In the study of mixtures of fluids, either with molecular simulation or using molecular-based equations of state (EOSs) such as the Statistical Associating Fluid Theory (SAFT), the unlike interaction between molecules of type i and j is described in terms of the like-like intermolecular-potential parameters. The energy parameter, ε_ij, is generally given in terms of a deviation from the Berthelot (geometric-mean) combining rule: ε_ij = (1 – k_ij) (ε_ii ε_jj)^1/2; the binary-interaction parameter, k_ij is normally treated as an adjustable parameter and is adjusted until the theoretical description best captures experimental binary-mixture data. However, it is not always possible to obtain k_ij by this procedure due either to the absence of appropriate mixture data, or to the large number of binary mixtures that may need to be considered in modern engineering applications. It is frequently assumed that k_ij represents merely a correction and it is inferred that large values indicate the (relative) inability of the theory at hand to provide a good description of the properties of the mixture. Thereby, in cases where an adjusted k_ij is unavailable it is standard procedure to assume k_ij = 0. In this work we question the practice of assuming k_ij = 0 and show that, theoretically, large deviations from the Berthelot rule may be expected, particularly for polar fluids. Extending the analysis of Hudson and McCoubrey [1], we propose a method [2] for calculating k_ij from fundamental principles that does not rely on experimental mixture data, requiring only single-component information such as the ionisation energy or the molecular polarisibility. The theory relates to a variety of mixtures although in the case of polar fluids it may be applied only to mixtures of small molecules. In some cases (e.g., highly non-ideal mixtures such as nitrogen + polyethylene, water + methane and water + hydrogen fluoride) we predict large, sometimes temperature-dependent k_ij values. Nevertheless, for the cases considered, use of predicted k_ij values in analyses of binary fluid mixtures leads to descriptions of (experimental) mixture data at least as good as, and usually far better than those obtained using the Berthelot rule. To test the theory we have examined a variety of binary mixtures using SAFT-VR [3,4]. For the alkane + perfluoroalkane mixtures considered, the use of our predicted k_ij values in phase-equilibrium calculations leads to the correct class of phase behaviour (according to the classification of van Konynenburg and Scott [5]), whereas the use of the Berthelot rule fails in this regard. The theory provides an excellent description of the thermodynamic properties of water vapour + methane and rationalises recent, apparently contradictory, models of the mixture of carbon dioxide + water [6,7].

References

[1] G.H. Hudson, J.C. McCoubrey, Trans. Faraday Soc. 56 (1960) 761–766.

[2] A.J. Haslam, A. Galindo, G. Jackson, (in press), Fluid Phase Equilib. (2008), doi: 10.1016/j.ßuid.2008.02.004

[3] A. Gil-Villegas, A. Galindo, P.J. Whitehead, S.J. Mills, G. Jackson, A.N. Burgess, J. Chem. Phys. 106 (1997) 4168–4186.

[4] A.Galindo, L.A. Davies, A. Gil-Villegas, G. Jackson, Mol. Phys. 93 (1998) 241–252.

[5] P.H. Van Konynenburg, R.L. Scott, Phil. Trans. R. Soc. Lond. A 298 (1980) 495–540.

[6] A. Valtz, A. Chapoy, C. Coquelet, P. Paricaud and D. Richon, Fluid Phase Equilib. 226 (2004) 333–344.

[7] M.C. dos Ramos, PhD Thesis, Universidad de Huelva, Huelva Spain, 2007;      M.C. dos Ramos, F.J. Blas, A. Galindo, J. Phys. Chem. C 111 (2007) 15924–15934.