Johann Fischer

Vapour liquid equilibria of the Lennard-Jones fluid from the NpT plus test particle method

Using an improved version of the recently suggested NpT + test particle method, phase equilibria are determined for the Lennard-Jones fluid in the temperature range T* = 0·70 to T* = 1·30 in steps of ΔT* = 0·05. For the final results, gas simulations are necessary only at the two highest temperatures; for T* = 1·20 and downwards the gas phase can be described with sufficient accuracy by the Haar-Shenker-Kohler equation. The resulting vapour pressures, bubble and dew densities can be correlated by the equations , , , with the critical temperature and density being T*c = 1·310 and ρ*c = 0·314, respectively. Then a detailed comparison with other simulation results and perturbation theory results is given. Outstanding findings are that the present data are rather smooth, that they match quite well the early data of Hansen and Verlet (1969, Phys. Rev., 184, 151) and are much closer to perturbation theory than most previous results. Finally, using the vapour pressure equation and directly calculated volume chan...

Molecular dynamics simulation of the liquid–vapor interface: The Lennard-Jones fluid

In this work we present new molecular dynamics simulation results for the liquid–vapor interface of the pure Lennard-Jones fluid. Our aims were further investigations on the simulation setup and the simulation parameters to obtain reliable data for the coexisting densities as well as for the surface tension. The influence of the cut-off distance to the interfacial properties is investigated and long-range corrections to both the dynamics and the surface tension are applied. It is found that the saturated liquid densities from the surface simulations agree with those from the NpT+test particle method within 1% for sufficiently large simulation boxes; the saturated vapor densities agree within 4%. In order to obtain reliable values for the surface tension, cut-off radii of at least 5 molecular diameters supplemented by a tail correction are required.

Influence of intermolecular potential parameters on orthobaric properties of fluids consisting of spherical and linear molecules

Model fluids consisting of spherical n/6 molecules and of linear two-centre Lennard-Jones molecules are considered. The orthobaric densities and the vapour pressures are calculated by using perturbation theory at liquid densities and second virial coefficients at gas densities. In order to classify the results the deviations from corresponding states principle are investigated. For spherical molecules, a steeper repulsive potential lowers the vapour pressure considerably but hardly effects the liquid saturation density. For linear molecules, an increasing elongation lowers the vapour pressure and increases the liquid saturation density. Finally, comparison with real Ar, CH4, N2, F2, C2H6, and CO2 is made.

Perturbation theory for the free energy of two‐center‐Lennard‐Jones liquids

Recently a perturbation theory for molecular liquids using hard dumbbells as reference system was suggested by Kohler et al. Here, with a somewhat modified approach, it is shown that this type of perturbation theory yields a nearly accurate equation of state even for the most anisotropic two‐center‐Lennard‐Jones molecules, for which simulation results have been reported. In addition to that, an investigation of the different approximations in this approach is given.

Vapour liquid equilibrium of a pure fluid from test particle method in combination with NpT molecular dynamics simulations

In order to determine the vapour liquid equilibrium of a pure fluid, the liquid and the vapour branch of the isotherms in the chemical potential μ vs pressure p-diagram, are constructed explicitly. The liquid branch is obtained by molecular dynamics simulations in an NpT-ensemble into which test particles are inserted to calculate the chemical potential. The vapour branch is obtained at lower temperatures by using the second virial coefficient, at higher temperatures it is determined again by simulations. As an example the two-centre Lennard-Jones fluid with elongation L = 0·505 is considered at temperatures ranging from 0·69 to 0·92 of the estimated critical temperature. As expected, the inaccuracies of the liquid chemical potential increase with decreasing temperature as a consequence of the increasing saturated density. The uncertainties in μ/RT range from 0·02 at the highest to 0·10 at the lowest temperature which creates an uncertainty in the reduced vapour pressure Pσ3/ϵ of the order of 0·002. Withi...

Thermodynamic perturbation theory for molecular liquid mixtures

A Weeks–Chandler–Andersen type perturbation theory for the Helmholtz energy of mixtures consisting of molecules with nonspherical cores is given. The correlation functions are obtained from a reference mixture of softly repulsive spherical particles. For that mixture the Percus–Yevick equation is solved with Baxter’s formalism. By a blip expansion a hard convex body system is determined for which the free energy is obtained from Boublik’s equation. For one‐center Lennard‐Jones liquids, the excess properties for mixtures agree with simulation results as good as those of the Baker–Henderson and the variational theory, while the pure substance properties are obtained better now. For mixtures of one‐center and two‐center Lennard‐Jones liquids, the excess volumes and the excess enthalpies are given for argon/nitrogen and argon/oxygen after fitting the unlike pair interaction to the experimental value of the excess Gibbs energy. The results resemble those obtained from simpler theories, but discrepancies with r...

