Spectroscopy, Solubility, and Modeling of Cosolvent Effects on Metal

results are presented for this system using the Peng−Robinson equation of state. .... Silvia De Dea , Dominic Graziani , David R. Miller , Rober...
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Ind. Eng. Chem. Res. 2001, 40, 980-989

Spectroscopy, Solubility, and Modeling of Cosolvent Effects on Metal Chelate Complexes in Supercritical Carbon Dioxide Solutions Erik J. Roggeman,† Aaron M. Scurto, and Joan F. Brennecke* Department of Chemical Engineering, University of Notre Dame, Notre Dame, Indiana 46556

Extraction of metals from aqueous solutions and solid matrixes with supercritical CO2 is an attractive, environmentally benign alternative to organic solvent extraction to remove metal contaminants. Here, new measurements are presented for the solubility of iron tris(pentane2,4-dionate) [Fe(acac)3], a representative metal chelate complex, in pure supercritical CO2 and in a mixture of supercritical CO2 and trichloromethane (chloroform), a typical organic cocontaminant, as a function of temperature and pressure. Solubilities ranged from 8.75 × 10-6 mole fraction to 1.34 × 10-3 mole fraction with an average uncertainty of just 12%. It is shown that the presence of 3 mol % chloroform increases the solubility of Fe(acac)3 by approximately a factor of 2. Thus, the co-extraction of organic contaminants with metals would be advantageous. In addition, spectroscopic measurements are presented of the local environment around the dissolved Fe(acac)3 in the CO2/chloroform mixture that show a cybotactic region that is enriched with chloroform, especially at lower pressures. Finally, thermodynamic modeling results are presented for this system using the Peng-Robinson equation of state. Using just one fit parameter, excellent agreement is obtained with the solubility data in pure CO2. Without any new adjustable parameters the model underpredicts the solubility in the CO2/3 mol % chloroform mixture. Thus, the solubility, spectroscopy, and modeling results suggest that the large increase in solubility with the cosolvent (co-contaminant) present is not just attributable to the bulk density increase when chloroform is added, but evidently is also due to the enrichment of the chloroform in the solvation sphere around the solute. 1. Introduction Elimination of metal ions from soils, sludges, and wastewater streams has become an increasingly important environmental priority. For soil contamination, fixation might be an option, but this is an unacceptable alternative for radioactive metals or when organic cocontaminants are present. In these cases, solvent extraction with an organic phase containing a chelating ligand might be an option.1,2 The metal ions react with the chelating agent to form a stable complex that is more soluble in the organic phase than the aqueous phase (or solid matrix), allowing for effective extraction of the metal. Unfortunately, this technique can result in residual organic solvent remaining in the solid matrix or contamination of the aqueous phase or sludge with the organic solvent. Replacement of the organic solvent with supercritical CO2 would overcome many of these difficulties as the CO2 would evaporate when the pressure was released. Carbon dioxide is nontoxic, inexpensive, nonflammable, and readily available, and it has a critical temperature just above ambient (Tc ) 31 °C and Pc ) 73.8 bar). Another difficulty with solvent extraction systems is that formation of the metal chelate complex might be mass-transfer-limited. Supercritical fluids (SCFs) have relatively low viscosity and high diffusivity, which might enhance complex formation in certain systems, increasing extraction efficiency. Also, the solvent properties of a SCF can be changed greatly by small temperature and * Author to whom correspondence should be addressed. Phone: (219) 631-5847. Fax: (219) 631-8366. E-mail: [email protected]. † Present address: IBM Inc., Hopewell Junction, NY 12533.

pressure changes in the region near its critical point, which can be used to enhance selective extraction. The research to date on metals chelates in supercritical (SC) CO2 has focused primarily on the use of two broad families, or types, of chelating agents. The first family is the β-diketonates.3-7 These compounds are known for having a high stability because of the resonance effects between the central carbon atoms and the complexed metal atom.8 The other common class of compounds for use in metal supercritical fluid extraction is the dithiocarbamates, which use sulfur atoms to interact with the metal ion instead of oxygen atoms.5 There have also been some investigations of phosphates9-11 and crown ethers.12 Studies of metal chelates in SC CO2 have examined both solubilities and extraction efficiencies. In particular, some solubility measurements of metal chelate complexes have been conducted in pure SC CO213-16,18 (for a review of some equilibrium solubilities, see Smart et al.17) Coupled with some of the more recent reports of metal chelate solubilities have been attempts to develop correlative models of the measured solubilities.18,19 One aspect of solubility measurements that has been largely overlooked is the solubility of metal chelates in modified SC CO2; few equilibrium studies have been performed.20 Organic modifiers would inevitably be present in the co-extraction of metals and organic cocontaminants from solid matrixes. One of the goals of this work is to provide a comparison of the solubilities of metal chelate complexes in pure CO2 and modified CO2. Extraction of metals from aqueous media and various types of solid matrixes have been performed successfully

