Ind. Eng. Chem. Res. 1990,29, 1682-1690
1682
GENERAL RESEARCH Fluorescence Spectroscopy Studies of Dilute Supercritical Solutions Joan F. Brennecke Department of Chemical Engineering, University of Notre Dame, Notre Dame, Indiana 46556
David L. Tomasko and Julie Peshkin Department of Chemical Engineering, University of Illinois, Urbana, Illinois 61801
Charles A. Eckert* School of Chemical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0100
Much of the unusual behavior in supercritical fluids (SCFs), including enhanced solubilities, synergistic effects of mixed solutes, and entrainer effects, may be explained by a region around the solute that has a higher density than the bulk. We present a new technique to investigate SCFs using fluorescence spectroscopy to probe the local interactions. In contrast to thermodynamic measurements, this technique determines the strength of interactions on a molecular scale, which is important in the development of more accurate thermodynamic models. The results indicate stronger solute/solvent interactions near the critical point and local densities that are liquid-like, even when the bulk density is quite low. In addition, we determine a quantitative value of the local density enrichment from the spectroscopic measurements. The local solvent density enhancement around the solute appears to correlate reasonably well with the isothermal compressibility, so we speculate that it may be possible to model solute/solvent clustering by knowing only pure solvent properties. We also present evidence of the importance of solute/solute interactions in dilute supercritical fluid solutions.
I. Introduction While supercritical fluids (SCFs) show potential for a variety of extraction and separation processes (Paulaitis et al., 1982,1983; McHugh and Krukonis, 1986; Eckert et ai., 1986a), to design these processes the engineer needs accurate and reliable mathematical models of the thermodynamics. Unfortunately, most standard equations of state do not represent adequately the phase behavior in the near supercritical region without adding several adjustable parameters. Perturbation equations and lattice gas models address the size and energy differences of the molecules better than simple cubic equations, but there still exists a need for a better understanding of the true intermolecular interactions to develop realistic models. These models are discussed in two recent review articles (Brennecke and Eckert, 1989a; Johnston et al., 1989a). The inadequacy of standard equation of state models for SCF solutions may result from much of the macroscopic phase behavior in the highly asymmetric SCF solutions being dependent on strong or specific interactions. In this situation, clear understanding of the molecular attractions and repulsions is especially important. While accurate thermodynamic models require accurate estimates of the potential and strength of specific interactions, it is impossible to obtain this information directly from standard thermodynamic measurements. For instance, analysis of solubility measurements is constrained by the choice of the equation of state model that must be used. The fluorescence spectroscopy results presented here give in-
* To whom
correspondence should be addressed.
0888-588519012629-1682$02.50/0
dications of the actual intermolecular interactions and provide a measure of the local density around the solute. Therefore, the real advantage of the fluorescence spectroscopy technique is that one can obtain independent determinations of local densities and the strength of interactions on the truly molecular scale. In addition, it is noninvasive and relatively nonperturbing to the system. Clearly, a combination of both thermodynamic and spectroscopic measurements will give a better understanding of supercritical fluid solutions and aid in the development of accurate phase equilibrium models. The molecular interactions of dilute solutes in SCFs are significantly different than those in normal liquids. Measurement of the infinite dilution partial molar volumes of several solutes in supercritical fluids was the first strong indication of the unusual behavior in these solutions. At high reduced pressures, where the solvents are incompressible, the infinite dilution partial molar volumes of several solutes in SCF ethylene and C02 at pressures of 50-250 bar and temperatures of 12-45 "C (Eckert et al., 1983; 1986b) were slightly positive. However, very sharp negative dips in D," were observed for solutes in the compressible region of the solvent, which is near the solvent critical point. These negative values were extremely large in magnitude (as large as -20000 cm3/mol) and were largest for the isotherms closest to the critical temperatures. See, for example, Figure 1. The extremely large negative infinite dilution partial molar volumes suggest the "condensation" of many solvent molecules when a molecule of solute is added to solution. This can be envisioned as the collapse of the solvent shell about the solute, the formation of solute/solvent clusters 1990 American Chemical Society
Ind. Eng. Chem. Res., Vol. 29, No. 8, 1990 1683
*:' -
v1 I,,
i
15000
-20000
0.004
'*OC
,
~
,[,y,, ,, ,,
0.008
,, ,,,, ,
0.012
I,I
0.016
DENSITY (g mo I/cc)
Figure 1. Infinite dilution partial molar volume of naphthalene in SCF ethylene at 285 K. The solid line is an estimated best fit. Data of Eckert et al. (1986).
