Quantitative Equilibrium Constants between CO2 and Lewis Bases

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J. Phys. Chem. 1996, 100, 10837-10848

10837

ARTICLES Quantitative Equilibrium Constants between CO2 and Lewis Bases from FTIR Spectroscopy J. Carson Meredith and Keith P. Johnston* Department of Chemical Engineering, UniVersity of Texas at Austin, Austin, Texas 78712

Jorge M. Seminario Department of Chemistry, UniVersity of New Orleans, New Orleans, Louisiana 70148

Sergei G. Kazarian and Charles A. Eckert School of Chemical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332 ReceiVed: October 26, 1995; In Final Form: January 22, 1996X

Equilibrium constants measured from the ν2 bending mode of CO2 by FTIR spectroscopy are reported for the electron donor-acceptor interactions of CO2 with three Lewis bases: triethylamine (TEA), pyridine (PYR), and tributyl phosphate (TBP). The average Kc values are 0.046 (CO2-TEA), 0.133 (CO2-PYR), and 1.29 (CO2-TBP) L/mol at 25 °C in the solvent pentane. For the CO2-TBP system, the average enthalpy of association, ∆H°, is -4.7 kcal/mol. Ab initio calculations indicate that steric repulsion of the ethyl groups in TEA cause the binding energy of the CO2-TEA complex to be weaker than that of the CO2-PYR complex by 1.34 kcal/mol, a trend that is in agreement with our spectroscopic data. The lattice fluid hydrogen bonding model was used in conjunction with the spectroscopically determined Kc values to predict bubble points for the CO2-TEA and CO2-TBP systems and CO2 sorption in a hypothetical polymer. These calculations indicate that these relatively weak specific interactions have a measurable effect on phase behavior and can influence sorption of CO2 in polymers.

Introduction Carbon dioxide is of current interest as an environmentally acceptable alternative to organic solvents in many chemical processing applications.1,2 CO2 is the least expensive solvent after H2O and is in plentiful supply. Its incorporation into chemical processes could actually reduce emissions to the atmosphere by replacing organic solvents. Recent research in this area has focused on identifying molecules that have favorable intermolecular interactions with CO2. Because of the low polarizability of CO2, along with the lack of a dipole moment, nonvolatile polar molecules, surfactants, and nearly all polymers are virtually insoluble. However, CO2 has a large quadrupole moment and both Lewis acid and base sites. There is evidence from microwave and radio-frequency spectroscopy,3,4 ab initio calculations,5-7 and infrared spectroscopy8-13 that CO2 acts as a Lewis acid in the presence of Bronsted and Lewis bases such as water, amines, amides, and basic polymers. These studies have illuminated the existence and structure of electron donor-acceptor (EDA) complexes between CO2 and bases but have not given quantitative thermodynamic values of the strength of the specific interactions. The present state of knowledge is far from conclusive as to the strength of these complexes and to what degree specific interactions influence certain thermodynamic properties. The Lewis acidity of CO2 can be important in practical applications where CO2 is a reaction medium or reaction partner.1,14 DeSimone et al. have synthesized highly soluble X

Abstract published in AdVance ACS Abstracts, March 15, 1996.

S0022-3654(95)03161-3 CCC: $12.00

poly(1,1-dihydroperfluorooctyl acrylate) in supercritical fluid (SCF) CO2.15 The CO2-acrylate interactions likely enhance the solubility of this polymer. Using this polymer as a stabilizer, they have recently synthesized PMMA in SCF CO2 by dispersion polymerization.16 CO2 shows promise as a replacement for phosgene in the production of isocyanates and urethanes from primary and secondary amines.17 A key in developing this technology is discovering molecules that activate CO2, an extremely stable molecule. McGhee et al.18 have recently used tertiary amines as co-bases to enhance reactivity of carbamates formed as intermediates in the production of urethanes. Walsh et al.19 discuss the importance of specific Lewis acidbase interactions in enhancing the solubilities of certain nonvolatile compounds in SCF CO2-cosolvent mixtures. They propose that weak specific interactions between CO2 and the cosolvent can inhibit the solubility enhancements due to the cosolvent that are seen in noninteracting solvents such as ethane. In an effort to design surfactants for use in CO2, Newman et al.20 examined the phase behavior of fluoroether functional surfactants in supercritical CO2. They proposed that the solubility of the fluorinated surfactants in CO2 was enhanced by the electron-donating capacity of the fluoroether functional groups. Yee et al.21 used FTIR spectroscopy to examine molecular interactions of CO2 dissolved in C2H6 and C2F6. From shifts in the ν2 frequency of CO2 and a semiempirical dielectric continuum model, they concluded that CO2 is more repulsive to C2F6 than C2H6 and that no specific attractive interactions exist between CO2 and perfluorinated molecules. Interestingly, © 1996 American Chemical Society

10838 J. Phys. Chem., Vol. 100, No. 26, 1996 deviations in the model indicated the possibility of specific interactions between CO2 and acetone, methanol, and toluene. Further indication of the need for a quantitative understanding of the Lewis acidity of CO2 can be seen in studies of the solubilities of CO2 in polymers. Fried and Li22 studied interactions of CO2 with cellulose acetate and with poly(methyl methacrylate) using IR spectroscopy. They concluded that shifts in the carbonyl stretching frequencies indicate interactions between CO2 and the polar carbonyl group. Also, the solubility of near-critical CO2 in glassy polymers shows a trend in the order: poly(vinyl acetate) > poly(methyl methacrylate) > poly(vinyl chloride).23 In fact, at 500 psia and 25 °C, the solubility of CO2 in PMMA is 75 wt % greater than in PVC. Wissinger report a solubility of CO2 in PMMA that is 205 wt % greater than that in polystyrene at 35 °C and 500 psia.24 The authors suggest that specific interactions between CO2 and the polar groups of PMMA and PVA are responsible for the enhanced solubilities. However, it is unclear what role physical forces and specific chemical interactions play in influencing the solubility of CO2 in polymers. Many studies have focused on identifying the nature of the interactions of CO2 through qualitative or empirical methods. A recent review outlines the importance of IR and Raman spectroscopy not only in improving SCF CO2 applications but also in understanding fundamentals such as hydrogen bonding and reverse micelle formation.25 Hyatt26 measured the shifts in IR frequencies of several probe compounds in both liquid and SCF CO2. Shifts in the ν(CdO) of acetone and cyclohexanone were slightly greater than in the solvent n-hexane and slightly less than those in aromatic solvents, indicating a low tendency for CO2 to interact with basic carbonyl groups. For the probe pyrrole, large shifts in the ν(N-H) stretching frequency indicated hydrogen bonding between pyrrole and CO2. Kim and Johnston27 measured transition energies, ET, for the dye phenol blue in CO2. On a plot of ET vs reduced density, CO2 coincides with C2H4 (Figure 3 of ref 27) although the polarizability/volume of C2H4 is 1.6 times that of CO2.27,28 This suggests that CO2 has a significant Lewis acidity toward phenol blue, a Lewis base. Sigman et al.29 measured π* dipolarity-polarizability values for 10 solvatochromic indicators in SCF CO2. They suggested that specific interactions, not accounted for in π*, are important. They also found β, the hydrogen-bonding basicity parameter, in SCF and liquid CO2 to be near zero, indicating a low tendency to donate electrons. On the basis of the above studies, there is considerable uncertainty concerning the nature and importance of the Lewis acidity of CO2. Direct IR spectroscopic measurements of the specific interactions of CO2 with basic monomers in the liquid phase promise to shed insight into the magnitude and role of the specific interactions. Dobrowolski and Jamro´z11 report an IR study of the ν3 and ν2 frequencies of CO2 dissolved in over 30 solvents. For highly basic solvents such as amines and amides, the ν2 frequency is split, a phenomenon they attribute to weak EDA complexes between the bases and CO2. However, in their experiments, CO2 was dissolved in pure base, so that the absorbance of free CO2 could not be calibrated. Consequently, equilibrium constants could not be determined. In this work, the Lewis acidity of CO2 is examined in a quantitative manner from its ν2 bending mode in the presence of Lewis bases. Three common Lewis bases are considered: triethylamine (TEA), pyridine (PYR), and tributyl phosphate (TBP). From changes in the absorbance of the “free” ν2 peak, equilibrium constants, Kc, for the EDA interactions are defined and measured. The CO2 and base are dissolved in an inert liquid

