Solvent strength of ionic liquid

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Solvent strength of ionic liquid / CO2 mixtures
Christopher P. Fredlakea, Mark J. Muldoona, Sudhir N.V.K. Akia, Tom
Weltonb and Joan F. Brenneckea*
aDepartment
of Chemical and Biomolecular Engineering, University of
Notre Dame, Notre Dame, IN-46556; jfb@nd.edu
bDepartment
of Chemistry, Imperial College, South Kensington campus,
London, SW7 2AZ, UK
----------------------------------------------------------------------------------------------Abstract
Previously we have shown that organic solutes can be extracted from
ionic liquids (ILs) with supercritical CO2 and that ILs can be induced to
separate from organic and aqueous mixtures by applying gaseous CO2
pressure. Thus, we are interested in the solvent strength of IL/CO2 mixtures.
Here we use 4-nitroaniline, N,N-diethyl-4-nitroaniline and Reichardt’s dye 33
to determine the Kamlet-Taft parameters for four different imidazolium based
ILs and their mixtures with CO2 at 25 and 40 °C. The effect of temperature and
carbon dioxide concentration on these parameters was determined. The
polarizability parameter depends weakly on the CO2 concentration. However,
the hydrogen bond donating ability and the hydrogen bond accepting ability
are virtually independent of CO2 pressure. The results indicate that the strong
interactions between ILs and probe molecules are not influenced by CO2.
-----------------------------------------------------------------------------------------------
1
Introduction
In this work we use three solvatochromic probes to characterize the
polarity/polarizability and hydrogen bond accepting and donating ability of
ionic liquid (IL)/CO2 mixtures. The solvent strength of these mixtures is of
particular interest for a variety of reasons.
First, we have shown that
supercritical CO2 can be used to extract solutes from ionic liquids.1-3 A variety
of researchers have used this strategy to recover products from IL solutions.4-7
Thus, the capacity of IL/CO2 mixtures for various solutes is of interest.
Second, we have also shown that CO2 can be used to induce phase splits in
IL/organic and IL/H2O mixtures.8,9 This is another reason to understand the
solvent strength of IL/CO2 mixtures and, eventually, IL/CO2/organic and
IL/CO2/H2O mixtures.
Third, a number of researchers have conducted
reactions in IL/CO2 mixtures.4-7,10-20 For instance, Cole-Hamilton has shown
the utility of performing hydroformylation reactions in an IL/CO2 biphasic
flow reactor.19 In this situation, the solvent strength of the IL/CO2 mixtures
will determine the range of feasible reactant and product compositions.
There have been numerous studies examining ionic liquid interactions
using solvatochromic probes.21-29 Recently one of our groups determined the
Kamlet-Taft parameters for a range of ionic liquids.29 The Kamlet-Taft model
breaks the solvent strength down into three component parts; the hydrogen
2
bond acidity (), hydrogen bond basicity () and dipolarity/polarizability
effects (*).30-33 It was found that  values were determined largely by the
cation, with the presence of the acidic C-H in the 2-position of imidazolium
ring increasing the hydrogen donating ability, with only a secondary anion
effect. The  values were found to be dominated by the anions of the IL. The 
values for bis(trifluoromethylsulfonyl)imide ([Tf2N]-) anion based ILs were
found to depend on the cations, suggesting that in this class of ILs, cationanion interactions may alter the relative anion-solute interaction strength. The
* values are similar in all ILs and higher than most organic solvents,
indicating strong ion-dye coloumbic interactions.
In this study we examine the effect on these parameters of adding CO2
to ILs. We know of only two other studies that have used solvatochromic
probes to examine IL/CO2 mixtures.34,35 Both were limited to a single IL, 1butyl-3-methylimidazolium hexafluorophosphate ([bmim][PF6]), and focused
solely on the polarity/polarizability of the solvent mixture.
Here we are
interested in polarity, polarizabiltiy, hydrogen bond donating ability, and
hydrogen bond accepting ability of several different imidazolium-based
IL/CO2 mixtures.
3
Experimental Section
The measurements were made in a high-pressure stainless steel cell (3
cm path length) equipped with sapphire windows. The sapphire window
assembly is similar to the one that we have used previously,36 although this cell
has a larger head space to accommodate the small but finite expansion of ILs
upon dissolution of CO2. The temperature of the IL was controlled to + 0.5 ºC
using an Omega model CS6071A P2 temperature controller and the
temperature was measured to + 0.5 ºC using a RTD probe. Omega cartridge
heaters were used to heat the cell to the required temperature. An Isco 260D
syringe pump was used to control the carbon dioxide pressure. The pressure in
the cell was measured to + 0.25 bar using a Heise PPM2 digital pressure
transducer. The UV-Vis measurements were made using a Cary 300Bio
spectrophotometer, which has an uncertainty of ± 0.5 nm. The max stated is the
average of five separate scans and the standard deviation estimated from these
replicates varied between 0.1 and 1.7 nm. Standard deviation of the max values
was used to determine the error bars given in Figures 1-7.
Coleman instrument grade CO2 (99.99%) obtained from Mittler
Supply, Inc., was used as received. Reichardt’s dye 30 and 33 and 4nitroaniline were purchased from Sigma-Alrdich and
N,N-diethyl-4-
nitroaniline was purchased from Oakwood Products Inc. All four probes were
4
used as received. [bmim][PF6] was purchased from Sachem Inc., and Clcontent was reported to be less than 3 ppm. We measured the concentration of
Cl- in this sample to be less than 10 ppm using a chloride ion specific electrode
(Cole-Parmer
27502-12).
bis(trifluoromethylsulfonyl)imide
1-butyl-3-methylimidazolium
([bmim][Tf2N]),
1-butyl-3-
methylimidazolium trifluoromethanesulfonate ([bmim][TfO]), and 1-butyl-3methylimidazolium tetrafluoroborate ([bmim][BF4]) were synthesized and
characterized as described previously.37,38 The halide content of [bmim][BF4]
and [bmim][Tf2N] were found to be < 10 ppm using a bromide ion specific
electrode (Cole-Parmer 27502-05) and [bmim][TfO] was synthesized halide
free, via direct methylation.
The ionic liquids were dried prior to use under high vacuum at 70 °C
for 72 hr. 3 mL of ionic liquid was loaded into the cell and the dye was added
in the form of a concentrated dichloromethane solution, enough solution being
added such that the absorbance was approximately 1. The dichloromethane
was then removed in-situ by placing the cell under vacuum at 70 °C until the
max remained constant. Carbon dioxide was added to the cell and the solution
stirred until equilibrium was reached. The water content of the ionic liquids
was determined by using the Karl-Fisher titration technique (Aquastar V-200
Volumetric titrator, EM Science) and found to be < 200 ppm in all cases.
5
Even at this low level the water concentration is still about two orders of
magnitude greater than the dye concentrations. However, since we dry the
samples until max is constant, we think it is reasonable to conclude that the
water is not significantly affecting the results.
The * parameter is determined using N,N-diethyl-4-nitroaniline, using
eqn.(1)