in solution, or a local density that is greater than the bulk density. One way of modeling this phenomenon is the use of density-dependent local composition (DDLC) mixing rules (Vidal, 1984, Johnston et al., 1987; Kim and Johnston, 1987a). Another method of looking at such a process might be a chemical theory description, in which the clusters are envisioned as actual complexes being formed. A number of experimental studies using spectroscopy have addressed the difference between local and bulk densities around the solute in SCF solutions. Kim and Johnston first suggested the link between the local density and the isothermal compressibility (Kim and Johnston, 1987b), showing that the local density is highest in the region of highest compressibility near the critical point. This idea was used to interpret and obtain local densities from absorption data of phenol blue in SCFs (Kim and Johnston, 1987b). Yonker and co-workers (Yonker et al., 1986) have studied the wavelength of maximum absorption of a chromophore in supercritical fluids and used that information to determine Kamlet-Taft x* values as a function of solvent density in the SC region. Kajimoto and co-workers (Kajimoto et al., 1988) have used both absorption and fluorescence to look at the complicated system of (N,N-dimethylamino)benzonitrile, which forms a charge-transfer (CT) complex in addition to the normal fluorescence. The Stokes shift and ratio of the CT to normal fluorescence were used to develop a simple aggregation model which uses a Langmuir-type adsorption description of the clustering phenomenon. Additional work has been done by using UV absorption measurements to quantify the clustering around solutes in solute/fluid/entrainer systems (Yonker and Smith, 1988; Kim and Johnston, 1987a). The shift in the wavelength of maximum absorption is used to determine the local composition about the solute. This vicinity is shown to be enriched with the entrainer, especially in the highly compressible region nearest the critical point. Johnston et al. (1989b) provides an excellent review of previous work using spectroscopic probes in supercritical fluids. There have been a number of modeling efforts that employ the concept of clustering in supercritical fluid solutions. Debenedetti (1987) has used a fluctuation analysis to estimate what might be described as a cluster size or aggregation number from the solute infinite dilution partial molar volumes. These calculations indicate the possible formation of very large clusters in the region of highest solvent compressibility, which is near the critical point. Also, Petsche and Debenedetti (1989) have performed molecular dynamics simulations of supercritical mixtures of neon and xenon that distinctly show the clustering of
solvents around the solute in the attractive case and a negative cluster or hole in the repulsive case. They indicate first shell densities as high as 4 times the bulk density. Lee and co-workers have calculated pair correlation functions of supercritical fluid systems as asymmetric as naphthalene/COp and pyrene/C02 (Cochran and Lee, 1989; Lee, 1989). Their results are also consistent with the theory of a more dense local environment. Donohue and co-workers (Walsh et al., 1987) recognized a different type of clustering: the formation of complexes between solutes in SCFs and "entrainers" (1-5%) added to the SCF. Entrainers such as methanol or acetone have been used to enhance solubility by specific interactions with the solute (Van Alsten, 1986;Schmitt and Reid, 1986). In Donohue's APACT (associated perturbed anisotropic chain theory), both association between alcohols molecules and solvation of the solute by the alcohol are taken into account. However, no complex formation is assumed to occur between the solute and the SCF solvent. Solute/solute interactions are also important in SCF solutions, as observed by Kurnik and Reid and Kwiatkowski and co-workers (Kurnik and Reid, 1982; Kwiatkowski et al., 1984), in the synergistic effects on the solubilities of mixed solutes. When a physical mixture of naphthalene and benzoic acid is extracted with SCF COB, the solubilities of both components are greater than the solubilities of the pure components. This phenomenon mole fraction. occurs at concentrations as low as 10-~-10-~ Frequently, equation of state models assume "infinite dilution" of the solutes due to the low solubilities. Clearly, recognition and a better understanding of these solute/ solute interactions are important for the prediction of SC phase equilibria. In this paper, we present new results of fluorescence spectroscopy studies of dilute organics in pure supercritical fluids. We compare those results to make observations about local densities and the strength of solute/solvent interactions in solution, especially near the critical point, as well as the importance of solute/solute interactions even at extremely low concentrations.
