J. Phys. Chem. B 1999, 103, 10007-10016
10007
Spectroscopic Measurement of Solute and Cosolvent Partitioning between Supercritical CO2 and Polymers N. H. Brantley,† D. Bush, S. G. Kazarian,‡ and C. A. Eckert* School of Chemical Engineering and Specialty Separations Center, Georgia Institute of Technology, Atlanta, Georgia 30332-0100 ReceiVed: June 22, 1999; In Final Form: September 3, 1999
Cosolvents exhibit significant effects on the partitioning behavior of dilute solutes between a supercritical CO2 fluid phase and cross-linked siloxane-based polymers. A spectroscopic technique was developed and applied that allows us to measure the partition coefficients of both the cosolvents and solutes between the two phases. The Sanchez-Lacombe lattice fluid equation of state was extended to represent a two-phase, four-component system and was quantitatively successful in representing the volumetric and phase-equilibria properties of such systems. We then apply the model and our data to investigate the magnitudes of stationaryphase effects in supercritical fluid chromatography and explore opportunities to use the model for a priori prediction of separation.
Introduction Supercritical fluids have been used for a number of polymer processes including polymer fractionation,1-4 extraction of molecules from polymer matrices,5-8 and impregnation of polymers with additives.9-12 An advantage of a supercritical fluid is that its solvent strength can be adjusted with pressure, which enables tuning of the selectivity and degree of extraction and the degree of loading during an impregnation process. In addition, supercritical fluids are soluble in many polymers, often resulting in substantial swelling of the polymer matrix, which enhances solute diffusivities. Moreover, supercritical fluids can be removed from the polymer phase through depressurization. The addition of a small amount of cosolvent to the supercritical fluid is often used to enhance the properties of the fluid by selective interaction with the solutes or simply by changing the polarity of the fluid. In a polymer system, both the fluid and cosolvent are generally soluble in the polymer, and their behavior affects significantly the solubility of solutes. A key parameter for the design of supercritical fluid extraction and impregnation processes involving polymers is the partition coefficient of the solutes between the two phases. However, much of the literature on supercritical fluid extraction and impregnation characterizes only the final polymer product to determine whether the process was successful. Experimental challenges, such as sampling at high pressure, have posed an obstacle for the measurement of thermodynamic properties in supercritical fluid extraction and impregnation systems. We show a spectroscopic method for the accurate determination of the thermodynamic partition coefficients for multicomponent systems consisting of polymer, supercritical fluid, cosolvent(s), and solute(s) and use this information to describe the effects of cosolvents on solute partitioning. The partitioning of naphthalene, acridine, and 2-naphthol between a supercritical fluid phase, including pure and CO2 modified with methanol* To whom correspondence should be addressed. E-mail: cae@che. gatech.edu. † Current address: Albemarle Process Development Center, Gulf States Road, Baton Rouge, LA 70805. ‡ Current address: Department Chemical Engineering, Imperial College, Prince Consort Road, London SW7 2BY, U.K.
d4 and 2-propanol-d8, and a cross-linked polymer phase, including poly(dimethylsiloxane) (PDMS) and poly(cyanopropylmethylsiloxane) (PCPMS), has been measured over a wide pressure range at 40 °C. A lattice fluid model including a term to account for the cross-linked nature of the polymer is evaluated for its use to describe the thermodynamics of these systems. One area of immediate application of this work is supercritical fluid chromatography (SFC). There are really two aspects of SFC where the effect of a cosolvent on solute partitioning is important. The obvious one is in the prediction or correlation of retention and selectivity, and we discuss the extent of these effects below. However, a perhaps narrower but more profound application is in the use of SFC to measure thermophysical properties, and that too is addressed. Theory. Sanchez-Lacombe Lattice Fluid Equation of State Thermodynamic models of supercritical fluid extraction and impregnation involving polymer systems are often complicated because of the dissimilarity of the two phases. However, lattice fluid models provide a good description of the polymer phase and have also been used to describe satisfactorily fluid phases. Gas sorption in many types of polymeric matrices13-15 and the resulting effects such as swelling and glass-transition temperature (Tg) depression16,17 have been modeled with generally good results. In addition, lattice fluid models have given adequate descriptions of solid solubilities in pure supercritical fluids,18-23 vapor-liquid equilibrium (VLE) of volatile components such as cosolvents,24,25 and high-pressure VLE of low-molecularweight chain molecules in compressed fluids.26,27 The convenience of lattice fluid models for describing both phases has been utilized for describing the partitioning of a third component in a supercritical fluid-polymer system. Condo et al. modeled the partition coefficients of five polar and nonpolar organic solids between supercritical CO2 and cross-linked PDMS swollen with CO2.28 West et al. used a lattice fluid model to describe the partitioning of three cosolvents between a modified supercritical CO2 phase and a swollen cross-linked PDMS phase.29 However, the extension of the lattice fluid model to
10.1021/jp9920646 CCC: $18.00 © 1999 American Chemical Society Published on Web 10/14/1999
10008 J. Phys. Chem. B, Vol. 103, No. 45, 1999 describe the partitioning of solutes between a cosolvent-modified supercritical fluid phase and a polymer phase has not been reported in the literature. The theory of Sanchez and Lacombe is a generalization of lattice fluid theory to multicomponent systems that assumes that the polymer has a flexible liquid structure. The SanchezLacombe (SL) theory has been further modified to account for the effects of polymer cross-linking, allowing a consistent and unified treatment of systems involving a swollen rubber. A full development of this theory can be found in the literature.30-32 Experimental Section Vincent et al. used an FTIR spectroscopic method to quantify the concentration of cosolvents in both a cross-linked PDMS phase and a high-pressure CO2 phase.33 The spectroscopic method developed in the present study was an extension of this method that allows the measurement of solute concentrations as low as a part per million in each phase. This degree of sensitivity, which is not possible using FTIR for the solutes in this study, is achieved using UV-visible spectroscopy. The optical cell was equipped with BaF2 windows, which are transparent in both the infrared and ultraviolet-visible regions of the spectrum, allowing partition coefficients to be measured for both cosolvent and solute in a single experiment. Swelling of the two polymers used in this study was measured by an elongation technique.33-35 Swelling data were necessary for the spectroscopic determination of the partition coefficients and were used to calculate the CO2-polymer binary interaction parameters for the application of the Sanchez-Lacombe lattice fluid model. Apparatus. The FTIR spectrometer was a Nicolet Impact 400D using Omnic 2.0 operating software. The detector was a liquid nitrogen cooled MCT detector, and the resolution was 2 cm-1. The UV-visible spectrometer was a Hewlett-Packard 6594. The detector was a 1024 element diode array with a resolution of 1.0 nm. Details of the design of the high-pressure optical cell used in this study can be found elsewhere.6 This cell has the advantage of allowing the fluid and polymer phases to be studied separately under identical conditions.36 A level sight gauge (model 11-T-32, Jerguson Gage & Valve Co.) with quartz windows was used to observe the swelling of the polymers. Materials. PDMS with an average molecular weight of 94 300 was purchased from Aldrich. PCPMS was purchased from Supelco (MTO-OV-105). SFC grade carbon dioxide (99.99% purity) was purchased from Matheson. Trace amounts of H2O was removed from the carbon dioxide using molecular sieves supplied by Matheson. Azo-tert-butane (97% purity) was purchased from Aldrich. The deuterated cosolvents, methanol-d4 (99.8% isotope purity) and 2-propanol-d8 (99%+ isotope purity) were purchased from Aldrich. The use of deuterated cosolvents was necessary in the infrared studies in order to separate their spectral features from absorbances due to supercritical CO2 and the polymer phases. Undeuterated cosolvents, methanol (99.8%, ACS Reagent) and 2-propanol (99.5%, ACS Reagent), were also purchased from Aldrich and used in the polymer swelling studies. Polymer Film Preparation. Azo-tert-butane (ATB) was employed to cross-link the polymers in this study. This chemical has been used to cross-link siloxane polymers coated on chromatographic columns and has been shown to leave no detectable residue.37 PDMS films were made as follows. Amounts of 11.052 g of PDMS and 1.144 g of ATB were dissolved in 45 mL of dichloromethane. Glass slides were then dipped in the mixture and allowed to dry under N2 for 24 h.