Meredith et al.

Figure 1. Schematic of the experimental apparatus.

solvent, pentane, incapable of forming specific interactions with CO2 or the bases. The use of an inert solvent allows calibration of the “free” ν2 CO2 peak, unaffected by the base. Changes in the ν2 absorbance are examined as the solvent changes from noninteracting (pentane) to interacting (pentane + base). For the strongest interaction, that of CO2 and TBP, Kc values are measured at a series of temperatures, and ∆H° and ∆S° values are determined. In addition, an ab initio calculation is carried out in order to compare the relative stabilities and geometries of the CO2-TEA and CO2-PYR complexes. In an effort to determine the importance of weak specific interactions on phase equilibria, we calculate the bubble points for binary mixtures of CO2-TEA and CO2-TBP and CO2 sorption in polymers. This is accomplished with the lattice fluid hydrogen bonding model (LFHB),30,31 a chemical association theory. The spectroscopically determined equilibrium constants are used directly in the LFHB calculations. In this way, the enhancement of solubility of CO2 in the base can be calculated as the specific interaction is turned on with the model. Experimental Section Pentane (Mallinckrodt, spectrophotometric grade), triethylamine (EM Science, 98%), tributyl phosphate (Aldrich, 99.9+%; FMC), pyridine (MCB, 99.9%), and carbon dioxide (Liquid Carbonic, 99.5%) were used as received, except for drying over molecular sieves (Mallinckrodt, Grade 514GT, 4 Å). Carbon dioxide was dried by flowing the liquid through a 10 cm3 stainless steel tube containing a desiccant, Ca2SO4. Figure 1 gives a schematic of the FTIR apparatus. Unless stated otherwise, all vessels and connections were of stainless steel construction. Solutions were prepared in a variable volume view cell (28 mL) with a magnetic stir bar. Carbon dioxide was added accurately by using a six-port switching valve (Valco Instruments, Model C6W) in conjunction with a sample loop. The sample loop volume was determined to be 30.2 ( 0.5 µL by the weight of water it contained at room temperature. A pressure gauge (Heise, Model H8315), connected to the CO2 syringe pump, indicated the pressure of CO2 in the sample loop to within (0.15 bar. A syringe pump (HIP, Model 87-6-5) filled

CO2 and Lewis Base Equilibrium Constants with pentane was connected to the back side of the view cell to control pressure in the system. The system pressure was monitored to within (0.35 bar with a pressure gauge (Heise, Model 54198) connected to the back of the view cell. A magnetically coupled gear pump (Micropump, Model 1850) provided recirculation between the view cell and IR cell. The infrared cell was equipped with an inlet and an outlet port and two ZnSe windows (Morton Advanced Materials). The ZnSe windows allowed transmission in the 600-700 cm-1 range necessary to observe the ν2 bending mode of CO2. The cell path length, l, was approximately 0.5 mm as determined by a micrometer measurement; however, the path length was never changed during the course of the experiments, and a precise determination was therefore not necessary. The product l, determined from the Beer’s law calibration of the ν2 mode, remained constant in all calculations. All spectra were recorded with a Perkin-Elmer Paragon 1000 FTIR spectrometer and consisted of 64 averaged scans at 2 cm-1 resolution. The spectrometer compartment was purged with dry nitrogen gas to eliminate atmospheric interference. A temperature controller (Omega Engineering) maintained the temperature of the IR cell to within 0.1 °C. Before each experiment, the entire sealed system (∼33 mL) was purged with nitrogen gas, and liquid pentane was introduced. Once a pure pentane baseline spectrum was recorded, CO2 was injected into the system. Initially, for calibration, this was done by using the six-port valve and sample loop. The CO2 was introduced as a liquid at 68.9 bar (1000 psig) and 22 °C. CO2 densities were determined by using an accurate equation of state.32 A calibration curve for the ν2 frequency was constructed by adding incremental amounts of CO2 to pentane and recording the spectrum. Each Lewis base was added as liquid using a glass Luer-Lock syringe after reducing the system pressure to about 0.3 bar. The base was usually added in 2.0 cm3 increments. After each incremental addition of base, the solution was allowed to mix for 10 min, and the spectrum was recorded. For the bases triethylamine and pyridine, all spectra were recorded at 25.0 °C. For tributyl phosphate, spectra were recorded at a series of temperatures between 25.0 and 55.0 °C. The pressure was 6.89 bar (100 psig) in all experiments to ensure that all of the CO2 was dissolved and that no gas pockets existed in the system. In addition, CO2 concentrations were chosen to ensure that absorption of the ν2 peak remained in the range 0.5-1.0. Results and Discussion FTIR Spectroscopy. Because of a depletion of electron density on the carbon atom, CO2 is a weak Lewis acid. Triethylamine, pyridine, and tributyl phosphate, due to the nitrogen and phosphoryl groups, are strong Lewis bases. In an EDA interaction, electron density is considered to be transferred from the highest occupied molecular orbital of the donor molecule into the lowest unoccupied molecular orbital of the acceptor.33 The strength, orientation dependence, and lifetime of these interactions are sufficiently greater than those of physical interactions (e.g., van der Waals forces) to justify their treatment as chemical, or specific, interactions.34 As the donor and acceptor molecules move close together to form a complex, the intramolecular bond lengths in each molecule change as the electron distribution changes. Primary bonds in each molecule, those involving the actual donor and acceptor atoms, increase in length when a complex is formed. This increase indicates a slight weakening of the primary bonds in the donor and acceptor molecules. In addition, the polarity of primary bonds in each molecule is enhanced due to formation of the complex.35 Each

