. We adopt a minimalistic model to capture the interactions, accounting for two features: first, the laser heats up the NLC locally; and second, the laser polarises the NLC and exerts an optical torque that tends to reorient molecules of the nematic phase. Because of this reorientation the liquid crystal exhibits small regions of biaxiality, where the nematic director is one symmetry axis and the axis of rotation for the reorientation of the molecules is the other one. We find that the relative strength of the viscous and the optical torques mediates the flow-induced response of the biaxial regions, thereby tuning the emergence, shape and location of the regions of enhanced biaxiality. The mechanistic framework presented here promises experimentally tractable routes toward novel optofluidic applications based on material-flow-light interactions.     

Anisotropic microstructure-induced reduction of the Rayleigh instability for liquid crystalline polymers

We analyze a macroscopic 3D model for flows of liquid crystalline polymers (LCPs), deduced from Doi-type [3,4] kinetic equations. The Doi model accounts for rigid-rod microstructure, which introduces elastic relaxation and polymer-induced viscosity in addition to a Newtonian solvent viscosity, thus capturing all effects contained in standard isotropic viscoelastic models for Maxwell and Oldroyd B fluids. The rod-like microstructure further introduces anisotropic effects in the form of drag on the rods, together with a short-range, Maier-Saupe intermolecular potential, whose critical points vary with LCP concentration and yield stable isotropic (at low density) and nematic (at high density) equilibrium phases. From this single model, we compare various physical mechanisms for reducing the capillary instability of inviscid cylindrical jets: solvent viscosity as studied by Rayleigh and Chandrasekhar; isotropic viscoelasticity, both with and without Newtonian solvent viscosity; anisotropic polymer friction; and finally, the nematic, highly aligned prolate phase at high LCP density. Realistic parameter values for LCPs correspond to a regime in which the LCP capillary number (polymer bulk free energy relative to surface tension) is above an identified critical value; in such regimes, the unstable growth rates of the isotropic and nematic phases are lowered arbitrarily close to zero if the molecular drag is sufficiently anisotropic even in the absence of solvent viscosity. In low capillary number regimes, where surface tension dominates LCP bulk free energy, the LCP growth rates are sandwiched below the inviscid Rayleigh curve and above an explicit positive lower bound.     

Thermodynamics of mixtures of non-spherical molecules

Thermodynamic properties of liquid mixtures in which strong anisotropic intermolecular forces exist are studied using the Padé approximant method used by Stell et al. for pure fluids. Equations for the third-order perturbation term are derived for a general intermolecular potential of multipolar type. Using a mixture of Lennard-Jones molecules as the reference system, the effects of adding point dipole, quadrupole and anisotropic overlap potentials are calculated. Numerical results are presented (at low pressures) for the effect of these forces on the excess functions, and on the vapor-liquid equilibrium curves. These anisotropic forces lead to positive deviations from Raoult's law. Strong polar and quadrupolar forces may cause liquid-liquid immiscibility to occur. Numerical calculations are presented to illustrate such behaviour; these systems have upper critical solution points.     

Liquid–vapour equilibrium of n -alkanes using interface simulations

Molecular Dynamics simulations were performed to calculate liquid–vapour coexisting properties of n-alkane chains up to 16 carbon atoms using interface simulations. The lattice sum or Ewald method on the dispersion forces of the Lennard–Jones potential was applied to calculate the full interaction. The liquid and vapour coexisting densities were obtained for two flexible force field models, NERD and TraPPE-UA, where the intermolecular interactions are of the Lennard–Jones type. We have recently shown [P. Orea, J. López-Lemus, and J. Alejandre, J. Chem. Phys. 123, 114702 (2005)] that the liquid–vapour densities for simple fluids do not depend on interfacial area and therefore it is possible to use a small number of molecules in a simulation. We show that the same trend is found on the simulation of these hydrocarbon molecules. The phase diagram of ethane/n-decane binary mixtures is also obtained at 410.95 K for the NERD model. The simulation results from this work were compared with those obtained using methods with interfaces using large cut-off distances and with methods without interfaces for the same potential model. In both comparisons, excellent agreement was found. The results of liquid density from the TraPPE-UA model are in good agreement with experimental data while those from the NERD model are underestimated at low temperatures. Our findings are consistent with results published by other authors for small hydrocarbons.     

