SAFT Dispersion Term

In the Huang and Radosz version of SAFT [71, 72] the Chen-Kreglewski dispersion term is used. This term is obtained from a fit to the physical property data of argon and is given by Eq. (89) [76], where t is a constant equal to 0.74048. The constants Dij are given by Chen and Kreglewski [76]. 

For mixtures, the van der Waals one-fluid mixing rules or the volume fraction mixing rules can be used. 

The van der Waals mixing rules are given by Eq. (90), where the combining rules are Eqs. (91) and (92), in which kj- is an adjustable binary interaction parameter. 

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The recently proposed Perturbed-Chain SAFT (PC-SAFT) model [75, 76] adopts the opposite idea here, a perturbation theory of second order is applied to the reference system of hard chains instead of hard spheres to develop a dispersion term for chain-Hke molecules ... 

In SAFT the dispersion term represents the interactions between individual segments, while in PC-SAFT the dispersion term represents the interactions of chains of segments. The expression for a derived by Gross and Sadowsld is Eq. (95), where the terms on the right-hand side are defined by Eqs. (96) and (97). 

The SAFT equation of state was proposed by Radosz, Gubbins, Jackson, and Chapman and is a model derived based on the perturbation theory of Weirtheim. SAFT is a noncubic equation with separate terms for the various effects (dispersion, polar, chain, hydrogen bonding). SAFT has already found extensive application in both polymer and oil industry, where different capabilities of the model have been exploited. In the oil industry, it is used for describing the complex multiphase equilibria of hydrogen bonding multicomponent systems, e.g., water-oil-alcohols (glycols). Several recent reviews of the SAFT equation of state are available, all of which present results for polymer solutions. 

For mixtures, only the dispersion part of the segment Flelmholtz energy requires the use of combining rules the composition dependence is built into the chain and association terms by the statistical thermodynamics. Gross and Sadowski presented a new parameterization of SAFT with constants for a wide range of substances that does not suffer from the numerical inconsistencies of the Huang-Radosz model. ... 

The most extensively apphed version of SAFT, due to Huang and Radosz " and commonly denoted SAFT-HR, corresponds to a similar level of theory. In SAFT-HR the dispersion interactions are described through the expression of Chen and Kreglewski, which was fitted to argon physical-property data, with the hard-sphere radial distribution function used in the chain and association terms. SAFT-HR has been applied to study the phase behaviour in a wide range of fluid systems and polymers." Comparisons with SAFT-HR are often provided when a new version of SAFT is developed to demonstrate the improved ability of a new equation however, it should be noted that when comparisons are made, it is probably more relevant to refer to one of the more recent second-generation SAFT equations described below. 

Deviations of real molecules from the reference system may occur, e.g., due to attractive interactions (dispersion), formation of hydrogen bonds (association), or the nonspherical shape of the molecules (which can be understood as the formation of chains from spherical segments). These contributions are usually assumed to be independent of each other and are accounted for by different perturbation terms. Depending on the kind of considered perturbation and on the expression used for its description, different models have been developed. One of the first models derived from that idea was the Statistical-Associating-Fluid Theory (SAFT) (Chapman et al. [12, 13] Huang and Radosz [14, 15]). 

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