J. Phys. Chem., Vol. 100, No. 26, 1996 10839 of these changes in the donor and acceptor molecules is responsible for changes in IR spectra. As mentioned in the Introduction, Dobrowolski and Jamro´z11 report the splitting of the ν2 peak of carbon dioxide dissolved in various Lewis bases. They attribute the appearance of the second peak, which usually occurs at 10-15 cm-1 below the original ν2 peak, to the formation of an electron donor-acceptor complex. The assignment of free and complex peaks requires a careful consideration of the nature of the ν2 vibration. Due to the symmetry of the CO2 molecule about its linear axis, the CO2 ν2 vibration is degenerate; that is, two vibrational degrees of freedom (bending) absorb at one wavelength.36 A question arises as to how the presence of Lewis base affects the degenerate components of the ν2 mode. These are labeled inplane or out-of-plane with respect to the plane defined by the lone pair of the electron donor (oxygen or nitrogen atoms) and the OdCdO axis. It is expected that the degeneracy of the ν2 mode of CO2 will be released due to interaction with the electron lone pair of the Lewis base, and the vibration will appear as a doublet shifted to a lower frequency with respect to the free peak. The in-plane component should have a larger shift than the out-of-plane since the in-plane interaction with the electron donor is more direct.6,7,13,37 These observations are seen in our spectra as well as others.8-11,13 Furthermore, decreases in the height of the higher frequency free CO2 peak indicate the amount of CO2 complexed with base. Figures 2-4 show spectra in the region of the ν2 vibration for the CO2-TBP, CO2-TEA, and CO2-PYR interactions, respectively. Although the spectra were recorded at different CO2 concentrations, they are normalized to the initial concentration of CO2 in Figures 2a, 3a, and 4a for clarity of presentation. In addition, the spectrum of pure pentane at the same conditions has been subtracted from each of the spectra. The location of the peak maximum is at 661.3 cm-1 in pure pentane, consistent with results of others.11 As Lewis base is added, several important changes occur in the ν2 vibration. Most important is the appearance of a second peak at a lower frequency. Also, the intensity of the high-frequency (free) peak falls due to the formation of the EDA complex. For the bases studied, the largest complex peaks were observed for the CO2-TBP system in Figure 2a. A linear baseline was used in Figure 2a to correct a slight slope in the spectra due to the presence of interfering TBP bands at 557 and 720 cm-1. The in-plane complex peak appears at 650 cm-1 for the CO2-TBP interaction and is broader than the free peak. However, the out-of-plane peak is likely buried under the free CO2 peak. To reveal the shape of the complex peaks, a free CO2 in pentane peak was subtracted from the total spectrum, as demonstrated in Figure 2b. The absorbance of the free CO2 peak was estimated by assuming that all of the peak height above 663 cm-1 is due to free CO2. Contributions from the buried out-of-plane complex peak were assumed to vanish above 663 cm-1. This should reveal the position and shape, but not the correct area of the complex doublet components. In Figure 2b, the doublet has peaks at 658 and 650 cm-1, presumably for the out-of-plane and in-plane components, respectively. The shape of this doublet is similar to that found for CO2 dissolved in PMMA and poly(vinyl acetate), where CO2 forms a complex with carbonyl groups (Figures 3 and 8 of ref 13). The relatively sharp complex peak indicates a well-defined structure. Curve resolution makes determination of the peak parameters and areas for the free and complex peaks possible. Resolution was accomplished with the Peaksolve program, which uses a Levenberg-Marquardt nonlinear optimization algorithm to arrive at optimized peak parameters based on initial estimates.

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Meredith et al.

Figure 2. (a, top) IR spectra in the ν2 region for the TBP-CO2 system at several TBP concentrations and 25.0 °C. Spectra are normalized to 0.206 M CO2. D/A ) mole ratio of donor to acceptor. XD ) mole fraction of donor. (b, middle) Subtraction of free CO2 in pentane peak to reveal complex doublet. (c, bottom) Peak resolution of the free and complex peaks at D/A ) 4.1.

Figure 3. (a, top) IR spectra in the ν2 region for the TEA-CO2 system at several TEA concentrations and 25.0 °C. Spectra are normalized to 0.176 M CO2. D/A ) mole ratio of donor to acceptor. XD ) mole fraction of donor. (b, middle) Subtraction of free CO2 in pentane peak to reveal complex doublet. (c, bottom) Peak resolution of the free and complex peaks at D/A ) 24.9.

There are four parameters for each resolved peak: maximum wavelength, height, width, and percent Lorentzian character. For all three systems investigated, sums of Gaussian and Lorentzian line shapes fit the spectra better than either shape alone. Using the results of the subtraction procedure for the

CO2-TBP system (Figure 2b), the out-of-plane and in-plane complex peak maxima were estimated to be at approximately 658 and 650 cm-1, respectively. These locations were each constrained to a range of (2 cm-1 in the Peaksolve program.

CO2 and Lewis Base Equilibrium Constants

Figure 4. (a, top) IR spectra in the ν2 region for the PYR-CO2 system at several PYR concentrations and 25.0 °C. Spectra are normalized to 0.259 M CO2. D/A ) mole ratio of donor to acceptor. XD ) mole fraction of donor. (b, middle) Subtraction of free CO2 in pentane peak to reveal complex doublet. (c, bottom) Peak resolution of the free and complex peaks at D/A ) 12.6.

The free peak shape was fixed at 97.7% Lorentzian character, the value obtained for CO2 in pentane. The three peaks, free, out-of-plane, and in-plane, require 12 parameters, 3 of which are fixed or constrained to a narrow range as described above.

