quantitative equilibrium constants between co2 and lewis bases from ftir spectroscopy

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Quantitative Equilibrium Constants between CO2 and Lewis Bases from FTIR Spectroscopy

J. Carson Meredith and Keith P. Johnston*

Department of Chemical Engineering, UniV ersity of Texas at Austin, Austin, Texas 78712

Jorge M. Seminario

Department of Chemistry, UniV ersity 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

ReceiV ed: October 26, 1995; In Final Form: January 22, 1996 X

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 K c 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 groupsin TEA cause the binding energy of the CO2-TEA complex to be weaker than that of the CO2-PYR complexby 1.34 kcal/mol, a trend that is in agreement with our spectroscopic data. The lattice fluid hydrogen bondingmodel was used in conjunction with the spectroscopically determined K c values to predict bubble points forthe CO2-TEA and CO2-TBP systems and CO2 sorption in a hypothetical polymer. These calculations indicatethat these relatively weak specific interactions have a measurable effect on phase behavior and can influencesorption of CO2 in polymers.

Introduction

Carbon dioxide is of current interest as an environmentallyacceptable alternative to organic solvents in many chemicalprocessing applications.1,2 CO2 is the least expensive solventafter H2O and is in plentiful supply. Its incorporation intochemical processes could actually reduce emissions to theatmosphere by replacing organic solvents. Recent research inthis area has focused on identifying molecules that havefavorable intermolecular interactions with CO2. Because of thelow polarizability of CO2, along with the lack of a dipolemoment, nonvolatile polar molecules, surfactants, and nearlyall polymers are virtually insoluble. However, CO2 has a largequadrupole moment and both Lewis acid and base sites. Thereis evidence from microwave and radio-frequency spectros-

copy,

3,4

ab initio calculations,

5-7

and infrared spectroscopy

8-13

that CO2 acts as a Lewis acid in the presence of Bronsted andLewis 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 andbases 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 thesecomplexes and to what degree specific interactions influencecertain thermodynamic properties.

The Lewis acidity of CO2 can be important in practicalapplications where CO2 is a reaction medium or reactionpartner.1,14 DeSimone et al. have synthesized highly soluble

poly(1,1-dihydroperfluorooctyl acrylate) in supercritical fluid

(SCF) CO2.15 The CO2-acrylate interactions likely enhancethe solubility of this polymer. Using this polymer as a stabilizer,they have recently synthesized PMMA in SCF CO2 by disper-sion polymerization.16

CO2 shows promise as a replacement for phosgene in theproduction of isocyanates and urethanes from primary andsecondary amines.17 A key in developing this technology isdiscovering molecules that activate CO2, an extremely stablemolecule. McGhee et al.18 have recently used tertiary aminesas co-bases to enhance reactivity of carbamates formed asintermediates in the production of urethanes.

Walsh et al.19 discuss the importance of specific Lewis acid-base interactions in enhancing the solubilities of certainnonvolatile compounds in SCF CO2-cosolvent mixtures. They

propose that weak specific interactions between CO2 and thecosolvent can inhibit the solubility enhancements due to thecosolvent that are seen in noninteracting solvents such as ethane.

In an effort to design surfactants for use in CO2, Newman etal.20 examined the phase behavior of fluoroether functionalsurfactants in supercritical CO2. They proposed that thesolubility of the fluorinated surfactants in CO2 was enhancedby the electron-donating capacity of the fluoroether functionalgroups. Yee et al.21 used FTIR spectroscopy to examinemolecular interactions of CO2 dissolved in C2H6 and C2F6. Fromshifts in the ν2 frequency of CO2 and a semiempirical dielectriccontinuum model, they concluded that CO2 is more repulsiveto C2F6 than C2H6 and that no specific attractive interactionsexist between CO2 and perfluorinated molecules. Interestingly,X Abstract published in Ad V ance ACS Abstracts, March 15, 1996.

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

S0022-3654(95)03161-3 CCC: $12.00 © 1996 American Chemical Society



deviations in the model indicated the possibility of specificinteractions between CO2 and acetone, methanol, and toluene.

Further indication of the need for a quantitative understandingof the Lewis acidity of CO2 can be seen in studies of thesolubilities of CO2 in polymers. Fried and Li22 studiedinteractions of CO2 with cellulose acetate and with poly(methylmethacrylate) using IR spectroscopy. They concluded that shiftsin the carbonyl stretching frequencies indicate interactionsbetween CO2 and the polar carbonyl group. Also, the solubilityof near-critical CO2 in glassy polymers shows a trend in theorder: poly(vinyl acetate) > poly(methyl methacrylate) > poly-(vinyl chloride).23 In fact, at 500 psia and 25 °C, the solubilityof CO2 in PMMA is 75 wt % greater than in PVC. Wissingerreport a solubility of CO2 in PMMA that is 205 wt % greaterthan that in polystyrene at 35 °C and 500 psia.24 The authorssuggest that specific interactions between CO2 and the polargroups of PMMA and PVA are responsible for the enhancedsolubilities. However, it is unclear what role physical forcesand specific chemical interactions play in influencing thesolubility of CO2 in polymers.

Many studies have focused on identifying the nature of theinteractions 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 butalso in understanding fundamentals such as hydrogen bondingand reverse micelle formation.25 Hyatt26 measured the shiftsin IR frequencies of several probe compounds in both liquidand SCF CO2. Shifts in the ν(CdO) of acetone and cyclo-hexanone were slightly greater than in the solvent n-hex-ane and slightly less than those in aromatic solvents, indi-cating a low tendency for CO2 to interact with basic carbonylgroups. For the probe pyrrole, large shifts in the ν(N-H)stretching frequency indicated hydrogen bonding betweenpyrrole and CO2. Kim and Johnston27 measured transitionenergies, E T, for the dye phenol blue in CO2. On a plot of E Tvs 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 Lewisacidity toward phenol blue, a Lewis base. Sigman et al.29

measured π * dipolarity-polarizability values for 10 solvato-chromic indicators in SCF CO2. They suggested that specificinteractions, not accounted for in π *, are important. They alsofound β, the hydrogen-bonding basicity parameter, in SCF andliquid CO2 to be near zero, indicating a low tendency to donateelectrons.