Growth of unidirectional molecular rows of cysteine on Au(110)-(1 x 2) driven by adsorbate-induced surface rearrangements

Using scanning tunneling microscopy we have studied the nucleation and growth of unidirectional molecular rows upon adsorption of the amino acid cysteine onto the anisotropic Au(110)-(1 x 2) surface under ultrahigh vacuum conditions. By modeling a large variety of possible molecular adsorption geometries using density-functional theory calculations, we find that in the optimum, lowest energy configuration, no significant intermolecular interactions exist along the growth direction. Instead the driving force for formation of the unidirectional molecular rows is an adsorbate-induced surface rearrangement, providing favorable adsorption sites for the molecules.     

Tilt-induced ferromagnetic ordering in anisotropic molecular monolayers

It is shown that orientational ordering of anisotropic organic molecules with permanent magnetic dipoles in a tilted film should result in a macroscopic magnetisation in the plane of the film. The important requirement here is that the molecules are strongly biaxial, and the corresponding biaxial orientational order parameter in the tilted phase is sufficiently large. The molecules should also be characterised by a reduced symmetry of the magnetic core compared with existing “single molecular magnets". Possible symmetry groups of the molecular magnetic core, which allow for the existence of nonzero average magnetic moment, are discussed in detail. The tilt-induced ferromagnetic ordering of such molecules may be determined by nonmagnetic intermolecular interactions including, for example, quadrupole-quadrupole electrostatic interaction or dispersion interaction between molecules of particular symmetry. Magnetic intermolecular interactions are not important here, and as a result the induced ferromagnetic state may be stable in any temperature range where the corresponding tilted film is stable. These general conclusions, which form a theoretical foundation for the existence of novel fluid low-dimensional magnetic materials, are based on symmetry arguments and are supported by a simple mean-field molecular model. We also discuss how such induced ferromagnetic ordering may be observed in Langmuir-Blodgett films which seem to be the best candidates for preparing these magnetic materials.     

The mean squared torque in pure and mixed dense fluids

The mean squared torque on a molecule can be obtained from infra-red or Raman band moments, and provides a direct measure of the strength of the anisotropic intermolecular forces. The expression for the mean squared torque on a molecule of species α in a fluid mixture is given in terms of the intermolecular potential and the angular pair correlation functions. This relation is made tractable by introducing a perturbation expansion in powers of the anisotropic potential strength for the angular pair correlation functions. Monte Carlo calculations of the mean squared torque are presented for a liquid of linear molecules having dipolar, quadrupolar and anisotropic overlap interactions. Comparison of the perturbation expansion to second order with these ‘exact’ results shows good agreement for μ*=μ/(εσ³)^1/2 and Q*=Q/(εσ⁵)^1/2 values less than about 0·5, and for values of the dimensionless overlap constant |δ| less than about 0·2. Finally, experimental values of the mean squared torque for both pure and mixed liquids are compared to the Monte Carlo and to the perturbation theory results.     

激波与火焰面相互作用数值模拟的GPU加速

为考察计算机图形处理器（GPU）在计算流体力学中的计算能力,采用基于CPU/GPU异构并行模式的方法对激波与火焰界面相互作用的典型可压缩反应流进行数值模拟,优化并行方案,考察不同网格精度对计算结果和计算加速性能的影响.结果表明,和传统的基于信息传递的MPI 8线程并行计算相比,GPU并行模拟结果与MPI并行模拟结果相同;两种计算方法的计算时间均随网格数量的增加呈线性增长趋势,但GPU的计算时间比MPI明显降低.当网格数量较小时（1.6×10⁴）,GPU计算得到的单个时间步长平均时间的加速比为8.6;随着网格数量的增加,GPU的加速比有所下降,但对较大规模的网格数量（4.2×10⁶）,GPU的加速比仍可达到5.9.基于GPU的异构并行加速算法为可压缩反应流的高分辨率大规模计算提供了较好的解决途径.     