max = 27.52 -3.182*
(1)
The  value is determined using the solvatochromic shift of 4nitroaniline relative to N,N-diethyl-4-nitroaniline, eqn (2)
 = [1.035 (2)max - (1)max + 2.64 kK]/2.80
(2)
where (1)max and (2)max are the absorbance maxima for 4-nitroaniline and
N,N-diethyl-4-nitroaniline, respectively.
The  values were determined by using the ET(30) (Reichardt’s dye,
RD30) and * values:
ET(30) / kcal mol-1 = hcRD30NA = 2.8591 x 10-3 RD30/cm-1 (3)
 = -0.186 x [10.91- RD30] - 0.72 *
(4)
In this study Reichardt’s dye 33 was used instead of Reichardt’s dye
30, as it was found that in the presence of small traces of water, carbonic acid
6
was formed when CO2 was added to the system, causing the Reichardt’s dye
30 to be protonated. Reichardt’s dye 33 is known to be more stable under
slightly acidic conditions and has been used previously in examining ionic
liquids.27 ET(33) numbers were converted to ET(30) values using the following
correlation (equation 5) that we determined by examining values of ET(30) and
ET(33) for common organic solvents.
The values obtained for common
organic solvents measured in our laboratory are shown in Table 1, where they
are compared with those reported in the literature39. There is generally good
agreement. In the few cases where there are significant differences (e.g.,
dichloromethane and pyridine) we believe the discrepancy may be due to lower
water content in the solvents we used.
ET(30) = 0.9986 ET(33) -8.6878
(5)
Clearly, there is a simple one-to-one correspondence between ET(30) and
ET(33). The ET(30) value obtained from eqn.(5) was used to obtain the value
of  according to eqn (4).
Results and Discussion
Kamlet-Taft parameters were obtained for four different ILs and
IL/CO2 mixtures at 25 and 40 °C as a function of CO2 pressure. An example of
7
a plot of the Kamlet-Taft parameters against CO2 pressure at 25 °C is shown
for [bmim][BF4] in Figure 1. As shown in Figure 1, addition of CO2 had very
little effect on  and  parameters and only a small decrease in * value was
observed, even after increasing the CO2 pressure to 50 bar (which is still below
the vapor pressure of CO2 at 25 °C). When the IL sample is under vacuum
(i.e., the lowest pressure points shown on the graph, ~10-5 bar) the Kamlet-Taft
parameters are the same as when the IL sample is exposed to either 1 bar inert
gas (e.g., nitrogen) or 1 bar of CO2. The * and  values for pure CO2 depend
on temperature and pressure and are very small compared to those of ILs (* ~
0 and  ~ 0.01 at 100 bar and 40 °C for CO240 compared to * = 1.04 and  =
0.41 for pure [bmim][BF4] at 25 °C). To our knowledge, the  for pure CO2
has not been determined experimentally but one would expect this value to be
essentially zero. Therefore, one would have expected a decrease in these values
for the IL/CO2 mixtures upon addition of large amounts of CO2. To the
contrary no such effect was observed even after increasing the CO2
concentration in the [bmim][BF4]/CO2 mixture to ~ 0.55 mole fraction
(solubility results are described in later sections). The implications of the
observed results in terms of the solvent-solute interactions are discussed in the
later parts of the manuscript.
8
Our previous studies indicate that CO2 solubility in ILs depends on the
nature of the ionic liquid;41,42 therefore, we felt it was more appropriate to plot
the Kamlet-Taft parameters as a function of CO2 concentration rather than
pressure. The solubility of CO2 in all four ILs of interest was measured in our
laboratory at the temperatures and pressure studied here.42 From these CO2
solubility measurements, we converted the CO2 pressure to concentration. At
25 °C and 40 °C, we performed the measurements up to about 50 bar and 100
bar, respectively. Both sets of conditions resulted in as much as 70 mole %
CO2 dissolved in the liquid phase. At 25 °C we were limited by condensation
of CO2 when its vapor pressure is reached. At 40 °C we performed the
experiments up to the pressure at which further increases resulted in no
significant increase in the CO2 mole fraction in the liquid phase.41,42
* values
Figures 2 and 3 demonstrate the effect of CO2 on the * values (a
measure of non-specific interactions such as polarizability, dipole-dipole
