Extraccion

5
Thermodynamic M o d e l i n g of Supercritical Fluid-Solute Phase Behavior

In this chapter we describe the methods used to calculate solubility isotherms as well as the entire phase diagram for binary and ternary solute-SCF mixtures. The objective of the first part of the chapter is to discuss the relevant physical properties of the solute and solvent pair that are needed to describe theintermolecular forces in operation between molecules in a mixture that ultimately fix solubility levels. A brief description is provided on the application of solubility parameters to supercritical fluids.

INTERMOLECULAR FORCES
The determination of whether a given solute will dissolve in a particular supercritical fluid solvent depends on the free volume differences between the solute and thesolvent, and the intermolecular forces in operation between solvent-solvent, solvent-solute, and solute-solute pairs in solution. We first address the issue of how intermolecular interactions affect solubility. To gain a better understanding of why certain solutes readily dissolve in certain SCF solvents, we use simplified expressions to interpret qualitatively the properties of the components thatfix the strength of their intermolecular forces (Prausnitz, 1969). Every molecule has a momentary dipole due to electron oscillations that induces a dipole in neighboring molecules resulting in a net attractive interaction that determines the solubility level of a nonpolar solute in a nonpolar solvent. For nonpolar molecules these momentary dipoles average to zero over time due to their rapidlychanging direction and magnitude. A simplified expression can be used to describe the induced dipole-induced dipole potential energy, known more commonly as dispersion energy.

rij=

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99

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Thermodynamic Modeling of Supercritical Fluid-Solute Phase Behavior

where Tij is the potential energy between an i and a j molecule, (Y is the polarizability, r is the distance between the twomolecules, and C1 is a constant. Since force is the derivative of potential energy with respect to intermolecular distance, equation 5.1 shows that the attractive force due to dispersion is independent of temperature and is very short-range. The polarizability is the key molecular property of the molecule that provides an indication of the strength of the solvent. Generally, within a given classof molecules, the polarizability increases with the size of the molecule since the more electrons a molecule has, the less tightly they are held (Castellan, 1971). For example, the polarizabilities of the noble gases increase from cm3 for helium, a very small molecule, to 40.1 X 2.0 x cm3 for xenon, a quite large molecule. Interestingly, xenon has a polarizability comparable to that of ethane orethylene. This helps to explain why xenon is such a good supercritical fluid solvent. In addition to dispersion forces between molecules, there can be an additional force of attraction between the molecules if they have permanent dipoles whose strength and direction are fixed as a result of their molecular structure. The simplified expression that accounts for permanent dipole4ipole potential energyis

where p is the strength of the dipole moment in debye, T is the absolute temperature, k is Boltzmann’s constant, and C2 is a constant. In this case, the force of attraction varies as the inverse seventh power of the intermolecular distance but it also varies inversely with temperature. Dipole-dipole interactions increase in strength with decreasing temperature since the effect of kT thermalenergy decreases sufficiently to allow the permanent dipoles of the two molecules to align. Here the key molecular parameter is the dipole moment, which has a large effect on the properties of the molecule if the magnitude of the dipole is larger than -1.0debye. Substances that are very polar at room conditions, such as acetone, typically have high critical temperatures ( T , = 234.9”C) since...