Limiting group activity coefficients

In eqn. (2.4.21) ti is the number of k groups present in species i, and In F][ is the residual contribution to the activity coefficient of group k in a pure fluid of species i molecules. The purpose of the last term is to ensure that, in the limit of pure species i (which is still a mixture of groups unless of course the molecules of species i consist of a single functional group), the residual term is zero. 

Hovorka, S., Dohnal, V., Roux, A.H., andRoux-Desgranges, G. Determination of temperature dependence of limiting activity coefficients for a group of moderately hydrophobic organic solutes in water. Fluid Phase Equilib., 201(1) 135-164, 2002. 

It is very satisfying and useful that the COSMO-RS model—in contrast to empirical group contribution models—is able to access the gas phase in addition to the liquid state. This allows for the prediction of vapor pressures and solvation free energies. Also, the large amount of accurate, temperature-dependent vapor pressure data can be used for the parameterization of COSMO-RS. On the other hand, the fundamental difference between the liquid state and gas phase limits the accuracy of vapor pressure prediction, while accurate, pure compound vapor pressure data are available for most chemical compounds. Therefore, it is preferable to use experimental vapor pressures in combination with calculated activity coefficients for vapor-liquid equilibria predictions in most practical applications. 

When it is necessary to estimate activity coefficients where no data or very limited data are available, estimates may be made by using a group contribution method. In this case, a molecule is divided into fimctional groups, or subgroups of the molecule. These subgroups are assumed to act independently of the molecule in which they appear. Molecular interactions are accounted for by properly weighted sums of group interactions. Fredenslund, Jones, and Prausnitz developed the method for UNIQUAC and named it as universal functional activity coefficient (UNIFAC). Smith, van Ness, and Abbott report the equations for the activity coefficients of multicomponent solutions and their parameters. These equations are very... 

Kojima and Togichi, 1979)] model and UNIFAC [UNIQUAC functional-group activity coefficient (Fredenslund et al., 1977)] model discussed earlier, have been developed. However, these models are limited to the range of classes of compounds and conditions of the regressed experimental data used in their development. 

Chapter 11 plus 1-5 of this chapter Uses estimated activity coefficients Structure — Calculations are lengthy and difficult — Limited applicability for functional groups — Fairly accurate... 

Liquid Solution Behavior. The component activity coefficients in the liquid phase can be addressed separately from those in the solid solution by direct experimental determination or by analysis of the binary limits, since y p = 1. Because of the large amount of experimental effort required to study a ternary composition field and the high vapor pressures encountered in the arsenide and phosphide melts, a direct experimental determination of ternary activity coefficients has been reported only for the Ga-In-Sb system (26). Typically, the available binary liquidus data have been used to fix the adjustable parameters in a solution model with 0,p determined by Equation 7. The solution model expression for the activity coefficient has been used not only to represent the component activities along the liquidus curve, but also the stoichiometric liquid activities needed in Equation 7. The ternary melt solution behavior is then obtained by extending the binary models to describe a ternary mixture without additional adjustable parameters. In general, interactions between atoms in different groups exhibit negative deviations from ideal behavior... 

An important first step in any model-based calculation procedure is the analysis and type of data used. Here, the accuracy and reliability of the measured data sets to be used in regression of model parameters is a very important issue. It is clear that reliable parameters for any model cannot be obtained from low-quality or inconsistent data. However, for many published experimentally measured solid solubility data, information on measurement uncertainties or quality estimates are unavailable. Also, pure component temperature limits and the excess GE models typically used for nonideality in vapor-liquid equilibrium (VLE) may not be rehable for SEE (or solid solubility). To address this situation, an alternative set of consistency tests [3] have been developed, including a new approach for modehng dilute solution SEE, which combines solute infinite dilution activity coefficients in the hquid phase with a theoretically based term to account for the nonideality for dilute solutions relative to infinite dilution. This model has been found to give noticeably better descriptions of experimental data than traditional thermodynamic models (nonrandom two liquid (NRTE) [4], UNIQUAC [5], and original UNIversal Eunctional group Activity Coefficient (UNIEAC) [6]) for the studied systems. 

A step forward in modelling is provided by the use of activity coefficient models and group contribution methods. One of the most valuable features of these methods is their applicabihty to multi-component systems imder the assumption that local compositions can be described in this case by a relationship similar to that obtained for binary systems. However, one of the main disadvantages of these methods is that they depend on an extremely large amount of experimental data. Furthermore, the absence of the volume and surface p>arameters p>oses a hindrance in the calculation of the binary interaction parameters for UNIQUAC and UNIFAC models. These limitations can be overcome by the use of quantum-based models, such as COSMO-RS (see, for instead, the works of Shah et al., (2002) and of Guo et al. (2007)). In this method no experimental data is needed as an input to model the ionic hquids, being the main constraint the extensive computational time and also that, in some cases, the comparison with experimental data is only qualitative. 

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