J. Phys. Chem., Vol. 100, No. 26, 1996 10841 The remaining nine parameters were found with the Peaksolve program. The resolved peaks for D/A ) 4.1 are shown along with the raw spectrum in Figure 2c. We were able to obtain a good fit to the data for all concentrations, with an average correlation coefficient of 0.9897. The appearance of the complex peak is less apparent in the CO2-TEA system (Figure 3a) than for the CO2-TBP system (Figure 2a). From these observations, one would expect the strength of the CO2-TEA interaction to be less than the CO2TBP interaction. In Figure 3b the complex doublet is estimated using the subtraction procedure discussed above and is heavily overlapped and broad, making it difficult to resolve both inplane and out-of-plane components. This shape is similar to that of interactions between CO2 and polymers with functional groups containing nitrogen such as poly(2-vinylpyridine) (Figure 7 of ref 13). The out-of-plane peak maximum was estimated to be at 659 ( 2 cm-1. The in-plane peak maximum was estimated to be at 645 ( 3 cm-1, with a greater uncertainty due to the broad complex line shape. The peaks were resolved in the same manner as for the TBP-CO2 system. An example of the resolved peaks and comparison to the original data is given in Figure 3c. The average correlation coefficient for the TEA-CO2 system was 0.9999. Figure 4a shows that changes in the ν2 peak for the CO2PYR system are intermediate between the other two systems. For clarity of presentation, a small pyridine adsorption at 675 cm-1 was subtracted out of Figure 4a using Peaksolve. The broad complex peak may suggest the presence of more than one complex structure. In addition to the lone pair of electrons on the nitrogen atom, pyridine possesses π-electrons which may also be donated to carbon dioxide. However, without more detailed structural information we assume the complex with nitrogen is dominant. Interfering bands from the base are most evident for pyridine, increasing the incertainty in the Kc values for this base in particular. These bands at 675 (small) and 702 cm-1 were resolved using the Peaksolve program. Figure 4a indicates how the large pyridine skeletal absorption at 702 cm-1 affects the high-frequency side of the ν2 peak. The complex peak is revealed through subtraction in Figure 4b and is remarkably similar to the shape found for CO2 in poly(2vinylpyridine) (Figure 7 of ref 13). The out-of-plane and inplane peak maxima are at approximately 657 ( 2 and 645 ( 3 cm-1. Figure 4c gives the curve fitting results for D/A ) 12.6. The average correlation coefficient was 0.98. Figure 5 shows spectra in the region of the CO2 ν3 asymmetric stretching vibration for the CO2-TBP system. When electron density donated to the carbon of CO2 leads to a complex, it is well-known that no new peaks arise for this stretching vibration.11,38 However, changes in the shape of the ν3 peak can give insight into the qualitative nature of CO2-base interactions. There is a decrease in peak width as base is added. This decrease is greatest for TBP and least noticeable for TEA, with PYR intermediate between them (ν3 peaks for the TEA and PYR systems are not shown). In addition, for all systems, there is an increase in intensity as base is added. There is significant right-hand-side asymmetry of the ν3 peak in the TBP system (Figure 5) and to a lesser extent in the PYR system. In the system containing TEA, the ν3 peak retains its symmetry. The magnitudes of these changes follow in general the properties of the bases in Table 1: density, dielectric constant, index of refraction, and dipole moment. The decrease in bandwidth and increase in intensity in the TBP and PYR systems are most likely due to a loss in rotational freedom. A loss in rotational freedom tends to decouple rotational and vibrational modes and sharpen the distribution of vibrational frequencies.36 The resulting

10842 J. Phys. Chem., Vol. 100, No. 26, 1996

Meredith et al.

Kc )

Figure 5. IR spectra in the ν3 region for the TBP-CO2 system at several TBP concentrations and 25.0 °C. Spectra are normalized to 0.206 M CO2. D/A ) mole ratio of donor to acceptor. XD ) mole fraction of donor.

TABLE 1: Selected Data for Solvents at 25 °C solvent

dielectric constant

refractive indexc

dipole momentd (D)

densityc (g/cm3)

pentane triethylamine tributyl phosphate pyridine

1.836a 2.42a 8.05b 12.3a

1.3575 1.3980 1.4226 1.5069

0.072 0.71 3.0 2.2

0.6262e 0.7326 0.9720 0.9782

e

a Reference 69. b Reference 56. c Reference 47. d Reference 70. Value at 20 °C.

decrease in bandwidth has uncovered the “hot” band (ν3 + ν2) - ν2, a well-known transition of CO2 which is responsible for the asymmetry in Figure 5.11,39 The “hot” transition exists but is not observable in less interacting solvents such as pentane and TEA because the wide ν3 band covers it. Rotational motion can be inhibited for several reasons including increased solvent density and solvent-solute interactions. Thompson and Jewell noted similar changes in the intensity and bandwidth of the carbonyl stretching band of acetone as the solvent is changed from n-hexane to pyridine (higher polarity and density).40 Indeed, as shown in Table 1, the density of the Lewis bases, especially TBP and PYR, is greater than that of pentane. However, density alone cannot explain the difference between the PYR and TBP systems. The density of PYR is higher than that of TBP, yet the ν3 spectra indicate that rotational motion is more inhibited in TBP. Therefore, short-range solute-solvent interactions must be responsible. This is reasonable considering the dipole moment of TBP, 3.0 D, is greater than that of pyridine, 2.2 D. While the ν3 band is not used for the calculation of equilibrium constants, this discussion is important because it illuminates the expected order of interaction strengths, namely, CO2-TBP > CO2-PYR > CO2-TEA, and will later provide a check on our quantitative results. Theory. We assume that only 1:1 complexes are formed between CO2 and the bases employed in this study according to

CO2 + B h CO2‚‚‚B

(1)

The equilibrium constant based on molar concentrations is defined by the law of mass action:

[CO2‚‚‚B] [CO2][B]

(2)

where [B] represents the concentration of base, and [CO2‚‚‚B], the concentration of complex. The spectroscopic data may be reduced to obtain the concentrations of free CO2 in order to calculate equilibrium constants using eq 2. The key is to calculate the amount of free CO2 based upon the peak at 661 cm-1. A calibration curve cannot be produced for the complex peak, since it will likely fail to obey Beer’s law. The Beer-Lambert law, A ) lC, is used to calibrate the ν2 free peak and is valid because only dilute solutions of CO2 were examined. The calibration of the CO2 ν2 free peak (661.3 cm-1) was carried out in pentane for CO2 concentrations from 0.03 to 0.18 mol/L. Concentration was calculated based upon the amount of CO2 injected through the sample loop. Ideal mixing was assumed in this and all subsequent calculations of concentration. The product of the extinction coefficient and the path length, l, was 16.0 L/(mol cm) with a correlation coefficient of 0.9990 and an integration range of 675-645 cm-1. The calibration was carried out twice to verify its precision and the reproducibility in l was ( 0.30 L/(mol cm). It was assumed that  for the free peak did not change upon addition of base to the pentane-CO2 solution. Experiments in our lab showed that the shape of the ν2 free peak does not differ appreciably for CO2 dissolved in pentane or CCl4. Furthermore it changes little for concentrations of polar bases up to 0.45 mole fraction. Once the spectral bands were resolved (Figures 2c, 3c, and 4c), the concentration of free CO2 was calculated from the calibration above and the area of the resolved free peak integrated from 675 to 645 cm-1. The concentrations of free base and complex were calculated by mass balance based on knowledge of the overall amounts of base, [B]0, and CO2, [CO2]0, in solution. For the CO2-TEA and CO2-PYR systems, the resulting equation for Kc is

