Transport coefficients of the Lennard-Jones model fluid. III. Bulk viscosity

In an extensive computer simulation study, the transport coefficients of the Lennard-Jones model fluid were determined with high accuracy from equilibrium molecular-dynamics simulations. In the frame of time-correlation function theory, the generalized Einstein relations were employed to evaluate the transport coefficients. This third of a series of four papers presents the results for the bulk viscosity. With comprehensive simulation data at over 350 state points, the temperature and density dependences of the bulk viscosity are characterized in this work over a wide range of fluid states. The bulk viscosity exhibits a large critical enhancement similar to that known for the thermal conductivity, but it extends much farther into the supercritical region and can be observed even at 4.5 times the critical temperature. An investigation of the pressure-fluctuation autocorrelation functions shows that the enhancement is caused by extremely slowly decaying pressure fluctuations.     

Transport and Helfand moments in the Lennard-Jones fluid. I. Shear viscosity

The authors propose a new method, the Helfand-moment method, to compute the shear viscosity by equilibrium molecular dynamics in periodic systems. In this method, the shear viscosity is written as an Einstein-type relation in terms of the variance of the so-called Helfand moment. This quantity is modified in order to satisfy systems with periodic boundary conditions usually considered in molecular dynamics. They calculate the shear viscosity in the Lennard-Jones fluid near the triple point thanks to this new technique. They show that the results of the Helfand-moment method are in excellent agreement with the results of the standard Green-Kubo method.     

Transport coefficients of the Lennard-Jones model fluid. II Self-diffusion

In an extensive computer simulation study, the transport coefficients of the Lennard-Jones model fluid were determined with high accuracy from equilibrium molecular-dynamics simulations. In the frame of time-correlation function theory, the generalized Einstein relations were employed to evaluate the transport coefficients. This second of a series of four papers presents the results for the self-diffusion coefficient, and discusses and interprets the behavior of this transport coefficient in the fluid region of the phase diagram. The uncertainty of the self-diffusion data is estimated to be 1% in the gas region and 0.5% at high-density liquid states. With the very accurate data, even fine details in the shape of the self-diffusion isotherms are resolved, and the previously little-investigated behavior of the self-diffusion coefficient at low-density gaseous states is analyzed in detail. Finally, aspects of the mass transport mechanisms on the molecular scale are explored by an analysis of the velocity autocorrelation functions.     

Transport coefficients of the Lennard-Jones model fluid. I. Viscosity

In an extensive computer simulation study, the transport coefficients of the Lennard-Jones model fluid were determined with high accuracy from equilibrium molecular-dynamics simulations. In the frame of time-correlation function theory, the generalized Einstein relations were employed to evaluate the transport coefficients. This first of a series of four papers presents the results for the viscosity, and discusses and interprets the behavior of this transport coefficient in the fluid region of the phase diagram. Moreover, the kinetic-kinetic, kinetic-potential, and potential-potential viscosity contributions are resolved over the whole range of fluid states, and their characteristic dependence on temperature and density is described. Finally, an additional analysis of the shear-stress correlation functions reveals aspects of the momentum-transport mechanisms on the molecular scale.     

Theoretical scheme for the shear viscosity of Lennard-Jones fluids

We use the shear viscosity expression from the Enskog theory of dense gases in a perturbative scheme for the Lennard-Jones (LJ) fluid. This perturbative scheme is formulated by combining the analytic rational function approximation method of Bravo Yuste and Santos [Phys. Rev. A 43, 5418 (1991)] for the radial distribution function of hard-sphere fluids and the well known Mansoori-Canfield/Rasaiah-Stell perturbation theory to determine an effective diameter for the LJ fluid. The scheme is reliable on a wide range of temperatures and densities, and is very accurate around the critical point. Using this information, we build an accurate empirical formula for the shear viscosity in the liquid phase, which fits the recent data [K. Meier et al., J. Chem. Phys. 121, 3671 (2004)] in the whole simulation range.     

