Solubility of solids in SCFs

Table 2. Comparison between the LC Mixing Rules and the van der Waals Mixing Rule for the Solubilities of Solids in SCFs at Various Temperatures"...

Another attractive feature of the new mixing rules is that they allow one to predict the solubilities of solids in SCFs using only data for the pure components and the intermolecular interactions. In this paper, the solubilities of sohd CCI4 in the SCF CF4 were predicted for three different temperatures. The energies of the intermolecular interactions (CF4 + CCI4, CF4 + CF4, and... 

At high pressure the solubility tends asymptotically to a value which is temperature dependent but very low. Generally, the solubility of solids in SCFs is well below 1 % w/w, and most often it ranges from 0.01 % w/w downward. In particular, there are very few compounds of molecular weight in the thousands that can be dissolved in SCCO2 to a detectable extent. 

Pressure is not the best independent variable with which to represent solubilities in SCFs. The quite confused representation of Figure 2.3-l(a) can be improved if the same solubility isotherms are plotted against the vapor density (i.e. the SCF density), as in Figure 2.3-1(b). This smooth dependence is embedded in a simple equation proposed by Chrastil [7] and recently modified by Mendez-Santiago and Teja [8] to correlate solubility of solids in SCFs ... 

Diffusivity values are higher in the supercritical phase than in the Hquid phase, so that species wiU diffuse faster through a supercritical fluid (SCF) than through a Hquid, implying faster solubility of solids in SCFs than in more normal liquids, and that SCFs wiU be more efl dent at penetrating through microporous materials thereby increasing the rate of mass transport... 

As can be seen from Eq. (14), the solubility of a solid in an SCE depends not only on solid-state parameters, such as sublimation pressure and molar volume V , but additionally on the fiigacity coefficient (]), . The fugacity coefficient is the supercritical analogue to the activity coefficient (5). The fugacity coefficient varies not only with the type of fluid but with temperature and pressure (53). Therefore, solubility of solids can be significantly influenced by changing the density of SCFs on alteration of temperature and/or pressure. The fugacity coefficient is the key variable that explains the different solubility of solids in SCFs compared with ordinary liquids. 

Various models of SFE have been published, which aim at understanding the kinetics of the processes. For many dynamic extractions of compounds from solid matrices, e.g. for additives in polymers, the analytes are present in small amounts in the matrix and during extraction their concentration in the SCF is well below the solubility limit. The rate of extraction is then not determined principally by solubility, but by the rate of mass transfer out of the matrix. Supercritical gas extraction usually falls very clearly into the class of purely diffusional operations. Gere et al. [285] have reported the physico-chemical principles that are the foundation of theory and practice of SCF analytical techniques. The authors stress in particular the use of intrinsic solubility parameters (such as the Hildebrand solubility parameter 5), in relation to the solubility of analytes in SCFs and optimisation of SFE conditions. 

Eqs. (l)-(3) show that the solubilities of sohds in an SCF depend among others on their fugacity coefficients (pf (pf and the calculations indicated that these coefficients were responsible for the large solubilities of solids in supercritical solvents. These solubilities are much larger than those in ideal gases, and enhancement factors of 10" -10 are not uncommon [1] they are, however, still relatively small and usually do not exceed several mole percent. Consequently, these supercritical solutions can be considered dilute and the expressions for the fugacity coefficients in binary and ternary supercritical mixtures simplihed accordingly. 

From Eqs. (9) and (10) one can see, that the calculation of the solubilities of solids in a SCF in the presence of an entrainer (cosolute or cosolvent) requires information about the properties of the pure components, the fugacity coefficients at infinite dilution and the values of K p. 

In a number of areas of modeling phase equilibria, the cubic equation of state (EOS) provided equal or even better results than the traditional approach based on the activity coefficient concept. In fact, for certain t5rpes of phase equilibria, the EOS is the only method that provided acceptable results. The solubility of solids in a supercritical fluid (SCF) constitutes such a case. For the solubility of a solid in a SCF [SCF (1) + solid solute (2)], one can write the well-known relation ... 

