(494a) Efficient Implementation of Wertheim's Theory: II. Master Equations for Asymmetric Solvation

Elliott (1996) showed that the solution for mole fractions of proton donors and acceptors not bonded could be reduced to a single nonlinear "master" equation. Normally, this determination requires solving a system of Nc^2*NA*ND coupled nonlinear equations by a linearly convergent iteration method like successive substitution, where Nc is the number of components, and NA and ND are the numbers of acceptor and donor types. Such a determination can be quite slow for multicomponent systems with many donor and acceptor types, and this determination is fundamental to each iteration on density required to match the system pressure before fugacities can be computed. The master equation method expedites the computation by a factor of roughly 3 for a binary mixture, roughly 9 for a ternary mixture, and so forth.

The method of Elliott (1996) required an assumption about the symmetric nature of solvation interaction between distinct molecules. Specifically, the "symmetric" assumption was that the solvation interaction could be factored as: alpha(i,j)=sqrt[alpha(i,i)*alpha(j,j)]. This assumption is applicable to mixtures of associating molecules where both pure compounds associate, and it applies to mixtures of "inert" molecules (like hydrocarbons) with associating molecules where the solvation interaction is zero. The symmetric assumption breaks down when considering mixtures of associating molecules with molecules that can either donate or accept protons but not associate, like ethers, esters, ketones, and some halocarbons. In this presentation, we show how the master equation method can be extended to approximate the solution for these asymmetric mixtures. The result is a compact relation that can facilitate understanding of peculiar phase behavior like lower critical solution temperatures, as well as expediting computations in general. As an "almost analytical" solution for multicomponent solutions with many site types, it puts Wertheim's theory on a similar computational basis with expedient models like Mercedes-Benz water, while retaining the rigor and generality of Wertheim's theory. Implications for interfacial density functionals will also be conjectured.

Reference:

Elliott, J.R. Ind. Eng. Chem. Res., 35:1624(1996).