11. Experimental Details A dilute mixture of a solute in supercritical fluid is introduced into a custom-built high-pressure optical cell, equipped for 90° detection with a 1.3-cm path length. The windows are 6-mm-thick fused quartz disks, which are sealed with viton O-rings. The pressure in the optical cell is measured with a Texas Instrument Model 140 pressure gauge, which has an accuracy of f0.2 bar. The temperature in the optical cell is controlled with a custom-built precision temperature controller that is good to f0.02 "C. The temperature is measured by recording the resistance of an Omega type 44032 thermistor. The heating and cooling elements are Melcor Model CP1.4-71-06L Peltier coolers. These serve as heaters by simply switching the leads to the modules. Four modules are fastened to the bottom of the cell. The spectrometer assembly incorporates a 1000-W xenon arc lamp with Kratos power supply, lenses, and monochromators. Detection is with a Hamamatsu 1P-28 photomultiplier tube, powered by a Keithley Model 247 high-voltage supply. A stepper motor on the emission monochromator is computer controlled and coordinated with the computer data acquisition of the singal from a Keithley Model 414a picoammeter. The spectrometer assembly is shown in Figure 2. The schematic of the high-pressure assembly used to introduce the sample into the optical cell is shown in Figure 3. The gas is compressed from the cylinder into
1684 Ind. Eng. Chem. Res., Vol. 29, No. 8, 1990
Monochromotor
n
Lens
I*i Xenon Arc
Lens
I I I
n
I/
"
Filter
High Pressure Optical Cell
Monochromator
Lamp
Figure 2. Schematic of fluorescence spectrometer assembly. is)
hTu A
I
&,T---. A
1
%=? 7
-5b---
The estimated accuracy or reproducibility of the overall intensity measurements is only f10-20%. Long-term decay of the lamp intensity, short-term lamp fluctuations, and slight variations in lens adjustments all contribute to the uncertainty. However, within one spectrum the variations are minimal, so the ratios of intensities in one scan used below are much more accurate, estimated f3-5%. 111. Results and Discussion We studied the following systems of dilute polycyclic aromatics in near room temperature supercritical fluids: pyrene in C02,CzH4,and CF3H; naphthalene in CO,; dibenzofuran in C 0 2 and C2H4;and carbazole in COz and CF,H. The solutes are generally ones that have solubility and, for naphthalene, partial molar volume data available in the literature and have strong fluorescence spectra. Many polycyclic aromatics do fluoresce in the ultraviolet-visible range, and pyrene, in particular, has a very high quantum yield. Its spectrum has been well-documented, and it has been used extensively as a probe of solvent environments. The solvents have convenient critical temperatures near ambient: C 0 2 (T, = 31 OC, P, = 73.8 bar), C2H, (T, = 9.2 OC, P, = 50.4 bar), CF3H (T,= 25.9 "C, P, = 48.3 bar). We explored the slightly supercritical region from about TR = 1.005-1.10 and PR= 1.01-2.00. This includes the highly compressible region where the partial molar volumes are extremely large and negative. Solute concentrations were relatively dilute, ranging from 3 X lo4 to 1 X mole fraction, and were held well below the saturation limit. The one exception is the series of runs with 5.5 X lo+ mole fraction pyrene in SCF ethylene. Although it is likely that the lowest pressure runs fell below the solubility limit, in this paper we present intensity ratio data, which are relatively insensitive to solute concentration. Fluorescence spectroscopy was the analytical method of choice for two reasons. First, one can detect the dilute solutions typical of SCFE of heavy organic hydrocarbons, which is often a limitation in absorption. Second, fluorescence spectra are very sensitive to the local solvent environment, and this is the region that we were trying to probe (Brennecke and Eckert, 198913). In fluorescence spectroscopy, the dilute sample is irradiated with the appropriate wavelength of ultraviolet light to place some of the molecules in their first excited state. The molecules fluoresce when they emit photons and lose energy back down to the ground state. The fluorescence spectra are relatively insensitive to the exact wavelength of excitation because even if the molecules are promoted into a higher excited vibrational level in the excited electronic state, they quickly lose energy in radiationless processes to the lowest vibrational level before they fluoresce (Lumb, 1978). There are two characteristics of the fluorescence spectra that we shall use to analyze the intermolecular interactions of solutes in SCFs. The first is particular to some nonfunctional polycyclic aromatics in which the intensity of a forbidden transition is used as a measure of the strength of solute/solvent interactions. Next, the presence of excimers, or excited state dimers, can indicate solute/solute interactions in solution. We summarize briefly the results of the excimer studies; details and discussion are in a complementary manuscript (Brennecke et al., 1990). Intensity Ratios. The intensity of the forbidden transition can be an exceedingly sensitive measure of the solute/solvent interactions. It is particularly well-documented for pyrene in a wide range of liquid organic solvents, but we also observed the same type of enhancement in the naphthalene spectra. Ham was the first to observe the enhancement of some weak or forbidden transitions