Brantley et al.
Figure 1. Schematic diagram of cell used for in situ spectroscopic measurement of cosolvent and solute partitioning between polymer and fluid phases.
The polymer-covered slides were then cured at 230 °C for 23.5 h. The polymer was washed with dichloromethane and vacuumdried. The degree of cross-linking was determined to be 1.03 × 10-4 mol/(g polymer) from equilibrium swelling in benzene at 25 °C.37-41 PCPMS films were made by a similar procedure, adding 6.966 g of polymer and 0.679 g of ATB to 25 mL of dichloromethane and then proceeding as above. The degree of cross-linking was estimated to be 8.16 × 10-5 mol/g polymer by using the equilibrium swelling in a benzene technique developed for PDMS. High-Pressure Swelling Experiments. The swelling of PDMS and PCPMS was measured for pure CO2 over a range 0-180 bar. The swelling of these two polymers in the cosolventmodified systems was measured over the range 70-180 bar, which is the range of pressure for which the solute partitioning measurements were made. In Situ Partitioning Experiments. Figure 1 is a schematic of the high-pressure optical cell used in this study. A polymer film was cut in the shape of a disk from a clean, dry polymer sheet as prepared above. This film was secured in path A of the cell, while path B contained no polymer film. The temperature was controlled to within (0.2 °C using Omega electric cartridge heaters and an Omega model CN9000A temperature controller. The pressure was measured to within (0.1 bar using a Druck model PDCR 911 pressure transducer attached to a Druck model DPI 260 readout. Before each partitioning experiment, the cell was evacuated, then purged with flowing CO2 (50 °C, 225 bar) for 24-48 h to extract any remaining cosolvent and solute from the prior experiment. Solute was added to the clean cell by first dissolving the solute in dichloromethane, then injecting an aliquot of this solution into the cell. The dichloromethane was allowed to evaporate in an N2 environment. With this method overall solute concentrations of 2.7 × 10-7 M were achieved. If cosolvent was to be used in the partitioning experiment, a predetermined volume was then injected into the cell while under the N2 environment. The partitioning experiments proceeded as follows. The cell was charged with CO2 to approximately 75 bar. The UV-visible spectra of the solute in path A of the cell (polymer containing) were monitored until there was no change in absorption intensity, indicating equilibrium partitioning. Upon reaching equilibrium, the UV-visible spectra of the solute was recorded through both the fluid and polymer cell paths. For experiments with a cosolvent present, the cell was then placed in the FTIR and spectra of both the fluid and polymer cell paths were measured. Details of cosolvent partitioning measurements can be found in the work by Vincent et al.33 The pressure was then increased incrementally up to approximately 180 bar, allowing equilibrium to be reached at each pressure and recording necessary spectra. Figure 2 shows sample UV-visible spectra of 2-naphthol in both the fluid and polymer phases taken during one of our partitioning experiments.
Solute and Cosolvent Partitioning
J. Phys. Chem. B, Vol. 103, No. 45, 1999 10009
Figure 2. UV-visible spectra of 2-naphthol in the fluid phase (dashed line) and polymer phase (solid line). Note that the path length of the fluid phase was much larger than the path length of the polymer phase, resulting in a larger absorbance in the fluid than in the polymer even though the 2-naphthol concentration is larger in the polymer.
The concentration of solute and/or cosolvent was determined from the measured spectra by applying Beer’s law. Solute concentrations were determined from the maximum absorbance of a peak in the UV-visible spectra. Peak height was used for quantification of the UV-visible data, since the peak area in this method of spectroscopy can change considerably depending on molecular environment (i.e., solvent). Cosolvent concentrations were determined from the integrated area of the 2ν(O-H) band of the alcohols. The area was utilized for IR quantification, since this absorbance was found to be relatively independent of molecular environment for the systems we studied. A correction was made to account for cosolvent or solute in the fluid phase surrounding the polymer in path A. In this correction the polymer length is determined from the highpressure swelling results. Molar absorptivites, which are necessary for the application of Beer’s law, were determined in pure CO2 and pure PDMS for both the solutes and cosolvents used in this study, and in the case of the solutes, they were measured in pure methanol and 2-propanol. Estimates of the cosolvent and solute molar absorptivities in the swollen polymer phase were obtained by averaging values in the pure components, weighing each component according to the molar composition of the swollen phase. In all cases, the difference between the molar absorptivities measured in the pure solvents was less than 8-16%. Thus, we estimate the error in the molar absorptivities determined for the swollen polymer phase to be less than these bracketing values and realistically to be about a few percent. Partition coefficients were calculated from Beer’s law by
K)
C p Ap f lf ) Cf Af p lp
(1)
where the subscripts p and f refer to the polymer phase and fluid phase, respectively, C is concentration, A is the spectroscopic absorbance, is the molar absorptivity, and l is path length. The experimental error for our data was estimated to be less than 5% at the lowest pressures studied and increases with pressure to approximately 15% at the highest pressures studied. The increase in error is due to the decrease in spectroscopic absorbance intensity resulting from lower concentrations of the solutes or cosolvents in the polymer phase as the pressure is increased. Experimental Results and Discussion Equilibrium Swelling. The equilibrium swelling of a crosslinked PDMS film and a cross-linked PCPMS film by pure CO2 at 40 °C is shown in Figure 3 as a function of pressure. The
Figure 3. Pressure dependence of the equilibrium swelling of crosslinked PDMS (b) and cross-linked PCPMS (4) in pure CO2 at 40 °C. The solid line is the SL EOS fit of the PDMS swelling data.
