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The vapor-liquid phase equilibria of square-well systems with hard-sphere diameters o, welldepths E, and ranges il = 1.25, 1.375, 1.5, 1.75, and 2 are determined by Monte Carlo simulation. The two bulk phases in coexistence are simulated simultaneously using the Gibbs ensemble technique. Vapor-liquid coexistence curves are obtained for a series of reduced temperatures between about T,. = T/T, = 0.8 and 1, where T, is the critical temperature. The radial pair distribution functions g(r) of the two phases are calculated during the simulation, and the results extrapolated to give the appropriate contact values g(a), g(/Za-), and g(;la-I-). These are used to calculate the vapor-pressure curves of each system and to test for equality of pressure in the coexisting vapor and liquid phases. The critical points of the squarewell fluids are determined by analyzing the density-temperature coexistence data using the first term of a Wegner expansion. The dependence of the reduced critical temperature Tr = kT,/q pressure P r = P,o-'/E, number density p: = pE d, and compressibility factor Z = P /(pkT), on the potential range il, is established. These results are compared with existing data obtained from perturbation theories. The shapes of the coexistence curves and the approach to criticality are described in terms of an apparent critical exponent 8. The curves for the square-well systems with il = 1.25, 1.375, 1.5, and 1.75 are very nearly cubic in shape corresponding to near-universal values ofp (flzO.325). This is not the case for the system with a longer potential range; when ;1 = 2, the coexistence curve is closer to quadratic in shape with a nearclassical value of p (PzO.5). These results seem to confirm the view that the departure of fl from a mean-field or classical value for temperatures well below critical is unrelated to longrange, near-critical fluctuations.

The influence of the form of the interaction potential on the thermodynamic properties of fluids is investigated. Differences in the potential profile of nonconformal interactions are taken into account by the steepness of the potential functions and used to define a relative softness between interactions. In the dilute gaseous phase, the system of interest is characterized by a relative softness relating its virial coefficient B(T) with respect to that of a reference system B 0 (T). For constant softness S, B(T) is obtained directly from B 0 (T) by linear relations involving only S. The conditions on which S is exactly or approximately constant are analyzed and shown to hold in a wide range of cases. Furthermore, it is shown how to invert B(T) to construct potentials whose form and parameters reproduce accurately the thermodynamic properties of the gas.

A new theory which accounts for the nonconformality of intermolecular potentials is used to obtain effective potentials which represent accurately the thermodynamic properties of simple and molecular fluids. This approximate nonconformal (ANC) theory introduces a constant softness (S) to incorporate deviations in conformality between the exact angle-averaged effective potential and a potential of reference. The softness S together with the molecular size and energy determine both the intermolecular potential and the thermodynamic properties of the fluid, i.e., the second virial coefficient, B(T). The theory is applied here to the pure noble gases and their mixtures. The cross interactions in the binary mixtures are determined from suitable mixing rules. The effective potentials of these molecules and for their cross interactions are obtained and compared with accurate pair potentials available from the literature. The ANC potentials agree very well with known pair interactions, except for He, and the pure and cross virial coefficients give excellent agreement with experimental results.

The adequacy of the recently developed bonded hard-sphere (BHS) theory in describing the critical behavior of the homologous series of the alkanes and perfluoroalkanes is examined in this work. A simple united atom model, formed from chains of tangent hard spheres, reproduces the major experimental trends and provides good quantitative agreement for systems with two or more carbon atoms. This simple model cannot, however, reproduce the anomalous behavior of the critical pressure of the alkane series: the values of the critical pressure and temperature for methane are smaller than expected. A more sophisticated distributed-site model, which takes explicit account of the backbone and substituent atoms, reproduces this anomalous behavior. The BHS theory has also been used to predict the upper critical solution temperatures of alkane + perfiuoroalkane mixtures. For most systems, the segment-segment parameters are fitted to the butane + perfluorobutane system, although in the case of mixtures containing methane, methane + perfluoromethane parameters must be used. Excellent qualitative agreement with experimental data is seen. This indicates the strength of the BHS approach as a type of group contribution method.

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The approximate nonconformal (ANC) theory recently proposed has been very successful in determining interaction potentials for the noble gases and their mixtures. The ANC theory is used here to obtain e †ective angle averaged potentials of all homodiatomic gases for which experimental second virial coefficient data are available :and The cross virial coefficients in the mixtures of homodiatomics among. themselves and with noble gases are predicted with excellent agreement with experiment for the heavier classical gases. The atomÈatom interactions, which should be an improvement over previous results, are also determined and shown to behave regularly with atomic number. The critical temperatures and volumes of these gases vary smoothly when scaled with the parameters of the ANC potential.

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