Ind. Eng. Chem. Res., Vol. 29, No. 8, 1990 1685 in benzene (1953). Bayliss (1969) described the solute/ solvent interactions as a mixing of states such that a weak solute transition can borrow intensity from other solute transitions or from transitions of the solvent. He used a perturbation treatment to show theoretical justification of his model. The enhanced band in pyrene is the transition from the lowest vibrational state of the excited electronic state to the lowest vibrational state of the ground electronic state (the 0-0 transition). Nakajima (1971) studied the fluorescence spectra of pyrene in various solvents and attributed the enhancement in the 0-0 transition to the reduction of molecular symmetry in the field of surrounding solvent molecules or to the distortion of the *-electron cloud by the environmental perturbation. The ground state of pyrene is a totally symmetrical Al, state, and the first excited electronic state has been assigned lBlu (Hara and Ware, 1980). The 0-0 band (designated Zl) is a transition from an ag vibration and is symmetry forbidden. In contrast, the third peak (4)for fluorescence is from the ground ap vibration in S1 to a bl, vibration in So and is strong, allowed, and relatively solvent-insensitive (Kalyanasundaram and Thomas, 1977). Therefore, the ratio 1 1 / 1 3 gives a good normalized value of the band enhancement. Clearly, Z1/13 is a measure of the local solvent environment because the mechanisms for the disruption of the symmetry mentioned above are nearest-neighbor or first-shell interactions. Nakajima reported values of Z1/Z3 ranging from 0.5 to 1.8 for pyrene in various solvents (Nakajima, 1971,1976). Kalyanasundaram and Thomas (1977) reported Z1/Z3 values for 39 solvents and mentioned that the ratio is independent of pyrene concentration, even in the range where excimers occur. Lianos and Georghiou (1979a,b) reported a threefold increase in Z1/Z3 in going form nonpolar heptane to methanol and attributed the reduction in symmetry to the formation of an actual 1:l complex between the pyrene and the alcohol. Perhaps the most extensive documentation of the increase in Z1/Z3 in various liquid organic solvents is two papers by Dong and Winnik (1982,1984). They observed 11/13 values ranging from 0.47 to 1.95 in 94 different solvents. They found that the higher the ratio, the stronger the solute/solvent interactions, and they developed the Py scale (Z1/I3) of solvent polarities to quantify their results. They compared the empirical P y scale to the Kamlet-Taft equation (Kamlet et al., 1977; Abboud et al., 1977; Kamlet et al., 1983) with generally good correlation with K*, the Kamlet-Taft solvent dipolarity/polarizability index. Therefore, the stronger the solute/solvent interaction, in terms of dipole, induced dipole, or even complex formation, the more the symmetry is disrupted, which allows the forbidden transition to take place with greater intensity. A higher 11/Z3 ratio indicates stronger solute/solvent interactions. In naphthalene, the fourth peak is the most stable one, so we recorded 1 1 / 1 4 . The ratios for naphthalene are much lower, ranging from about 0.3 to 0.45. We are first interested in showing that Z1/Z3 and Z1,!14 are good measures of the strength of solute/solvent interactions in SCFs, just as they are in different organic liquids. The ratio of the intensity of the first to the third peak (11/Z3) of pyrene in SCF C02, C2H4,and CF3H is shown in Figure 4 as a function of reduced density. Both C02 and C2H4 are nonpolar yet polarizable; in addition, C02 has a substantial quadrupole moment. On the other hand, CF3H has a considerable dipole moment of 1.65 D. Therefore, even with the nonpolar pyrene one would expect dipole/induced dipole forces with CF,H. The recorded Z1/13 values fall exactly as expected: CF3H highest
0.7 o,5
I
PYRENE at TR (solvent) = 1.01
y2= 3 0.3 0.b 0.b 1.b
'
io-'
' ' ' 1.b REDUFED DENSITY 1.4
2.b
1.6
Figure 4. Comparison of I 1 / & for pyrene in three different supercritical fluids.
PYRENE IN SCF
fc
0.501, ,
0.40.0
, ,
,
-
,! 2
C2H4
5.5 x 10-6 9.2 C
0.5 1 .o BULK DENSIM (gmol/cc
, ,
,
, ,
* io2)
Figure 5. 11/13of pyrene in SCF ethylene at 11 and 35 OC.
(strongest interactions), followed by C02 and C2H4. Note that along the constant mole fraction isotherm in a particular fluid the Z1/13 is lower near the critical point and increases slightly as the pressure is raised to a hundred bar above the critical point. This is not an indication of weaker forces nearer the critical point; it is simply a reflection of the changing solvent density, which is lower near the critical point. Changing solute concentration should not affect the peak intensity ratio. This brings up a very important observation. Not only does the nature of the solvent (dipolarity, polarizability, acidity, basicity) affect Z1/Z3, as shown by Kalyanasundaram and Thomas (1977) and Dong and Winnik (1982, 1984), but the solvent density changes Z1/13 (lower densities give lower values of Z1/13). Clearly, at the reduced temperatures shown in Figure 4, one would have to take into account the strong possibility of local densities that are different than the bulk density in the highly compressible region where the partial molar volumes are very large and negative. However, at temperatures further removed from the critical point, where the compressibility is relatively low and free of anomalies, a plot of ZJZ3 versus bulk density for a particular solvent might be a good measure of the effect of density on the ratio. Such is likely to be the case in Figures 5-9 for the lower curves, which are 19-26 "C above the critical temperature. We shall use this later to determine local densities. Because 11/13 for pyrene (or 1 1 / 1 4 for naphthalene) decreases with decreasing density, a superior way to compare the data is at constant density, at temperatures near and far from the critical point. This introduces a small complication in the analysis since in liquids the intensity ratio can be a function of temperature (Thomas, 1989). For
1686 Ind. Eng. Chem. Res., Vol. 29, No. 8, 1990
1.50
0
1
;
0
/ c
35
1.30 1.40: 1'
,
"I
-
-
i
20
-
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PYRENE IN SCF CFJH
-
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PYRENE IN SCF CO?