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using SC CO2 and a variety of chelating ligands.21,22 For a review on aqueous extraction using chelating agents and SC CO2, see Erkey.23 The presence of polar modifiers (e.g., methanol) or water greatly increases overall extraction efficiency.20,24 Also, there have been successful attempts to use a chelating agent with another extractant (e.g., tributyl phosphate) in a synergistic extraction scheme.10,11,25,26 Although modeling of the extraction process has been limited, Erkey and coworkers have developed a detailed model of the extraction of copper(II) from aqueous solutions with SC CO2.27 Because the metal complexes of many of the conventional ligands mentioned above are only sparingly soluble in SC CO2, Yazdi and Beckman28 synthesized a series of CO2-philic chelating agents consisting of fluoroalkyl-, fluoroether-, and silicone-containing polymer tails attached to traditional chelating headgroups. These compounds and their metal complexes have large solubilities in CO2, which make them very attractive. Conversely, the specially synthesized ligands would be much more expensive than conventional chelating agents, which might make their cost prohibitive in a commercial process. As mentioned above, one of the goals of this investigation is to determine the influence of cosolvents on metal chelate solubilities and extraction efficiencies in SC CO2. Thus, new measurements and a new modeling approach are presented of the solubility of a metal chelate complex with and without a cosolvent present. To help explain the solubility increase that is observed with the added cosolvent on a molecular basis, spectroscopic measurements are presented of the local composition of cosolvent around the solute in the mixture. For heavy organic solutes, it has been shown spectroscopically that the local environment can be enriched with the cosolvent. This is true for both supercritical29-36 and liquid37-41 solutions. This might contribute to the enhanced solubility and extraction efficiency increases that are measured when a modifier is added to the SCF phase. A more detailed discussion of this physical phenomenon in supercritical solutions can be found in Zhang et al.35 Previous researchers have used a variety of spectroscopic techniques to measure preferential solvation, including shifts in absorption or fluorescence peak energies29,30,37,38,40,42 and changes in peak intensity.35,39,41 This work will explore the use of both wavelength shifts and peak intensity changes in the ultraviolet-visible (UV-vis) spectrum. A high-pressure cell was used to allow direct UV-vis spectroscopic measurements of SCF solutions. Thus, this report will present new solubility measurements with and without added chloroform for iron tris(pentane-2,4-dionate), which is also known as iron acetylacetonate [abbreviated Fe(acac)3], in SC CO2. A schematic of this complex is shown in Figure 1. Spectroscopic measurements will be presented of the preferential solvation of the Fe(acac)3 by trichloromethane (chloroform) in a CO2/chloroform mixture. Finally, equation of state modeling results will be presented for the Fe(acac)3 systems. 2. Experimental Section 2.1. Materials. SFC-grade CO2 (>99.99%) (CAS registry number 124-38-9) from Scott Specialty Gases (Philadelphia, PA) was used for the spectroscopic experiments, and Coleman instrument-grade CO2 (99.99%) (Mittler Supply, Inc., South Bend, IN) was used for the

Figure 1. Schematic of the structure of iron tris(pentane-2,4dionate), which is also known as iron acetylacetonate and abbreviated Fe(acac)3.

solubility measurements. The chloroform (CHCl3, CAS registry number 67-66-3) was either HPLC-grade (99.9%) from Sigma-Aldrich (Milwaukee, WI) or spectrophotometry-grade (99%) from J. T. Baker. It should be noted that commercial chloroform contains between 0.5 and 1% ethanol as a stabilizer because of its tendency to react with air to form phosgene and HCl. The methanol (CH3OH, CAS registry number 67-56-1) was HPLCgrade (99.93%) from Sigma-Aldrich (Milwaukee, WI). Both chloroform and methanol were kept under N2 to prevent contamination from air and water. No steps were taken to further purify any of these materials. Iron(III) tris-acetylacetonate (CAS registry number 14024-18-1) was purchased from Sigma-Aldrich, and was of 99.7% purity. Because of the hygroscopic nature of most chelates, Fe(acac)3 was stored in an airtight container with calcium carbonate and dried in a 60 °C oven for 3 h prior to use. 2.2. Solubility Measurements. The solubility results reported here were measured using a static sampling technique, a schematic of which is shown in Figure 2. A stainless steel high-pressure vessel (Hoke, Inc.) of roughly 50 mL in volume was used as a saturation chamber. The two ends of the vessel were fitted with 1/4-in. NPT to 1/16-in. HIP adapters (HIP, Inc., Erie, PA). Glass wool was placed in the hollow regions of the adapters to prevent small particles from being entrained. Roughly 25 mL of 5-mm-diameter glass beads were placed in the vessel to reduce the total volume of the system and to increase mixing. Agitation was accomplished with the help of a 1-in. Teflon-coated magnetic stirring bar inserted into the vessel with the glass beads. The vessel was placed in a small water bath atop a magnetic stirrer. The bath was heated with an immersion heater (Fisher, Inc.; model 11-463-15) controlled by a PID temperature controller (Omega, Inc.; model CN6071A) using a calibrated Pt-100 RTD with an accuracy of (0.1 °C. The bath was stirred with a 2-in. Teflon-coated magnetic stirring bar. The vessel was connected through the wall of the water bath to a Valco, Inc. six-port sampling valve (Houston, TX; model C6WE) with a 251.6 ( 0.5 µL sample loop. The sampling valve was heated to the temperature of the water bath with heating tape (Omega, Inc.; model FWH171-020), which was manually controlled by a Variac (model 3PN1010) temperature controller and monitored with a type-K thermocouple (Omega, Inc.). The CO2 or CO2/cosolvent

