Friedrich Kohler

Perturbation theory with a hard dumbbell reference system. I. Application to liquid nitrogen

We present a perturbation theory of molecular fluids which uses an anisotropic reference assembly. At each orientation, the potential is divided according to the Weeks–Chandler–Andersen (WCA) prescription into a reference potential e0 which contains the repulsive forces and a perturbation e1 containing the attractive forces. To compute the properties of the reference system, a second perturbation is made about a reference system consisting of equivalent hard dumbells using the analogue of the WCA‐blip function theory. The thermodynamic properties of the hard dumbell system are computed from an analytic equation of state due to Boublik and Nezbeda, and the correlation functions using a method developed by the authors. The theory is applied to a two‐center Lennard–Jones model of nitrogen at high densities and shown to predict pressures in good agreement with computer simulations.

Excess properties of binary mixtures of 2,2,4-trimethylpentane with one polar component

Abstract The excess proerties (g E , h E , v E , c p E ) of 2,2,4-trimethylpentane with several polar components of different polarity [acetonitrile, 2-butanone, bisdichloroethylether, t-butylchloride, chlorobenzene] have been determined. If the dipole-dipole interaction could be averaged over the different orientations, the net effect should be a spherical but temperature dependent contribution to the interaction potential. This would give rise to a negative c p E which could be estimated from the difference between g E and h E . The investigation has shown that the experimental values of c p E are the more positive, the stronger the dipole moment of the polar molecule. Obviously, there exist preferred orientations between the dipolar molecules, which cannot be broken up easily for stronger dipole moments.

The pϱT properties of ethanol + hexane

Abstract The pϱT behavior of ethanol, hexane and its mixture has been investigated with the aim to cover the whole region from low pressure-low temperature thermodynamic excess properties up to the critical curve. The mixture exhibits a positive azeotrope which persists over the whole range. The positive excess volume shows a remarkable temperature dependence. Whereas the thermodynamic evaluation and the comparison to model calculations will be the subject of a future paper, all experimental results are put together in this paper.

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.

Intermolecular force parameters for unlike pairs

Abstract A combining rule is suggested for spherically symmetric two-parameter pair potentials. The efficiency of this rule is demonstrated for several gaseous and liquid mixtures.

Local composition in liquid mixtures

Abstract Nonrandomness and local compositions in model liquid mixtures have been investigated by computer simulation (molecular dynamics) and perturbation theory. The computer simulation represents nonrandomness due to both attractive and repulsive forces, whereas perturbation theory is restricted to the effect of repulsive forces (size differences). In the case of mixtures of equal-sized molecules, the quasichemical approximation of Rushbrooke and Guggenheim gives good results concerning both the magnitude of the effect and its concentration dependence. For a quantitative description, some corrections are necessary for the difference in coordination number around strongly and weakly interacting molecules. Perturbation theory neglects the effect of nonrandomness. However, as emphasized by Rushbrooke and Guggenheim, this effect is not of great thermodynamic significance. For mixtures of molecules of different sizes, packing effects (included in perturbation theory) are dominant, and may be of opposite sign to the effect caused by attractive forces.

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 .

MODEL FOR ALKANOL + ALKANE MIXTURES : EXTENSION AND EXPERIMENTAL VERIFICATION

A recently developed model for 1-alkanol+alkane mixtures is extended to methanol mixtures and to the non-polar mixing partners tetrachloromethane and benzene. The model contains chemical and physical terms, which are combined in a thermodynamically consistent way. For our calculations on methanol mixtures, we have measured gE of methanol+ hexane via static vapor pressure measurements. In order to check the model predictions for systems with higher alkanols and alkanes, we have also determined gE of 1-octanol+tetradecane by measuring the melting curve. The reproduction of the excess properties of methanol+hexane, the agreement between predicted and measured values of gE for 1-octanol+ tetradecane, and the capability to deal also with other non-polar mixing partners demonstrate the power and reliability of the model.

A new representation for thermodynamic properties of a fluid

It is proposed to consider the contribution of the nonisolated molecular pairs to the configurational Helmholtz energy, i.e., the quantity f*/RT−Bρ, where the product of the second virial coefficient B times molar density ρ covers the contribution of the isolated pairs. Especially illuminating is the difference function Δ = (f*/RT−Bρ)real  fluid −(f*/RT−Bρ)hard  body  fluid. From the few examples given it seems that this difference function is of a general nature provided that the anisotropy of the hard bodies corrsponds to the anisotropy of the molecules of the real fluid. The difference function can be correlated empirically in a simple way and can be used for estimating thermodynamic properties at intermediate and low densities from high density results.

The virial coefficients and the equation of state behavior of the polar components chlorodifluoromethane, fluoromethane and ethanenitrile

Abstract Demiriz, A.M., Kohlen, R., Koopmann, C., Moeller, D., Sauermann, P., Iglesias-Silva, G.A. and Kohler, F., 1993. The virial coefficients and the equation of state behavior of the polar components chlorodifluoromethane, fluoromethane and ethanenitrile. Fluid Phase Equilibria, 85: 313-333. Burnett p,ϱ,T measurements are reported for chlorodifluoromethane, fluoromethane and ethanenitrile. Some isochoric data on fluoromethane are added. Literature data on fluoromethane are also used. It is shown that the virial coefficients of these polar molecules depend on the fourth power of the reduced dipole moment, a much more dramatic dependence than that of the cohesive energy of the liquid. The second virial coefficient becomes much more negative and the third much more positive compared with those of non-polar molecules. The fourth, which can be neglected for non-polar molecules, becomes negative again and is important for highly polar molecules.