C
l y2
30 C u 50 C 0
0 % '
"
" 0.5 "
"
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BULK DENSITY (gmoi/cc
o o
*
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10' )
'
Figure 6. 11/13of pyrene in SCF fluoroform a t 30 and 50 "C. Solute mole fraction. concentration is 3 x
= 31 C
T, 0 6 1 00
1.5
I
,
l
l
,
r
,
I
0.5
3.0 x lo-'
=
,
,
,
1.o
,
,
T--T;
BULK DENSITY (gmol/cc*: 0') Figure 8. 11/13of pyrene in SCF carbon dioxide a t 35 and 50 OC.
0.38 ' .5 I I
!
I
1 ~
09
PYRENE IN S C F CF,H
-
y2
= 50 x
T,
= 26 C
10-6
~
% / y2 cNAPHTHALENE = 3.5 IN SCF C 0 2 I
~
0
7 00
~
I
,
,
,
, 05
,
I
I
I
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BULK DENSITY (gmoI/cc*102) Figure 7. I1/&of pyrene in SCF fluoroform a t 30 and 50 "C. Solute concentration is 5 x IO4 mole fraction.
Figure 9. 11/14of naphthalene in SCF carbon dioxide a t 35 and 45
instance, if the symmetry disruption is due to hydrogen bonding (which is not occurring in this case), raising the temperature would break hydrogen bonds, reducing the interaction and lowering the value of the intensity ratio. However, the temperature ranges investigated here are relatively small, and at constant density the ratios are the same at both low and high temperatures when operating outside the region where one might expect clustering to occur. Therefore, we believe the only significant temperature effect on the intensity ratios is due to clustering, as discussed below. 11/13and 1,/14ratios are shown in Figures 5-9 for pyrene in COz, CzH4, and CF3H and for naphthalene in C02 at several solute concentrations. Comparison of Figures 6 and 7 confirms that the ratios are relatively independent of solute concentration. In all cases, the ratios 11/13and 11/14 are higher nearer the critical point when two temperatures at constant density are compared. This indicates much stronger solute/soluent interactions closer to the critical point. For instance, in Figure 6, the ratio 11/13is plotted versus bulk solution density for a 3 X mole fraction solution of pyrene in SCF fluoroform at 30 and 50 "C. The critical temperature of CF3H is 26 OC, so the upper curve is closer to the critical point. The two curves seem to merge at higher pressure, where the compressibility is low and the sovlent is very dense. This is what one might anticipate, because at those pressures the solution is at liquid-like densities and the solution is out of the region of large negative partial molar volumes, where clustering is most likely to occur.
As mentioned previously, IJ13 and IJ14 are strong functions of solvent density. They could be considered measures of local density about the solute, based on the discussion of the mechanisms of forbidden band enhancement. Some clustering may occur even at temperatures far removed from the critical point; in fact, even in attractive liquid mixtures the first shell solvent density is somewhat greater than the bulk density. However, the data at a temperature 20-30 "C from the critical temperature are the best measures available of the effect of solvent density on 11/13or 11/14.Such is the case for all the higher temperature curves in Figures 5-9. The relationship appears to be somewhat linear; however, we know of no theoretical justification for such a fit. In Figure 6, for instance, the lower solid line is a linear least-squares fit of the low compressibility points of the 11/13ratio of pyrene in SCF CF3H, i.e., the data at 50 "C. In fact, all of the lower lines in Figures 5-9 are linear least-squares fits of the higher temperature data. It follows that a measure of the density enrichment of the 30 "C points in Figure 6 that are above the line can be obtained by moving horizontally to the line and reading the density. For instance, the local density at point A (bulk density 0.008 mol/cm3) may actually be like the local density at the bulk density at point B, 0.013 mol/cm3. Using this method, we determined a measure of solvent density enrichment or augmentation of pyrene in C02,CzH4,and CF3H, as well as naphthalene in SCF C02. These are shown in Tables I-V. The augmented density is the local density increase over that which would exist without clustering in an
OC.