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Figure 2. Schematic of the experimental apparatus to measure the solubility of Fe(acac)3 in CO2 and CO2/CHCl3 mixtures. A, Isco syringe pump; B, high-pressure vessel; C, magnetic stirring bar; D, magnetic stirrer; E, Valco sampling/switching valve; F, vent valve; G, solute elution valve; H, valve fitted with syringe adapter; I, collection flask.

solution was delivered to the saturation vessel with a syringe pump (Isco, Inc., Lincoln, NE; model 260D) and was used as a back-pressure regulator throughout the run. The pressure was measured with a digital Heise gauge (Heise, Inc.; model 901A-5000), accurate to (0.34 bar. The dried Fe(acac)3 was charged, in excess (∼2 g, order of magnitude excess), into the vessel, which was flushed with CO2 several times to remove air and then pressurized. An equilibration time of 40 min at each new pressure was found to give consistent solubility results. The solution was sampled by placing the sampling valve into the load position and opening the attached vent valve to allow several volumes to pass through the sample loop, which resulted in a momentary loss of about 1 bar pressure in the vessel until the Isco pump could respond. The vent was then shut, and the pressure and temperature were allowed to return to the desired set-point. The sample valve was turned to the inject position and the restrictor valve (HIP, Erie, PA; model 15-11AF1) was slightly opened to allow the CO2 solution to slowly vent into a 25-mL volumetric flask filled with about 5 mL of methanol. Roughly 10-15 mL of methanol was then flushed through the loop to dissolve the fine particles of precipitated metal chelate in the loop and lines. About 30 mL of air was then forced through the loop and restrictor to remove any residual collection solvent. This was repeated three times for each pressure for use in error analysis. The 25 ( 0.02 mL collection solution was analyzed with a UV-vis spectrometer (Cary; model Cary 1) at 274 nm and compared with a calibration curve. From the molarity of the collection solution, the volumes of the collection flask and sample loop, and the density of pure CO2 at the experimental conditions, the mole fraction solubility in the supercritical solution was obtained. Because the solubility of Fe(acac)3 in SC CO2 was much less than 1%, the mixture density was assumed to be the pure component CO2 density as calculated by the ultra-accurate equation of state of Span and Wagner.43 From the mixture density and molarity of the SC solution, the mole fraction solubility was determined. This method was verified to be accurate to within 10% of published values for the solubility of phenanthrene in CO2.44 Cosolvent mixtures were prepared with the aid of a second Isco, Inc., syringe pump (model 260D) filled with pure CO2. Both pumps were cooled to 1 °C with a Fischer water bath (model 1016), and the pure CO2 pump pressurized to 137.9 bar. Roughly 12 mL of chloroform was injected with a syringe directly into the top of the empty pump with the piston withdrawn to

about 40 mL. The syringe was weighed before and after the injection to determine the number of moles of CHCl3 added. The corresponding number of moles of CO2 to produce a 3 mol % solution was calculated. Using the density of CO2 at the temperature and pressure of the pure CO2 pump, the necessary volume was metered into the pump with the chloroform, after it had been flushed with CO2 to remove any residual air. The chloroform/ CO2 solution was heated to 45 °C, where the mixture is single phase at the pressures investigated here, as determined experimentally by Scurto et al.45 The pressure was continuously varied between 138 and 345 bar, intermittent with static equilibration periods, for 3 h to properly mix the solution. 2.3. Preferential Solvation Measurements. Concentrations of the liquid solutions from the solubility measurements and preferential solvation of the solution were determined from UV-vis spectroscopy using a Cary 1 model spectrometer from Varian. The wavelength range of the instrument is 190-900 nm. The accuracy is (0.2 nm, and the repeatability of peak positions is (0.5 nm. Accuracy refers to the range in the wavelength of maximum absorption and repeatability to the average deviation of repeated trials for a maximum of known wavelength. The spectrometer is connected to a computer, which uses a manufacturersupplied software package for data processing and manipulation. For the supercritical fluid experiments, instead of a standard sealed liquid cell, a high-pressure cell was used. This high-pressure cell is essentially a stainless steel cube, which has been described in detail elsewhere.46 Quartz windows sealed into the block with lead gaskets are on three sides of the cube, to allow effective transmission of UV-vis light through the cell and to provide an additional viewport into the cell. A thermocouple was placed inside the cell with a high-pressure fitting to record system temperature, and an Omega CN6071A PID autotune temperature controller controlled the temperature to within (0.1 °C. The temperature controller used a Watlow 120 V C2A4 50 W heating cartridge to heat the cell to the desired system temperature. An Isco model 260D syringe pump was used to supply pure CO2 or modified CO2 to the pressure cell through 1/16-in. stainless steel pressure tubing. For the preferential solvation measurements, the pressure cell was precharged with the chelate complex Fe(acac)3 by adding the solid complex with a spatula into the cell and then sealing the thermocouple in place. Typical Fe(acac)3 concentrations were on the order of