On the basis of the above studies, there is considerableuncertainty concerning the nature and importance of the Lewisacidity of CO2. Direct IR spectroscopic measurements of thespecific interactions of CO2 with basic monomers in the liquidphase promise to shed insight into the magnitude and role of the specific interactions. Dobrowolski and Jamroz11 report an

IR study of the ν3 and ν2 frequencies of CO2 dissolved in over30 solvents. For highly basic solvents such as amines andamides, the ν2 frequency is split, a phenomenon they attributeto weak EDA complexes between the bases and CO2. However,in their experiments, CO2 was dissolved in pure base, so thatthe absorbance of free CO2 could not be calibrated. Conse-quently, equilibrium constants could not be determined.

In this work, the Lewis acidity of CO2 is examined in aquantitative manner from its ν2 bending mode in the presenceof 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, K c, for the EDA interactions are definedand measured. The CO2 and base are dissolved in an inert liquid

solvent, pentane, incapable of forming specific interactions withCO2 or the bases. The use of an inert solvent allows calibrationof the “free” ν2 CO2 peak, unaffected by the base. Changes inthe ν2 absorbance are examined as the solvent changes fromnoninteracting (pentane) to interacting (pentane + base). Forthe strongest interaction, that of CO2 and TBP, K c values aremeasured at a series of temperatures, and ∆ H ° and ∆S ° valuesare determined. In addition, an ab initio calculation is carriedout in order to compare the relative stabilities and geometriesof the CO2-TEA and CO2-PYR complexes.

In an effort to determine the importance of weak specificinteractions on phase equilibria, we calculate the bubble pointsfor binary mixtures of CO2-TEA and CO2-TBP and CO2

sorption in polymers. This is accomplished with the lattice fluidhydrogen bonding model (LFHB),30,31 a chemical associationtheory. The spectroscopically determined equilibrium constantsare used directly in the LFHB calculations. In this way, theenhancement of solubility of CO2 in the base can be calculatedas the specific interaction is turned on with the model.

Experimental Section

Pentane (Mallinckrodt, spectrophotometric grade), triethyl-amine (EM Science, 98%), tributyl phosphate (Aldrich, 99.9+%;FMC), pyridine (MCB, 99.9%), and carbon dioxide (LiquidCarbonic, 99.5%) were used as received, except for drying overmolecular sieves (Mallinckrodt, Grade 514GT, 4 Å). Carbondioxide was dried by flowing the liquid through a 10 cm3

stainless steel tube containing a desiccant, Ca2SO4. Figure 1gives a schematic of the FTIR apparatus. Unless statedotherwise, all vessels and connections were of stainless steelconstruction. Solutions were prepared in a variable volume viewcell (28 mL) with a magnetic stir bar. Carbon dioxide wasadded accurately by using a six-port switching valve (ValcoInstruments, Model C6W) in conjunction with a sample loop.The sample loop volume was determined to be 30.2 ( 0.5 µLby the weight of water it contained at room temperature. Apressure gauge (Heise, Model H8315), connected to the CO2

syringe pump, indicated the pressure of CO2 in the sample loopto within (0.15 bar. A syringe pump (HIP, Model 87-6-5) filled

Figure 1. Schematic of the experimental apparatus.

10838 J. Phys. Chem., Vol. 100, No. 26, 1996 Meredith et al.



with pentane was connected to the back side of the view cell tocontrol pressure in the system. The system pressure wasmonitored to within (0.35 bar with a pressure gauge (Heise,Model 54198) connected to the back of the view cell. Amagnetically 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 outletport and two ZnSe windows (Morton Advanced Materials). TheZnSe windows allowed transmission in the 600-700 cm-1 rangenecessary to observe the ν2 bending mode of CO2. The cell

path length, l, was approximately 0.5 mm as determined by amicrometer measurement; however, the path length was neverchanged during the course of the experiments, and a precisedetermination 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 recordedwith a Perkin-Elmer Paragon 1000 FTIR spectrometer andconsisted of 64 averaged scans at 2 cm-1 resolution. Thespectrometer compartment was purged with dry nitrogen gasto eliminate atmospheric interference. A temperature controller(Omega Engineering) maintained the temperature of the IR cellto within 0.1 °C.

Before each experiment, the entire sealed system (∼33 mL)was purged with nitrogen gas, and liquid pentane was intro-duced. Once a pure pentane baseline spectrum was recorded,CO2 was injected into the system. Initially, for calibration, thiswas done by using the six-port valve and sample loop. TheCO2 was introduced as a liquid at 68.9 bar (1000 psig) and 22°C. CO2 densities were determined by using an accurateequation of state.32 A calibration curve for the ν2 frequencywas constructed by adding incremental amounts of CO2 topentane and recording the spectrum. Each Lewis base wasadded as liquid using a glass Luer-Lock syringe after reducingthe system pressure to about 0.3 bar. The base was usuallyadded in 2.0 cm3 increments. After each incremental additionof base, the solution was allowed to mix for 10 min, and thespectrum was recorded. For the bases triethylamine andpyridine, all spectra were recorded at 25.0 °C. For tributylphosphate, spectra were recorded at a series of temperaturesbetween 25.0 and 55.0 °C. The pressure was 6.89 bar (100psig) in all experiments to ensure that all of the CO2 wasdissolved and that no gas pockets existed in the system. Inaddition, CO2 concentrations were chosen to ensure thatabsorption of the ν2 peak remained in the range 0.5-1.0.