Ind. Eng. Chem. Res., Vol. 29, No. 8, 1990 1687 Table I. Augmented Densities of 3 X lo-* Mole Fraction Pyrene in SCF C 0 2 at 35 OC augmented pressure, psia density, mol/cm3 compressibility, bar-' 1977 1712 1460 1291 1202 1166 1142 1096 1072 1039
0.0040 0.0031 0.0033 0.0026 0.0049 0.0064 0.0061 0.0048 0.0045 0.0032
0.0019 0.0028 0.0052 0.0128 0.0518 0.1560 0.0989 0.0547 0.0470 0.0413
Table 11. Augmented Densities of 3.5 X 10" Mole Fraction Naphthalene in SCF COz at 35 OC augmented pressure, psia density, mol/cm3 compressibility, bar-' 2046 1880 1715 1549 1374 1294 1217 1188 1159 1141 1099
PYRENE IN SCF COa
0.0006 0.0005 -0.0010 0.0018 0.0010 0.0009 0.0025 0.0022 0.0034 0.0036 0.0028
0.0018 0.0021 0.0027 0.0038 0.0070 0.0113 0.0285 0.0753 0.1698 0.1019 0.0583
-
0
PYRENE IN SCF CHFj
u u '1.0.6 0
-
y2
-m
= 3
lo-'
.
T = 3 0 C
0
L
m z w c3
-
-0.2 0
n
I
v
0.4
-
0
-
n
c1 m
v)
-
-0.i
m W
I
,
0
o
W
Table 111. Augmented Densities of 5.5 Pyrene in SCF C2H, at 11 OC augmented pressure, psia density, mol/cm3 1833 1578 1416 1257 1124 1040 954 862 816 769 1005 1002 816 814 768 764 763 760 755 750 745 736 735 724 724 725 715 705 700 680 679 659
0.0044 0.0045 0.0029 0.0052 0.0034 0.0050 0.0054 0.0063 0.0055 0.0057 0.0049 0.0036 0.0050 0.0040 0.0060 0.0069 0.0086 0.0064 0.0074 0.0100 0.0107 0.0079 0.0089 0.0089 0.0071 0.0086 0.0059 0.0084 0.0074 0.0074 0.0077 0.0070
X
lo4 Mole Fraction
I
c3
20.0
I
. . .
r
I
. . . .
,
. .
*
*
0.0
compressibility, bar-' 0.0014 0.0018 0.0022 0.0029 0.0038 0.0048 0.0066 0.0120 0.0211 0.1420 0.0054 0.0055 0.0211 0.0218 0.1575 0.3295 0.4063 0.5567 0.3267 0.2049 0.1564 0.1147 0.1147 0.0895 0.0895 0.0895 0.0783 0.0704 0.0681 0.0596 0.0593 0.0544
equivalent normal liquid of that bulk density. In these experiments, the local density is as much as 2.5 times the bulk density. At these conditions, the local density is less than that at very high pressures (Le.) 1000 psi or more above the critical point) but still very liquid-like in nature. For instance, for pyrene in SCF fluoroform at a bulk density of 0.35 g/cm3, the local density is almost 0.6 g/cm3.
y2 =
1 '. 0 E 0.8
5.5 lo-6 n
___z
0.4
V
Figure 12. Relationship of the augmented density to the isothermal compressibility of pyrene in supercritical ethylene.
Even more dramatically, the lower temperature isotherms (nearer the critical temperature) return to the higher temperature lines at very low densities, as shown for pyrene in SCF carbon dioxide, ethylene, and fluoroform in Figures 5, 6, and 8. These low-density data are at conditions where the compressibility is smaller than at slightly higher pressures. The compressibility correlates very well with the infinite dilution partial molar volume, so these points are on the decreasing portion of the DZm curve shown in Figure 1and, subsequently, at a state where one would anticipate less clustering. We demonstrate that the clustering does indeed diminish at lower compressibilities in Figures 10-12, where the augmented density (local density increase over that in a normal liquid of
1688 Ind. Eng. Chem. Res., Vol. 29, No. 8, 1990 Table IV. Augmented Densities of 3 X lo-' Mole Fraction Pyrene in SCF CFSH at 30 "C augmented pressure, psia density, mol/cm3 compressibility, bar-' 1789 0.0013 0.002 1539 0.0020 0.002 1371 0.0021 0.003 1209 0.0030 0.004 0.007 1031 0.0025 912 0.0032 0.011 868 0.0037 0.016 812 0.0039 0.041 779 0.0051 0.140 744 0.0064 0.138 1786 0.0008 0.002 1546 0.0036 0.002 1371 0.0020 0.003 0.005 1219 0.0037 1030 0.0022 0.007 910 0.0008 0.011 875 0.0035 0.014 802 0.0045 0.051 778 0.0052 0.176 744 0.0060 0.138 803 0.0026 0.051 774 0.0052 0.170 770 0.0049 0.193 767 0.0047 0.205 758 0.0056 0.200 755 0.0056 0.190 750 0.0054 0 167 744 0.0060 0.142 711 0.0047 0.129 720 0.0051 0.088 700 0.0049 0.070 680 0.0045 0.060 658 0.0041 0.057 636 0.0041 0.053 626 0.0028 0.053 604 0.0019 574 0.0019 566 0.0014 Table V. Augmented Densities of 5 X lo6 Mole Fraction Pyrene in SCF CF3H at 30 "C augmented pressure, psia density, mol/cm3 compressibility, bar-' 1548 0.0025 0.002 1328 0.0028 0.002 1060 0.0029 0.007 901 0.0045 0.011 857 0.0047 0.016 815 0.0055 0.14 770 0.0061 0.19 750 0.0064 0.17
equivalent bulk density) is shown with the isothermal compressibility for pyrene in supercritical COP,CF3H,and C2H4. These values are the difference between the lowtemperature data points and a linear fit of the higher temperature points. It appears that the highest augmented densities correspond reasonably well with the highest isothermal compressibilites for carbon dioxide and fluoroform. For ethylene, the compressibility maximum is at a somewhat higher density than the experimental augmented density maximum. The ethylene data are taken at a temperature closer to the critical temperature than either C 0 2 or CzH4,so there is more experimental uncertainty in those data, as shown by the considerable scatter in the points in Figure 12. As a result, we believe that further investigations are needed to make conclusive statements about the apparent link between the augmented density and the solvent isothermal compressibility. Invariably, any such relationship will break down arbitrarily close to the critical point because the solvent com-
PYRENE
IN ETHYLENE
C
P=53 BAR
T=ll
350.0
400.0
450.0
Figure 13. Excimer formation in dilute supercritical fluid solutions.