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10-4 mole fraction. The exact concentration was not important as the relative intensities of two peaks in the absorption spectrum were measured. However, it was important that the concentration was low enough to justify the assumption, described later, of infinite dilution of the solute and high enough to provide a sufficiently intense absorbance signal. For the modified SC CO2 phases, the appropriate amount of liquid cosolvent was initially added to the pump, and then the pump was filled with CO2, as described above for the solubility measurements. The water jacket surrounding the pump cylinder was used to heat the pump to 60 °C, which was well above the temperature needed to maintain a single homogeneous phase.45 A pressure gauge, a Heise Digital Pressure Indicator (model 901A-5000), was connected in-line to measure the system pressure to within (0.34 bar. The system pressure was controlled by adding additional CO2 to increase the pressure in the cell and venting some of the homogeneous CO2 solution, when necessary, to reduce it. After time was given to allow the temperature and pressure within the cell to equilibrate, UV-vis spectra could be taken of the resulting supercritical solution. 3. Thermodynamic Modeling There have been two methods proposed in the literature to model the solubility of metal chelates in SC CO2: regular solution theory (RST)14,19 and an equation of state approach.18 Although, there seems to be some correlation between the solubility parameter of a metal chelate and its solubility in CO2, RST can neither qualitatively nor quantitatively model the solubility data.47,48 Use of a cubic equation of state (EOS) for modeling solubility data was first attempted by Cross et al.18 This investigation will use the equation of state approach to model the solubility data in both pure CO2 and CO2 modified with 3 mol % chloroform. The equation of state approach has already been shown to be a viable technique in modeling the solubility of a wide variety of organic solutes in supercritical fluids.49 This approach uses the EOS to predict the mixture fugacity coefficient, φˆ 2, of the chelate in the SC phase. The solubility of the supercritical fluid in the solid phase is negligible, and therefore, at equilibrium, the fugacity of the pure solid phase is equal to the mixture fugacity of the chelate in the supercritical fluid phase. Because the vapor pressure of the solid is low, the fugacity coefficient of the sublimated vapor is approximately equal to 1. At supercritical conditions, the Poynting correction (exponential term) is usually less than 10, but the fugacity coefficient, φˆ 2, can be quite small (e.g., between 10-3 and 10-6). Thus, it is primarily responsible for the large deviations from ideality and the large solubility enhancements of solutes in SCFs. Recently, Xu et al.50 illustrated that modeling solid/ fluid equilibrium with an equation of state is not always reliable with conventional numerical algorithms. This is because the solubility resulting from the equifugacity condition is a necessary, but not sufficient, condition for equilibrium. Sometimes, there exist multiple roots (solubilities) to the equifugacity criterion, and only the thermodynamically stable root or roots is the correct solution. Xu et al.50 use the tangent plane method51 for stability and a technique based on interval analysis52 to develop a method that guarantees identification of the thermodynamically stable (correct) solution to the solid/fluid equilibrium problem. That methodology is used in this investigation.

There are many different equations of state that can be used in the above formulation. Here, we have used the Peng-Robinson EOS53 with van der Waals-1 mixing rules (equations 1a and 1b), as first investigated for metal chelate systems by Cross et al.18 NC NC

am )

∑ ∑ yi yj xaiaj (1 - kij) i)1 j)1

(1a)

NC

bm )

yi bi ∑ i)1

(1b)

The mixture attractive and volume parameters, am and bm, respectively, are used in the equation of state. The volume root (compressibility factor) is used to calculate the fugacity coefficient, which is used to determine the solubility. The original Peng-Robinson formulation incorporates the principles of corresponding states theory to determine both the attractive, a, and the volume, b, parameters. This presents a problem in modeling metal chelate systems, because the critical properties of metal chelates, needed to find a and b, cannot be measured because the compounds usually degrade at temperatures around the normal boiling point. It was proposed by Cross et al.18 to regress the critical properties from the mixture solubility data. Because there are up to four possible parameters to be fit, a good representation of the data by the model would be expected, but this leaves little confidence in using the model to extrapolate, or even interpolate, the data. To reduce the number of parameters in this work, the critical temperature, Tc, and critical pressure, Pc, were estimated from Joback’s group contribution method,54 neglecting the contribution of the metal ion center. Joback’s method uses the normal boiling point, which, to our knowledge, is not available for Fe(acac)3. Nonetheless, the boiling point was estimated from the enthalpy of vaporization55 and the vapor pressure at the triplet point (approximately the melting point). The vapor pressure at the melting point was determined by extrapolating sublimation pressure data of Ribeiro da Silva et al.56 to the melting point, where the sublimation pressure and the vapor pressure are equal. This procedure yielded a boiling point for Fe(acetylacetonate)3 of 343 °C, which is close to published values of other tris acetylacetonates (pentanedionates), e.g., 340 °C for Cr(acac)3.57 The enthalpy of vaporization and the vapor pressure at the melting point were used to extrapolate the vapor pressure to a reduced temperature of 0.7, i.e., T ) 0.7 × Tc, so the Pitzer acentric factor could be determined from its definition,54 i.e., ω ) -log(Pvap/Pc)TR)0.7 - 1. The resulting critical properties are listed in Table 1. From eq 7, the Peng-Robinson equation of state was used to calculate the fugacity coefficient; the experimental solid density was from Roof;58 and the experimental sublimation pressure was from Fedotova et al.59 In this study, a modified Simplex method was used to regress the binary interaction parameter, k12. The objective function was the average absolute deviation (AAD). N

AAD )

exp pred |y2,i - y2,i | ∑ i)1

(2)

This objective function was chosen because it lends more

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Table 1. Pure-Component Parameters for CO2, Fe(acac)3, and CHCl3 component

CO2

Fe(acac)3

CHCl3

MW Tc [K] Pc [bar] ω Tb [°C] Vs [cm3/mol] Ad Bd bvdW σ

44.01 304.13 73.77 0.225

353.18 799.95a 19.56a 0.983b 343b 269.6c 37.578e 13733.3e 171.9 f 5.56

119.38 536.4 53.7 0.218 61.2

13.8 2.40

33.4 3.22

a Joback method, ref 54. b Estimated from method discussed in text. c Reference 58. d ln(Psub[Pa]) ) A - B/T[K]. e Reference 59. f Bondi method, ref 68.