interactions, and dipole-induced dipole interactions) for the ILs at 25 and 40
°C, respectively. The results indicate that * values for pure ILs are relatively
high compared to organic solvents, as shown in Table 2. Furthermore, these
values are independent of the choice of the anion, consistent with findings
previously reported by one of our groups.29
Note that the [bmim][Tf2N]
9
symbol at the lowest pressure is hidden under the [bmim][PF6] symbol in
Figure 3.
The results shown in Figures 2 and 3 are on a widely expanded scale,
therefore any effect of temperature and CO2 concentration on these values
should be drawn with caution. For example, in [bmim][BF4] the * value
decreased from 1.035 to 1 at 25 °C, as the CO2 concentration increased from 0
to 0.55 mole fraction. An increase in the temperature from 25 to 40 °C had
very little or no effect on the * values. The observed small decrease in this
value with an increase in the temperature and CO2 concentration was found to
be within our error limits. Baker et al. reported a similar temperature
dependence for pure [bmim][PF6].27 Even though we are above the critical
temperature and pressure of pure CO2 for some measurements, the conditions
studied are still well below the IL/CO2 mixture critical points.41 Therefore the
values reported at these conditions are of a liquid mixture of IL and CO2. The
* values for pure CO2 depend on pressure and ranged between –1.0 to 0.1.40
Clearly these values are very small compared to the * values for pure ILs and
the IL/CO2 mixtures studied here (* ~ 1.0). * arises solely from changes in
the spectrum of N,N-diethyl-4-nitroaniline, from non-specific interactions with
the solvent/solvent mixture. Therefore the addition of CO2 to the ionic liquid
might affect the value in one of two ways. The CO2 might interact with the dye
10
directly, or it might interact with the ionic liquid ions in such a way as to
disrupt their interactions with the dye. Our results clearly show that, even at
high concentrations, CO2 does not do either of these.
 values
 values represent hydrogen bond donating ability (acidity) and the
effect of CO2 on this parameter for four ionic liquids at 25 and 40 °C is shown
in Figures 4 and 5, respectively (the error bars are larger than those for * due
to the propagation of error, as this parameter depends on two probe molecules).
 values were found to be independent of the choice of anion indicating that it
depends solely on the cation, once again consistent with results for pure ILs
previously reported by one of our groups.29 A small decrease in the  values
was observed as the temperature was increased from 25 to 40 °C.
 arises from the differential solvation effects on the UV spectra of
Reichardt’s dye and N,N-diethyl-4-nitroaniline. We have demonstrated above
that the addition of CO2 has no effect on the spectrum of N,N-diethyl-4nitroaniline, and any effects seen must arise from solvation of Reichardt’s dye.
This could result from direct interaction of the CO2 with the dye or by the CO2
interacting with the ionic liquid cation in such a way as to disrupt its hydrogen
bond to the Reichardt’s dye. It was found that CO2 had no effect on  values
11
even when the concentration of CO2 was increased to greater than 0.6 mole
fraction. Therefore, the hydrogen bond from the cation to the Reichardt’s dye
is not affected by the presence of large amounts of CO2. Recent measurements
show that the solubility of CO2 in ionic liquids is unaffected by changing the
hydrogen bond donating ability of the cation.42-44 Hence, these measurements
support the conclusion that there is no strong interaction between the CO2 and
the cation of the ionic liquid.
 values
Theparameter is a measure of the hydrogen bond accepting ability
(basicity) of the solvent. The values of  can be seen in Figures 6 and 7 (as
with the  parameter, the error bars are larger than those for * as this
parameter also depends on two probe molecules). It was found that the 
values were dependent on the choice of anion and that increasing temperature
and CO2 concentration had little effect on the values for all the liquids studied.
Once again, the strong interaction between the ionic liquids and the probe