Figure 4. Pressure dependence of the equilibrium swelling of crosslinked PDMS (O) and cross-linked PCPMS (4) in the methanol-d4-modified CO2, and cross-linked PDMS (0) in 2-propanol-d8--modified CO2 at 40 °C. The overall cosolvent concentrations are 0.30 M. The solid line is the SL EOS prediction of the swelling of PDMS in the presence of methanol-d4-modified CO2.
equilibrium swelling is expressed in terms of the ratio of the swollen volume to the original volume. The unswollen PDMS and PCPMS film thicknesses were measured to be 0.017 ( 0.002 and 0.036 ( 0.002 cm, respectively, using calipers. The swelling measurements of PDMS were consistent with literature data, exhibiting a sigmoidal shape versus pressure.33-35 No literature data for the swelling of PCPMS were available. The swollen volume of PDMS and PCPMS at 180 bar is approximately double its volume under atmospheric conditions. There is very little difference between the swelling of PDMS and the swelling of PCPMS under these conditions. The equilibrium swelling of PDMS at 40 °C in the presence of a 0.30 M methanol-modified CO2 solution and a 0.30 M 2-propanol modified CO2 solution over the pressure range 70180 bar is shown in Figure 4. Below approximately 82 bar, there are two fluid phases in addition to the polymer phase. The swollen volume in this two-phase region was measured to be up to 150% more than the swollen volume by pure CO2. Above the phase transition around 82 bar, in which only a single fluid phase is present, the swollen volume was measured to be less than 10% more in the cosolvent-modified system, decreasing as the pressure was increased. These data compared well to the cosolvent-modified CO2 swelling behavior of PDMS under similar conditions reported by Vincent et al.33 The equilibrium swelling of PCPMS at 40 °C in the presence of a 0.30 M methanol-modified CO2 solution is also shown in Figure 4. These swelling data in the range 70-180 bar show behavior nearly identical to that of PDMS as described above.
10010 J. Phys. Chem. B, Vol. 103, No. 45, 1999
Figure 5. Pressure dependence of the partition coefficient of cosolvents between the polymer phase and fluid phase at 40 °C: (O) methanol-d4 partitioning between PDMS and modified CO2 phases; (0) methanold4 partitioning between PCPMS and modified CO2 phases; (4) 2-propanol-d8 partitioning between PDMS and modified CO2 phases. Solid line is SL EOS fit of methanol partitioning between PDMS and 0.30 M methanol-d4-modified CO2.
In addition, the swelling behavior at lower pressures is very similar to literature data for PDMS at similar conditions. Equilibrium Cosolvent Partitioning. The equilibrium partition coefficients of the cosolvents methanol and 2-propanol between the fluid and polymer phases are plotted in Figure 5 as a function of pressure. Methanol partitioning was measured for both PDMS and PCPMS, whereas 2-propanol was measured only for PDMS. The overall cosolvent concentration was 0.30 M, and the experimental temperature was 40 °C. The general trend of the three measured isotherms was the same: partition coefficients on the order of 10 near 80 bar, then a rapid decrease with increasing pressure with magnitudes between 2 and 4 at the highest pressures studied. The decrease in KC was most probably due to the increase in the solvating power of carbon dioxide, concomitant with the density increase.38-40 Thus, there was a significantly higher concentration of cosolvent in the polymer phase under all conditions. The solute partitioning studies discussed in the next section examine what effects the cosolvent partitioning had on solute partitioning. Figure 5 shows that the partition coefficients of methanol were significantly higher in the PCPMS system compared to the system containing PDMS. Methanol’s higher affinity for the PCPMS environment suggests that the polarity of the polymer phase affects the partitioning of a polar cosolvent. Equilibrium Solute Partitioning. The equilibrium partition coefficients of naphthalene between the fluid and PDMS phases are plotted in Figure 6 as a function of pressure. The three sets of data presented include fluid phases of pure CO2, methanolmodified CO2, and 2-propanol-modified CO2, with both cosolvents at an overall concentration of 0.30 M. From these data we see that naphthalene partitioning follows the same trend in all three systems. At the lowest pressures studied (∼75 bar), partitioning greatly favors the polymer phase by a factor of 102103. As CO2 was added and pressure increased to approximately 90 bar, we see naphthalene partition coefficients decrease rapidly by over 2 orders of magnitude. Above 90 bar, naphthalene partition coefficients decrease only slightly with the addition of CO2, resulting in a partition coefficient between 2 and 3 at the highest pressures studied. Comparing the data for pure CO2 and the data for the two cosolvent-modified systems reveals that naphthalene partition coefficients were significantly decreased for pressures below about 90 bar with the addition of a cosolvent. However, above 90 bar naphthalene partition coefficients are nearly equal within experimental error for all
Brantley et al.
Figure 6. Pressure dependence of the partition coefficient of naphthalene between PDMS and fluid at 40 °C: (b) pure CO2; (0) 0.30 M methanol-d4-modified CO2; (4) 0.30 M 2-propanol-d8-modified CO2. The lines are the SL EOS fit of naphthalene partitioning: (solid line) pure CO2; (dotted-dashed line) 0.30 M methanol-d4-modified CO2; (dashed line) 0.30 M 2-propanol-d8-modified CO2.
Figure 7. Pressure dependence of the partition coefficient of 2-naphthol between PDMS and fluid at 40 °C: (b) pure CO2; (0) 0.30 M methanol-d4-modified CO2; (4) 0.30 M 2-propanol-d8-modified CO2. The lines are the SL EOS fit of 2-naphthol partitioning: (solid line) pure CO2; (dotted-dashed line) 0.30 M methanol-d4-modified CO2; (dashed line) 0.30 M 2-propanol-d8-modified CO2.
three systems studied. We attribute this result to the decrease in the effect of the cosolvent on the solvent strength of the fluid phase as CO2 density is increased, since our experiments were run at constant cosolvent concentration, not mole fraction. A comparison of the two cosolvents shows that 2-propanol has a larger effect on naphthalene partition coefficients than methanol for the conditions we studied. The equilibrium partition coefficients of 2-naphthol between the fluid and PDMS phases are plotted in Figure 7 as a function of pressure. Again, the three sets of data presented include fluid phases of pure CO2, methanol-modified CO2, and 2-propanolmodified CO2, with both cosolvents at an overall concentration of 0.30 M. The partition coefficients of 2-naphthol follow the same trend as that of naphthalene, having large values at low pressures and decreasing with increasing pressure. We do note slight differences from the naphthalene data, however. The effect of cosolvent on the partition coefficients of 2-naphthol at high pressures was different from its effect on naphthalene. We see similar partition coefficients for both 2-naphthol and naphthalene when the fluid phase is pure CO2. However, at high pressures the addition of a cosolvent may have very slightly increased the partition coefficient of naphthalene, whereas the data for 2-naphthol indicate a slight decrease in its partition coefficient with the addition of a cosolvent. We suggest that since 2-naphthol is more polar than naphthalene, it was affected more by the presence of the polar cosolvent. The fact that 2-naphthol favors the cosolvent-modified fluid phase more than naphthalene
Solute and Cosolvent Partitioning
Figure 8. Pressure dependence of the partition coefficient of acridine between PDMS and fluid at 40 °C: (b) pure CO2; (0) 0.30 M methanol-d4-modified CO2; (4) 0.30 M 2-propanol-d8-modified CO2. The lines are the SL EOS fit of acridine partitioning: (solid line) pure CO2; (dotted-dashed line) 0.30 M methanol-d4-modified CO2; (dashed line) 0.30 M 2-propanol-d8-modified CO2.