Results and Discussion

FTIR Spectroscopy. Because of a depletion of electrondensity on the carbon atom, CO2 is a weak Lewis acid.Triethylamine, pyridine, and tributyl phosphate, due to thenitrogen and phosphoryl groups, are strong Lewis bases. In anEDA interaction, electron density is considered to be transferredfrom the highest occupied molecular orbital of the donormolecule into the lowest unoccupied molecular orbital of theacceptor.33 The strength, orientation dependence, and lifetimeof these interactions are sufficiently greater than those of physical interactions (e.g., van der Waals forces) to justify theirtreatment as chemical, or specific, interactions.34 As the donorand acceptor molecules move close together to form a complex,the intramolecular bond lengths in each molecule change as theelectron distribution changes. Primary bonds in each molecule,those involving the actual donor and acceptor atoms, increasein length when a complex is formed. This increase indicates aslight weakening of the primary bonds in the donor and acceptormolecules. In addition, the polarity of primary bonds in eachmolecule is enhanced due to formation of the complex.35 Each

of these changes in the donor and acceptor molecules isresponsible for changes in IR spectra. As mentioned in theIntroduction, Dobrowolski and Jamroz11 report the splitting of the ν2 peak of carbon dioxide dissolved in various Lewis bases.They attribute the appearance of the second peak, which usuallyoccurs at 10-15 cm-1 below the original ν2 peak, to theformation of an electron donor-acceptor complex.

The assignment of free and complex peaks requires a carefulconsideration of the nature of the ν2 vibration. Due to thesymmetry 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 questionarises as to how the presence of Lewis base affects thedegenerate components of the ν2 mode. These are labeled in-plane or out-of-plane with respect to the plane defined by thelone pair of the electron donor (oxygen or nitrogen atoms) andthe OdCdO axis. It is expected that the degeneracy of the ν2

mode of CO2 will be released due to interaction with the electronlone pair of the Lewis base, and the vibration will appear as adoublet shifted to a lower frequency with respect to the freepeak. The in-plane component should have a larger shift thanthe out-of-plane since the in-plane interaction with the electrondonor is more direct.6,7,13,37 These observations are seen in our

spectra as well as others.

8-11,13

Furthermore, decreases in theheight of the higher frequency free CO2 peak indicate theamount of CO2 complexed with base.

Figures 2-4 show spectra in the region of the ν2 vibrationfor the CO2-TBP, CO2-TEA, and CO2-PYR interactions,respectively. Although the spectra were recorded at differentCO2 concentrations, they are normalized to the initial concentra-tion of CO2 in Figures 2a, 3a, and 4a for clarity of presentation.In addition, the spectrum of pure pentane at the same conditionshas been subtracted from each of the spectra. The location of the peak maximum is at 661.3 cm-1 in pure pentane, consistentwith results of others.11 As Lewis base is added, severalimportant changes occur in the ν2 vibration. Most important isthe appearance of a second peak at a lower frequency. Also,

the intensity of the high-frequency (free) peak falls due to theformation of the EDA complex. For the bases studied, thelargest complex peaks were observed for the CO2-TBP systemin Figure 2a. A linear baseline was used in Figure 2a to correcta slight slope in the spectra due to the presence of interferingTBP bands at 557 and 720 cm-1. The in-plane complex peakappears at 650 cm-1 for the CO2-TBP interaction and is broaderthan the free peak. However, the out-of-plane peak is likelyburied under the free CO2 peak. To reveal the shape of thecomplex peaks, a free CO2 in pentane peak was subtracted fromthe total spectrum, as demonstrated in Figure 2b. The absor-bance of the free CO2 peak was estimated by assuming that allof 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 theposition and shape, but not the correct area of the complexdoublet components. In Figure 2b, the doublet has peaks at658 and 650 cm-1, presumably for the out-of-plane and in-planecomponents, respectively. The shape of this doublet is similarto that found for CO2 dissolved in PMMA and poly(vinylacetate), where CO2 forms a complex with carbonyl groups(Figures 3 and 8 of ref 13). The relatively sharp complex peakindicates a well-defined structure.

Curve resolution makes determination of the peak parametersand areas for the free and complex peaks possible. Resolutionwas accomplished with the Peaksolve program, which uses aLevenberg-Marquardt nonlinear optimization algorithm toarrive at optimized peak parameters based on initial estimates.

CO2 and Lewis Base Equilibrium Constants J. Phys. Chem., Vol. 100, No. 26, 1996 10839



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

CO2-TBP system (Figure 2b), the out-of-plane and in-planecomplex peak maxima were estimated to be at approximately658 and 650 cm-1, respectively. These locations were eachconstrained to a range of (2 cm-1 in the Peaksolve program.

Figure 2. (a, top) IR spectra in the ν2 region for the TBP-CO2 systemat several TBP concentrations and 25.0 °C. Spectra are normalized to0.206 M CO2. D / A ) mole ratio of donor to acceptor. X D ) molefraction of donor. (b, middle) Subtraction of free CO2 in pentane peakto reveal complex doublet. (c, bottom) Peak resolution of the free andcomplex peaks at D / A ) 4.1.

Figure 3. (a, top) IR spectra in the ν2 region for the TEA-CO2 systemat several TEA concentrations and 25.0 °C. Spectra are normalized to0.176 M CO2. D / A ) mole ratio of donor to acceptor. X D ) molefraction of donor. (b, middle) Subtraction of free CO2 in pentane peakto reveal complex doublet. (c, bottom) Peak resolution of the free andcomplex peaks at D / A ) 24.9.




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 whichare fixed or constrained to a narrow range as described above.

The remaining nine parameters were found with the Peaksolveprogram. The resolved peaks for D / A ) 4.1 are shown alongwith the raw spectrum in Figure 2c. We were able to obtain agood fit to the data for all concentrations, with an averagecorrelation coefficient of 0.9897.