Kc )

[CO2]0 - A/l (A/l)([B]0 - [CO2]0 + A/l)

(3)

where A and  are the area and extinction coefficient of free CO2. The TBP-CO2 system is more complicated than the others since TBP self-associates, forming linear dimers due to the interaction of the highly polar phosphoryl groups.41,42 This selfassociation competes with the CO2-TBP association and must be accounted for in the calculation of Kc. Fortunately, the dimerization of TBP has been the subject of several studies. The most reliable results seem to be those of Dyrssen and Petkovic.41,42 From distribution studies of tripropyl phosphate between water and wet hexane/TBP mixtures, they reported the dimerization constant of TBP, K2 ) [TBP2]/[TBP]2, to be 2.4 L/mol.41 From IR investigations in dry n-hexane, Petkovic obtained a K2 value of 2.9 ( 0.1 L/mol.42 A conflicting result was obtained by Rytting et al., who reported K2 ) 0.21 L/mol and ∆H° ) -27.5 kJ/mol.43 However, these values were calculated by assuming the heat of dilution of TBP data in isooctane was entirely due to the breaking of TBP dimers. This assumption probably accounts for the disparity in K2. On the basis of the above results, a K2 value of 2.9 ( 0.1 L/mol at 25 °C was used. The equation for Kc becomes

Kc )

[CO2]0 - A/l (A/l)([TBP]0 - [CO2]0 + A/l - 2[TBP2])

(4)

CO2 and Lewis Base Equilibrium Constants

J. Phys. Chem., Vol. 100, No. 26, 1996 10843 TABLE 2: Equilibrium Constants at 25 °C acid-base pair CO2-TEA CO2-TBP CO2-PYR SO2-trimethylamine phenol-tributylamine methanol-TEA H2O-TEA I2-PYR phenol-PYR H2O-PYR I2-benzene a

Figure 6. Equilibrium constants, Kc, for the TBP-CO2 interaction at 25 °C as a function of TBP concentration. The concentration dependence is attributed to TBP dimerization, as discussed in the text.

Spectra were recorded for a series of temperatures between 25.0 and 50.0 °C for the CO2-TBP system. Equilibrium constants were calculated at each of these temperatures from eq 4. For condensed phase interactions, the enthalpy of complex formation, ∆H°, may be derived from the temperature dependence of Kc according to the van’t Hoff relation

d ln(Kc)

∆H° ) -R

d(1/T)

- RT2a

(5)

where a is the coefficient of thermal expansion, a ) -1/ν(∂ν/ ∂T)P. It is necessary to include the -RT2a term in the calculation of ∆H° because the concentrations are in units of mol/L, which depend on temperature.44,45 However, these corrections are small (3%). Values of a were estimated using pure-component values in a linear mixing rule based on mole fractions. The standard free energy and entropy of complex formation are evaluated as ∆G° ) -RT ln Kc and ∆S° ) (∆H° - ∆G°)/T. Results. For the CO2-TEA interaction, the average Kc is 0.0463 ( 0.0036 L/mol, and there is moderate variation in Kc. In fact Kc varies between 0.0845 ( 0.0034 and 0.0303 ( 0.0025 L/mol over a concentration range of 0.098 < XTEA < 0.43. Uncertainty is greatest for the smallest ratio of donor to acceptor because the amount of complex CO2 is very small, and the change in the ν2 free peak due to formation of complex is small. As more donor is added, the uncertainty drops due to the increasing amount of bound CO2. For the CO2-PYR complex, only two concentrations of base were investigated. We obtained a Kc value of 0.125 ( 0.0061 L/mol at XPYR ) 0.19 and 0.140 ( 0.0049 L/mol at XPYR ) 0.27. Figure 6 shows the Kc values obtained for the CO2-TBP EDA complex from eq 4. Unlike the CO2-TEA and CO2PYR values, there is an obvious dependence on the concentration of base. Kc varies approximately linearly with XTBP. The values of Kc vary between 0.266 ( 0.089 and 2.60 ( 0.18 L/mol for XTBP between 0.04 and 0.34. This solvent dependence will be discussed in detail when the enthalpies are presented. Even at XTBP ) 0.04, the Kc for the CO2-TBP complex is a full order of magnitude greater than for the CO2-TEA complex. The order of strengths of the CO2 interactions is just as expected from the qualitative observations of the ν2 and ν3 peaks: CO2TBP > CO2-PYR > CO2-TEA. It is worth noting here that we originally calculated Kc by a simpler method.46 The complex CO2 peaks were fit as one

Kc (L/ mol) 0.046a 1.29a 0.133a 2550 29.2 6.8 7.0 157 80 5.3 0.246

∆H° (kJ/ mol) -19.5 -46.0 -28.9 -25.1 -34.1 -25.1 -6.8

solvent

ref

C5H12 C5H12 C5H12 C7H16 CCl4 CCl4 C6H12 C7H16 C7H16 C6H12 C7H16

this work this work this work 45 45 45 45 45 45 45 45

These values are averaged over the concentrations studied.