Scaling Function Between the Exponential-6 and the Generalized Lennard-Jones Potential Functions

The van der Waals forces for non-bonded interaction can be expressed either by the Exponential-6 or by the Lennard-Jones(m-n) potential functions, whereby m > n. Hitherto a relationship exists between the Exponential-6 and the Lennard-Jones(12-6) potential functions, with a scaling factor = 13.772 at or near the equilibrium and = 12.0 for long range interaction. This paper attempts to develop relationships between Exponential-6 and a more generalized Lennard-Jones(m-n). Analysis reveals that the relationship exists only when n = 6 and that two sets of scaling factors (as functions of index m) applies for the relationship between Exponential-6 and the Lennard-Jones(m-6), whereby m > 6.     

Thermodynamic properties of Lennard-Jones chain molecules: renormalization-group corrections to a modified statistical associating fluid theory

A modified version of the statistical associating fluid theory (SAFT), the so-called soft-SAFT equation of state (EOS), has been extended by a crossover treatment to take into account the long density fluctuations encountered when the critical region is approached. The procedure, based on White's work from the renormalization group theory [Fluid Phase Equilibria 75, 53 (1992); L. W. Salvino and J. A. White, J. Chem. Phys. 96, 4559 (1992)], is implemented in terms of recursion relations where the density fluctuations are successively incorporated. The crossover soft-SAFT equation provides the correct nonclassical critical exponents when approaching the critical point, and reduces to the original soft-SAFT equation far from the critical region. The accuracy of the global equation is tested by direct comparison with molecular simulation results of Lennard-Jones chains, obtaining very good agreement and clear improvements compared to the original soft-SAFT EOS. Excellent agreement with vapor-liquid equilibrium experimental data inside and outside the critical region for the n-alkane series is also obtained. We provide a set of transferable molecular parameters for this family, unique for the whole range of thermodynamic properties.     

Molecular theory of thermal conductivity of the Lennard-Jones fluid

In this paper the thermal conductivity of the Lennard-Jones fluid is calculated by applying the combination of the density-fluctuation theory, the modified free volume theory of diffusion, and the generic van der Waals equation of state. A Monte Carlo simulation method is used to compute the equilibrium pair-correlation function necessary for computing the mean free volume and the coefficient in the potential-energy and virial contributions to the thermal conductivity. The theoretical results are compared with our own molecular dynamics simulation results and with those reported in the literature. They agree in good accuracy over wide ranges of density and temperature examined in molecular dynamics simulations. Thus the combined theory represents a molecular theory of thermal conductivity of the Lennard-Jones fluid and by extension simple fluids, which enables us to compute the nonequilibrium quantity by means of the Monte Carlo simulations for the equilibrium pair-correlation function.     

A reexamination of virial coefficients of the Lennard-Jones fluid

The fourth-order virial coefficients have been calculated exactly to five decimal places for pure fluids of the Lennard-Jones potential at many points in the phase diagram. The calculations were performed through direct evaluation of the integrals, or diagrams, which make up the density expansion of the radial distribution function: included were the standard fast Fourier transform method of evaluating the simply connected diagrams and the evaluation of the bridge diagram for the fourth order in density by expansion in Legendre polynomials. The polynomial-order dependence of the bridge diagram calculation and the range dependence of the simply connected diagrams of the fourth order are found to have more significance than was thought from previous studies, especially in the low-temperature range. This result was confirmed by direct evaluation of the diagrams which construct the virial coefficients, as given by Rowlinson, Barker, and coworkers. This calculation confirmed that numerical convergence has not been achieved at the precision levels previously reported in the literature. These differences, though minor at higher temperatures, can be seen to be more significant at the lower temperature ranges. Received: 31 July 2000 / Accepted: 18 September 2000 / Published online: 21 December 2000     