J. Phys. Chem. B, Vol. 103, No. 45, 1999 10011
Figure 10. Pressure dependence of the partition coefficient of 2-naphthol between PCPMS and fluid at 40 °C: (b) pure CO2; (0) 0.30 M methanol-d4-modified CO2.
TABLE 1: Solvent, Polymer, and Cosolvent Parameters for the Lattice Fluid Model
CO2 PDMS methanol 2-propanol
Mw (g/mol)
* (kJ/mol)
ν* (cm3/mol)
r
44.01 308,000 32.04 60.10
2.73 3.96 3.90 3.32
5.88 13.11 3.24 3.89
5.25 21280 10.72 15.83
TABLE 2: Solid Parameters for the Lattice Fluid Model Mw * ν* (g/mol) (kJ/mol) (cm3/mol) naphthalene 128.17 2-naphthol 144.17 acridine 179.22
5.59 4.29 5.66
12.53 4.35 11.13
r 9.33 22.90 14.10
∆Hfus Tm Fsolid (kJ/mol) (K) (g/cm3) 19.4 18.8 20.7
353 1.144 396 1.280 380 1.005
Modeling Results and Discussion Figure 9. Pressure dependence of the partition coefficient of naphthalene between PCPMS and fluid at 40 °C: (b) pure CO2; (0) 0.30 M methanol-d4-modified CO2.
at high pressures, which suggests that the change in polarity of the fluid phase upon addition of a polar cosolvent influenced the solute’s partition coefficient more than the change in the polarity of the polymer phase. Also, hydrogen bonding with the cosolvent gives the same result. The equilibrium partition coefficients of acridine between the fluid and PDMS phases are plotted in Figure 8 as a function of pressure. Again, the three sets of data presented include fluid phases of pure CO2, methanol-modified CO2, and 2-propanolmodified CO2, with both cosolvents at an overall concentration of 0.30 M. The partitioning behavior of acridine was very similar to 2-naphthol and can be explained similarly. Figures 9 and 10 show the equilibrium partition coefficients of naphthalene and 2-naphthol, respectively, between the fluid and PCPMS phases as a function of pressure. For this polymer, methanol was the only cosolvent studied. The general trend of these two solutes for PCPMS was the same as that for PDMS. In addition, the magnitudes of the partition coefficients for the solute naphthalene were very similar in both polymers. However, the magnitudes of the partition coefficients of 2-naphthol were significantly larger in PCPMS. This result indicates that the 2-naphthol molecules favored the more polar environment of the PCPMS compared to PDMS. Also, we did not see a reduction of 2-naphthol’s partition coefficient at higher pressures upon the addition of the cosolvent as we did see for the PDMS experiment. This may be due in part to a higher concentration of methanol in the PCPMS phase than in the PDMS phase for a given pressure in the higher pressure region, which was discussed previously and is shown in Figure 5.
There were four components in our experiments: CO2 (1), cross-linked polymer (2), cosolvent (3), and solute (4). There are two phases present: the fluid and the polymer. The CO2, cosolvent, and solute all partition between them. We assume the polymer solubility in the fluid phase to be negligible. Equilibrium Calculations. The Sanchez-Lacombe modified lattice fluid model was used to calculate the chemical potentials in each phase, with the composition of the components in the lattice determined by applying a modified Newton-Raphson procedure41 until the equilibrium conditions were satisfied. Interaction parameters for the binary pairs CO2-polymer, CO2cosolvent, and CO2-solid were determined prior to modeling our cosolvent and solute partitioning data, from our polymer swelling data, from literature CO2-cosolvent vapor-liquid equilibrium (VLE) data, and from literature solid solubility in CO2 data. Lattice Fluid Parameters. The lattice fluid parameters for CO2, PDMS, methanol, and 2-propanol, which we used in this work, are listed in Table 1. We found no parameters for PCPMS in the literature and little thermodynamic data to regress parameters. However, since our experimental results show that the volumetric properties of this polymer are very similar to the properties of PDMS when exposed to CO2 and cosolventmodified CO2, we used the PDMS parameters as an estimate of the PCPMS parameters. The lattice fluid parameters and necessary thermodynamic data for the solutes of this study are listed in Table 2. The parameters were calculated by the method described by Sanchez and Lacombe.30 The data required in the method were estimated by the DIPPR 801 thermophysical property database for naphthalene and acridine. Data from the MSDS supplied by Aldrich was used for 2-naphthol.