Description of polyatomic real substances by two-center Lennard-Jones model fluids

Abstract Bohn, M., Lustig, R. and Fischer, J., 1986. Description of polyatomic real substances by two-center Lennard-Jones model fluids. Fluid Phase Equilibria, 25: 251–262. For O2, CO, CS2, C2H4, Cl2 and Br2 orthobaric properties were calculated by perturbation theory on the basis of two-center Lennard-Jones (2CLJ) model molecules. The LJ-parameters σ and e were determined by fitting the vapour pressure and the bubble density at one temperature about halfway between the triple point and 0.8 Tc. The elongation L in the model was fixed to give the correct temperature variation of the vapour pressure. The temperature variation of the orthobaric liquid density turned out to be less dependent on L, and could be satisfactorily reproduced. With the parameters determined from the orthobaric properties of the liquid, second virial coefficients were calculated. This was also done for Ar, Kr, Xe, CH4, N2, F2 and C2H6 for which the parameters have been determined previously in a similar way. The agreement between the predicted and the experimental second virial coefficients is excellent for C2H4 and C2H6. For O2, N2, CO and F2 it is still better than for the spherical molecules. The agreement for Cl2 and CS2 is less satisfactory.

An accurate Van der Waals-type equation of state for the Lennard-Jones fluid

A new equation of state (EOS) is proposed for the Helmholtz energyF of the Lennard Jones fluid which represents the thermodynamic properties over a wide range of temperatures and densities. The EOS is written in the form of a generalized van der Waals equation.F =Fu +Fv. WhereFu is a hard body contribution andFA an anttractive dispersion force contribution. The expression forFH is closely related to the hybrid Barker Henderson pertubation theory. The construction ofFA is accomplished with the Setzmann Wagner optimization procedure on the basis of virial coefficients and critically assessed computer simulation data. A comparison with the EOS of Johnson et al. shows improvement in the description of the vapor liquid coexistence properties, thepvT data. and in peculiar, of the calorie properties. A comparison with the EOS of Kolafa and Nezbeda which appeared after the bulk of this work was finished shows still by about 30%.

Determination of an effective intermolecular potential for carbon dioxide using vapour-liquid phase equilibria from NpT + test particle simulations

Abstract Molecular simulations according to the NpT + test particle method are used for the determination of vapour-liquid phase equilibria of six model potentials of the two-centre Lennard-Jones plus point quadrupole (2CLJQ) type. By fitting to experimental saturation properties of carbon dioxide, an optimized effective 2CLJQ potential for this substance is found to have the parameters ϵ/k = 125.317 K, σ = 3.0354 A, L = I/σ = 0.699, and Q★2 = Q/ϵσ5 = 3.0255; the resulting quadrupole moment Q differs from the most recent experimental value by only 9%. Using this potential, densities and enthalpies of carbon dioxide are obtained again by molecular simulations as functions of temperature and pressure in large parts of the fluid region extending from 230 to 570 K, and pressures up to 400 MPa. The results show that effective potentials obtained by fitting to experimental saturation properties also yield good predictions of the thermodynamic properties for polar substances.

Prediction of thermodynamic properties of fluid mixtures by molecular dynamics simulations: methane-ethane

NPT and NVT molecular dynamics simulation results are reported for the fluid methane-ethane mixture. Methane is modelled as Lennard-Jones fluid and ethane as a two-centre Lennard-Jones fluid with parameters obtained some time ago by fitting WCA-type perturbation theory results to two experimental vapour pressures and one bubble density for each substance. It has also already been shown that these effective pair potentials yield good predictions of the pressures and internal energies of the pure substances in the whole fluid region. In order to obtain an effective potential between the unlike molecules, previously derived fluctuation formulas for the dependence of the mixture excess properties on the unlike molecule interaction parameters are used. A test of these fluctuation formulas shows their statistical uncertainties to be small. Hence, the unlike interaction parameters can be determined from one mixture simulation and a fit to one experimental excess volume and one excess enthalpy. Then second virial...