Scaling analysis of the temperature dependence of intrinsic viscosity

The scaling predictions for the temperature dependence of the intrinsic viscosity of flexible polymers are briefly reviewed. When the predictions are fit to a power law over a fixed range of chain length, a relation between the exponent and prefactor of the Mark–Houwink–Sakurada equation emerges. In comparing with the experimental data compilation of Rai and Rosen, we conclude that real polymer systems are nowhere near the true good solvent limit, even when the exponent matches the good solvent prediction. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1989–1991, 1997     

Critical point estimation of the Lennard-Jones pure fluid and binary mixtures

The apparent critical point of the pure fluid and binary mixtures interacting with the Lennard-Jones potential has been calculated using Monte Carlo histogram reweighting techniques combined with either a fourth order cumulant calculation (Binder parameter) or a mixed-field study. By extrapolating these finite system size results through a finite size scaling analysis we estimate the infinite system size critical point. Excellent agreement is found between all methodologies as well as previous works, both for the pure fluid and the binary mixture studied. The combination of the proposed cumulant method with the use of finite size scaling is found to present advantages with respect to the mixed-field analysis since no matching to the Ising universal distribution is required while maintaining the same statistical efficiency. In addition, the accurate estimation of the finite critical point becomes straightforward while the scaling of density and composition is also possible and allows for the estimation of the line of critical points for a Lennard-Jones mixture.     

Systematic investigation of theories of transport in the Lennard-Jones fluid

Three kinetic theories of transport are investigated for the single-species Lennard-Jones model fluid. Transport coefficients, including diffusion, shear, and bulk viscosity, are calculated from these theories for the Lennard-Jones fluid across the fluid regions of the phase diagram. The results are systematically compared against simulation. It is found that for each transport property considered, there is at least one theoretical result based on approximations that have been systematically derived from a first-principles starting point that is quantitatively useful over a wide range of densities and temperatures. To the authors' knowledge, this article constitutes the first such compendium of results for the Lennard-Jones model fluid that has been assembled.     

Thermal properties of the metastable supersaturated vapor of the Lennard-Jones fluid

p, rho, T data of the supersaturated vapor of the Lennard-Jones fluid are obtained by molecular dynamics simulations. The metastable state points are identified before a phase separation takes place. An estimation of the location of the spinodal is given. The results are compared to two theoretically based equations of state and one empirical equation of state which was parametrized also taking into account metastable state points. The pressure obtained by simulation is found to be lower than that from both theoretically based equations of state, which do not account for the inhomogeneous density distribution of the supersaturated vapor.     

The viscosity of argon at very high pressure, up to the melting line

The viscosity of argon has been measured as a function of pressure at 223.15 K, 301.15 K and 323.15 K by means of a vibrating wire viscometer. The measurement of the 223.15 K isotherm has been carried out right up to the melting pressure (7790 bar).     

The self-diffusion coefficient in stable and metastable states of the Lennard-Jones fluid

Molecular-dynamics simulations have been employed to calculate the self-diffusion coefficient of a Lennard-Jones fluid for 198 sets of state parameters in the range of temperatures 0.35 ≤ k_BT/? ≤ 2.0 and densities 0.005 ≤ ρσ³ ≤ 1.2. Calculations have been made in stable and metastable states to the boundary of spontaneous nucleation in a model containing 2048 interacting particles. Results of computations, performed in the parameter range of stable states, are compared with the results of previous papers. Equations have been formulated, which describe the dependences of the self-diffusion coefficient on temperature and density and on temperature and pressure in the whole range of parameters including both the stable and metastable (supersaturated vapor, superheated and supercooled liquid) states of fluid.     