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TABLE 3: Binary Interaction Parameters Determined for CO2-Solute, ζ14
naphthalene 2-naphthol acridine
35 °C
45 °C
40 °C (average)
1.023 0.896 0.999
1.039 0.902 0.978
1.031 0.899 0.988
CO2-Polymer Swelling Equilibrium. The solid line in Figure 3 is the SL equation of state (EOS) fit of our experimental volumetric behavior of cross-linked PDMS when exposed to pure CO2 at 40 °C. Our choice of CO2 parameters results in a discontinuity in the first derivative of the fit near 90 bar. This indicates a vapor-liquid transition in the fluid phase, but as shown, the parameters allow for a reasonable fit of the volumetric behavior of the polymer. The regressed CO2-PDMS binary interaction parameter was determined to be ζ12 ) 1.045. Fitting our experimental volumetric behavior of cross-linked PCPMS using the PDMS lattice fluid parameters resulted in a CO2-polymer binary interaction parameter of ζ12 ) 1.052. These values are used in all subsequent calculations to describe the interaction of CO2 with the polymer. CO2-Cosolvent Vapor-Liquid Equilibria. The binary interaction parameters for the SL EOS were determined from literature high-pressure vapor-liquid equilibria data for methanol42,43 and 2-propanol44 with CO2 at 40 °C. The regressed CO2-methanol binary interaction parameter was determined to be ζ13 ) 0.913, and for CO2-2-propanol ζ13 ) 0.875. CO2-Solute Solubility. The CO2-solute binary interaction parameters were determined from solubility data at 35 and 45 °C for naphthalene,45-50 2-naphthol,51,52 and acridine51-53 (see Table 3). CO2-Polymer-Cosolvent Sorption and Swelling. West et al. showed that a single polymer-cosolvent binary interaction parameter was acceptable for describing both swelling and sorption in the high-pressure range (approximately 80-180 bar).29 The polymer-cosolvent binary interaction parameter was found from a fit of cosolvent partitioning data. The fluid phase consisted of only CO2 and cosolvent, since the cross-linked polymer was assumed to be insoluble. The solid line in Figure 5 shows the result of fitting the partitioning of methanol between the PDMS and fluid phases. The regressed PDMS-methanol binary interaction parameter was determined to be ζ23 ) 0.890. We see that the model was capable of capturing both the shape of the isotherm and magnitude of the partition coefficients. This binary interaction parameter was used to predict the volumetric behavior of this system, and the results are shown as the solid line in Figure 4. The model predicted a fairly accurate swelling isotherm above 85 bar, with only a slight negative deviation. However, the model was not able to capture the higher degree of swelling at pressures below 85 bar, suggesting some kind of composition (pressure) dependence of ζ23. The binary interaction parameters for the PDMS-2-propanol pair and the PCPMS-methanol pair were determined to be ζ23 ) 0.942 and ζ23 ) 0.910, respectively. The model was again able to capture both the shape and magnitude of the partitioning isotherms, and the volumetric predictions were similar to that for the PDMS-methanol system described previously. CO2-Polymer-Solute Sorption. To model the partitioning behavior of our solutes without a cosolvent present, the fluid phase was considered to be pure CO2, since the solutes were infinitely dilute. The binary interaction parameters for the polymer-solute pairs were determined by fitting experimental data. The solid lines in Figures 6-8 are the result of fitting the partitioning of naphthalene, 2-naphthol, and acridine between
TABLE 4: Binary Interaction Parameters Determined for Polymer-Solute, ζ24 naphthalene 2-naphthol acridine
PDMS
poly(cyanopropylmethylsiloxane)
0.750 0.870 0.785
0.760 0.890
CO2 and PDMS, respectively. The model successfully captured the large decrease in the solutes’ partition coefficients upon increasing pressure. The correlation was most accurate at higher pressures, away from the critical point of CO2. The binary interaction parameters for the polymer-solute pairs, ζ24, determined from these fits are listed in Table 4. CO2-Polymer-Cosolvent-Solute Sorption. For this system the fluid phase was considered to be a mixture of CO2 and cosolvent with the solutes present at infinite dilution. Six binary interaction parameters are necessary to model a four-component system with the SL EOS. With five of these parameters already determined, we fit our data by adjusting the sixth parameter, which corresponds to the cosolvent-solute pair, ζ34. However, the effect of ζ34’s magnitude on the model’s predicted solute partition coefficients was small. For example, we found that changing ζ34 from 1.00 to 0.50 shifted the predicted solute partitioning isotherms by only about 10%. Since the results were insensitive to this parameter, no further attempt was made to determine it; we set ζ34 ) 1.00 for all systems. The dotted-dashed lines in Figures 6, 7, and 8 are the results of the model’s prediction of naphthalene, 2-naphthol, and acridine partitioning, respectively, with methanol as a cosolvent. The predicted isotherms decreased in value with increasing pressure but not to the extent of the experimental data. Also, the model underpredicted the solute’s partition coefficients over most of the conditions studied, with an initial underprediction of about 200-500%. The accuracy of the prediction increased with pressure, resulting in fairly accurate predictions at the highest pressures studied. Similar results were obtained from fits of solute partitioning with the cosolvent 2-propanol, as shown by the dashed lines in Figures 6, 7, and 8 for naphthalene, 2-naphthol, and acridine, respectively. Results for the polymer PCPMS were very similar to those obtained for PDMS. Because of the insensitivity of the model’s prediction to ζ34, there were slight discrepancies between the predicted and experimental solute partition coefficients for these fourcomponent systems. However, by a sensitivity analysis, we found the predictions to be very responsive to changes in the polymer-solute binary interaction parameter, ζ24. Modifying this value improved solute partition coefficient predictions. This larger dependence on ζ24 compared with that on ζ34 may have resulted from the polymer existing in one phase only, whereas the cosolvent was present in both phases. Thus, the interactions of the solute with the polymer played a larger role in determining the solute’s distribution between the two phases. To apply the model to systems containing other components, ideally one would have available all necessary lattice fluid parameters (or data from which the parameters can be fit) and thermodynamic data from which binary interaction parameters can be regressed. However, all data are not always available. For example, the lattice fluid parameters for PCPMS were not available for this work. We were able to show, however, that using parameters from a polymer with a similar molecular structure, PDMS, gave qualitatively adequate results. Similar results would be expected if parameters were not available for a solute. Methods also exist for obtaining estimates of lattice fluid parameters by group contribution techniques.54,55 Thus,
Solute and Cosolvent Partitioning
J. Phys. Chem. B, Vol. 103, No. 45, 1999 10013
at least for a first approximation, one should be able to estimate parameters for nearly any system to be used in the lattice fluid model. In addition to the methods described in this work, binary interaction parameters for solvent-polymer and cosolventpolymer can be fit from solubility data. For the cosolventpolymer binary interaction parameter, swelling of the polymer in the pure liquid cosolvent would be adequate in many systems. A technique to obtain data rapidly to fit the solute-polymer binary interaction parameters is SFC, which will be discussed in the next section. Application to SFC A powerful experimental technique to measure the thermophysical properties of solutes at infinite dilution in supercritical fluids rapidly and accurately is chromatography.38-40,56-59 Not only does SFC yield partition coefficients and cosolvent effects but also this technique requires only small amounts of material, inherently offers the ability to use impure solutes, allows measurement of multiple solutes simultaneously, and does not require high-pressure sampling. SFC is also an attractive analytical technique compared to either gas or liquid chromatography for difficult separations because the mobile (fluid) phase can be “tuned” with simple changes in pressure to achieve better chromatographic retention.60-62 A major obstacle for the use of SFC for thermophysical property measurements is the proper characterization of the polymeric stationary phase. Pressure changes of the mobile phase or small additions of cosolvent can lead to large changes in the composition or volumetric properties of the stationary phase. For example, cross-linked PDMS, a common stationaryphase material for capillary SFC, can uptake over 40 wt % of solvent and almost double in volume when exposed to highpressure CO2.34,35,63 The addition of a cosolvent to the fluid phase has been shown to cause even more pronounced changes in the polymer phase.33 These stationary-phase effects have often been assumed to be negligible when calculating thermophysical properties from SFC retention data.38-40,56-59 The high-pressure spectroscopic measurements shown here are time-intensive and require specialized equipment; SFC is clearly an easier and more rapid method for measurement of thermophysical properties. However, since stationary-phase effects may introduce errors in the calculation of thermophysical properties from retention data, these may be corrected by using the Sanchez-Lacombe lattice fluid model. Stationary-Phase Corrections. We first estimate the magnitude of stationary-phase effects in an SFC. Roth64 analyzed retention of a solute in a two-phase, four-component system such as those studied in this work. With the stationary phase typically a cross-linked polymer, the stationary-phase mole fraction, which is utilized in Roth’s original analysis, is not well defined. A more meaningful variable is the volume fraction of component i in the stationary phase, φis. Vincent et al. give the results of substituting stationary-phase volume fractions in Roth’s analysis to determine the ratio of a solute’s infinite dilution fugacity coefficients in the fluid phase (ln(φ∞4f/φ∞4f,0)) upon the addition of a cosolvent.33 Their results are given in
ln
φ∞4f φ∞4f,0
) ln
k4 + k4,0
V
( ) ( )( )
∫0x ζf dx + ∫0x Vpf ζ′3p 3f
3f
∂φ3p dx + ∂x3f ∂µ∞
1 4p ∫0x RT ∂φ3p 3f
∂φp dx (2) ∂x3f
Figure 11. Total correction required to convert retention time data to infinite dilution fugacity coefficients for 2-naphthol at 40 °C and 3.5 mol % methanol concentration: (b) our calculations including solute contribution; (4) Vincent et al. calculation not accounting for solute contribution.
