Conformal solution theory

Configurational energy for clathrates, 12 Configurations, superposition of, 258 Conformal solution theory, 137 Coordination polymerization, 148, 162, 170... 

Equation (9.83) is also the basis for the compound energy model. The excess energy of the mixture is here represented by any type of equation, for example a power series [15, 16], Equation (9.83) has also been derived using the conformal solution theory after Blander [14] and as an extension of the molten salts models presented by Flood, Fprland and Grjotheim [17],... 

Fickett in "Detonation Properties of Condensed Explosives Calculated with an Equation of State Based on Intermolecular Potentials , Los Alamos Scientific Lab Rept LA-2712 (1962), pp 34-38, discusses perturbation theories as applied to a system of deton products consisting of two phases one, solid carbon in some form, and the other, a fluid mixt of the remaining product species. He divides these theories into two classes conformal solution theory, and what he chooses to call n-fluid theory. Both theories stem from a common approach, namely, perturbation from a pure fluid whose props are assumed known. They differ mainly in the choice of expansion variables. The conformal solution method begins with the assumption that all of the intermolecular interaction potentials have the same functional form. To obtain the equation of state of the mixt, some reference fluid obeying a common reduced equation of state is chosen, and the mixt partition function is expanded about that of the reference fluid... 

Theory conformal solution theory and dipole interaction. 

Chimowitz and coworkers [9,10] emphasized the synergism caused by the cross exponential terms exp(—XiA 23) on the entrainer effect, and Jonah and Cochran [12] related the coefficients Ka to the limiting values of the Kirkwood-Buff (KB) integrals and used the conformal solution theory to discuss the entrainer effect. 

They showed that the Peng-Robinson equation of state using mixing rules based on conformal solution theory can predict the fluid phase equilibrium of high molecular weight liquids in supercritical fluids more accurately than others (18.19). 

It is obvious from the foregoing discussion that the enthalpies of mixing for charge-unsymmetrical systems do not follow the simple conformal solution theory. When the anion in a strontium halide-alkali metal halide mixture from chloride to bromide and from bromide to iodide is changed, the enthalpy of mixing is decreasing. For all systems, the enthalpy interaction parameter, k, is a linear function of 512 with the usual exception for lithium-containing systems. Two important features of the k versus 512 plot should be emphasized ... 

A general method of predicting the effective molecular diameters and the thermodynamic properties for fluid mix-tures based on the hard-sphere expansion conformal solution theory is developed. The method of Verlet and Weis produces effective hard-sphere diameters for use with this method for those fluids whose intermolecular potentials are known. For fluids with unknown potentials, a new method has been developed for obtaining the effective diameters from isochoric behavior of pure fluids. These methods have been extended to polar fluids by adding a new polar excess function, to account for polar contributions in a mixture. A new set of pseudo parameters has been developed for this purpose. The calculation of thermodynamic properties for several fluid mixtures including CH —C02 has been carried out successfully. 

It is important to realize that the diameters needed for thermodynamic calculations do not necessarily represent a true minimum attainable separation distance between molecules. The objective is rather to determine optimal or effective diameters which give best results when used with a particular method of dealing with the contributions of molecular attraction. In this chapter the effective diameters sought are to be used specifically with the hard-sphere expansion (HSE) conformal solution theory of Mansoori and Leland (3). This theory generates the proper pseudo parameters for a pure reference fluid to be used in predicting the excess of any dimensionless property of a mixture over the calculated value of this property for a hard-sphere mixture. The value of this excess is obtained from a known value of this type of excess for a pure reference fluid evaluated at temperature and density conditions made dimensionless with the pseudo parameters. For example, if Xm represents any dimensionless property for a mixture of n nonpolar constituents at mole fractions xu x2,. . . x -i at temperature T and density p, then ... 

The GHBL perturbation procedure is remarkably accurate and the HSE-VW method is only slightly better in its overall agreement with the machine-calculated results. This comparison is not completely valid in that the conformal solution theory uses pure component data while in the perturbation theory each term is calculated from molecular parameters. 

Using conformal solution theory models for the prediction of mixture thermodynamic behavior is becoming increasingly popular for industrial calculations. The attractiveness of the conformal solution approach stems largely from the fact that it is faster computationally than purely theoretical methods and yet has a sufficiently good basis in theory to allow extension to complex molecular interactions (e.g., multipole, dispersion, and steric effects), which would be difficult using purely empirical methods. 

The formulation of conformal solution theory which has received the widest use to date is the so-called VDW one-fluid theory (I). Strictly, the VDW one-fluid theory applies to mixtures of similar size molecules... 

The first of these developments is perturbation theory. Its application to solution theory was perhaps first made by H. C. Longuet-Higgins in his conformal solution theory (Longuet-Higgins 1951). The formal theory of statistical mechanical perturbation theory is very simple in the canonical ensemble. If denotes the intermo-lecular potential energy of a classical A-body system (not necessarily the sum of pair potentials), the central problem is to evaluate the partition function. 

An extension of the conformal solution theory was given "by Davis and Rice.IT They assimie the same model ionic melt as Reiss et al, but their model also includes short-range dispersion interactions as a perturbation to the pair potential of Reiss and coworkers. 

Helmholtz free energy (1.2.8) molar Helmholtz free energy parameter m the conformal solution theory (4.3.1)... 

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