The appearance of the complex peak is less apparent in theCO2-TEA system (Figure 3a) than for the CO2-TBP system(Figure 2a). From these observations, one would expect thestrength of the CO2-TEA interaction to be less than the CO2-TBP interaction. In Figure 3b the complex doublet is estimatedusing the subtraction procedure discussed above and is heavilyoverlapped and broad, making it difficult to resolve both in-plane and out-of-plane components. This shape is similar tothat of interactions between CO2 and polymers with functionalgroups containing nitrogen such as poly(2-vinylpyridine) (Figure7 of ref 13). The out-of-plane peak maximum was estimatedto be at 659 ( 2 cm-1. The in-plane peak maximum wasestimated to be at 645 ( 3 cm-1, with a greater uncertaintydue to the broad complex line shape. The peaks were resolvedin the same manner as for the TBP-CO2 system. An exampleof the resolved peaks and comparison to the original data isgiven in Figure 3c. The average correlation coefficient for theTEA-CO2 system was 0.9999.

Figure 4a shows that changes in the ν2 peak for the CO2-PYR system are intermediate between the other two systems.For clarity of presentation, a small pyridine adsorption at 675cm-1 was subtracted out of Figure 4a using Peaksolve. Thebroad complex peak may suggest the presence of more thanone complex structure. In addition to the lone pair of electronson the nitrogen atom, pyridine possessesπ -electrons which mayalso be donated to carbon dioxide. However, without moredetailed structural information we assume the complex withnitrogen is dominant. Interfering bands from the base are mostevident for pyridine, increasing the incertainty in the K c valuesfor this base in particular. These bands at 675 (small) and 702cm-1 were resolved using the Peaksolve program. Figure 4aindicates how the large pyridine skeletal absorption at 702 cm-1

affects the high-frequency side of the ν2 peak. The complexpeak is revealed through subtraction in Figure 4b and isremarkably similar to the shape found for CO2 in poly(2-vinylpyridine) (Figure 7 of ref 13). The out-of-plane and in-plane peak maxima are at approximately 657 ( 2 and 645 ( 3cm-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 asymmetricstretching vibration for the CO2-TBP system. When electrondensity donated to the carbon of CO2 leads to a complex, it iswell-known that no new peaks arise for this stretching vibra-tion.11,38 However, changes in the shape of the ν3 peak cangive 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, withPYR intermediate between them (ν3 peaks for the TEA and PYRsystems are not shown). In addition, for all systems, there isan increase in intensity as base is added. There is significantright-hand-side asymmetry of the ν3 peak in the TBP system(Figure 5) and to a lesser extent in the PYR system. In thesystem containing TEA, the ν3 peak retains its symmetry. Themagnitudes of these changes follow in general the propertiesof the bases in Table 1: density, dielectric constant, index of refraction, and dipole moment. The decrease in bandwidth andincrease in intensity in the TBP and PYR systems are most likelydue to a loss in rotational freedom. A loss in rotational freedomtends to decouple rotational and vibrational modes and sharpenthe distribution of vibrational frequencies.36 The resulting

Figure 4. (a, top) IR spectra in the ν2 region for the PYR-CO2 systemat several PYR concentrations and 25.0 °C. Spectra are normalized to0.259 M CO2. D / A ) mole ratio of donor to acceptor. X D ) molefraction of donor. (b, middle) Subtraction of free CO2 in pentane peakto reveal complex doublet. (c, bottom) Peak resolution of the free andcomplex peaks at D / A ) 12.6.




decrease in bandwidth has uncovered the “hot” band (ν3 + ν2)- ν2, a well-known transition of CO2 which is responsible forthe asymmetry in Figure 5.11,39 The “hot” transition exists butis not observable in less interacting solvents such as pentaneand TEA because the wide ν3 band covers it. Rotational motion

can be inhibited for several reasons including increased solventdensity and solvent-solute interactions. Thompson and Jewellnoted similar changes in the intensity and bandwidth of thecarbonyl stretching band of acetone as the solvent is changedfrom 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 betweenthe PYR and TBP systems. The density of PYR is higher thanthat of TBP, yet the ν3 spectra indicate that rotational motionis more inhibited in TBP. Therefore, short-range solute-solventinteractions must be responsible. This is reasonable consideringthe 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 calculationof equilibrium constants, this discussion is important becauseit illuminates the expected order of interaction strengths, namely,CO2-TBP > CO2-PYR > CO2-TEA, and will later providea check on our quantitative results.

Theory. We assume that only 1:1 complexes are formedbetween CO2 and the bases employed in this study accordingto

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

where [B] represents the concentration of base, and [CO2‚‚‚B],the concentration of complex. The spectroscopic data may bereduced to obtain the concentrations of free CO2 in order tocalculate equilibrium constants using eq 2. The key is tocalculate the amount of free CO2 based upon the peak at 661cm-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 wereexamined. The calibration of the CO2 ν2 free peak (661.3 cm-1)was carried out in pentane for CO2 concentrations from 0.03 to0.18 mol/L. Concentration was calculated based upon theamount of CO2 injected through the sample loop. Ideal mixingwas assumed in this and all subsequent calculations of concen-tration. The product of the extinction coefficient and the pathlength, l, was 16.0 L/(mol cm) with a correlation coefficientof 0.9990 and an integration range of 675-645 cm-1. Thecalibration was carried out twice to verify its precision and thereproducibility 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 inour lab showed that the shape of the ν2 free peak does not differappreciably for CO2 dissolved in pentane or CCl4. Furthermoreit changes little for concentrations of polar bases up to 0.45mole fraction. Once the spectral bands were resolved (Figures2c, 3c, and 4c), the concentration of free CO2 was calculatedfrom the calibration above and the area of the resolved freepeak integrated from 675 to 645 cm-1. The concentrations of free base and complex were calculated by mass balance basedon 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 K c is

where A and are the area and extinction coefficient of freeCO2.