where the numerical subscripts refer to the component and the subscripts p and f refer to the polymeric stationary phase and fluid mobile phase, respectively. In this equation, the subscript “0” refers to the condition of zero cosolvent, φ∞4f is the infinite dilution fugacity coefficient of the solute in the mobile phase, k4 is the capacity factor of the solute, x3f is the mole fraction of cosolvent in the mobile phase, ζ3f is called the mixing expansivity; ζ′3p is called the cosolvent expansivity, φ1p and φ3p are the volume fractions of CO2 and cosolvent in the stationary phase, respectively, and µ∞4p is the infinite dilution chemical potential of the solute in the stationary phase. The second term on the right-hand side of eq 20 is a fluid-phase property, while the third and fourth terms are associated with the volumetric and partitioning behavior of the stationary phase, respectively. The cosolvent effect is defined as the solubility augmentation caused by the addition of a cosolvent to the fluid. Ekart et al. used a truncated form of eq 2, retaining only the first term on the right-hand side, to evaluate the cosolvent effects for anthracene and 2-naphthol as solutes in a carbon dioxidemethanol (x3f ) 0.035) mixture relative to pure CO2.56 Vincent et al. utilized experimental swelling data, the theory of FloryHuggins, and independent fugacity coefficient data to estimate the contributions of the second, third, and fourth terms on the right-hand side of eq 2, which amounted to a correction of approximately 30% near the critical region. In this work we use the SL EOS with binary interaction parameters determined from spectroscopic data to refine the calculation performed by Vincent et al., calculating the second, third, and fourth terms on the right-hand side of eq 2 with a single equation of state. Vincent et al. had to utilize experimental data, a model specifically for the fluid phase, and a separate model for the polymer phase. The result is shown in Figure 11 as a function of pressure at 40 °C. The corrected cosolvent effect is compared with the data of Vincent et al. in Figure 11. Our isotherm is similar in shape to Vincent et al.’s, but we consistently predict a larger total correction. At pressures above about 90 bar the difference is relatively small when compared to the Ekart’s value of ln(k4/ k4,0) equal to -1.7 for this system at 35 °C and 100 bar. However, near the critical pressure our results indicate a total correction about 5 times more than that calculated by Vincent et al. This difference is largely due to the inclusion of the effects of solute partitioning. Our results do not change the conclusions reached by Vincent et al.: the total corrections may be very large near the critical pressure but are less significant at higher pressures. However,
10014 J. Phys. Chem. B, Vol. 103, No. 45, 1999
Brantley et al.
Figure 12. Logarithm of the ratio of SL EOS predicted capacity factors of 2-naphthol and acridine (′′) relative to naphthalene (′) as a function of pressure with a pure CO2 mobile phase at 40 °C.
the inclusion of solute partitioning effects considerably changes the magnitude of the total correction. In addition, our results show that a single equation of state, namely, the SL EOS, can be used to calculate the necessary corrections to SFC-measured capacity factors when determining thermophysical properties. These stationary-phase correction results also show that SFC operating away from the critical point is a viable option, compared to spectroscopic techniques, for determining the partition coefficients necessary for fitting the lattice fluid model. Thus, one should be able to measure partitioning coefficients using SFC operating above the critical point (>100 bar should give good results) and then fit the model to these data points. Since the model predicts the correct shape of the partitioning curve, only a single data point is required for each fit. Retention and Separation Prediction. We now investigate the use of the SL lattice fluid model for a priori prediction of the retention of solutes in SFC. The actual retention time of a solute depends on a number of experimental conditions, but predictions of the relative retention of solutes are much more useful than the actual retention time. Relative retention can be used to determine the effect of cosolvents on the retention of a solute, the order in which multiple solutes will elute on the same chromatograph, and the effect of changing system parameters such as stationary-phase material on the retention of a solute. In this work we evaluate the use of the SL model to predict the order of elution of solutes used in this study and to predict the effects of changing the stationary phase from PDMS to PCPMS. For two experiments the ratio of capacity factors of the solute(s) is given in terms of the partition coefficient K as
ln
() ()
V′′p V′f k′′4 K′′4 ) ln + ln + ln k′4 K′4 V′p V′′f
(3)
The prime and double prime represent the two different experiments. Using the SL EOS, we can predict all of the terms on the right-hand side of eq 3. We assumed a column diameter of 25 µm and unswollen stationary-phase thickness of 1 µm when calculating the ratio of mobile- and stationary-phase volumes. These dimensions are common in capillary SFC. We start by predicting the retention of 2-naphthol and acridine relative to naphthalene using a PDMS stationary phase at 40 °C. Figure 12 shows the results for a mobile phase consisting of pure CO2. The results for mobile phases consisting of CO2 with 3.0 mol % methanol and CO2 with 3.0 mol % 2-propanol can be found elsewhere.65 For all three mobile phases and all
Figure 13. Logarithm of the ratio of SL EOS predicted capacity factors of solutes using a poly(cyanopropylmethylsiloxane) (kcyano) stationary phase relative to PDMS (kPDMS) at 40 °C. Solid lines indicate a pure CO2 fluid phase. Dotted-dashed lines indicate a methanol-modified CO2 fluid phase.