Entropy of flexible liquids from hierarchical force–torque covariance and coordination

ABSTRACT

New theory is presented to calculate the entropy of a liquid of flexible molecules from a molecular dynamics simulation. Entropy is expressed in two terms: a vibrational term, representing the average number of configurations and momentum states in an energy well, and a topographical term, representing the effective number of energy wells. The vibrational term is derived in a hierarchical manner from two force–torque covariance matrices, one at the molecular level and one at the united-atom level. The topographical term comprises conformations and orientations, which are derived from the dihedral distributions and coordination numbers, respectively. The method is tested on 14 liquids, ranging from argon to cyclohexane. For most molecules, our results lie within the experimental range, and are slightly higher than those by the 2PT method, the only other method currently capable of directly calculating entropy for such systems. As well as providing an efficient and practical way to calculate entropy, the theory serves to give a comprehensive characterisation and quantification of molecular structure.     

Discrimination in racemates of small chiral molecules

A comparison of similar chiral molecules provides information about the impact of molecular characteristics on selectivity. In this article, the intermolecular structure in racemic fluids is the basis for comparing the molecules: the radial distribution between atoms on identical molecules is compared with the corresponding distribution for atoms from a mirror-image pair. A difference in these distributions signals an enantiomeric imbalance in the local distribution of molecules. The structure in the racemic fluids is explored using Monte Carlo (MC) simulations and the integral equation theory of Chandler, Silbey and Ladanyi (CSL) [1982, Molec. Phys., 46, 1335].

Racemic fluids are examined for several categories of chiral molecules. First, symmetrically shaped molecules have been considered in order to isolate local excesses attributable to energetic contributions. Second, racemates of hard chiral molecules have been examined. Here, enantiomeric imbalances can only originate from asymmetry in the molecular shape. Finally, both the molecular shape and the interaction strengths have been varied in order to explore the competition between steric and energetic effects. Within each category, the number of chiral molecules is large and a selection mechanism is required to identify those molecules which are expected to show large local excesses. An appropriate selection criterion (chirality index) has been defined and evaluated for 400 000 chiral molecules. Based on the results of this assessment, 24 racemates have been chosen for detailed examination by MC simulations and integral equation theories.     

Early dynamics of guest-host interaction in dye-doped liquid crystalline materials

We have studied in detail the early dynamics of laser-induced molecular reorientation in a dye-doped liquid crystalline (LC) medium that exhibits a significant enhancement of the optical Kerr nonlinearity due to guest-host interaction. Experimental results agree quantitatively with theory based on a model in which the anisotropic dye excitation helps reorient the LC molecules through a mean-field intermolecular interaction.     

Hydrogen bonding in liquid water: An ab initio QM/MM MD simulation study

Pattern and dynamics of hydrogen bonds in liquid water were investigated by a quantum mechanical/molecular mechanical molecular dynamics (QM/MM MD) simulation at Hartree–Fock (HF) level of theory. A large subregion of the whole system comprising two complete coordination shells was treated quantum mechanically in order to include all polarization and charge transfer effects and to obtain accurate data about structure and dynamics of the intermolecular bonds. The results of this investigation are in agreement with recent experimental findings and suggest that in liquid water every molecule forms in average 2.8, but almost as a rule less than four intermolecular hydrogen bonds.     

Calculation and optical measurement of laser trapping forces on non-spherical particles

Optical trapping, where microscopic particles are trapped and manipulated by light is a powerful and widespread technique, with the single-beam gradient trap (also known as optical tweezers) in use for a large number of biological and other applications. The forces and torques acting on a trapped particle result from the transfer of momentum and angular momentum from the trapping beam to the particle. Despite the apparent simplicity of a laser trap, with a single particle in a single beam, exact calculation of the optical forces and torques acting on particles is difficult. Calculations can be performed using approximate methods, but are only applicable within their ranges of validity, such as for particles much larger than, or much smaller than, the trapping wavelength, and for spherical isotropic particles. This leaves unfortunate gaps, since wavelength-scale particles are of great practical interest because they are readily and strongly trapped and are used to probe interesting microscopic and macroscopic phenomena, and non-spherical or anisotropic particles, biological, crystalline, or other, due to their frequent occurance in nature, and the possibility of rotating such objects or controlling or sensing their orientation. The systematic application of electromagnetic scattering theory can provide a general theory of laser trapping, and render results missing from existing theory. We present here calculations of force and torque on a trapped particle obtained from this theory and discuss the possible applications, including the optical measurement of the force and torque.     