Figure 4. Experimental solubility of Fe(acac)3 in CO2 modified with 3 mol % CHCl3 at 60 °C and model predictions from the PR EOS with zero (k23 ) 0) and one (k23 ) -0.1291) adjustable parameter.

two data points, we accept this discrepancy. The solubility was also measured in CO2 modified with 3 mol % chloroform. These data are illustrated in Figure 4. As seen in Figure 3, the isotherms of the chelate in pure CO2 behave similarly to those of other solids dissolved in SC CO2 in that they increase with pressure and temperature at higher pressures. The typical crossover pressure is observed at roughly 162 bar. The crossover pressure results from the competing effects of density and changes in the sublimation pressure with changes in temperature. Chloroform was chosen as a model contaminant for mixed metal/organic wastes, where effective extraction of both the organic and the metal would be desirable. The solubility of the chelate complex in an organic-modified SC CO2 phase would therefore be more pertinent. Upon addition of 3 mol % chloroform, the solubility increases by an average of 192%. Upon inspection of the residual Fe(acac)3 after depressurization, there was no evidence of phase changes, i.e., melting, nor did our model, which can identify solid/ liquid/vapor (SLV) equilibrium, indicate such. Therefore, we are confident that the measurements are simple solid/fluid equilibrium. The error bars in the figures and the error in Table 2 are a propagation of all experimental errors, including the standard deviation of the three sample concentrations taken for each condition, the uncertainty in the sample loop and collection solvent volumes, and the uncertainty in the temperature and pressure measurements. 4.2. Modeling. The solubility of Fe(acac)3 in supercritical carbon dioxide with and without the chloroform co-contaminant was modeled with the Peng-Robinson EOS using the van der Waals mixing rule. Because of the lack of critical property data, the Joback group contribution method was used to estimate the critical temperature and pressure. The boiling point of the

Figure 3. Experimental solubility of Fe(acac)3 in pure CO2 at 40 and 60 °C, along with results from the PR EOS model. There is only one regressed parameter in the model, k12, at each temperature.

weight to the higher solubilities, which generally have less experimental error and are sufficiently away from the mixture critical point, where the equation of state has better accuracy. However, the difference between the model and the experimental data is reported below as the more commonly used average absolute relative deviation (AARD). 4. Results and Discussion 4.1. Solubility. The solubility of Fe(acac)3 in SC CO2 was experimentally measured at 40 and 60 °C with pressures ranging from 90 to 300 bar (see Table 2 and Figure 3). There are two data points in the literature for this system in the pressure range investigated here.60 The present measurements are slightly higher (30-40%) than those values. Because Di Giacomo et al.60 did not include comparisons of the performance of their apparatus to others and because they have only

Table 2. Experimental Solubility of Fe(acac)3 in Pure CO2 at 40 and 60 °C and in CO2 Modified with 3 mol % CHCl3a CO2 (1)/Fe(acac)3 (2) 40 °C P [bar] 90.1 137.9 172.4 206.9 237.9 275.8 a

60 °C (

y2 10-5

3.06 × 1.55 × 10-4 2.07 × 10-4 2.63 × 10-4 2.90 × 10-4 3.17 × 10-4

10-6

4.4 × 1.3 × 10-5 3.2 × 10-5 1.9 × 10-5 2.3 × 10-5 2.1 × 10-5

60 °C/3% CHCl3 (3) (

y2 10-6

8.75 × 1.20 × 10-4 2.41 × 10-4 3.57 × 10-4 4.72 × 10-4 5.76 × 10-4

10-6

6.0 × 8.9 × 10-6 2.1 × 10-5 2.7 × 10-5 5.0 × 10-5 4.3 × 10-5

y2

(

4.33 × 10-4 7.33 × 10-4 9.78 × 10-4 1.21 × 10-3 1.34 × 10-3

1.3 × 10-5 6.5 × 10-5 6.0 × 10-5 8.2 × 10-5 7.9 × 10-5

Also shown are the corresponding error estimates determined from the propagation of all experimental errors.