broad single peak, ignoring the splitting of the degeneracy of the ν2 mode. The concentration of free CO2 was calibrated using the absorbance at peak maximum instead of peak areas. The product l was 1.89 (L)/mol. The Kc values for the CO2TEA system with this simpler approach were about 25% smaller than those obtained using the rigorous method of this paper. For the CO2-PYR system, Kc was about 10% smaller, and for the CO2-TBP system, about 50% smaller. These differences are relatively small for the range of Kc values presented for the systems in Table 2. Table 2 gives the averaged values of Kc for each EDA interaction of CO2 in this study and lists Kc values for other EDA and hydrogen-bonded complexes of tertiary amines and pyridine. For comparison purposes, an attempt was made to find Kc values in solvents similar to that used in this study (i.e., hydrocarbons). The bases employed in this study are all relatively strong. Because of the low values for Kc, CO2 is a weak Lewis acid. For example, the Kc for the CO2-TEA interaction is 2 orders of magnitude less than that for the methanol-TEA and H2O-TEA interactions. Likewise, the Kc for the CO2-PYR interaction is 1 or 2 orders of magnitude less than that of the phenol-PYR and H2O-PYR complexes. For these bases, CO2 is 1-2 orders of magnitude weaker as a Lewis acid compared to these common protic Lewis acids. The strength of the CO2-base complexes seems to be roughly equivalent to that of the weak I2-benzene complex. In aqueous solution, the pKa of pyridine (pKa ) 5.17) is significantly lower than that of TEA (pKa ) 10.72).47 Furthermore, the hydrogen-bonding basicity parameters, β, of TEA and PYR are 0.71 and 0.64, respectively.48 However, pyridine forms a complex with CO2 which is stronger by a factor of three, according to the values of Kc. We postulate that steric repulsion between CO2 and the ethyl groups on TEA is the primary reason. The planar structure of pyridine leads to less steric hindrance, allowing the nitrogen atom to move closer to the carbon of CO2. Indeed, our ab initio calculations indicate that the preferred geometry of the pyridine complex allows the nitrogen to be closer to the carbon in CO2 than in the TEA-CO2 complex (see Appendix A for details of the calculations). Figure 7 shows the energetically favorable geometries from the ab initio calculations for the TEA-CO2 and PYR-CO2 complexes. The carbon-nitrogen distance is 3.12 Å for TEA-CO2 and 2.85 Å for PYR-CO2, and the PYR-CO2 complex is more strongly bound by 1.34 kcal/mol. The oxygens of CO2 are closer to the ethyl groups of TEA than to the aromatic C-H groups of pyridine. The ethyl groups are repelled by the nearby oxygens on CO2. This steric effect distinguishes CO2 from most protic Lewis acids where access to the electron accepting proton is usually not as hindered. Torsional rotations about the C-N bonds in TEA produce higher energy configurations due to repulsion. Such rotations are not present for pyridine. In this

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Meredith et al.

Figure 7. Lowest energy geometries from ab initio calculations for the (a) TEA-CO2 and (b) PYR-CO2 complexes.

obtained.45 This could be due to uncertainty in the ∆H° or K2 values used for the TBP-TBP dimerization. Additionally, the assumption that a 1:1 complex is formed between CO2 and TBP could be somewhat oversimplified. For example, if two CO2 molecules associate with each TBP, the ∆H° will be about half what we obtained. However, it is not possible to discriminate between the two types of complexes with our spectroscopic data. The solvent dependence of Kc is in general due to both nonspecific solvation effects and competition with the TBP selfassociation.45 We consider the latter to be more important here because of the relatively strong TBP self-association. However, the uncertainties in ∆H° and ∆S° and the lack of values at higher concentrations of base makes a quantitative thermodynamic description of the solvent effect on Kc difficult. One component of the complex, TBP, is also a component of the solvent. As TBP is added, the solvent environment likely becomes more ordered because of the dimerization of TBP. The property -T∆S° is positive for bimolecular complex formation because translational and rotational degrees of freedom are lost.49 However, in the more ordered solvent medium, less entropy is lost upon forming the CO2-TBP complex, since entropy is also gained in breaking TBP-TBP interactions. Other studies indicate a similar solvent dependence of Kc when one of the components of the complex also associates with the solvent. A theoretical treatment, which considers the effect of selfassociation of D on the complex formation between A and D, predicts a linear increase in Kc with concentration of D,50 which agrees with our data in Figure 6. Drago et al.51 measured the equilibrium constant for adduct formation between N,N-dimethylacetamide (DMA) and I2 in both benzene and CH2Cl2, a Lewis acid. After correcting for specific interactions with the solvent (benzene-I2 and CH2Cl2-DMA), the Kc value in CH2Cl2 was 23 L/mol, significantly greater than the value in benzene, 6.9 L/mol. Modeling of Phase Behavior

Figure 8. van’t Hoff plot for the TBP-CO2 interaction at two [TBP]/ [CO2] ratios.

TABLE 3: Values Calculated from Spectroscopic Data for the CO2-TBP Interaction (T ) 25 °C) XTBP

Kc (L/mol)

∆G° (kJ/mol) ∆H° (kJ/mol) -T∆S° (kJ/mol)

0.084 0.686 ( 0.074 0.934 ( 0.27 -20.2 ( 8.7 0.12 0.891 ( 0.069 0.287 ( 0.19 -18.5 ( 5.5

21.2 ( 8.9 18.8 ( 5.7

case the difference in the average interaction energy for CO2PYR versus CO2-TEA will be even larger than the difference for the optimized geometries. The van’t Hoff plot for the CO2-TBP interaction is given in Figure 8. The temperature dependence of the ν2 peak was measured at 2 molar ratios of donor to acceptor: 4.1 and 6.1. This allows for the calculation of enthalpy and entropy of association at each concentration. Table 3 gives the results of these calculations. The enthalpy values are -20.3 ( 8.7 and -18.6 ( 5.5 kJ/mol at donor to acceptor ratios of 4.1 (XTBP ) 0.084) and 6.1 (XTBP ) 0.12), respectively. These ∆H° values are higher than may be expected for the relatively low Kc values

Specific chemical interactions may be described with association theories based upon well-defined molecular models. Most association theories involve the assumption of separability of the molecular interactions into physical and chemical interactions, for example, the lattice fluid hydrogen-bonding (LFHB) model. The LFHB model is described in detail elsewhere;30,52 a summary is presented in Appendix B of this paper. The equilibrium constants determined from IR spectroscopy serve as input parameters to characterize the strength of specific interactions in the LFHB model. The LFHB model will be used below to predict vapor-liquid phase equilibria in an effort to determine the effect of these weak chemical interactions. In doing so, it is assumed that the equilibrium constants determined in a ternary system of base-CO2-inert solvent are applicable to a binary system of base-CO2. Figure 9 gives the bubble point curves calculated for the binary TEA-CO2 system using the LFHB model. The calculations were carried out at 25 °C. The physical parameters used for CO2 were those of Panayiotou and Sanchez.53 We used the triethylamine parameters of Sanchez and Lacombe.54 The physical binary interaction parameter, ζ12, is defined by 12 ) ζ12(1122)1/2. We found that when ζ12 is used to fit the solubility of CO2 in n-alkanes, ζ12 scales with molecular weight of the n-alkane. Since n-heptane has a molecular weight similar to that of TEA, we used ζ12 ) 1.05, which fit the solubility of CO2 in n-heptane. Since alkanes do not have chemical interactions with CO2, ζ12 was chosen independently of chemical interactions. The dashed curve in Figure 9 is the bubble point

CO2 and Lewis Base Equilibrium Constants

Figure 9. Comparison of the LFHB predictions of the bubble points for the CO2-TEA binary system at 25 °C with the specific interaction turned off and on. Kc ) 0.046 L/mol. Experiment: ref 55.

