Soft-SAFT

Johnson et aVsf proposed equation of state to treat LJ chains in which the free energy of the chain fluid was obtained using the free energy and radial distribution function of a monomer LJ fluid, the expressions for which were fitted to simulation data. This approach was extended to mixtures by Ghonasgi et al. and Bias and Vega, who referred to the approach as the soft-SAFT equation of state. 

The equation of Johnson et alf is one of most accurate available for LJ chains, since it is heavily based on computer simulation data. Equally the soft-SAFT equation is very accurate for modelling mixtures of associating LJ fluids. In their extension to mixtures Bias and Vega performed extensive simulations on model homo- and heteronuclear fluids and their mixtures to test the soft-SAFT approach, before application of the theory to real fluids in a subsequent paper was undertaken by the authors. Soft-SAFT has been applied to the study of alkanes and their binary and ternary mixtures, perfluoro-alkanes, alcohols, carbon dioxide,polymers, and more recently room temperature ionic liquids.  

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Vega and co-workers have applied the method of White to the soft-SAFT... 

Mac Dowell N, Llovell F, Sun N, Hallett JP, George A, Hunt PA, Welton T, Simmons BA, Vega LF (2014) new experimental density data and soft-SAFT models of alkylimidazolium ([CnClim]+) chloride (C1-), methylsulfate ([MeS04]-), and dimethylphosphate ([Me2P04]-) based ionic liquids. J Phys Chem B 118 6206-6221... 

Some molecular-based equations of state such as lattice models, chain fluid theories and SAFT-type approaches have also been used to model ionic liquids and their behaviour in mixtures. The advantage of building a model for the molecule describing the physics of the system is related to a major predictive ability, hence enhancing the possibility of extending the range of application of the equation. In the next sections of this chapter, some examples of successful applications and current limitations of the use of one of these tools, the soft-SAFT equation, will be presented and discussed. 

As other SAFT-typ>e equations, soft-SAFT is written in terms of the total Helmholtz energy of the system. When applied to ionic liquids, the residual Helmholtz energy is written as ... 

Expressions for and a i, the second and third-order perturbation terms, were derived for an arbitrary intermolecular reference potential (Twu et al., 1975). A detailed derivation of these expressions is given elsewhere (Gubbins Two, 1978). This term in the soft-SAFT EoS involves an additional molecular parameter, Q, the quadrupolar moment. 

Fig. 1. Schematic representations of the [Cn-mim][PF6] ionic liquid. Left the soft-SAFT simplified model right all atom model.

The correlations were done using the molecular parameters from n=2 till n=8, both included. The density AAD% for this series of ionic liquids is 0.09%. Using these correlations and keeping constant the volume and energy of association soft-SAFT can be used to predict the behaviour of heavier members of the series (see Fig. 3). 

Fig. 4. Pressme-density diagram for [C2-mim]frf2N] (squares), [Q-inim]frf2N] (circles), [O-mim]frf2N] (triangle up) and [C8-mim]frf2N] (crosses). S)mibols experimental data (Gomes de Azevedo et al, 2005 Gardas et al., 2007) solid lines soft-SAFT calculations.

The molecular parameters fitted to single-phase equilibrium data were used in a transferable manner to calculate interfacial properties. The only additional parameter within the soft-SAFT+DGT approach is the influence parameter. In this work we have optimized this parameter for each pure compoimd using interfacial tension experimental data from the triple to the critical point (Carvalho et al., 2008). The resulting values are given in Table 1. 

Soft-SAFT+DGT results compared to experimental data (Carvalho et al., 2008) are presented in Fig. 5. As in the experimental case a decreasing interfacial tension value with the alkyl chain length is obtained. This behaviour is very surprising as it is contrary to the other chemical families where the interfacial tension increases as the chain length increases. 

Fig. 5. Vapour-liquid interfacial tensions of the [Cn-mim][Tf2N] ionic liquid family, as a function of temperature, from top to bottom [C2-mim][Tf2N], [C3-mim][Tf2N], [C4-mim][Tf2N], [C5-mim][Tf2N], [C6-mim][Tf2N] and [C7-mim][Tf2N]. Symbols experimental data (Carvalho et al., 2008) lines soft-SAFT+DGT calculations.

Fig. 6. Prediction of the solubility of [C2-mim][Tf2N] Oeft) and [C4-mim][Tf2N] (right) in CO2 at three different temperatures. Symbols experimental data (Raeissi Peters, 2009), lines soft-SAFT calculations.

Fig. 8. Solubility of water in [Cn-rnim][Tf2N]. Left Pressure-composition diagram of a water + [C2-mim][Tf2N] mixture at 292.75K (squares), 303.15K (diamonds), 323.2K (circles) and 353.15K (triangles). Experimental data was taken from reference (Husson et al., 2010). Right Pressure-composition diagram of a water + [C4-rnim][Tf2N] mixture at 353.15K. Symbols experimental data (Nebig et al., 2007) lines soft-SAFT predictions.

Belkadi, A. HadjKali, M.K. Llovell, F. Gerbaud, V. Vega, L.F. (2010). Soft-SAFT modeling of vapor-liquid equilibria of nitriles and their mixtures. Fluid Phase Equilib. 289,191-200. 

Colina, C.M. Turrens, L.F. Olivera-Fuentes, C. Gubbins, K.E. Vega, L.F. (2002). Predictions of the Joule-Thomson Inversion Curve for the n-Alkane Series and Carbon Dioxide from the Soft-SAFT Equation of State. Ind. Eng. Chem. Res. 41,1069-1075. 

Llovell, F. Vega, L.F. (2006a). Global Fluid Phase Equilibria and Critical Phenomena of Selected Mixtures Using the Crossover Soft-SAFT Equation. /, Phys, Chem, B 110, 1350-1362. 

Llovell, F. Peters, C.J. Vega, L.F. (2006). Second-order thermodynamic derivative properties of selected mixtures by the soft-SAFT equation of state. Fluid Phase Ecjuilib. 248,115-122. 

Llovell, F. Valente, E. Vilaseca, O. Vega, L.F. (2010b). Modelling complex associating mixtures with [Cn-mim][Tf2N] Ionic Liquids with the soft-SAFT equation. Submitted. 

Ramies, J. C. Vega, L. F. (2001). Vapor-liquid equilibria and critical behavior of heavy n-alkanes using transferable parameters from the soft-SAFT equation of state. Ind. Eng. Chem. Res. 40,2532-2543. 

Vega, L.F. Llovell, F. Bias, F. J. (2009). Capturing the Solubility Minima of n-Alkanes in Water by Soft-SAFT. J. Phys. Chem. B 113, 7621-7630. 

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