The TBP-CO2 system is more complicated than the otherssince TBP self-associates, forming linear dimers due to theinteraction of the highly polar phosphoryl groups.41,42 This self-association competes with the CO2-TBP association and mustbe accounted for in the calculation of K c. Fortunately, thedimerization of TBP has been the subject of several studies.The most reliable results seem to be those of Dyrssen andPetkovic.41,42 From distribution studies of tripropyl phosphatebetween water and wet hexane/TBP mixtures, they reported the

dimerization constant of TBP, K 2 ) [TBP2]/[TBP]2, to be 2.4L/mol.41 From IR investigations in dry n-hexane, Petkovicobtained a K 2 value of 2.9 ( 0.1 L/mol.42 A conflicting resultwas obtained by Rytting et al., who reported K 2 ) 0.21 L/moland ∆H° ) -27.5 kJ/mol.43 However, these values werecalculated by assuming the heat of dilution of TBP data inisooctane was entirely due to the breaking of TBP dimers. Thisassumption probably accounts for the disparity in K 2. On thebasis of the above results, a K 2 value of 2.9 ( 0.1 L/mol at 25°C was used. The equation for K c becomes

Figure 5. IR spectra in the ν3 region for the TBP-CO2 system atseveral TBP concentrations and 25.0 °C. Spectra are normalized to0.206 M CO2. D / A ) mole ratio of donor to acceptor. X D ) molefraction of donor.

TABLE 1: Selected Data for Solvents at 25 °C

solvent dielectricconstant refractiveindexc dipolemomentd (D) densityc

(g/cm3)

pentane 1.836a 1.3575 0.072 0.6262e

triethylamine 2.42a 1.3980 0.71 0.7326tributyl phosphate 8.05b 1.4226 3.0 0.9720pyridine 12.3a 1.5069 2.2 0.9782

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

CO2 + B h CO2‚‚‚B (1)

K c )[CO2‚‚‚B]

[CO2][B](2)

K c )[CO2]0 - A / l

( A / l)([B]0 - [CO2]0 + A / l) (3)

K c )[CO2]0 - A / l

( A / l)([TBP]0 - [CO2]0 + A / l - 2[TBP2])(4)




Spectra were recorded for a series of temperatures between25.0 and 50.0 °C for the CO2-TBP system. Equilibriumconstants were calculated at each of these temperatures fromeq 4. For condensed phase interactions, the enthalpy of complexformation, ∆ H °, may be derived from the temperature depen-dence of K c according to the van’t Hoff relation

where a is the coefficient of thermal expansion, a ) -1/ ν(∂ν / ∂T )P. It is necessary to include the - RT 2a term in thecalculation of ∆ H ° because the concentrations are in units of mol/L, which depend on temperature.44,45 However, thesecorrections are small (3%). Values of a were estimated usingpure-component values in a linear mixing rule based on molefractions. The standard free energy and entropy of complex

formation are evaluated as ∆G° ) - RT ln K c and ∆S ° ) (∆ H °- ∆G°)/ T .

Results. For the CO2-TEA interaction, the average K c is0.0463 ( 0.0036 L/mol, and there is moderate variation in K c.In fact K c varies between 0.0845 ( 0.0034 and 0.0303 ( 0.0025L/mol over a concentration range of 0.098 < X TEA < 0.43.Uncertainty is greatest for the smallest ratio of donor to acceptorbecause the amount of complex CO2 is very small, and thechange in the ν2 free peak due to formation of complex is small.As more donor is added, the uncertainty drops due to theincreasing amount of bound CO2. For the CO2-PYR complex,only two concentrations of base were investigated. We obtaineda K c value of 0.125 ( 0.0061 L/mol at X PYR ) 0.19 and 0.140( 0.0049 L/mol at X PYR ) 0.27.

Figure 6 shows the K c values obtained for the CO2-TBPEDA complex from eq 4. Unlike the CO2-TEA and CO2-PYR values, there is an obvious dependence on the concentra-tion of base. K c varies approximately linearly with X TBP. Thevalues of K c vary between 0.266 ( 0.089 and 2.60 ( 0.18 L/molfor X TBP between 0.04 and 0.34. This solvent dependence willbe discussed in detail when the enthalpies are presented. Evenat X TBP ) 0.04, the K c for the CO2-TBP complex is a full orderof magnitude greater than for the CO2-TEA complex. Theorder of strengths of the CO2 interactions is just as expectedfrom the qualitative observations of the ν2 and ν3 peaks: CO2-TBP > CO2-PYR > CO2-TEA.

It is worth noting here that we originally calculated K c by asimpler method.46 The complex CO2 peaks were fit as one

broad single peak, ignoring the splitting of the degeneracy of the ν2 mode. The concentration of free CO2 was calibratedusing the absorbance at peak maximum instead of peak areas.The product l was 1.89 (L)/mol. The K c values for the CO2-TEA system with this simpler approach were about 25% smallerthan those obtained using the rigorous method of this paper.For the CO2-PYR system, K c was about 10% smaller, and forthe CO2-TBP system, about 50% smaller. These differencesare relatively small for the range of K c values presented for the

systems in Table 2.Table 2 gives the averaged values of K c for each EDA

interaction of CO2 in this study and lists K c values for otherEDA and hydrogen-bonded complexes of tertiary amines andpyridine. For comparison purposes, an attempt was made tofind K c values in solvents similar to that used in this study (i.e.,hydrocarbons). The bases employed in this study are allrelatively strong. Because of the low values for K c, CO2 is aweak Lewis acid. For example, the K c for the CO2-TEAinteraction is 2 orders of magnitude less than that for themethanol-TEA and H2O-TEA interactions. Likewise, the K cfor the CO2-PYR interaction is 1 or 2 orders of magnitudeless 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. Thestrength of the CO2-base complexes seems to be roughlyequivalent to that of the weak I2-benzene complex.