Ind. Eng. Chem. Res., Vol. 40, No. 3, 2001 985 Table 3. Binary Interaction Parameters Used for the PR EOS Modeling, Along with the Resulting %AARD system

T [°C]

CO2/Fe(acac)3

40 60 60 60

CO2/Fe(acac)3/ 3% CHCl3 a

k12

k13

k23

0.1528 0.1590 0.1590 0.0525a 0 0.1590 0.0525a -0.1291

%AARD (w/o first pt) 11.3 (3.8) 15.3 (4.7) 27.6 (35.4) 5.7 (2.3)

Regressed from vapor-liquid equilibrium data of ref 45 at 60

°C.

chelate and its acentric factor were estimated by its experimental heat of vaporization and sublimation pressure near the melting point. The lines in Figure 3 show the results of the EOS model for both isotherms in pure CO2, regressing the temperature-dependent binary interaction parameter. Thus, there is only one adjustable parameter in this approach, and fair results are obtained, despite the fact that the method used to estimate critical properties was not originally intended for use with metal chelates. The solid line in Figure 4 shows the EOS model for the solubility of Fe(acac)3 in SC CO2 modified with 3 mol % chloroform at 60 °C. The binary interaction parameter between the CO2 solvent and the chloroform was regressed from vapor/liquid equilibria information45 at 60 °C. The interaction parameters between the chelate and solvent were taken from the binary solubility data (see Table 3). The interaction between the chelate and chloroform was set to zero for the model results shown in Figure 4. The model representation of the experimental data is fair but indicates that the equation of state underpredicts the interactions involved. This might be anticipated from a careful examination of the local composition results, as will be discussed below. To force a good representation from the model to the solubility of Fe(acac)3 in a 3 mol % CHCl3/ CO2 mixture, one can regress the Fe(acac)3/CHCl3 binary interaction parameter, k23, from the experimental data of the ternary system. As shown in Figure 4, the best fit (%AARD ) 5.7%) occurs with a k23 of -0.1291. This indicates that the geometric mean for the attractive parameter a23 is too small. An interaction parameter this large and negative usually indicates that chemical, rather than just physical, effects are present. A summary of the binary interaction parameters and the resulting average absolute relative deviation between the model and the experimental data from Figures 3 and 4 is shown in Table 3. The %AARD is shown with and without the lowest pressure point, which contributes the greatest amount to the %AARD. It should be restated that the objective function for the regressions was not %AARD, but AAD, which usually offers a more physically realistic representation. 4.3. Preferential Solvation. Because the solubility of Fe(acac)3 is significantly greater with added cosolvent, spectroscopy was used to measure the preferential solvation of metal chelates in SC CO2/cosolvent mixtures. Unfortunately, Fe(acac)3 does not exhibit any solvatochromic shifts with solvent density or added cosolvent, although it was reported to do so by Tingey et al.61 In fact, they used spectral shifts in peak maxima of Fe(acac)3 to estimate the local compositions of methanol around Fe(acac)3 in CO2/methanol mixtures. They formed the metal chelate in situ from FeCl3‚6H2O using a large (∼2500-fold) excess (mole:mole) of chelating agent. When the preformed metal chelate complex and, therefore, no excess chelating agent, is used, it was

found that the absorption spectrum of Fe(acac)3 does not shift with changing solvent environment. This is evident from literature data62,63 for Fe(acac)3 in liquid solvents, which show that the predominant peaks for Fe(acac)3 in ethanol are at 272, 351, and 431 nm. In chloroform, they are at 274, 353, and 437 nm, and in dioxane, they are at 273, 353, and 434 nm. In SC CO2, the peaks are at 272, 354, and 431 nm. In other words, there is no significant change in the absorption wavelengths of Fe(acac)3 with changing solvent environment. The apparent shifts measured by Tingey and co-workers were likely due to the presence of large quantities of excess chelating ligand in their system. Their method of complex formation might have also resulted in the extraction of chromium and nickel from the stainless steel vessel, forming a mixture of metal chelate complexes, which would have altered the observed spectra. Thus, the local compositions reported in Tingey et al. are actually just an artifact of their experimental technique. As a result, a new spectroscopic method was sought to determine the local compositions around metal chelate complexes in CO2/cosolvent mixtures. Fortunately, in Fe(acac)3, the intensities of the intraligand transition (π f π*) at ∼272 nm and the metal-to-ligand chargetransfer transition (n f d*) at ∼434 nm are very sensitive to the solvent environment.63 In ethanol at room temperature, this peak ratio is 9.33, in chloroform it is 16.2, and in dioxane it is 7.94.62,63 In this laboratory, the ratios in liquid chloroform at 60 °C were found to range from about 8.84 to 13.1 at pressures from 138 to 276 bar. The ratio in SC CO2 ranges between approximately 6.23 and 7.12 for pressures from 138 to 276 bar and temperatures from 40 to 60 °C. Thus, the changes in the peak intensity ratio of Fe(acac)3 could be used to estimate local compositions in SC CO2/ chloroform mixtures. The changes in peak intensity ratio were measured in 3 mol % chloroform/CO2 solutions at 60 °C. This temperature ensured that the mixture was a single phase at the pressures investigated, as confirmed by Scurto et al.45 To determine local compositions, it was also necessary to measure the intensity ratios in both pure SC CO2 and pure chloroform as a function of temperature and pressure. Table 4 shows the change in peak ratio for Fe(acac)3 in pure liquid chloroform at 60 °C for the range of experimental pressures investigated, as well as the values of the peak ratio in pure CO2 and in the 3 mol % chloroform/CO2 mixture. These experiments were performed in the same high-pressure optical cell used for the supercritical mixture. Note that these peak ratios are comparable to those reported by Barnum62 at room temperature. Measurement of the local composition of methanol around Fe(acac)3 was also attempted, but small changes in the shape of peaks in the Fe(acac)3/ CO2/methanol system spectra from those in spectra for either of the pure solvents precluded this investigation. To obtain estimates of local compositions from these data, the method developed by Kim and Johnston64 was followed. It assumes a linear contribution to the intensity ratio of the two solvents based upon volume fractions. Equation 3 can be used to directly calculate the local solvent mole fractions around the chelate complex solute.