molecules are not disrupted by the presence of large concentrations of CO2.
Any effect on the  value, which arises from the differential solvation
effects on the UV spectra of 4-nitroaniline and N,N-diethyl-4-nitroaniline, of
the ionic liquid/CO2 mixtures must arise from solvation of 4-nitroaniline.
12
Again this could result from direct interaction of the CO2 with the dye or by
the CO2 interacting with the ionic liquid anion in such a way as to disrupt
hydrogen bonding between the 4-nitroaniline and the anion of the ionic liquid.
One might conclude based on these results that no such interaction occurs, yet
infrared spectroscopy and solubility studies show that CO2 in ionic liquids
interact with the anion.42-44 One possible explanation could just be that the
CO2-anion interaction is significantly weaker than the hydrogen bond between
the ionic liquid and 4-nitroaniline and is incapable of disrupting the interaction.
Comparison with literature values of Kamlet-Taft studies in ionic liquids
Table 2 compares the values of the Kamlet-Taft parameters for neat
ionic liquids from this study with those previously reported in the literature.
The ILs used in this study are from different batches than those used in the
study of pure ILs that was previously published by one of our groups.29 The
values obtained in both studies compare reasonably well, although the  value
for [bmim][Tf2N] differed from the previously reported value by 0.073
(10.5%).
Baker et al. has also published the Kamlet-Taft parameters for neat
[bmim][PF6], as a function of increasing temperature and water content.27 The
 value obtained in the current study is in close agreement with that of Baker et
al., while our  value is lower, but this may be due to the different correlation
13
that was used to calculate 27 However, our values differ significantly
(particularly in the case of ) from those reported by Huddleston et al.28 It
should be noted that these researchers used different probes (nitrophenol and
nitroanisole) than those used here, which could amount for the observed
differences. The differences may also be explained by the higher water content
of the ILs used in that particular study (2 wt% water for [bmim][[BF4] and 0.21
wt % water for [bmim][PF6]).28
Comparison with other solvatochromic studies in ionic liquids / CO2
mixtures.
Previously, Eckert and co-workers examined the effect of CO2 pressure
on the * value in [bmim][PF6] at 35 and 50 °C.35 From their study they
concluded that increasing CO2 concentrations had little effect on the * value
in [bmim][PF6], consistent with the * values reported here for not just
[bmim][PF6], but three other ILs, as well. Baker et al. examined the
fluorescence of pyrene with added CO2 pressure in [bmim][PF6].34 The ratio of
first and third emission bands (I1/I3) of pyrene is a measure of polarizability
(similar to that of *), and it was found that the addition of CO2 changed I1/I3
only modestly, from 2.02 to 1.92. They believed that this relatively small
decrease was due to the CO2 disrupting some of the IL-pyrene interactions.
14
Literature values of solvatochromic studies in organic / CO2 mixtures
Kelly and Lemert previously examined phenol blue in CO2 expanded
organic liquid mixtures (acetone, methanol, toluene, tetrahydrofuran and
cyclohexane).45 Phenol blue is a commonly used solvatochromic probe that is
sensitive to both specific (hydrogen bond accepting and donating ability) and
non-specific interactions. In contrast to the IL/CO2 mixtures, a large decrease
in the solvent strength of the organic liquid was observed with addition of CO2
except in the case of cyclohexane. In the case of cyclohexane, the solvent is
“non-polar” in nature. Therefore, the addition of another non-polar solvent
such as CO2 results in a less dramatic change. In fact, cyclohexane has been
compared to CO2 in polarity.40,46 In the case of the other organic solvents the
expansion of the solvent upon addition of CO2 amounts comparable to those
investigated here for the ILs results in a dramatic decrease in the solvent
strength47,48. By contrast, addition of large quantities of CO2 to ILs does not
lead to a large degree of solvent expansion,41,42 therefore the IL-probe