pressures studied, we predict that the order of retention will be, in order of least retained to most, naphthalene < 2-naphthol < acridine. We now predict the effects of changing the stationary phase from PDMS to PCPMS on the relative retention of naphthalene and 2-naphthol in pure CO2 and 3.0 mol % modified CO2 at 40 °C. The results of these predictions are shown in Figure 13. The model predicts that both solutes will be retained longer on a PCPMS stationary phase than on a PDMS stationary phase, regardless of whether methanol is used as a cosolvent. In addition, the predicted effect of changing from PDMS to PCPMS is much greater on 2-naphthol than on naphthalene. Although no experimental results were available for comparison, these predictions are consistent with expected results. 2-Naphthol should interact much more strongly with PCPMS than with naphthalene, which should result in longer retention times for 2-naphthol. Thus, the SL lattice fluid model can be used to calculate stationary-phase corrections and predict a priori the relative retention of solutes in SFC. Using improved models accounting for specific interactions should aid in making more quantitative predictions. Evaluating other models was beyond the scope of this work. When using the SL model, binary interaction parameters must be known for each binary pair in the system. Spectroscopically measured partitioning data used here ensured reliable predictions of partitioning and thus relative retention. However, it would be more useful if the binary interaction parameters could be reliably fit from data more easily obtained, such as actual chromatographic data. Then the binary interaction parameters could be determined from a small number of experiments, then used to predict the retention behavior at other conditions. Our results show that using data such as partition coefficients measured away from the critical point is a viable option. Conclusions In this work we applied in situ UV-visible and FTIR spectroscopy to study the partitioning of solutes and cosolvents, respectively, between a high-pressure fluid phase and a crosslinked polymer phase. The cosolvent and solute partitioning data, along with experimentally measured polymer swelling data, literature CO2-cosolvent VLE data, and literature CO2-solid solubility data were used to determine binary interaction parameters for the Sanchez-Lacombe lattice fluid model. The extension of this model to other systems was discussed, and
Solute and Cosolvent Partitioning the relevance of our results to supercritical fluid chromatography was investigated. Experimentally, it was shown that the CO2-induced swelling behavior of PDMS and PCPMS was nearly identical for the systems we studied. For both polymers, adding a cosolvent resulted in increased polymer swelling, with the greatest effect at the lower pressures studied (∼75 bar). Over the range of pressures studied, the cosolvents methanol and 2-propanol resulted in similar swelling behavior of PDMS. Cosolvent partitioning behavior shows that there was nearly an order of magnitude higher cosolvent concentration in the polymer phase than in the fluid phase at pressures near 80 bar. The partition coefficients decreased with increasing pressure, resulting in values of approximately 3-4 at pressures near 180 bar. The increased partitioning of methanol in PCPMS compared to PDMS indicates that the cosolvent has a higher affinity for the more polar environment of PCPMS, possibly as a result of hydrogen bonding of the methanol to the cyano functionality of the polymer. The solute partitioning measurements showed that for all conditions studied the solute concentration was higher in the polymer phase than in the fluid phase. The partition coefficients decreased from values over 103 near 75 bar to values between 1 and 5, depending on the system studied. The effect of adding a cosolvent was found to be a reduction in the solute partition coefficient, with the effect largest at lower pressures and decreasing with increasing pressure. Our data suggest that the increase in solvent strength of the fluid phase upon increasing pressure or adding a cosolvent was the primary factor in decreasing the solute partition coefficient. The chemical nature of the solute did affect its partitioning behavior, with the greatest effect seen with the polar polymer phase, PCPMS, and a polar solute. The Sanchez-Lacombe equation of state was shown to be successful in representing quantitatively the volumetric and phase equilibria properties of a four-component system consisting of CO2, cross-linked polymer, cosolvent, and solute. The model could easily be applied to other systems, utilizing existing lattice fluid parameters or estimating them from compounds of similar molecular structure or group contribution techniques. Methods other than those utilized in this work, such as SFC, are available for obtaining data to fit binary interaction parameters. We have successfully used the SL lattice fluid model to calculate stationary-phase corrections, which can be significant in the near-critical region. These results show that SFC, without any corrections, is a viable technique for determining thermophysical properties away from the critical point. We have also shown the ability of the model to predict a priori the relative retention of solutes in SFC. More investigations are needed to make the predictions quantitative in nature, but our results show that this lattice fluid model gives good qualitative descriptions of the relative retention. Acknowledgment. We greatly appreciate the help and advice of Dr. Charles L. Liotta, Dr. Barry West, Mr. Sam Edge, Mr. Birkin Weith, and Mr. Jeff Andrews. References and Notes (1) Kumar, S. K.; Suter, U. W.; Reid, R. C. Fluid Phase Equilib. 1986, 29, 373-382. (2) Folie, B.; Kelchtermans, M.; Shutt, J. R.; Schonemann, H.; Krukonis, V. J. Appl. Polym. Sci. 1997, 64, 2015-2030. (3) Pradhan, D.; Chen, C. K.; Radosz, M. Ind. Eng. Chem. Res. 1994, 33, 1984-1988.