Correlation of the Solubility of Solids in Various SCF. The new LC mixing rules were also tested for the solubility of a large number of solid solutes in various SCFs. The critical temperatures and pressures of solids and SCFs were taken from refs 24 and 25. The molar volumes of the solids and their saturated vapor pressures were taken from ref 25. The saturated vapor pressure of perylene was found in ref 26. The results are compared with the van der Waals mixing rules in Table 2, which shows that they are comparable. The parameters of SRK EOS (a and b) can be expressed by combining one of eqs 17a—c with one of eqs 18a—c. Only a few combinations have been included in Table 2 the other ones have also been tested and provided comparable results. 

Of these featores, the pressure-dependence of SCF properties dominates or influences virtually every process conducted on polymers. Pressure governs such properties as density, solubility parameter, and dielectric constant changes of more than an order of magnitude are common when pressure is sufficiently increased to transform a gas into a supercritical fluid. This chapter primarily compiles experimental data on the pressure dependence of physical properties of fluid phase polymer-SCF mixtures. Phase equilibria are addressed, including the solubility of polymers in SCFs, the solubility of SCFs in liquid polymers, and the three-phase solid-fluid-fluid equilibria of crystalline polymers saturated with SCFs. Additional thermodynamic properties include glass transition temperature depressions of polymers, and interfacial tension between SCF-swollen polymers and the SCF. The viscosity of fluid phase polymer-SCF mixtures is also treated. 

Several authors [3-9] studied the solubility of polymers in supercritical fluids due to research on fractionation of polymers. For solubility of SCF in polymers only limited number of experimental data are available till now [e.g. 4,5,10-12], Few data (for PEG S with molar mass up to 1000 g/mol) are available on the vapour-liquid phase equilibrium PEG -CO2 [13]. No data can be found on phase equilibrium solid-liquid for the binary PEG S -CO2. Experimental equipment and procedure for determination of phase equilibrium (vapour -liquid and solid -liquid) in the binary system PEG s -C02 are presented in [14]. It was found that the solubility of C02 in PEG is practically independent from the molecular mass of PEG and is influenced only by pressure and temperature of the system. 

This equation is analogous to Eq. 5 of Ch. 1 for the solubility of a solid in a SCF. In this equation, the subscript 2 refers to the liquid component. The superscript s refers to saturation conditions at temperature T. Pj refers to the saturation vapor pressure of the liquid at temperature T. The variable uf is the molar volume of the liquid, ( )2 is the fugacity coefficient at saturation pressure and is the fiigacity coefficient in the high pressure gas mbrture. For a detailed derivation of this equation, see Prausnitz. " As is stated in the derivation, it is the escaping tendency of the liquid into the supercritical fluid phase, as described by the fugacity coefficient, ( >2, which is responsible for the enhanced solubility of liquids in compressed gases. 

To our knowledge, no successful prediction of the solubilities of solid substances in SCFs has been made. Because of the physical meaning of the parameters contained in the LC mixing rules, such an attempt becomes possible. Indeed, the new parameters depend on the intermolecular energies which can be calculated independently. 

Figure 1. Comparison between predicted (O) and experimentaF ( ) solubilities of solid CCI4 in the SCF CF4 at 249 K. Parameter a is given by eq 17a and parameter b by eq 18a. The LCs are given by the Wilson equations (eqs 9 and 10).

We can now explain the sudden increase in the solubility of naphthalene in supercritical ethylene reported at 50 bar and 12°C. This solubility increase is a result of being very close to the LCEP for this system, which is 51.9 bar and 10.7°C (Diepen and Scheffer, 1948a). As shown in table 3.3, the LCEP usually occurs very close to the critical point of the pure SCF for most of the solid-SCF systems reported in the literature even though there is a large solubility enhancement, the amount of solid in the SCF phase at the LCEP is quite low. 

Schmitt (1984) verified the entrainer behavior reported by Kurnik and Reid. Schmitt and Reid (1984) show that very small amounts of an entrainer in the SCF-rich phase have very little effect on the solubility of a second component in that phase. This observation is consistent with the work of Kohn and Luks for ternary mixtures at cryogenic temperatures. The data of Kurnik and Reid have been corroborated for the naphthalene-phenanthrene-carbon dioxide system (Gopal et al., 1983). Lemert and Johnston (1989, 1990) also studied the solubility behavior of solids in pure and mixed solvents at conditions close to the upper critical end points. Johnston finds that adding a cosolvent can reduce the temperature and pressure of the UCEP while simultaneously increasing the selectivity of the solid in the SCF-rich phase. In these studies Johnston found the largest effects with a cosolvent capable of hydrogen bonding to the solute. 