interactions remain intact.
Literature values of CO2 solubility in ionic liquids
There are several reports in the literature regarding the CO2 solubility
in [bmim][PF6], and there is a certain degree of discrepancy in the literature
values, varying within 15%.41,42,49,50 The values used here to convert pressure
15
to composition for [bmim][PF6] are those found in Aki et al.42 However, this
discrepancy does not effect the conclusions of the current study, as the general
trends will be the same irrespective of the exact CO2 solubility values used.
Conclusions
The results of this study indicate that the addition of large amounts of
CO2 into ionic liquids has only a marginal effect on the solvating power of ILs.
This is true for not just the polarity/polarizability, but also for the hydrogen
bond donating and accepting ability of the IL/CO2 solvent mixture. It is also
the case for all four of the ILs studied. Of course, the strength of these
interactions determine not only how the ionic liquid interacts with solutes but
also how it interacts with itself. Unlike in organic solvents, ionic liquids do not
expand to a great degree when CO2 is added, allowing ionic liquids to maintain
their solvent strength even at high CO2 compositions. This lack of expansion
seems to derive from the fact that dissolved CO2 does not greatly affect the
strength of the interionic interactions in the ionic liquid. Processes taking place
in ILs that are influenced by specific solute-solvent interactions are not likely
to be affected by the addition of CO2.
16
Acknowledgements
Acknowledgment is made to the Donors of the Petroleum Research
Fund, administered by the American Chemical Society, for partial support of
this research. The work described herein was also supported by the National
Science Foundation (CTS-9987627), and the State of Indiana 21st Century
Research and Technology Fund (#909010455).
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C. J. Chang, C. Y. Day, C. M. Ko and K. L. Chiu, Fluid Phase Equilib.,
1997, 131, 243.
(48)
A. Kordikowski, A. P. Schenk, R. M. VanNielen and C. J. Peters, J.
Supercrit. Fluids, 1995, 8, 205.
(49)
A. P. S. Kamps, D. Tuma, J. Z. Xia and G. Maurer, J. Chem. Eng.
Data, 2003, 48, 746.
(50)
Z. M. Liu, W. Z. Wu, B. X. Han, Z. X. Dong, G. Y. Zhao, J. Q. Wang,
T. Jiang and G. Y. Yang, Chem.-Eur. J., 2003, 9, 3897.
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C. Reichardt, Chem. Rev., 1994, 94, 2319.
22
List of Tables:
Table 1: Reichardt’s dye 33 in various organic solvents and comparison of the
values obtained in the current study with those reported in the literature at
ambient conditions.
Table 2: Kamlet Taft parameters for ionic liquids and common organic
solvents determined in the current study and comparison with the literature
values.
23
List of Figures:
Figure 1: Kamlet-Taft parameters for [bmim][BF4]/CO2 mixtures at 25 °C
Figure 2: Dependence of * on anion and carbon dioxide in IL/CO2 mixtures
at 25 °C;  [bmim][PF6]; ■ [bmim][BF4]; ▲ [bmim][Tf2N]; ▼ [bmim][TfO]
Figure 3: Dependence of * on anion and carbon dioxide in IL/CO2 mixtures
at 40 °C;  [bmim][PF6]; ■ [bmim][BF4]; ▲ [bmim][Tf2N]; ▼ [bmim][TfO]
Figure 4: Dependence of  on anion and carbon dioxide in IL/CO2 mixtures at
25 °C;  [bmim][PF6]; ■ [bmim][BF4]; ▲ [bmim][Tf2N]; ▼ [bmim][TfO]
Figure 5: Dependence of  on anion and carbon dioxide in IL/CO2 mixtures at
40 °C ;  [bmim][PF6]; ■ [bmim][BF4]; ▲ [bmim][Tf2N]; ▼ [bmim][TfO]
Figure 6: Dependence of  on anion and carbon dioxide in IL/CO2 mixtures at
25 °C;  [bmim][PF6]; ■ [bmim][BF4]; ▲ [bmim][Tf2N]; ▼ [bmim][TfO]
Figure 7: Dependence of  on anion and carbon dioxide in IL/CO2 mixtures at
40 °C;  [bmim][PF6]; ■ [bmim][BF4]; ▲ [bmim][Tf2N]; ▼ [bmim][TfO]
24
Table 1:
Solvent
Current study
max, nm
ET(33),
kcal mol-1
Literature Values39
max, nm
ET(33),
kcal mol-1
Acetonitrile
518.5
55.15
516.1
55.4
Ethanol
472.3
60.53
471.0
60.7
Methanol
443.9
64.42
442.6
64.6
Acetone
548.8
52.1
549.8
52
Dichloromethane
584.0
48.96
575.28
49.7
Pyridine
589.1
48.53
585.9
48.8
1-butylimidazole
543.6
52.57
1-butanol
494.8
57.79
497.24
57.5
1-octanol
514.4
55.58
1,1,1-trifluoroethanol
415.9
68.75
25
Table 2:

[bmim][PF6]
± ±
1.05 ±


(1.032)
[bmim][PF6]27*


0.92
[bmim][PF6]28


0.91
[bmim][Tf N]
±
±
0.97 ±


(0.984)
±
±
1.04 ±


(1.047)
[bmim][BF4]28


1.09
[bmim][TfO]
±
±
1.03 ±


(1.006)
Water51

0.14; 
 1.13
Methanol51


0.73
Acetonitrile29


0.799
Acetone29


0.704
Dichloromethane29


0.791
Pyridine51


0.87
[bmim][BF4]

*
Solvent
* = 20°C, Values in parenthesis are from Crowhurst et al.29
26
1.1
25 °C
*

0.9
0.7

0.5

0.3
0
10
20
30
40
50
60
CO2 pressure, bar
Figure 1:
27
1.09
25 °C
1.07
*
1.05
1.03
1.01
0.99
0.97
0.95
0.0
0.1
0.2
0.3
0.4
0.5
0.6
[CO2], mole fraction
Figure 2:
28
0.7
1.08
40 °C
1.06
*
1.04
1.02
1.00
0.98
0.96
0.0
0.2
0.4
0.6
0.8
[CO2], mole fraction
Figure 3:
29
0.74
25 °C
0.70

0.66
0.62
0.58
0.54
0.0
0.1
0.2
0.3
0.4
0.5
0.6
[CO2], mole fraction
Figure 4:
30
0.7
0.72
40 °C

0.68
0.64
0.60
0.56
0.0
0.2
0.4
0.6
0.8
[CO2], mole fraction
Figure 5:
31
0.6
25 °C
0.5

0.4
0.3
0.2
0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
[CO2], mole fraction
Figure 6:
32
0.7
0.6
40 °C
0.5

0.4
0.3
0.2
0.1
0.0
0.2
0.4
0.6
0.8
[CO2], mole fraction
Figure 7:
33
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