In aqueous solution, the pK a of pyridine (pK a ) 5.17) issignificantly lower than that of TEA (pK a ) 10.72).47 Further-more, the hydrogen-bonding basicity parameters, β, of TEA andPYR are 0.71 and 0.64, respectively.48 However, pyridine formsa complex with CO2 which is stronger by a factor of three,according to the values of K c. We postulate that steric repulsionbetween 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 preferredgeometry of the pyridine complex allows the nitrogen to becloser to the carbon in CO2 than in the TEA-CO2 complex(see Appendix A for details of the calculations). Figure 7 showsthe energetically favorable geometries from the ab initiocalculations for the TEA-CO2 and PYR-CO2 complexes. Thecarbon-nitrogen distance is 3.12 Å for TEA-CO2 and 2.85 Åfor PYR-CO2, and the PYR-CO2 complex is more stronglybound by 1.34 kcal/mol. The oxygens of CO2 are closer to theethyl groups of TEA than to the aromatic C-H groups of pyridine. The ethyl groups are repelled by the nearby oxygenson CO2. This steric effect distinguishes CO2 from most proticLewis acids where access to the electron accepting proton isusually not as hindered. Torsional rotations about the C-Nbonds in TEA produce higher energy configurations due torepulsion. Such rotations are not present for pyridine. In this

Figure 6. Equilibrium constants, K c, for the TBP-CO2 interaction at25 °C as a function of TBP concentration. The concentration depen-dence is attributed to TBP dimerization, as discussed in the text.

∆ H ° ) - Rd ln(K c)

d(1/ T )- RT

2a (5)

TABLE 2: Equilibrium Constants at 25 °C

acid-base pairK c (L/ mol)

∆ H ° (kJ/ mol) solvent ref

CO2-TEA 0.046a C5H12 this workCO2-TBP 1.29a -19.5 C5H12 this workCO2-PYR 0.133a C5H12 this workSO2-trimethylamine 2550 -46.0 C7H16 45phenol-tributylamine 29.2 -28.9 CCl4 45methanol-TEA 6.8 -25.1 CCl4 45H2O-TEA 7.0 C6H12 45I2-PYR 157 -34.1 C7H16 45phenol-PYR 80 -25.1 C7H16 45H2O-PYR 5.3 C6H12 45I2-benzene 0.246 -6.8 C7H16 45

a These values are averaged over the concentrations studied.




case the difference in the average interaction energy for CO 2-PYR versus CO2-TEA will be even larger than the differencefor the optimized geometries.

The van’t Hoff plot for the CO2-TBP interaction is given inFigure 8. The temperature dependence of the ν2 peak wasmeasured 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 ( X TBP )0.084) and 6.1 ( X TBP ) 0.12), respectively. These∆ H ° valuesare higher than may be expected for the relatively low K c values

obtained.45 This could be due to uncertainty in the ∆ H ° or K 2values used for the TBP-TBP dimerization. Additionally, theassumption that a 1:1 complex is formed between CO2 and TBPcould 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 discriminatebetween the two types of complexes with our spectroscopic data.

The solvent dependence of K c is in general due to bothnonspecific solvation effects and competition with the TBP self-association.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 higherconcentrations of base makes a quantitative thermodynamicdescription of the solvent effect on K c difficult. One componentof the complex, TBP, is also a component of the solvent. AsTBP is added, the solvent environment likely becomes moreordered because of the dimerization of TBP. The property-T ∆S ° is positive for bimolecular complex formation becausetranslational and rotational degrees of freedom are lost.49

However, in the more ordered solvent medium, less entropy islost upon forming the CO2-TBP complex, since entropy is alsogained in breaking TBP-TBP interactions. Other studiesindicate a similar solvent dependence of K c when one of thecomponents of the complex also associates with the solvent. Atheoretical treatment, which considers the effect of self-association of D on the complex formation between A and D,predicts a linear increase in K c with concentration of D,50 whichagrees with our data in Figure 6. Drago et al.51 measured theequilibrium constant for adduct formation between N , N -di-methylacetamide (DMA) and I2 in both benzene and CH2Cl2, aLewis acid. After correcting for specific interactions with thesolvent (benzene-I2 and CH2Cl2-DMA), the K c value in CH2-Cl2 was 23 L/mol, significantly greater than the value inbenzene, 6.9 L/mol.

Modeling of Phase Behavior

Specific chemical interactions may be described with as-

sociation theories based upon well-defined molecular models.Most association theories involve the assumption of separabilityof the molecular interactions into physical and chemicalinteractions, for example, the lattice fluid hydrogen-bonding(LFHB) model. The LFHB model is described in detailelsewhere;30,52 a summary is presented in Appendix B of thispaper.

The equilibrium constants determined from IR spectroscopyserve as input parameters to characterize the strength of specificinteractions in the LFHB model. The LFHB model will be usedbelow to predict vapor-liquid phase equilibria in an effort todetermine the effect of these weak chemical interactions. Indoing so, it is assumed that the equilibrium constants determinedin 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 calcula-tions were carried out at 25 °C. The physical parameters usedfor CO2 were those of Panayiotou and Sanchez.53 We used thetriethylamine parameters of Sanchez and Lacombe.54 Thephysical binary interaction parameter, ζ12, is defined by 12 )ζ12(1122)1/2. We found that when ζ12 is used to fit the solubilityof CO2 in n-alkanes, ζ12 scales with molecular weight of then-alkane. Since n-heptane has a molecular weight similar tothat of TEA, we used ζ12 ) 1.05, which fit the solubility of CO2 in n-heptane. Since alkanes do not have chemicalinteractions with CO2, ζ12 was chosen independently of chemicalinteractions. The dashed curve in Figure 9 is the bubble point

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

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

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

X TBP K c (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 21.2 ( 8.9

0.12 0.891 ( 0.069 0.287 ( 0.19 -18.5 ( 5.5 18.8 ( 5.7




calculation for a system neglecting specific interactions betweenCO2 and TEA; only the physical interactions are considered.The solid curve, however, includes the weak specific interactionbetween TEA and CO2. The average K c, 0.046 L/mol, obtainedfrom 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 isenhanced by about 11% (13% increase in weight fraction).Although the interaction is weak, it has a noticeable effect onmacroscopic phase equilibria. The effect is strongest in themidrange of concentration because it is here that the largestnumber of cross interactions may be formed. Limited bubblepoint data were available which allow comparison at the highand low ends of concentration.55 Unfortunately, data were notavailable in the midrange of concentration.

