Michael Bohn

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.

Prediction of excess properties for liquid mixtures: results from perturbation theory for mixtures with linear molecules

Abstract A Weeks—Chandler—Andersen type perturbation theory is used to predict excess properties of liquid binary mixtures of spherical and linear dumbbell-like molecules and mixtures with two dumbbell-like components. The calculations are improved by the introduction of a new blip formalism. A combining rule used previously for mixtures of spherical molecules is extended to mixtures with nonspherical ones and criteria are given as to when reasonable results can be expected. This is demonstrated for 20 binary mixtures. It is also shown that fitting the unlike interaction to one excess property ( g E or h E ) always gives good results for the other excess properties, provided that the electric moments are not too big. Finally, it is shown for the mixture Xe + C 2 H 6 , that the perturbation theory can reproduce the temperature variation of the excess properties almost within experimental error.

Excess properties of liquid mixtures from perturbation theory: results for model systems and predictions for real systems

Abstract Mixtures consisting of spherical and linear molecules are treated with a Weeks-Chandler-Andersen type perturbation theory. For model mixtures of spherical molecules the excess properties obtained from perturbation theory are in excellent agreement with the simulation results of Singer for all energy and size ratios. The concentration dependence of the excess properties is investigated and shown to become asymmetric for g E only as a consequence of different molecular sizes. For mixtures of spherical with linear molecules the effect of the molecular shape on the excess quantities is demonstrated. As to the properties of real mixtures, for spherical or nearly spherical molecules they can be predicted with fair accuracy using merely pure component properties by applying a previously suggested combinating rule or its improvement. Finally, an extension of the combining rule to nonspherical molecules is attempted and yields good predictions for the mixtures Ar/C 2 H 6 , CH 4 /C 2 H 6 , Kr/C 2 H 6 and Xe/C 2 H 6 .

Effect of molecular elongation on the quadrupolar free energy in diatomic fluids

This paper reports results obtained from computer simulations of pure fluids composed of two-centre Lennard-Jones plus point quadrupole molecules. Simulations were performed over a range of quadrupole moments 0 ⩽ Q 2 ⩽ 4 and a range of molecular elongations 0 ⩽ l ⩽ 0·793. The principal results reported are values of the quadrupolar contribution to the Helmholtz free energy AQ , which was computed via Kirkwoods coupling parameter method. We show how AQ responds to changes in both Q and l. Results are also presented for the configurational internal energy, the quadrupolar internal energy, and site-site pair distribution functions. The simulation results are used to test two forms of first-order perturbation theory; neither form of the theory satisfactorily predicts the simulation results when both the quadrupole moment and the molecular elongation are large.

The Haar-Shenker-Kohler equation: A fundamental equation of state for gases

Haar and Shenker and later Kohler and Haar related the residual Helmholtz energy A res of a realistic fluid to that of a hard body fluid by A res/RT = Bρ + A H res/RT - B Hρ, where B and B H are the second virial coefficients. By comparison with the simulation data of Adams and of Yao et al. for a Lennard-Jones fluid we show that the Haar-Shenker-Kohler equation yields very accurate chemical potentials and pressures for the gas up to densities ρσ3 = 0·2. The chemical potential equation of Powles is also discussed.

Specific heat of simple liquids

Residual specific heats c v/* are calculated from a Weeks-Chandler-Andersen-type perturbation theory for Lennard-Jones (LJ) and two-centre-Lennard-Jones (2CLJ) liquids. For spherical molecules the theory predicts that as the density is increased up to slightly above three times the critical density (ρc), c v/* increases to 2R. Corresponding states considerations indicate that rotational degrees of freedom in 2CLJ fluids make no contributions to c v/*. Comparing with real liquids, the theoretical predictions of c v/* agree, within the accuracy of the experiments, with experimental data for liquid argon, methane, and oxygen, at densities ρ/ρc > 2·5. For ethane, the theoretical predictions of c v/*, assuming a 2CLJ fluid with elongation L = 0·67, are too low. This deficiency in the theory for long molecules is attributed to the neglect of the angle-dependence of the background correlation function. However, computer simulation results for c v/* in 2CLJ fluids of elongation L = 0·67 agree with the perturbatio...

