(226f) Evolving the SAFT-VR Equation of State Into a General Modeling Platform for Complex Fluids

SAFT-VR is an equation of state (EOS) based on the statistical associating fluid theory (SAFT) originally developed by Wertheim¹ and turned into a practical EOS by Gubbins and co-workers.²  SAFT-VR has come to refer to the version of SAFT in which the reference system is the hard sphere plus square well (HS-SW) fluid, and the square well is of variable range.  By using the SAFT theory to model the formation of chains of HS-SW monomers (complete association), by adjusting the parameters in the square well, homonuclear chain molecules (e.g., alkanes) can be modeled very accurately, and the prediction of the thermodynamic properties and phase envelopes of alkanes and their mixtures, and mixtures of alkanes with other low molecular weight species (including polymer-solute systems) represented some of the earliest successes of SAFT-VR.  Two elements of SAFT-VR have contributed to its success: first, the parameters that are found to fit the first few members of a homologous series were proven to be transferable to arbitrary length alkanes, including polymers; second, because SAFT-VR corresponds to a physical model, it can be compared to simulations of the same model to ensure the accuracy of the theory before it is applied to real systems.  By using the SAFT theory with incomplete association, one can also model associating systems (such as alcohols).

In the spirit of SAFT-VR, we have embarked on a series of modifications of the EOS that are based on the same principles as the original theory.  Using the results of modern critical phenomena, we incorporated crossover near the critical point.³  By using the results of perturbation theory for hard sphere mixtures, we developed a hetero-SAFT-VR, enabling the modeling of heteronuclear chains,⁴ which also makes it possible to model branched chain fluids.  Drawing on the results of liquid state theory for mixtures of ions and dipoles,⁵ we replaced the HS-SW monomer with ionic HS-SW and dipolar HS-SW monomers, enabling SAFT-VR to now describe such complex fluids as electrolytes in solution and ionic liquids.⁶   Combining all of these elements has made it possible to develop a group-contribution version of SAFT-VR that retains the essential elements of the original SAFT-VR: that is, transferability of parameters (i.e., parameters for groups need only be fitted once) and connection to a physical model that can be simulated in order to verify the accuracy of the theory.⁷  The result is a general, molecular-based modeling platform applicable to a wide complex fluid systems. 

References

1    Wertheim, M. S., Journal of Statistical Physics, 35, 19--34 (1984); Wertheim, M. S., Journal of Statistical Physics, 35, 35--47 (1984); Wertheim, M. S., Journal of Statistical Physics, 42, 459--476 (1986); Wertheim, M. S., Journal of Statistical Physics, 42, 477-492 (1986).

2    Chapman, W. G., Gubbins, K. E., Jackson, G. and Radosz, M., Fluid Phase Equil., 52, 31-38 (1989); Chapman, W. G., Jackson, G. and Gubbins, K. E., Mol Phys, 65, 1057-1079 (1988).

3    McCabe, C. and Kiselev, S. B., Fluid Phase Equilib., 219, 3-9 (2004); McCabe, C. and Kiselev, S. B., Ind. Eng. Chem. Res., 43, 2839-2851 (2004); Sun, L. X., Zhao, H. G., Kiselev, S. B. and McCabe, C., Fluid Phase Equilib., 228, 275-282 (2005); Sun, L. X., Zhao, H. G., Kiselev, S. B. and McCabe, C., J. Phys. Chem. B, 109, 9047-9058 (2005).

4    McCabe, C., Gil-Villegas, A., Jackson, G. and del Rio, F., Mol. Phys., 97, 551-558 (1999); Peng, Y., Zhao, H. G. and McCabe, C., Mol. Phys., 104, 571-586 (2006).

5    Zhao, H. G., Ding, Y. and McCabe, C., J. Chem. Phys., 127, article number 084514 (2007); Zhao, H. G. and McCabe, C., J. Chem. Phys., 125, 4504-4515 (2006).

6    Zhao, H. G., dos Ramos, M. C. and McCabe, C., J. Chem. Phys., 126, 4503 (2007).

7    Peng, Y., Goff, K. D., dos Ramos, M. C. and McCabe, C., Fluid Phase Equilib., 277, 131-144 (2009); Peng, Y., Goff, K. D., dos Ramos, M. C. and McCabe, C., Industrial & Engineering Chemistry, 49, 1378-1394 (2010); dos Ramos, M. C., Haley, J. D., Westwood, J. R. and McCabe, C., Fluid Phase Equilib., in press, (2011); dos Ramos, M. C. and McCabe, C., Fluid Phase Equilib., in press, (2011).