Interatomic Lennard-Jones potentials of linear and branched alkanes calibrated by Gibbs ensemble simulations for vapor-liquid equilibria

We propose Lennard-Jones potential parameters for interatomic interactions of linear and branched alkanes based on matching the results of Gibbs ensemble simulations of vapor-liquid equilibria to experimental data. The alkane model is similar as in the OPLS-AA, but multiple atom types for carbon based on the number of covalently bonded hydrogen atoms are necessary to accurately reproduce liquid densities and enthalpies of vaporization with the errors of 2.1% and 3.3%, respectively, for hydrocarbons of various chain lengths and structures. We find that the attraction energies of the carbon atoms are almost proportional to the number of covalent hydrogen atoms with each increasing the carbon energy parameter by approximately 0.033 kcal/mol. Though the present force field outperforms the OPLS-AA force field for alkanes we studied, systematic deviations for vapor pressures are still observed with errors of 15%-30%, and critical temperatures are slightly underestimated. We think that these shortcomings are probably due to the inadequacy of the two-parameter Lennard-Jones potential, and especially its behavior at short distances.     

Influence of the chain length on the dynamic viscosity at high pressure of some amines: Measurements and comparative study of some models

This work reports the dynamic viscosity data (a total of 72 points) of a series of primary amines which exhibit small association consisting of pentylamine, hexylamine and heptylamine at four temperatures between (293.15 and 353.15) K (every 20 K), and pressures up to 100 MPa (every 20 MPa) which allows to study the influence of the chain length. A falling body viscometer with an uncertainty of ±2% was used to perform these measurements.The variations of dynamic viscosity are discussed with respect to their behavior due to chain length. Six different models, most of them with a physical and theoretical background, are studied in order to investigate how they take the chain length influence and effect into account through their required model parameters. The evaluated models are based on the empirical Vogel–Fulcher–Tamman (VFT) representation (combined with Tait-like equation), the rough hard-sphere scheme, the concept of the free-volume, the friction theory and a correlation derived from molecular dynamics. A recent scaling viscosity model has also been considered. These models need some adjustable parameters except the molecular dynamic correlation which is entirely predictive. Overall a satisfactory representation of the viscosity of these amines is found for the different models within the considered T, p range taking into account their simplicity. Moreover it has been verified that the viscosity is a unique function of TV^γ where the exponent γ is related to the steepness of the intermolecular repulsive potential (T: temperature, and V: specific volume).     

An accurate expression for radial distribution function of the Lennard-Jones fluid

A simple and accurate expression for radial distribution function (RDF) of the Lennard-Jones fluid is presented. The expression explicitly states the RDF as a continuous function of reduced interparticle distance, temperature, and density. It satisfies the limiting conditions of zero density and infinite distance imposed by statistical thermodynamics. The distance dependence of this expression is expressed by an equation which contains 11 adjustable parameters. These parameters are fitted to 353 RDF data, obtained by molecular dynamics calculations, and then expressed as functions of reduced distance, temperature and density. This expression, having a total of 65 constants, reproduces the RDF data with an average root-mean-squared deviation of 0.0152 for the range of state variables of 0.5  T^*  5.1 and 0.35  ρ^*  1.1 (T^*=kT/ε and ρ^* = ρσ³ are reduced temperature and density, respectively). The expression predicts the pressure and the internal energy of the Lennard-Jones fluid with an uncertainty that is comparable to that obtained directly from the molecular dynamics simulations.     

A mode-coupling theory treatment of the transport coefficients of the Lennard-Jones fluid

We apply mode-coupling theory to study shear viscosity and self-diffusion coefficient of the Lennard-Jones fluid throughout the entire fluid region of the phase diagram. Theoretical results are compared with the extensive simulation data and good agreement is found. In addition, theory is compared to the experimental data on the transport coefficients of inert gas fluids.     

Self-assembly of long chain alkanes and their derivatives on graphite

We combine scanning tunneling microscopy (STM) measurements with ab initio calculations to study the self-assembly of long chain alkanes and related alcohol and carboxylic acid molecules on graphite. For each system, we identify the optimum adsorption geometry and explain the energetic origin of the domain formation observed in the STM images. Our results for the hierarchy of adsorbate-adsorbate and adsorbate-substrate interactions provide a quantitative basis to understand the ordering of long chain alkanes in self-assembled monolayers and ways to modify it using alcohol and acid functional groups.