The excess properties of nitric oxid mixtures

The excess properties of the three mixtures of nitric oxid with methane, krypton, and nitrogen are calculated and compared with experimental values. As nitric oxid is strongly dimerized in the liquid state, the calculation involves the assignment of potential parameters to the nitric oxid monomer and dimer, the statistical mechanical calculation of the excess properties of the fictitious mixtures with monomer and with dimer, and the calculation of the equilibrium properties in the pseudoternary system formed by monomer, dimer, and second component. The comparison with experimental values shows that the calculation gives the correct order of excess values, but fails in some numerical details.ZusammenfassungDie Exzeß-Eigenschaften der drei Stickstoffoxid-Mischungen mit Methan, Krypton und Stickstoff werden berechnet und mit experimentellen Werten verglichen. Da Stickstoffoxid im flüssigen Zustand überwiegend dimerisiert vorliegt, beinhaltet die Berechnung die Festlegung der Potentialparameter des Stickstoffoxid-Monomeren und -Dimeren, die statistisch-mechanische Berechnung der Exzeßeigenschaften der fiktiven Mischungen mit Monomer und mit Dimer, und die Berechnung der Gleichgewichtseigenschaften in dem pseudoternären System, das durch Monomer, Dimer und zweite Komponente gebildet wird. Der Vergleich mit den experimentellen Werten zeigt, daß die Berechnung die richtige Reihenfolge und Größenordnung der Exzeß-Werte wiedergibt, aber in manchen numerischen Details versagt.

Studies on phase equilibria of two-centre Lennard-Jones fluids

Several results concerning the phase equilibria of two-centre Lennard-Jones (2CLJ) fluids are presented. Firstly, a comparison of chemical potential values for the elongation L = 0·63 obtained from perturbation theory shows qualitative agreement with the simulation results of Romano and Singer and excellent agreement with results of Guillot and Guissani except at the highest density. The complete saturation curve of the 2CLJ-0·63 fluid is then calculated by combining the Romano-Singer results, the Haar-Shenker-Kohler equation and perturbation theory. For the 2CLJ-fluids with L = 0·05, 0·10, and 0·20 the low-temperature saturation curves are calculated by perturbation theory as well as the pseudocritical points. At that point the packing fraction of the hard molecular cores has the constant value η = 0·165 in going from L = 0 to L = 0·3292 and falls off slightly for higher elongations. The reduced hard sphere diameter d/σ, however, shows a distinct minimum at about L = 0·27.

Prediction of gas PVT data with effective intermolecular potentials using the Haar-Shenker-Kohler equation and computer simulations

Abstract Gas PVT data are predicted for argon, methane, oxygene, ethane, and ethylene for densities up to two-thirds of the critical density ρ c and temperatures up to three times the critical temperature. The underlying molecular interactions are Lennard-Jones and two-centre Lennard-Jones potentials with parameters determined previously with our WCA-type perturbation theory by fitting only to one saturated liquid density and to one or two vapour pressures. These potentials were taken as input for the Haar-Shenker-Kohler (HSK) equation and, for the non-spherical molecules, also for molecular dynamics (MD) simulations at a density about 2 3 ρ c . Technically, the simulations were performed with vectorized codes on a CYBER 205. The agreement of the MD pressures with the experimental data is found to be within the statistical uncertainties of the simulations which are estimated to be at most 0.3 MPa. The HSK pressures agree with the experimental pressures within 0.3 MPa near the saturation curve but always become somewhat too high at higher temperatures.

Thermodynamic perturbation theory for mixtures of spherical and tetrahedral molecules

A Weeks-Chandler-Andersen type perturbation theory (PT) is presented for the Helmholtz energy of liquid mixtures consisting of spherical and tetrahedral molecules. Use is made of a hard fused sphere anisotropic reference system. The excess properties g E, h E and v E are predicted for the mixtures CS2/CCl4 and Ar, Kr, Xe, CH4/CF4. CCl4 and CF4 are modelled as tetrahedrons, the other substances are treated as spheres. The consequences of molecular shape on the prediction of excess values is discussed. The tetrahedrons are modelled with and without an additional interaction site at the centre of mass. The influence on the excess properties turned out to be small. For the system Xe/CF4 the shape influence on the concentration dependence of the excess properties is small, and is compared with experiment. For the CF4 mixtures it is shown that unlike interaction parameters determined in the liquid phase predict the excess virial coefficients almost within the experimental accuracy.