Liquid-state theory of hydrocarbon-water systems: application to methane, ethane, and propane

Lue, L. and Blankschtein, D. (1992) Liquid-state theory of hydrocarbon-water systems: application to methane, ethane, and propane. Journal of Physical Chemistry B, 96 (21). pp. 8582-8594. ISSN 1520-6106 (http://pubs.acs.org/doi/abs/10.1021/j100200a069)

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Abstract

We have studied the structural and bulk thermodynamic properties of hydrocarbon (methane, ethane, and propane)-water systems as well as pure water using the site-site Omstein-Zemike (SSOZ) equation under a variety of different closure relations in order to compare the quantitative predictive Capabilities of the various closures. For the hydrocarbon-water systems, the simple point-charge (SPC) potential was used to model water, and the optimized potentials for liquid simulation (OPLS) were used to model the hydrocarbons. For pure water, predictions were also made for other water potential models. We solved the SSOZ equation with the hypemetted-chain (HNC) closure to determine the pair correlation functions of water. We then analyzed the structural and bulk thermodynamic properties of methane, ethane, and propane at infinite dilution in water using various closure relations for the hydrocarbonwater pair correlation functions. We find that the HNC closure, which is the closure that has been utilized almost exclusively to predict bulk thermodynamic properties of interaction-site fluids, performs rather poorly. Specifically, we find that the HNC closure consistently underpredicts the magnitudes of both the solute partial molar volume and the solute-solvent interaction energy, grossly overpredicts the magnitude of the residual chemical potential, and gives the incorrect sign of the enthalpy of solution. On the other hand, we find that two recently developed closures, the Martynov-Sarkisov (Mas) and Ballone-Pastore-Galli-Gazzillo (BEG) closures, which have not been utilized so far in conjunction with the SSOZ equation, yield reasonable predictions of the structural and bulk thermodynamic properties of the hydrocarbon-water systems studied. In particular, utilizing the SSOZ-BEG equation, the predicted temperature variation of the residual chemical potential over the relatively broad range 5-80 OC was found to be in very good agreement with the experimental data. Note that the residual chemical potential is directly related to the Henry's law constant, which, in tum, can be utilized to predict solubilities. In addition, we have developed an analytical expression for the residual chemical potential, appropriate for interaction-site fluids, in terms of pair and direct correlation functions at full coupling for the various closures examined in this paper. To date, an expression of this type was available only for the HNC closure. This new expression facilitates the calculation of the residual chemical potential by eliminating the previous need to perform a numerical integration over the coupling constant, thus making the computation of the chemical potential simpler and more efficient. Finally, we have also tested the accuracy of the equivalent-site approximation (ESA), a perturbation method which was developed by Curro and Schweizer to study long polymeric chains by treating all the sites in a given molecule as equivalent, on the predictions of the structural and bulk thermodynamic properties of propane at infinite dilution in water. Note that of all the n-alkanes, propane poses the most severe challenge to the ESA. Interestingly, we find that, already for propane, the ESA yields predictions of bulk thermodynamic properties which are within 5% of those obtained using the rigorous calculations.

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