Chemistry Reference
In-Depth Information
compositions and their effect on the phase behavior. For that purpose, in Section 8.3
we introduce the main ideas behind the derivation of composition expansions for
the thermodynamic properties of a dilute system whose infinite dilution reference
systems are described by the solvation formalism of Section 8.2. Then we discuss
the development of thermodynamically consistent perturbation expansions for the
species residual properties in multicomponent dilute mixtures (Section 8.3.1), pro-
vide a microscopic interpretation of the expansion coefficients (Section 8.3.2),
analyze special cases for which the thermodynamic consistency is well established
(Section 8.3.3), discuss some modeling implications behind
ad hoc
irst-order trun-
cated expansions (Section 8.3.4), and interpret the microscopic mechanisms behind
synergistic solvation effects involving cosolutes or cosolvents to provide a molecu-
lar argument on the unsuitability of the vdW-1f mixing rules for the description of
weakly attractive solutes in compressible solvents (Section 8.3.5).
8.2 SOLVATION FORMALISM FOR INFINITELY
DILUTE TERNARY SYSTEMS
The behavior of dilute solutes in compressible media has been traditionally associ-
ated with supercritical solubility enhancement and related phenomena, frequently
analyzed in terms of the solute mechanical partial molecular properties at infinite
dilution, that is, volume and enthalpy, as well as those of the pure solvent counterpart
(Debenedetti and Kumar 1986, 1988). There are compelling reasons behind the use
of these partial molecular properties at infinite dilution: (a) they are the pressure and
temperature first derivatives of the corresponding chemical potentials, therefore, the
choice of suitable approximations based on well-established limiting behavior for
the pair correlation functions leads to the development of well-behaved and accurate
correlations, and (b) they are rigorously related to volume integrals over the micro-
structure of the solvent around the infinite dilute solute according to the Kirkwood-
Buff fluctuation formalism of mixtures (Kirkwood and Buff 1951). Consequently,
the resulting macroscopic modeling will capture the relevant underlying physics
(O'Connell, Sharygin, and Wood 1996). In fact, the solute partial molecular volume
at infinite dilution has been often used to interpret the pressure dependence of the
isothermal solubility of sparingly soluble species (Kumar and Johnston 1988), and
not surprisingly, to make contact between the evolution of solubility (or the corre-
sponding solute partial molecular fugacity coefficient) and the underlying changes
in the solvent microstructure around the infinitely dilute solute (Debenedetti and
Mohamed 1989) to facilitate the modeling or correlation of solubility data (Cochran,
Lee, and Pfund 1990; O'Connell and Liu 1998).
Despite the referred advantages, the modeling of mechanical partial molecular
properties of solutes at infinite dilution is intrinsically problematic, that is, they
scale as the solvent isothermal compressibility (Levelt Sengers 1991), with finite
prefactors associated with the magnitude of the molecular solute-solvent interaction
asymmetry (Chialvo and Cummings 1995) as we will illustrate below. However,
in an effort to facilitate the regression of experimental data, Wood and coworkers
(Sedlbauer, Yezdimer, and Wood 1998) and O'Connell and coworkers (O'Connell,