Figure 10 shows the bubble point curve calculated for theTBP-CO2 system at 25 °C. Parameters for tributyl phosphatewere obtained from liquid density and vapor pressure data56

using a nonlinear regression technique. The regressed param-eters for TBP were T * ) 526 K, P* ) 289 MPa, and F* )1079 kg/m3, which yielded a 0.01% error in the liquid densityand a 0.02% error in the vapor pressure over the temperaturerange 25-45 °C. The CO2 lattice fluid parameters of Panay-iotou53 were used in this case also. The value of ζ12 corre-sponding to the n-alkane with a molecular weight near that of

TBP was too high. Therefore, ζ12 for the CO2-TBP systemwas chosen to be 1.15 in order to fit approximately the bubblepoint data, but after K c and K 2 had been fixed. The self-

association of TBP is taken into account in both the solid anddashed curves in Figure 10. However, the additional effect of the cross-association between TBP and CO2 is included in thesolid line. An average of K c of 1.29 L/mol was used for theTBP-CO2 interaction; the literature value of K 2 ) 2.9 L/molwas used for the self-association of TBP.42 At X TBP ) 0.5 thesolubility of CO2 is increased by 23% (28% increase in weightfraction) due to the TBP-CO2 interaction. Even though K c isan order of magnitude greater than in the TEA-CO2 system,the increase in solubility when the specific interactions areincluded is about twice that for the TEA-CO2 system. This isbecause the TBP-CO2 interaction competes with the TBP self-association, an interaction which is a degree of magnitudestronger. The LFHB predictions are compared to the bubble

point data of Page et al.57 Only a few bubble points wereavailable at this temperature, but the calculation is close toagreement except for the point at 3.6 MPa. Nevertheless, ouroriginal intent was not to fit the curves to data, but to show theeffect 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 considera 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 physicalparameters and ζ12 ) 1.0, a specific interaction between CO2

and an electron donating site on each structural unit of thepolymer is included. Two hypothetical values of K c areconsidered, 0.1 and 0.5 L/mol, which are similar in magnitudeto those obtained for TBP-CO2.59 Figure 11 gives the sorptionof CO2 in PMMA calculated with the LFHB model at 25 °C.For K c ) 0.5 L/mol, there is good agreement with sorption data23

when the specific interactions are included (solid line). Evenmore interesting is the great difference in sorption compared toa system with the same physical parameters, but incapable of forming specific interactions (no K c). 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 interac-tions can account for the large differences in CO2 sorptionbetween interacting and noninteracting polymers. A recent IRstudy indicates the presence of specific intermolecular interac-tions between CO2 and carbonyl groups in PMMA and suggests

Figure 9. Comparison of the LFHB predictions of the bubble pointsfor the CO2-TEA binary system at 25 °C with the specific interactionturned off and on. K c ) 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 interactionturned off and on. K c ) 1.29 L/mol. Experimental points are from ref 57.

Figure 11. LFHB predictions of CO2 sorption in PMMA at 25.0 °Cwith and without specific interactions. Experimental data of CO2

sorption in PMMA is shown also (ref 23).




that specific interactions influence the solubility of CO2 in otherpolymers.13 However, because we arbitrarily set ζ12 ) 1.0, ourresults do not fully illuminate the influence of physicalinteractions, and the difference in solubility cannot be attributedsolely to specific interactions without further study.

Conclusions

This study presents the first quantitative measurements of equilibrium constants for EDA interactions between CO2 and

Lewis bases in solution, in contrast with earlier qualitativestudies.11 The detection and assignment of the out-of-plane andin-plane complex ν2 peaks is in agreement with previousspectroscopic studies and ab initio calculations of CO2-basecomplexes. The strengths of the interactions are in the followingorder: CO2-TBP > CO2-PYR > CO2-TEA. Although TEAis in general a stronger base than PYR, CO2 interacts morestrongly with PYR due to steric repulsion with the ethyl groupsof TEA. Our ab initio calculations confirm this spectroscopi-cally observed trend, which illustrates the steric differencesbetween CO2-Lewis base complexes and protic Lewis acid-Lewis base complexes. The strong concentration dependenceof K c values for the CO2-TBP interaction indicates theimportance of competition with a second specific interaction,

namely, the self-association of TBP.The LFHB model quantifies the effect of specific interactionsbetween CO2 and Lewis bases on phase equilibria. Thecalculations show that the solubility of CO2 in TEA is enhancedby 13% at X TEA ) 0.5 when EDA bonding is included. Forthe strongest interaction, CO2-TBP, the solubility is increasedby 28% due to specific interactions. This increase would havebeen much larger if the solubility enhancement in TBP werenot hindered by the self-association of TBP. This study of thespecific interactions of CO2 with monomers sheds significantinsight into interactions with polymers and polymeric surfac-tants. Assuming that K c for the specific interaction betweenCO2 and a carbonyl group (PMMA) is of the same order as K cfor the interaction with the phosphoryl group of TBP, the

solubility of CO2 is increased by a factor of 7-16 compared tothe case without specific interactions. Thus, even weak specificinteractions can have significant effects on polymer-CO2 phasebehavior. 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 addimportant specific interactions that raise solubility in CO2. Inaddition, the combination of spectroscopically determinedequilibrium constants and an association theory represents apowerful approach in molecular thermodynamics.

