T. W. Leland’s research while affiliated with Rice University and other places

A new method for the calculation of thermodynamic properties of simple fluid mixtures constitutes an extension of the approach defined earlier as the “van der Waals” conformal solution theory. This extension is made possible by advances in the analytical representation of the thermodynamic properties of a mixture of hard spheres which permit the properties to be calculated directly, without the use of a reference fluid. A new hard-sphere excess function, defined as a property of the mixture less the value of this property for the hard-sphere mixture, is obtained by a new conformal solution theory using a single pure fluid as a reference substance. Although the reference substance properties could be experimentally measured values, this work obtains them from an analytical form of the Barker-Henderson perturbation theory.This new method improves prediction of the effects of large molecular size differences on the excess properties of the mixture. It uses the reference fluid to account for most of the temperature dependence of the cut-off parameter needed to define the molecular diameters in the direct hard-sphere mixture calculations and the calculations need only the high temperature limit of the cut-off parameters, even far below the critical temperature. The new method extends the original vdW conformal solution method to lower temperatures and provides an opening for inclusion of three-body interactions.Conventional excess mixing functions for several binary liquid mixtures calculated by the new method are compared with the predictions of other theories and with both experimental and Monte Carlo data.

An equation of state is proposed for the mixture of hard spheres based on an averaging process over the two results of the solution of the Percus–Yevick integral equation for the mixture of hard spheres. Compressibility and other equilibrium properties of the binary mixtures of hard spheres are calculated and they are compared with the related machine‐calculated (Monte Carlo and molecular dynamics) data. The comparison shows excellent agreement between the proposed equation of state and the machine‐calculated data.

The variational technique proposed earlier for the calculation of the equilibrium thermodynamic properties of simple pure fluids, melting transitions, and simple pure solids is extended to binary mixtures of simple fluids. The working inequality is introduced and the variational parameters are characterized. For a case study, the present variational approach is applied in predicting the thermodynamic properties of the liquid mixture of argon and krypton at zero pressure and 115.77°K. The thermodynamic and excess properties of this mixture over that of the pure systems (at zero pressure and in liquid state) are calculated and compared with the results of the available Monte Carlo calculations, experimental measurements, and several theories of solutions. Preliminary investigation indicates good agreement between the result of the present variational technique with the experimental and machine‐calculated data. Variations of the thermodynamic properties of the binary mixture, with the variation of the ratios of the force constants of the potential functions of the two components, are calculated at 97°K, zero pressure, and equal mole fractions. These values are compared with the existing values of the Monte Carlo calculations.

An approximation of a type devised by van der Waals has been shown to be superior to the random mixing approximation, and to theories derived from it, when applied to mixtures of molecules of different sizes. In this paper, van der Waals's approximation is extended to a two-fluid model, and so takes into account the departures from a random distribution induced by differences of intermolecular energy. The treatment is further extended to mixtures of molecules of different shapes. The two-fluid van der Waals approximation is compared with the experimental excess thermodynamic functions for ten simple binary mixtures. These yield unambiguous evidence that the intermolecular energy between unlike molecules is less than the geometric mean of that between the like molecules by up to 2 %. Independent and quantitative confirmation of such differences is provided by recent measurements of the second virial coefficients and of the critical temperatures of the same mixtures.

Calculation of fugacities of components in a gaseous or liquid solution directly from the corresponding states principle requires an improvement in the pseudo‐critical constants for the mixture. The derivation of the pseudo‐criticals must take into account deviations from the simple two parameter corresponding states principle which require additional parameters incorporated into the definition of the pseudo‐criticals. In this work parameters called molecular shape factors are introduced into the pseudo‐criticals. A generalized correlation for these shape factors is presented. Use of the shape factors greatly improves the calculation of vapor‐liquid equilibrium ratios for nonpolar hydrocarbon mixtures with large differences in molecular size and shape. Excellent results are obtained both in the low pressure and in the retrograde region when the pseudo‐reduced properties of the vapor and liquid lie within the range of accurately known properties of a reference fluid and the reduced temperatures for each component is greater than approximately 0.6.

The central problem in the theory of mixtures is the calculation of the free energy of mixing of molecules of different sizes. An explicit calculation of this free energy is made for a mixture in which all intermolecular potentials are of the form uαα(r)=(σαα/r)n, where σαα is a distance characteristic of the interaction of two molecules of species α, and where σαβ= 1/2(σαα+σββ) when α≠β. This result follows from a solution of Percus-Yevick integral equation for the pair distribution function of a mixture of hard spheres. The form of the free energy provides a criterion by which existing theories can be judged, and it is shown that an approximation of the type originally suggested by van der Waals is superior to approximations based on the concept of random mixing. Molecules that differ only in size mix with a small and negative excess free-energy. The recommended approximation is confirmed by comparison with experiment.

The accurate measurement of low-temperature volumetric properties of fluids is becoming increasingly important in the field of cryogenics. These properties are necessary for the prediction of the physical behavior of cryogenic systems and are utilized also in the calculation of thermodynamic properties.