Molecular simulation of liquid crystals

This article reviews recent progress in the computer simulation of liquid crystals at the molecular level. It covers the use of simple rigid-body models of the constituent molecules, and more detailed modelling via atomistic force fields. Bulk mesophases, inhomogeneous systems, and interfaces are discussed. Recent progress in calculating elastic properties and dynamics is summarised. As well as presenting an overview, some specific topics of recent interest are highlighted: the biaxial nematic phase, chiral phases, ionic liquid crystals, and charge-transfer systems.     

GPU accelerated simulations of bluff body flows using vortex particle methods

We present a GPU accelerated solver for simulations of bluff body flows in 2D using a remeshed vortex particle method and the vorticity formulation of the Brinkman penalization technique to enforce boundary conditions. The efficiency of the method relies on fast and accurate particle-grid interpolations on GPUs for the remeshing of the particles and the computation of the field operators. The GPU implementation uses OpenGL so as to perform efficient particle-grid operations and a CUFFT-based solver for the Poisson equation with unbounded boundary conditions. The accuracy and performance of the GPU simulations and their relative advantages/drawbacks over CPU based computations are reported in simulations of flows past an impulsively started circular cylinder from Reynolds numbers between 40 and 9500. The results indicate up to two orders of magnitude speed up of the GPU implementation over the respective CPU implementations. The accuracy of the GPU computations depends on the Re number of the flow. For Re up to 1000 there is little difference between GPU and CPU calculations but this agreement deteriorates (albeit remaining to within 5% in drag calculations) for higher Re numbers as the single precision of the GPU adversely affects the accuracy of the simulations.     

Perturbation theory for equilibrium properties of molecular fluids

Perturbation theory for the angular pair correlation function g(r₁₂ ω ₁ ω ₂), using a fluid with isotropic intermolecular forces as the reference system, is applied to the calculation of a variety of macroscopic properties. Comparisons with experiment are made for methane, oxygen and nitrogen (and carbon monoxide for infra-red and Raman band moments) in the dense fluid and liquid states. Theoretical expressions are given and calculations made for thermodynamic properties (isothermal compressibility, pressure, configurational energy, entropy and specific heat) both along and away from the vapour-liquid co-existence curve, for infra-red and Raman band moments, and for neutron scattering cross sections. Excellent agreement with experiment is obtained for all properties, except for the infra-red and Raman band moments; this latter comparison is inconclusive because of large experimental uncertainties. The anisotropic intermolecular forces are found to have very little effect on the liquid isothermal compressibility, in agreement with the first-order theory. Molecular anisotropy has a relatively small effect on the configurational energy and on the Helmholtz free energy, but the effect is large for pressure and specific heat. The pressure is more sensitive to short-range anisotropic forces than the other properties, whereas the specific heat is particularly sensitive to the long-range anisotropic forces. Mean squared torques (derived from infra-red and Raman band moments) are very sensitive to the strengths of the anisotropic forces, and are more sensitive to higher terms in the multipole series than are the other properties. The structure factors for oxygen and nitrogen are found to be little affected by the anisotropic forces.     

Evaluation of the SSC/LHNC,SSCF and PY approximations for short ranged,anisotropic potentials

Three approximations for the orientational correlation function of molecular fluids—the single super chain/linearized hypernetted chain (SSC/LHNC), single super chain f-expansion (SSCF) and Percus-Yevick (PY) approximation—are evaluated in the dense liquid state for a fluid inter-acting with short ranged anisotropic interactions. These interactions are prototypical of the forces that determine the non-spherical shape of symmetric linear molecules. We find that SSC/LHNC is very poor, failing to predict many of the structural features present in the Monte Carlo (MC) simulation results. The PY and SSCF approximations produce much better results; however, neither approximation is completely satisfactory.