Em ) y12Zm

( )

( )

E1 E3 + y32Zm Z12 Z32

(3)

986

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Table 4. Experimental Values of the Peak Intensity Ratio for Fe(acac)3 in Pure CO2, Pure Chloroform, and a 3 mol % Chloroform/CO2 Mixture at 60 °C as a Function of Pressurea Fe(acac)3 peak ratios (Ei ) A272 nm/A431 nm) at 60 °C

P [bar] 140.7 142.0 148.2 174.8 179.3 180.6 207.5 213.0 213.7 239.9 244.8 247.5 277.9 281.0 282.0

local mole E1 fraction (y23) E3 Em pure CO2 pure CHCl3 CO2/3% CHCl3 CO2/3% CHCl3 7.547

0.167

7.868

0.161

7.953

0.144

7.966

0.126

7.914

0.103

6.41 8.964 10.28 6.55 Figure 5. Comparison of the local composition of chloroform around Fe(acac)3 in a 3 mol % CHCl3/CO2 mixture with the percent increase in the solubility of Fe(acac)3 in CO2 when 3 mol % chloroform is added to the CO2. The solubility increases are at the same molar density (see text).

6.67 11.15 12.35 6.95 12.88 7.08

a Also shown are the local compositions of chloroform around Fe(acac)3 in the chloroform/CO2 mixture that were calculated from these data (see text).

E is a measurement of solvent strength (here, the intensity ratio of two of the characteristic peaks), and the subscript 1 refers to the primary solvent (CO2), 3 to the other solvent (chloroform), and m to the mixture at an intermediate composition. Zm, Z12, and Z32 refer to the coordination number around a solute molecule in the mixture, in pure solvent 1, and in pure solvent 3, respectively. To evaluate eq 3, eqs 4-6 must be used to estimate the necessary parameters.

( )( ) ( )( ) ( ) ( )( ) ( ) ( ) ( )( ) ( )

Zm Fm Z12 Fm Z32 ) y1 + y3 Z12 Z12 F1 r Z12 F3 y1Fm E1 y3Fm E°1 E3 ) + E 1 F1 r E1 E°3 F3

y1Fm E°3 E1 Zm y3Fm E3 ) + Z32 E3 F3 r E3 E°1 F1

( )

Z°32 ) Z°12

r

r

Z°32 Z°12

r

Z°12 Z°32

(4)

(5)

of the supercritical mixture were estimated using the Peng-Robinson equation of state53 with binary interaction parameter k13 obtained from regressing the vaporliquid equilibrium data of Scurto et al.45 and the Span and Wagner EOS43 for pure CO2. Because it is known that the Peng-Robinson EOS has some difficulties in estimating supercritical densities, the density was calculated both for the pure CO2 and for the supercritical chloroform/CO2 mixture. The ratio of these values (mixture/pure CO2) was then multiplied by the Span and Wagner CO2 density to estimate the chloroform/ CO2 density. It is recognized that an EOS cannot provide extremely accurate values for supercritical fluid mixtures densities. Only experimental density measurements, which were not available in conjunction with this study, can provide accurate values. Nonetheless, this estimation technique has been used in previous work35 and it is believed to provide reasonable estimates and the appropriate trends. The size parameter for the chelate complex, which for Fe(acac)3 was calculated to be 171.9 cm3/mol, was estimated using a well-known method outlined by Bondi.68 For CO2 and CHCl3, the actual van der Waals size parameter was used

bvdW )

7

2 + 10 exp [ /9(R0.825 - R0.825 23 32 )] 0.825 2 + 10 exp [7/9(R21 - R0.825 12 )]

(6)

In these equations, y1 and y3 are the mole fractions of solvent and cosolvent, respectively; Fm, F1, and F3 are the mixture, pure solvent, and pure cosolvent densities, respectively; E°1 and E°3 are the experimentally measured peak ratios recorded at the reference state (the highest pressure studied); the subscript r indicates that the properties within must be evaluated at the same reduced number density as that of the system, i.e., bmFm; (Z°32/Z°12) is a reference coordination number ratio; and Rij is the ratio of molecular radii of molecule i to molecule j. A more detailed discussion of these calculations can be found in Kim and Johnston64 and Zhang et al.35 The SC CO2 density was found from the equation of state of Span and Wagner.43 The chloroform density was calculated at elevated pressures using interpolated isothermal compressibility factors from Easteal and Woolf65 and Kumagai and Takahashi66 and normal liquid densities from Morgan and Lowry.67 The densities

0.0401677RTc Pc

along with the conventional mixing rules

bm )

∑i ∑j yi yj bij ) y21b1 + 2y1 y3b13 + y23b3 b13 )

[

]

1/3 b1/3 1 + b3 2

3

With these data, estimation of the local composition around Fe(acac)3 is possible. Figure 5 presents the local solvation results for chloroform around Fe(acac)3 in a supercritical CO2/3 mol % chloroform mixture. This local solvation trend is similar to those found in the literature for other supercritical systems.29,31,32 As the system density and pressure increase, the extent of local solvation decreases. The local compositions range from over four times the bulk loading at low densities to about twice the bulk loading at high densities. These results indicate that, like other organic solutes, metal chelate complexes can