J. Phys. Chem. B, Vol. 103, No. 45, 1999 10015 (4) Pratt, J. A.; Lee, S. H.; McHugh, M. A. J. Appl. Polym. Sci. 1993, 49, 953-966. (5) Burgess, A. N.; Jackson, K. J. Appl. Polym. Sci. 1992, 46, 13951399. (6) Kazarian, S. G.; Vincent, M. F.; Eckert, C. A. ReV. Sci. Instrum. 1996, 67, 1586-1589. (7) Vincent, M. F.; Kazarian, S. G.; Eckert, C. A. AIChE J. 1997, 40, 1838-1848. (8) McHugh, M. A.; Krukonis, V. J. Supercritical Fluid Extractions Principles and Practice, 2nd ed.; Butterworth-Heinemann: Boston, 1994. (9) Boggess, R. K.; Taylor, L. T.; Stoakley, D. M.; St. Clair, A. K. J. Appl. Polym. Sci. 1997, 64, 1309-1317. (10) Kazarian, S. G.; Brantley, N. H.; West, B. L.; Vincent, M. F.; Eckert, C. A. Appl. Spectrosc. 1997, 51, 491-494. (11) West, B. L.; Kazarian, S. G.; Vincent, M. F.; Brantley, N. H.; Eckert, C. A. J. Appl. Polym. Sci. 1998, 69, 911-919. (12) Berens, A. R.; Huvard, G. S.; Korsmeyer, R. W.; Kunig, F. W. J. Appl. Polym. Sci. 1992, 46, 231-242. (13) Conforti, R. M.; Barbari, T. A.; Vimalchand, P.; Donohue, M. D. Macromolecules 1991, 24, 3388-3394. (14) Barbari, I. A.; Conforti, R. M. J. Polym. Sci., Part B: Polym. Phys. 1992, 30, 1261-1271. (15) Pope, D. S.; Sanchez, I. C.; Koros, W. J.; Fleming, G. K. Macromolecules 1991, 24, 1779-1783. (16) Wissinger, R. G.; Paulaitis, M. E. J. Polym. Sci., Part B: Polym. Phys. 1987, 25, 2497-2510. (17) Condo, P. D.; Sanchez, I. C.; Panayiotou, C. G.; Johnston, K. P. Macromolecules 1992, 25, 6119-6127. (18) Leblans-Vinck, A. M.; Koningsveld, R.; Kleintjens, L. A.; Diepen, G. A. M. Fluid Phase Equilib. 1985, 20, 347-354. (19) Gilbert, S. W.; Eckert, C. A. Fluid Phase Equilib. 1986, 30, 1116. (20) Van Der Haegen, R.; Koningsveld, R.; Kleintjens, L. A.; Van Opstal, L. Fluid Phase Equilib. 1988, 43, 1-19. (21) Johnston, K. P.; Peck, D. G.; Kim, S. Ind. Eng. Chem. Res. 1989, 28, 1115-1125. (22) Balbuena, P. C.; Enrique, G. L. Fluid Phase Equilib. 1991, 62, 225-238. (23) Gupta, R. B.; Johnston, K. P. Fluid Phase Equilib. 1994, 99, 135151. (24) Kumar, S. K.; Suter, U. W.; Reid, R. C. Ind. Eng. Chem. Res. 1987, 26, 2532-2542. (25) Ormanoudis, C.; Panayiotou, C. G. Fluid Phase Equilib. 1993, 89, 217-228. (26) Klein, T.; Schulz, S. Ind. Eng. Chem. Res. 1989, 1073-1081. (27) Bharath, R.; Yamane, S.; Inomata, H.; Adschiri, T.; Arai, K. Fluid Phase Equilib. 1993, 83, 183-192. (28) Condo, P. D.; Sumpter, S. R.; Lee, M. L.; Johnston, K. P. Ind. Eng. Chem. Res. 1996, 35, 1115-1123. (29) West, B. L.; Bush, D.; Brantley, N. H.; Vincent, M. F.; Kazarian, S. G.; Eckert, C. A. Ind. Eng. Chem. Res. 1998, 37, 3305-3311. (30) Sanchez, I. C.; Lacombe, R. H. Macromolecules 1978, 11, 11451156. (31) Sanchez, I. C.; Lacombe, R. H. J. Phys. Chem. 1976, 80, 23522362. (32) Sanchez, I. C.; Panayiotou, C. G. Equation of State Thermodynamics of Polymer and Related Solutions. In Models for Thermodynamic and Phase Equilibria Calculations; Sandler, S. I., Ed.; Marcel Dekker: New York, 1993; pp 187-286. (33) Vincent, M. F.; Kazarian, S. G.; West, B. L.; Berkner, J. A.; Bright, F. V.; Liotta, C. L.; Eckert, C. A. J. Phys. Chem. B 1998, 102, 21762186. (34) Shim, J. J.; Johnston, K. P. AIChE J. 1989, 35, 1097-1106. (35) Fleming, G. K.; Koros, W. J. Macromolecules 1986, 19, 2285. (36) Kazarian, S. G.; Vincent, M. F.; West, B. L.; Eckert, C. A. J. Supercrit. Fluids 1998, 13, 107-112. (37) Richter, B. E.; Kuei, J. C.; Park, N. J.; Crowley, S. J.; Bradshaw, J. S.; Lee, M. L. J. High Resolut. Chromatogr. Chromatogr. Commun. 1983, 6, 371-374. (38) Berger, T. A.; Deye, J. F. Anal. Chem. 1990, 62, 1181-1185. (39) Yonker, C. R.; Smith, R. D. Anal. Chem. 1989, 61, 1348-1353. (40) Yonker, C. R.; Smith, R. D. J. Chromatogr. 1990, 505, 139-146. (41) Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed.; Cambridge University Press: New York, 1992. (42) Suzuki, K.; Sue, H.; Itou, M.; Smith, R. L.; Inomata, H.; Arai, K.; Saito, S. J. Chem. Eng. Data 1990, 35, 63-66. (43) Ohgaki, K.; Katayama, T. J. Chem. Eng. Data 1976, 21, 53-55. (44) Yaginuma, R.; Nakajima, T.; Tanaka, H.; Kato, M. J. Chem. Eng. Data 1997, 42, 814-816. (45) Chang, H.; Morrell, D. G. J. Chem. Eng. Data 1985, 30, 74-78. (46) Tsekhanskaya, Y. V.; Iomtev, M. B.; Mushkina, E. V. Russ. J. Phys. Chem. 1964, 38, 1173-1175.
10016 J. Phys. Chem. B, Vol. 103, No. 45, 1999 (47) Iwai, Y.; Fukuda, T.; Koga, Y.; Arai, Y. J. Chem. Eng. Data 1991, 36, 430-432. (48) King, M. B.; Alderson, D. A.; Fallah, F. H.; Kassim, D. M.; Kassim, K. M.; Sheldon, J. R.; Mahmud, R. S. Some Vapour/Liquid and Vapour/ Solid Equilibrium Measurements of Relavance for Supercritical Extraction Operations and their Correlation. In Chemical Engineering at Supercritical Fluid Conditions; Paulaitis, M. E., Penninger, J. M. L., Gray, R. D., Davidson, P., Eds.; Ann Arbor Science: Ann Arbor, MI, 1983; pp 31-80. (49) McHugh, M. A.; Paulaitis, M. E. J. Chem. Eng. Data 1980, 25, 326-329. (50) Sako, S.; Ohgaki, K.; Katayama, T. J. Supercrit. Fluids 1988, 1, 1-6. (51) Schmitt, W. J.; Reid, R. C. J. Chem. Eng. Data 1986, 31, 204212. (52) Dobbs, J. M.; Johnston, K. P. Ind. Eng. Chem. Res. 1987, 26, 14761482. (53) Hansen, P. C. Binary Supercritical Fluid Enhancement Factors for Separation Processes. Ph.D. Thesis, University of Illinois, 1985. (54) High, M. S.; Danner, R. P. AIChE J. 1990, 36, 1625-1632.
Brantley et al. (55) Lee, B. C.; Danner, R. P. AIChE J. 1996, 42, 837-849. (56) Ekart, M.; Bennett, K. L.; Ekart, S. M.; Gurdial, G. S.; Liotta, C. L.; Eckert, C. A. AIChE J. 1993, 39, 235-248. (57) Bartle, K. D.; Clifford, A. A.; Jafar, S. A. J. Chem. Eng. Data 1990, 35, 355-360. (58) Bartle, K. D.; Clifford, A. A.; Jafar, S. A. J. Chem. Soc., Faraday Trans. 1990, 86, 855-860. (59) Crow, J. A.; Foley, J. P. J. Microcolumn Sep. 1991, 3, 47. (60) Chester, T. L.; Pinkston, J. D.; Raynie, D. E. Anal. Chem. 1994, 66, 106R-130R. (61) Kirschner, C. H.; Taylor, L. T. Anal. Chem. 1993, 65, 78-83. (62) Levy, J. M.; Ritchey, W. M. HRC & CC, J. High Resolut. Chromatogr. Chromatogr. Commun. 1985, 8, 503-509. (63) Garg, A.; Gulari, E.; Manke, C. Macromolecules 1994, 27, 56435653. (64) Roth, M. J. Phys. Chem. 1996, 100, 2372-2375. (65) Brantley, N. H. Spectroscopic Investigations of Polymers Processed by High Pressure and Supercritical CO2. Ph.D. Thesis, Georgia Institute of Technology, 1999.
