Modeling Association in the Saft Equation Using Ab Initio Quantum Chemistry

Angelo Lucia, University of Rhode Island, Dept of Chem. Engineering, Kingston, RI 02881, Leah Octavio, Chemical Engineering, University of Rhode Island, Dept of Chem. Engineering, Kingston, RI 02881, Donald P. Visco Jr., Tennessee Technological University, Box 5013, Cookeville, TN 38505, Eudes E. Fileti, Universidade Federal do ABC, Santo Andre SP, Brazil, and Sylvio Canuto, Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, San Paulo, Brazil.

Recently, ab initio quantum chemistry calculations (specifically Moller-Plesset and Coupled-Cluster methods in Gaussian 98) by Fileti et al. (2004) have been used to show that hydrogen bonding strengths in alcohol-water mixtures depend on which molecule serves as the proton donor and which molecule serves as the proton acceptor. In particular, gas phase potential energies at 0 K for both self association and cross association have been determined and results clearly show that cross association is stronger if water serves as the proton donor while hydrogen bonds in which alcohol is the proton donor are weaker. Similar results hold for the liquid phase as well.

The original Statistical Associating Fluid Theory (SAFT) equation of state (Chapman et al., 1990; Huang and Radosz, 1990), and its many variations (e.g., simplified SAFT, PC-SAFT, and SAFT-VR), are well established as reliable mathematical tools for modeling the phase behavior of fluid mixtures. The primary advantages of the SAFT approach are that it takes into account the shape and size differences in fluid molecules and incorporates the effects of any association between molecules (e.g., hydrogen bonding). Unfortunately, relative hydrogen bonding effects modeled by SAFT are usually very poor and do not properly describe association when multiple hydrogen bonding sites are available.

The purpose of this poster is to

1) Provide further evidence that the association term in the SAFT formalism often predicts relative hydrogen bonding energies for mixtures that are grossly in error when the assumption of equal association strengths is used.

2) Describe a new methodology for determining unequal site-site association strengths and hydrogen bonding energies by fitting the SAFT association strengths directly to binding energies calculated from ab initio quantum chemistry.

In SAFT, in order to reduce the number of independent parameters, it is frequently assumed that the cross association bonding volumes are equal and that cross association bonding energies are equal. These assumptions lead directly to equal association strengths. Numerical examples are presented that clearly illustrate that using equal association strengths in the SAFT formalism often predicts relative hydrogen bonding energies that are completely different than those predicted by ab initio quantum chemistry calculations (e.g., Coupled Cluster methods and density functional theory). This, in turn, can lead to incorrect values for mole fractions of un-bounded sites, erroneous compressibility factors, and poor predictions of phase equilibrium. To resolve these difficulties, a new global optimization-quantum chemistry methodology for separating the determination of association strengths from non-associating SAFT parameters is proposed such that the resulting hydrogen bonding energies match more closely, in a relative sense, those predicted by quantum chemistry. Thus SAFT association parameters are not correlated to experimental vapor pressure and liquid density data but rather are fit to first principles information (i.e., using hydrogen bonding measurements to determine hydrogen bonding parameters). Numerical results for various associating mixtures, including ethanol and water and hydrogen fluoride and water, are presented to illustrate the efficacy of the proposed global optimization-quantum chemistry approach and clearly show that there are significant differences between the calculated mole fractions of un-bonded sites for equal and unequal association strengths.