Ind. Eng. Chem. Res., Vol. 40, No. 3, 2001 987

Figure 6. Solubility of Fe(acac)3 in CO2 and a 3 mol % CHCl3/ CO2 mixture at 60 °C as a function of molar density.

be preferentially solvated by cosolvents that are intermediate in size and volatility between the metal chelate and CO2. This preferential solvation might, at least in part, account for the solubility increase found when chloroform was added to CO2. Figure 6 is a plot of the logarithm of the experimental solubilities as a function of density. As has been observed by many researchers, these plots are relatively linear.69 However, at a given density, the solubility of Fe(acac)3 in the CO2/chloroform mixture is significantly higher than that in pure CO2. Although the EOS model can predict the significant density increase at a particular temperature and pressure with the addition of a 3 mol % chloroform, it does not account for specific interactions or strong attractions that might result in preferential solvation of the solute by the co-contaminant. The distinct difference in the two curves in Figure 6 suggests that the density increase is not the only factor responsible for the increase in the solubility of Fe(acac)3 in the CO2/chloroform mixture. Moreover, the spectroscopic measurements presented herein show that the local compositions of chloroform around Fe(acac)3 in SC CO2 are substantially greater than the bulk values. Shown in Figure 5 is a plot of the solubility increase experienced by Fe(acac)3 when 3 mol % chloroform is added to the SC CO2. These increases are calculated at the same bulk solution density. This was accomplished by interpolating the binary solubility data to find the Fe(acac)3 solubility at the same mixture density (in mol/cm3) rather than the same pressure of the cosolvent case. This approach should eliminate the effect of the increased density at a particular pressure when 3 mol % chloroform is added and, therefore, represent the true solubility enhancement. If the increased solubility was entirely an effect of density, then the percent solubility increase at the same mixture density should tend to zero. One can see that the region of greatest enhancement in solubility roughly correlates with the region of greatest local composition enhancement. Thus, it is concluded that the increased solubility of Fe(acac)3 in SC CO2 with 3 mol % chloroform is likely due in part to the increased solution density, but is also due to the preferential solvation of the solute by the chloroform. 5. Conclusions New measurements of the solubility of Fe(acac)3 in SC CO2 with and without the polar modifier or cocontaminant chloroform, have been presented. Fe(acac)3 shows modest solubility in pure CO2, similar to that of

phenanthrene.44 As both temperature and pressure increase, the solubility of this complex increases when the pressure is above the crossover pressure, which is roughly 160 bar. Upon addition of 3 mol % chloroform, the solubility at a given pressure increases by about a factor of 2, confirming that the present of an organic co-contaminant, such as chloroform, would reduce the cost of supercritical fluid extraction of metal contaminants. In addition, spectroscopic measurements are presented of the extent of local solvation around the metal chelate complex, Fe(acac)3, in a SC CO2/3 mol % chloroform mixture. Modeling results are presented for the solubility of Fe(acac)3 in SC CO2 with and without 3 mol % chloroform using the Peng-Robinson equation of state with van der Waals mixing rules. Using a single binary interaction parameter between Fe(acac)3 and CO2 provided a good correlation for the two pure CO2 isotherms, but the solubility in the cosolvent system was underpredicted. The solubility, spectroscopic local composition, and modeling results suggest that both density increases and local composition enhancements play a role in determining the solubility increase of Fe(acac)3 in SC CO2 when a cosolvent is added. Thus, a detailed understanding of complex extraction systems would require an accurate view of the molecular-scale interactions, as well as the mean field effects reflected in the equation of state. Nonetheless, the EOS method predicts the correct trends in the temperature, pressure, and cosolvent effects and, thus, will be an effective tool in the design of separation processes and equipment for the in situ extraction of metals with ligands in supercritical fluids. Acknowledgment Acknowledgment is made to the Department of Energy (DE-FG07-96ER14691 and DE-FG02-98ER14924) and the National Science Foundation (EEC97-00537CRCD) for financial support of this work. List of Symbols R ) attractive function for PR EOS φˆ 2 ) fugacity coefficient F ) density [mol/cm3] σ ) van der Waals diameter ω ) acentric factor A ) Antoine equation constant, ln(Psub[Pa]) ) A - B/T[K] aij ) Peng-Robinson attractive parameter B ) Antoine equation constant, ln(Psub[Pa]) ) A - B/T[K] bi ) PR, vdW, or Bondi volume parameter [cm3/mol] Ei ) absorbance peak ratio EOS ) equation of state exp ) experimental f ) fugacity [bar] kij ) binary interaction parameter MW ) molecular weight [g/(g mol)] NC ) number of components P, Psub, Pvap ) system, sublimation, and vapor pressures, respectively Pc ) critical pressure [bar] PR ) Peng-Robinson pred ) predicted from model R ) gas constant [83.14 bar cm3/(mol K)] Rij ) ratio of diameters SC ) supercritical Tb ) normal boiling point [°C]

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Tc ) critical temperature [K] TR ) reduced temperature (T/Tc) vdW ) van der Waals Vs ) solid molar volume [cm3/mol] yi ) bulk mole fraction yij ) local mole fraction of i around j Z ) compressibility factor Zij ) coordination number

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Received for review July 17, 2000 Revised manuscript received October 20, 2000 Accepted October 22, 2000 IE000665+