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Ind. Eng. Chem. Res. 1993,32,1482-1487
Chemical-Physical Interpretation of Cosolvent Effects in Supercritical Fluids Simon S. T. Ting, David L. Tomasko,+Stuart J. Macnaughton, and Neil R. Foster' School of Chemical Engineering and Industrial Chemistry, University of New South Wales, P.O. Box 1, Kensington, N.S.W. 2033,Australia
Cosolvent effects in supercritical fluids can be considerable for systems where the cosolvent interacts strongly with the solute. It is shown in a companion paper that strong interactions occur between naproxen ((S)-6-methoxy-cy-methyl-2-naphthaleneacetic acid) and various polar cosolventa in supercritical C02. A chemical-physical model proposed by Ekart and Eckert that incorporates chemical equilibria into the Soave-Redlich-Kwong equation of state was used here to study these systems. The model was found to describe these systems well, and the associated equilibrium constants obtained could be correlated with the cosolvent cy, P, and ?r* solvatochromic parameters by a linear free energy relationship. This correlation suggests that both physical and chemical forces are important in the solvation process of naproxen in polar cosolvent-supercritical C02 mixtures. The model coupled with the correlation represents a step toward predicting solubilities in cosolventmodified supercritical fluids using nonthermodynamic data. This method of modeling cosolvent effects allows a more intuitive interpretation of the data than either a purely physical equation of state or ideal chemical theory can provide.
Introduction It is believed that the relatively high solubilities of nonvolatile solutes in supercritical fluids result partially from clustering of solvent molecules around the solute molecules, creating a local density which is greater than the bulk (Kim and Johnston, 1987a;Kajimoto et al., 1988; Petache and Debenedetti, 1989; Cochran and Lee, 1989; Brennecke et al., 1990a). This effect has been found to be greatest close to the critical point. With the introduction of cosolventa,various workers (Kim and Johnston, 1987b; Yonker and Smith, 1988) have found that the cosolvent concentration in the vicinity of the solute is also greater than the bulk. Although direct evidence is yet required to confirm the existence of distinct species being formed between polar solutes and polar cosolvents in supercritical fluids, an excited-state naphthalene-triethylamine complex (an exciplex) was found to be formed in the naphthalene/triethylamine/COzsystem studied by Brennecke et al. (1990b). Donohue and co-workers (Walsh et al., 1987, 1989; Walsh and Donohue, 1989) have also used the concept of complex formation between the solute and cosolvent in supercritical fluid systems. However, spectroscopicanalysis of synthetic liquid solution mixtures was used to provide evidence of the formation of separate species and to obtain the related equilibrium constant. Evidence of complexing was also inferred by Lemert and Johnston (1991) for the hydroquinoneln-tributyl phosphate/supercritical COz system. It is shown in a companion paper (Ting et al., 1993)that purely physical models like the Peng-Robinson (Peng and Robinson, 1976) and the Soave-Redlich-Kwong (Soave, 1972)equations of state together with a binary interaction parameter could be used to correlate the solubility of polar organicslike naproxen in polar cosolvent-supercritical C02 mixtures. The binary interaction parameters between the naproxen and the cosolvent, k23, for the alcohol systems were unusually large and negative. Often a large positive kij is required to correct for the overprediction of the energy parameter given by the classical van der Waals (vdW) ~
* To whom correspondence should be addressed.
+ Present address: Department of Chemical Engineering, The
Ohio State University, Columbus, OH 43210-1180.
0888-588519312632-1482$04.00/0
1-fluidmixing rules implying that the interactions between
i and j species are relatively weak and of a physical nature. Thus a large and negative kij would be indicative of strong chemical-type interactions between the i and j species in these systems. It is probable that the strong interactions encountered in this study are the result of specific interactions between the cosolventa and the solute, naproxen. These specific interactions are likely to occur via hydrogen bonding. Should these interactions result in complex formation, a suitable model that incorporates chemical equilibria could be used to describe these systems. Several workers (Heidemann and Prausnitz; 1976; Hu et al., 1984; Ikonomou and Donohue, 1986, 1988; Hong and Hu, 1989; Anderko and Malanowski, 1989;Elliot et al., 1990;Wenzel and Korp, 1990; Anderko, 1991; Suresh and Elliot, 1991; Lemert and Johnston, 1991;Ekart and Eckert, 1992)have incorporated chemical equilibria into an equation of state (EOS), and these are grouped under the category of chemical-physical models. Such models are more realistic than either a purely physical cubic EOS or ideal chemical theory for systems where both types of interactions exist. However,the extra realism resulta in a more complex model containing several adjustable parameters. In this work, achemical-physical model (Ekart, 1992;Ekartand Eckert, 1992) is used to correlate the data for the six naproxen/ cosolvent/supercritical C02 ternary systems presented earlier (Ting et al., 1993). This model was chosen because it has the flexibility to handle any degree of chemical association with only two adjustable parameters.
Theory The chemical-physical model proposed by Ekart and Eckert (1992), which will be referred to as EECP, incorporates chemical equilibria into the Soave-RedlichKwong (SRK) EOS. In this model only one physical parameter and one chemical parameter are required even if an infinite chemical equilibriais considered. The model assumes that no complex formation resulta from the interaction between the primary supercritical solvent and the solute. Self-association of cosolvents, such as occurs between alcohols, is also not accounted for. 0 1993 American Chemical Society
Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993 1483 The chemical interaction between the solute and the cosolvent can be related through an infinite equilibria whereby every AiBj is assumed to exist and they are at equilibrium with the monomers:
fluid phase is calculated according to
-
iA + j B AiBj (1) The equilibrium constant for this reaction can be written as Kij
vij pl-(i+j) - ziz‘qzji j g vi&
(2)
where the (p’s represent the fugacity coefficients which are determined from an EOS, the z’s are the true mole fractions, and P i s the system pressure. This formulation results in the equilibrium constant being only temperature dependent. As opposed to true compositions, apparent compositions are the measured experimental values. While the true number of moles (nT)in solution decreases when complexation occurs, the apparent number of moles (no) remains the same. The ratio nT/nO (