pressibility diverges while the augmented density, by its nature, is a finite quantity. Nonetheless, these data indicate that clustering decreases at lower densities where the compressibility decreases, confirming that clustering is most important in the region of high solvent compressibility. In summary, the 11/13and 11/14ratios in the fluorescence spectra of pyrene and naphthalene in supercritical carbon dioxide, ethylene, and fluoroform indicate much stronger solute/solvent interactions nearer the critical point and yield liquid-likedensities in the highly compressible region. These are much greater than the bulk density of the supercritical fluid. Excimer Formation. The formation of excimers reveals the presence of solute/solute interactions. Excimers are excited-state dimers that result in a broad structureless band at significantly longer wavelengths than the normal fluorescence. While they are not dimers in the sense of a ground-state complex, their existence does indicate that there is sufficient interaction in the approximately 104-s lifetime of the excited state (Turro, 1978) to form the excited-state complex. We have observed the formation of pyrene excimers even at extremely low concentrations in supercritical fluids. Figure 13 shows the spectra of pyrene in SCF C 0 2 at two concentrations. A t a mole fraction of just 5.5 x IO4, significant excimer formation takes place. While we do not observe excimers for any of the other solutes in this study, we did observe solute/solute quenching from the intensity plots for naphthalene at 2 x mole fraction, dibenzofuran at less than 1 x mole fraction, and carbazole at about 1 X mole fraction. These solutes have much lower excimer quantum yields (Birks, 1970), so we would not anticipate seeing significant excimer formation in the spectra at these concentrations. The pyrene excimer formation is SCFs is somewhat greater than one observes in liquids. For example, the 5.5 X 10+ mole fraction sample in Figure 13 corresponds to a5x M solution. To obtain a similar level of excimer M formation in liquid cyclohexane requires a 2 x solution (Birks, 1970). This strongly suggests that the once common practice of neglecting solute/solute interactions in models when the solute is below 1-2 mol '70 is unsubstantiated and that our concept of infinite dilution in SCFs may need to be reevaluated. IV. Applications We have described a new technique to measure directly the intermolecular interactions in dilute SCF solutions and presented quantitative results that indicate a significant enrichment of the first solvent shell over that which would occur in normal liquids of the same bulk density. While
Ind. Eng. Chem. Res., Vol. 29, No. 8, 1990 1689 these measurements provide a better understanding of the molecular structure of SCF solutions, the real application of these experiments is in guiding the development of a thermodynamic model that reflects better the true interactions in solution and the investigation of processes that take advantage of the unique clustering in SCFs. Even though the spectra measure intermolecular interactions directly, the observations have not yet been linked quantitatively to equation of state parameters. However, the trends are unmistakable: increased solute/solvent interactions and local density in the regions of high compressibility. There are several viable ways to account for the observed strong interactions or clustering. First, one could address explicitly the clustering using a chemical theory model of the aggregation. Alternately, the attractive term in an equation of state could be modified to account for the effect of the compressibility (or density) on the strength of the interactions. Finally, one could adjust the mixing rules of a standard equation of state to augment the unlike pair interaction energy in the region of high compressibility. Whatever the mathematical method, the results presented here make it clear that the equation of state must account for local densities rather than bulk densities. The excimer results suggest that solute/solute interactions are important, even in very dilute SCF solutions, so the solute like pair interactions should not be discarded in any model development. Moreover, these data are a physical measure of criticality and can be used by theoreticians calculating radial distribution functions of these highly asymmetric SCF solutions. Enhanced local densities that can be carefully controlled with small changes in temperature and pressure may be attractive for a variety of other processes in SCFs. For instance, increased local concentrations of reactants could increase reaction rates in SCFs. This feature coupled with the strong pressure effect on the reaction rate constant and improved separations could make SCFs more attractive as reaction media. In addition, clustering may partially explain the remarkable enhancement of solute solubilities with entrainers. Understanding how entrainers aggregate around solutes may help in the selection of entrainers for extraction processes. Finally, we believe that the degree of clustering at the upstream conditions may have a profound effect on the morphology of solids formed from the expansion of SCF solutions. There appears to be potential for the formation of uniformly sized particles for ceramics and other applications by this method if the appropriate process conditions can be identified and predicted.