Acknowledgment. The authors gratefully acknowledgeNational Science Foundation Grant CTS-928769, the Separa-tions Research Program of the University of Texas at Austin,

and Unilever Research for funding this research. A specialthanks is due to Carl Harrison, Lenore LaValle, and the Perkin-Elmer corporation for the use of the Paragon 1000 spectrometer.In addition, we thank Julie Seiberg for her work in collectingthe TEA-CO2 bubble points.

Appendix A

Ab Initio Calculation. Present density functional theory(DFT) methods are strictly ab initio in character.60,61 They canbe directly derived from the electronic (Born-Oppenheimerapproximated) time-independent nonrelativistic Schrodingerequation of a molecular system:62

where H ˆ is the Hamiltonian operator, E is the total energy, andΨ is the N -electron wave function. Using the electronic densitydefined as

the Hohenberg-Kohn theorems63 and the Kohn-Sham proce-dure64 allow to calculate the total energy of the system as

where T s is the kinetic energy of a system of noninteractingelectrons, υext is the potential due to the nuclei, and E xc is theso called exchange-correlation energy. All terms in the right-hand side of eq 8 can be calculated exactly, except for the E xc

that need to be approximated. There are several good ap-proximations for E xc. We have used the combination of theBecke-3 (B3)65 exchange functional with the Lee-Yang-Parr(LYP)66 correlation functional. Both functionals are approxima-tions that contain the density and its gradient. In addition, theB3 exchange functional computes a portion of the exchange

energy in the same fashion as the Hartree-Fock exchangeenergy is calculated yet using the noninteractive wave function.

We use the above formalism as implemented in the Gaussian-92/DFT67 and Gaussian-9468 programs with two standard basissets. One is the 6-31+g** that has one set of six contractedGaussian functions for the core orbitals, two sets of three, andone Gaussian functions for the valence orbitals. In addition, ithas one set of sp-diffuse functions and one set of d-polarizationfunctions centered in the carbon, nitrogen, and oxygen atoms.The other basis set is the 6-311++G** which in addition tothe former has one more set of functions for the valence orbitals,and one set of s-diffuse and p-polarization functions centeredon 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 assumedto be separable into physical and chemical terms:

The physical interactions may be described with the well-knownlattice fluid model.54 The chemical interactions are treated byconsidering the number of pair interactions between donor andacceptor groups. In this way, the existence of specific molecularassociates is not invoked a priori; the emphasis is placed oncounting the number of possible donor-acceptor interactions.The lattice fluid equation of state is given by

where F, T ˜ , and P are the reduced density, temperature, andpressure, respectively. Three characteristic parameters, T *, P*,and F*, are required to describe the physical interactions, withT ˜ ) T / T *, P ) P / P*, and F ) F / F*. In eq 10, r ˜ is the modifiedaverage chain length, a function of the physical parameters andthe number of specific interactions at equilibrium.

1. TEA-CO2. In the TEA-CO2-pentane system, TEA hasone electron-donor site and CO2 has one electron-acceptor site.There are no specific interactions between pentane and thesolutes. The number of electron donor-acceptor interactions H ˆΨ) E Ψ (6)

F( r b1) ) N ∫d r b2 d r b3 ... d r b N |Ψ( r b1 r b2 r b3... r b N )|2 (7)

E ) T s +∫υext( r b) F( r b) d r b +12∫∫d r b1 d r b2

F( r b1) F( r b2)

| r b1 - r b2| +

E xc(F) (8)

Q ) QPQC (9)

F2 + P + T ˜[ln(1 - F) + F(1 - 1/ r ˜)] ) 0 (10)




at equilibrium is N 12. Minimizing the Gibbs free energy withrespect to N 12, holding all other variables constant, yields

where N 1 and N 2 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 mol-ecules in their close packed fluid state. Equation 11 can beused to find the fraction of EDA bonds, or alternatively, the

percentage of free base or CO2, at equilibrium. G°12 is usuallyan adjustable parameter which describes hydrogen bonding in

a particular system, but in this case, it is related to the measuredequilibrium constant, K c. The relation is

where ν* ) RT */ P*. Using a spectroscopically determinedequilibrium constant adds physical meaning to the model byeliminating adjustable association parameters.

Finally, for a binary system, the lattice fluid and chemical(specific) parts of the chemical potential are given by eqs 56and 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 equilibriumat 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 followingequations for the equilibrium of 1-1 (TBP self-association) and1-2 (TBP-CO2) bonds:

where G°11 and G°12 are related to their respective equilibriumconstants with eq 12. K 11, the equilibrium constant for self-association of TBP, is known from the literature,56 and K 12, the

constant for the TBP-CO2 interaction is taken as the averageK c obtained in the FTIR experiments.

The physical part of the chemical potential expression is givenby eq 56 of ref 30. For TBP, the chemical part of the chemicalpotential expression is given by eq 63 of ref 30 and for CO 2, itis given by eq 64 of ref 30.

3. Polymer-CO2. The LFHB model is used to describeCO2-polymer phase behavior for poly(methyl methacrylate)(PMMA). We assume a 1:1 EDA complex between CO2 andeach carbonyl site on PMMA. The equation of state is eq 10,and the lattice fluid part of the chemical potential is given byeq 56 of ref 30. For PMMA-CO2, the equilibrium of specificinteractions is described by

where component 2 is the polymer and a is the number of electron donating sites per polymer molecule. The chemicalpart 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 experimentaland calculated results (3 pages). Ordering information is givenon any current masthead page.

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JP953161B


quantitative equilibrium constants between co2 and lewis bases from ftir spectroscopy

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