The enhancement factor measures the extent of solubility in excess of that generated from the vapor pressure of the pure solid. This provides a convenient way of comparing the solubilities of solids with different vapor pressures. As the actual solubility of a solid is heavily influenced by the SCF density, the enhancement factor displays a similar dependence on density. Values of the enhancement factor typically vary between 10 and 10, although enhancement factors as high as 10 have been reported for some systems [10]. 

The solubility of a given solute also depends on the type of SCF as shown in Table 1.2-4. Fluoroform has the highest mass density under the conditions shown but displays the lowest affinity for naphthalene. The variation in the solubility of naphthalene in different SCFs therefore suggests that there are varying degrees of intermolecular interaction between the solid and SCF. The different levels of intermolecular interaction can be explained in terms of solvent polarity. 

The difference between solid solubilities in a given SCF depends mainly on the solid vapor pressure and intermolecular interactions between the solvent and solute. The individual solubilities of solids can vary greatly although most values are well below 10 mol%. The differences between enhancement factors are less pronounced [14,15], however, which suggests that the vapor pressure of the solid exerts the primary influence on solubility. Intermolecular interactions between the solvent and solute depend on the types of functional groups present in their chemical structures. In general, the intermolecular interactions are dominated by dispersion forces, which accounts for the similar values of the enhancement factor for many solids. 

To use a SCF as a solvent for extracting solutes, the solubility of any solute in a SCF must be substantial. It is generally observed that the capacity of a SCF to dissolve a solute is directly related to the density of the SCF. For example, consider the solubility characteristics of solid naphthalene in supercritical ethylene shown in Figure 3.3.15(a) (McHugh and Krukonis, 1986). The solubility of solid naphthalene increases by more than an order of magnitude from a very low value when the ethylene pressure exceeds the Pc = 49.7 atm of ethylene (at T > Tc = 9.4 C, of ethylene). The variation of the density of ethylene near its critical point may be seen in Figure 3.3.15(b), a plot of reduced density, = (p/pc) against reduced pressure Pn = (P/Pc) and reduced temperature... 

Principles and Characteristics Supercritical fluid extraction uses the principles of traditional LSE. Recently SFE has become a much studied means of analytical sample preparation, particularly for the removal of analytes of interest from solid matrices prior to chromatography. SFE has also been evaluated for its potential for extraction of in-polymer additives. In SFE three interrelated factors, solubility, diffusion and matrix, influence recovery. For successful extraction, the solute must be sufficiently soluble in the SCF. The timescale for diffusion/transport depends on the shape and dimensions of the matrix particles. Mass transfer from the polymer surface to the SCF extractant is very fast because of the high diffusivity in SCFs and the layer of stagnant SCF around the solid particles is very thin. Therefore, the rate-limiting step in SFE is either... 

Applications The majority of SFE applications involves the extraction of dry solid matrices. Supercritical fluid extraction has demonstrated great utility for the extraction of organic analytes from a wide variety of solid matrices. The combination of fast extractions and easy solvent evaporation has resulted in numerous applications for SFE. Important areas of analytical SFE are environmental analysis (41 %), food analysis (38 %) and polymer characterisation (11%) [292], Determination of additives in polymers is considered attractive by SFE because (i) the SCF can more quickly permeate throughout the polymer matrix compared to conventional solvents, resulting in a rapid extraction (ii) the polymer matrix is (generally) not soluble in SCFs, so that polymer dissolution and subsequent precipitation are not necessary and (iii) organic solvents are not required, or are used only in very small quantities, reducing preparation time and disposal costs [359]. 

To model the solubility of a solute in an SCF using an EOS, it is necessary to have critical properties and acentric factors of all components as well as molar volumes and sublimation pressures in the case of solid components. When some of these values are not available, as is often the case, estimation techniques must be employed. When neither critical properties nor acentric factors are available, it is desirable to have the normal boiling point of the compound, since some estimation techniques only require the boiling point together with the molecular structure. A customary approach to describing high-pressure phenomena like the solubility in SCFs is based on the Peng-Robinson EOS [48,49], but there are also several other EOS s [50]. 

The enhancement of solvent power obtained by compressing a gas into its critical region can be demonstrated dramatically. An estimate of the solubility of a solid in an SCF solvent can be made using the following expression ... 

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