Figure 10. Comparison of the LFHB predictions of the bubble points for the CO2-TBP binary system at 25 °C with the specific interaction turned off and on. Kc ) 1.29 L/mol. Experimental points are from ref 57.

calculation for a system neglecting specific interactions between CO2 and TEA; only the physical interactions are considered. The solid curve, however, includes the weak specific interaction between TEA and CO2. The average Kc, 0.046 L/mol, obtained from the FTIR measurements was used to calculate this curve. The effect of the specific interaction is greatest at 50 mol % CO2, where the mole fraction solubility of CO2 in TEA is enhanced by about 11% (13% increase in weight fraction). Although the interaction is weak, it has a noticeable effect on macroscopic phase equilibria. The effect is strongest in the midrange of concentration because it is here that the largest number of cross interactions may be formed. Limited bubble point data were available which allow comparison at the high and low ends of concentration.55 Unfortunately, data were not available in the midrange of concentration. Figure 10 shows the bubble point curve calculated for the TBP-CO2 system at 25 °C. Parameters for tributyl phosphate were obtained from liquid density and vapor pressure data56 using a nonlinear regression technique. The regressed parameters for TBP were T* ) 526 K, P* ) 289 MPa, and F* ) 1079 kg/m3, which yielded a 0.01% error in the liquid density and a 0.02% error in the vapor pressure over the temperature range 25-45 °C. The CO2 lattice fluid parameters of Panayiotou53 were used in this case also. The value of ζ12 corresponding to the n-alkane with a molecular weight near that of

J. Phys. Chem., Vol. 100, No. 26, 1996 10845

Figure 11. LFHB predictions of CO2 sorption in PMMA at 25.0 °C with and without specific interactions. Experimental data of CO2 sorption in PMMA is shown also (ref 23).

TBP was too high. Therefore, ζ12 for the CO2-TBP system was chosen to be 1.15 in order to fit approximately the bubble point data, but after Kc and K2 had been fixed. The selfassociation of TBP is taken into account in both the solid and dashed curves in Figure 10. However, the additional effect of the cross-association between TBP and CO2 is included in the solid line. An average of Kc of 1.29 L/mol was used for the TBP-CO2 interaction; the literature value of K2 ) 2.9 L/mol was used for the self-association of TBP.42 At XTBP ) 0.5 the solubility of CO2 is increased by 23% (28% increase in weight fraction) due to the TBP-CO2 interaction. Even though Kc is an order of magnitude greater than in the TEA-CO2 system, the increase in solubility when the specific interactions are included is about twice that for the TEA-CO2 system. This is because the TBP-CO2 interaction competes with the TBP selfassociation, an interaction which is a degree of magnitude stronger. The LFHB predictions are compared to the bubble point data of Page et al.57 Only a few bubble points were available at this temperature, but the calculation is close to agreement except for the point at 3.6 MPa. Nevertheless, our original intent was not to fit the curves to data, but to show the effect of the weak interaction on a macroscopic property. The final calculation with the LFHB model considers CO2 sorption in a polymer. In an effort to determine the effect of weak specific interactions on the sorption of CO2, we consider a hypothetical polymer with the physical parameters of PMMA: T* ) 696 K , P* ) 503 MPa , and F* ) 1269 kg/ m3.58 After calculating CO2 sorption with only physical parameters and ζ12 ) 1.0, a specific interaction between CO2 and an electron donating site on each structural unit of the polymer is included. Two hypothetical values of Kc are considered, 0.1 and 0.5 L/mol, which are similar in magnitude to those obtained for TBP-CO2.59 Figure 11 gives the sorption of CO2 in PMMA calculated with the LFHB model at 25 °C. For Kc ) 0.5 L/mol, there is good agreement with sorption data23 when the specific interactions are included (solid line). Even more interesting is the great difference in sorption compared to a system with the same physical parameters, but incapable of forming specific interactions (no Kc). At 3.447 MPa (500 psia) the difference in the weight fraction of dissolved CO2 is 1090%, a factor of 12. Figure 11 indicates that weak specific interactions can account for the large differences in CO2 sorption between interacting and noninteracting polymers. A recent IR study indicates the presence of specific intermolecular interactions between CO2 and carbonyl groups in PMMA and suggests

10846 J. Phys. Chem., Vol. 100, No. 26, 1996

Meredith et al.

that specific interactions influence the solubility of CO2 in other polymers.13 However, because we arbitrarily set ζ12 ) 1.0, our results do not fully illuminate the influence of physical interactions, and the difference in solubility cannot be attributed solely to specific interactions without further study.

where H ˆ is the Hamiltonian operator, E is the total energy, and Ψ is the N-electron wave function. Using the electronic density defined as

Conclusions

the Hohenberg-Kohn theorems63 and the Kohn-Sham procedure64 allow to calculate the total energy of the system as

This study presents the first quantitative measurements of equilibrium constants for EDA interactions between CO2 and Lewis bases in solution, in contrast with earlier qualitative studies.11 The detection and assignment of the out-of-plane and in-plane complex ν2 peaks is in agreement with previous spectroscopic studies and ab initio calculations of CO2-base complexes. The strengths of the interactions are in the following order: CO2-TBP > CO2-PYR > CO2-TEA. Although TEA is in general a stronger base than PYR, CO2 interacts more strongly with PYR due to steric repulsion with the ethyl groups of TEA. Our ab initio calculations confirm this spectroscopically observed trend, which illustrates the steric differences between CO2-Lewis base complexes and protic Lewis acidLewis base complexes. The strong concentration dependence of Kc values for the CO2-TBP interaction indicates the importance of competition with a second specific interaction, namely, the self-association of TBP. The LFHB model quantifies the effect of specific interactions between CO2 and Lewis bases on phase equilibria. The calculations show that the solubility of CO2 in TEA is enhanced by 13% at XTEA ) 0.5 when EDA bonding is included. For the strongest interaction, CO2-TBP, the solubility is increased by 28% due to specific interactions. This increase would have been much larger if the solubility enhancement in TBP were not hindered by the self-association of TBP. This study of the specific interactions of CO2 with monomers sheds significant insight into interactions with polymers and polymeric surfactants. Assuming that Kc for the specific interaction between CO2 and a carbonyl group (PMMA) is of the same order as Kc for the interaction with the phosphoryl group of TBP, the solubility of CO2 is increased by a factor of 7-16 compared to the case without specific interactions. Thus, even weak specific interactions can have significant effects on polymer-CO2 phase behavior. As a basis for rational and structure-based design of molecules for use in CO2, this work suggests that pyridine, phosphoryl groups, and other Lewis basic groups can add important specific interactions that raise solubility in CO2. In addition, the combination of spectroscopically determined equilibrium constants and an association theory represents a powerful approach in molecular thermodynamics. Acknowledgment. The authors gratefully acknowledge National Science Foundation Grant CTS-928769, the Separations Research Program of the University of Texas at Austin, and Unilever Research for funding this research. A special thanks is due to Carl Harrison, Lenore LaValle, and the PerkinElmer corporation for the use of the Paragon 1000 spectrometer. In addition, we thank Julie Seiberg for her work in collecting the TEA-CO2 bubble points. Appendix A Ab Initio Calculation. Present density functional theory (DFT) methods are strictly ab initio in character.60,61 They can be directly derived from the electronic (Born-Oppenheimer approximated) time-independent nonrelativistic Schro¨dinger equation of a molecular system:62