V. Conclusions Fluorescence spectroscopy is presented as a new experimental technique to study directly the intermolecular interactions in dilute SCF solutions. Intensity ratios indicate increased local densities (2-3 times that of the bulk density) about solutes in supercritical fluids in the highly compressible region where the infinite dilution partial molar volume of the solute is very large and negative. The fluorescence spectra provide quantitative measures of the augmented density, which can be as much as 0.006 mol/cm3 for a bulk density of only 0.003 mol/cm3. These are the first experimental results to show clustering of nonpolar solvents around nonpolar solutes and demonstrate that high local densities in SCFs are not limited to solutes that one would expect to have strong specific hydrogen-bonding, acid-base, charge-transfer, dipole-dipole, or induced dipole-dipole interactions with the solvent.
Excited-state dimers are present in SCF solutions as dilute as 5 X lo* mole fraction, which suggests that the concept of infinite dilution in these asymmetric mixtures may need to be reexamined. These data are important in understanding the structure of supercritical fluid solutions on a molecular scale so phase equilibria models can reflect better the true intermolecular interactions. Also, the increased local densities suggest potential for increased rates of reactions, exploitation of entrainer effects, and improved particle formation from the expansion of SCF solutions.
Acknowledgment We gratefully acknowledge funding support for this work from the US. Environmental Protection Agency, through the Advanced Environmental Control Technology Research Center at the University of Illinois, supported under Cooperative Agreement CR-806819; from the US. Department of Energy, under Grants DE-FG22-88PC88922 and DE-FG22-84PC70801; from the Hazardous Waste Research Information Center of the State of Illinois, under Grant SENR HWR 89-062; and from the National Science Foundation and E. I. du Pont de Nemours & Co., for fellowship support. We are grateful to Du Pont also for furnishing the fluoroform used. In addition, we acknowledge the very helpful advice of Dr. Curt Frank, Department of Chemical Engineering, Stanford University. Registry No. COz, 124-38-9; C,H,, 74-85-1; CF3H, 75-46-7; pyrene, 129-00-0; naphthalene, 91-20-3; dibenzofuran, 132-64-9; carbazole, 86-74-8.
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Receiued for review December 7 , 1989 Accepted April 16, 1990
Dynamics of Fluid Mixing at a T-Junction with Implications on Natural Gas Processing Shaw H. Chen* and Jane J. Ou Department of Chemical Engineering, University of Rochester, Rochester, New York 14627
Alexander J. Dukat Columbia Gas System Service Corp., 1600 Dublin Road, P.O. Box 2318, Columbus, Ohio 43216
Jayathi Y. Murthy Creare R & D Inc., P.O. Box 71, Hanover, New Hampshire 03755
A mathematical model was developed for the representation of both composition and temperature fields downstream from a T-junction where two natural gas streams of different composition and temperature meet. The work was motivated by a long-term goal to examine the effects of the dynamics of mixing on liquid yields in view of the fact that thermodynamic considerations of the retrograde condensation alone were found to be inadequate. The results from the present engineering analysis were compared to those obtained from computational fluid dynamics based on the k-t turbulence model. Both the jet trajectory and cross section were in reasonable agreement with each other, and the jet center temperature and species concentration were in quantitative agreement. However, the present approach has advantages in its conceptual simplicity and ease of implementation for practical applications.
I. Introduction The accumulation of liquids in pipeline systems has been a nuisance and sometimes a cause of hazard to the
* Author t o whom correspondence should be addressed. 0888-5885/90/2629-1690$02.50/0
transmission and service of natural gas. In an effort to enable design engineers to predict the quantity of liquid formation from conditions prevailing in the pipeline, the American Gas Association took an initiative by funding a research program conducted at the University of Mich0 1990 American Chemical Society