H ˆ Ψ ) EΨ

(6)

F(b r 1) ) N∫db r 2 db r 3 ... db r N|Ψ(b r 1b r 2b r 3...b r N)|2

r F(b) r db r+ E ) Ts + ∫υext(b)

(7)

F(b r 1) F(b r 2) 1 db r 1 db r2 + ∫∫ 2 |b r1 - b r 2| Exc(F) (8)

where Ts is the kinetic energy of a system of noninteracting electrons, υext is the potential due to the nuclei, and Exc is the so called exchange-correlation energy. All terms in the righthand side of eq 8 can be calculated exactly, except for the Exc that need to be approximated. There are several good approximations for Exc. We have used the combination of the Becke-3 (B3)65 exchange functional with the Lee-Yang-Parr (LYP)66 correlation functional. Both functionals are approximations that contain the density and its gradient. In addition, the B3 exchange functional computes a portion of the exchange energy in the same fashion as the Hartree-Fock exchange energy is calculated yet using the noninteractive wave function. We use the above formalism as implemented in the Gaussian92/DFT67 and Gaussian-9468 programs with two standard basis sets. One is the 6-31+g** that has one set of six contracted Gaussian functions for the core orbitals, two sets of three, and one Gaussian functions for the valence orbitals. In addition, it has one set of sp-diffuse functions and one set of d-polarization functions centered in the carbon, nitrogen, and oxygen atoms. The other basis set is the 6-311++G** which in addition to the former has one more set of functions for the valence orbitals, and one set of s-diffuse and p-polarization functions centered on the Hydrogen atoms. Appendix B LFHB Model. Although its title refers to hydrogen bonding, the LFHB model is valid for systems exhibiting any type of specific interaction. The canonical partition function is assumed to be separable into physical and chemical terms:

Q ) QPQC

(9)

The physical interactions may be described with the well-known lattice fluid model.54 The chemical interactions are treated by considering the number of pair interactions between donor and acceptor groups. In this way, the existence of specific molecular associates is not invoked a priori; the emphasis is placed on counting the number of possible donor-acceptor interactions. The lattice fluid equation of state is given by

˜ + T˜ [ln(1 - F˜ ) + F˜ (1 - 1/r˜)] ) 0 F˜ 2 + P

(10)

where F˜ , T˜ , and P ˜ are the reduced density, temperature, and pressure, respectively. Three characteristic parameters, T*, P*, and F*, are required to describe the physical interactions, with T˜ ) T/T*, P ˜ ) P/P*, and F˜ ) F/F*. In eq 10, r˜ is the modified average chain length, a function of the physical parameters and the number of specific interactions at equilibrium. 1. TEA-CO2. In the TEA-CO2-pentane system, TEA has one electron-donor site and CO2 has one electron-acceptor site. There are no specific interactions between pentane and the solutes. The number of electron donor-acceptor interactions

CO2 and Lewis Base Equilibrium Constants

J. Phys. Chem., Vol. 100, No. 26, 1996 10847

at equilibrium is N12. Minimizing the Gibbs free energy with respect to N12, holding all other variables constant, yields

(N1 - N12)(N2 - N12) ) N12rNυ˜ exp(G°12/RT)

(11)

where N1 and N2 are the total number of base and CO2 molecules, respectively, and G°12 is the Gibbs free energy of formation for the EDA complex, from the unassociated molecules in their close packed fluid state. Equation 11 can be used to find the fraction of EDA bonds, or alternatively, the percentage of free base or CO2, at equilibrium. G°12 is usually an adjustable parameter which describes hydrogen bonding in a particular system, but in this case, it is related to the measured equilibrium constant, Kc. The relation is

Kc ) ν* exp(-G°12/RT)

(12)

where ν* ) RT*/P*. Using a spectroscopically determined equilibrium constant adds physical meaning to the model by eliminating adjustable association parameters. Finally, for a binary system, the lattice fluid and chemical (specific) parts of the chemical potential are given by eqs 56 and 57, respectively, of ref 30. The equation of state (eq 9) and the chemical potential expressions are used together with eqs 11 and 12 to predict binary vapor-liquid phase equilibrium at 25 °C for a triethylamine-CO2 mixture. 2. TBP-CO2. The self-association of TBP changes the equations that describe specific interactions in the LFHB model. A derivation similar to that for TEA-CO2 yields the following equations for the equilibrium of 1-1 (TBP self-association) and 1-2 (TBP-CO2) bonds:

(N1 - N11 - N12)(N1 - N11) ) rNυ˜ N11 exp(G°11/RT)

(13)

(N1 - N11 - N12)(N2 - N12) ) rNυ˜ N12 exp(G°12/RT)

(14)

where G°11 and G°12 are related to their respective equilibrium constants with eq 12. K11, the equilibrium constant for selfassociation of TBP, is known from the literature,56 and K12, the constant for the TBP-CO2 interaction is taken as the average Kc obtained in the FTIR experiments. The physical part of the chemical potential expression is given by eq 56 of ref 30. For TBP, the chemical part of the chemical potential expression is given by eq 63 of ref 30 and for CO2, it is given by eq 64 of ref 30. 3. Polymer-CO2. The LFHB model is used to describe CO2-polymer phase behavior for poly(methyl methacrylate) (PMMA). We assume a 1:1 EDA complex between CO2 and each carbonyl site on PMMA. The equation of state is eq 10, and the lattice fluid part of the chemical potential is given by eq 56 of ref 30. For PMMA-CO2, the equilibrium of specific interactions is described by

(N1 - N12)(aN2 - N12) ) N12rNυ˜ exp(G°12/RT)

(15)

where component 2 is the polymer and a is the number of electron donating sites per polymer molecule. The chemical part of the chemical potential for CO2 is given by eq 57 of ref 30 and by eq 58 of ref 30 for the polymer. Supporting Information Available: Tables of experimental and calculated results (3 pages). Ordering information is given on any current masthead page. References and Notes (1) Reetz, M.; Ko¨nen, W.; Strack, T. Chimia 1993, 47, 493. (2) Carbon Dioxide Chemistry: EnVironmental Issues; Paul, J., Pradier, C. M., Eds.; The Royal Society of Chemistry: Cambridge, UK, 1994.

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