J . Phys. Chem. 1990, 94, 7692-7700
7692
adsorption energy, so equating expressions 43 and 44 and subtracting the chemical term -uodofrom the latter yields (45)
and recognizing uod0as the equivalent of the term J(pf4) du, we again have eq 13 for the electrical energy. In the case where the surface charge arises from an acid/base dissociation process, rather than from adsorption, one again has a constant potential process for which eq 44 is applicable, where the “chemical” term, is now a function of the bulk hydrogen ion concentration (pH), and the chemical dissociation work (pK,), and uo is the fraction of ionized groups at e q u i l i b r i ~ m . ~ ~ The energy density integral for the NLBP equation has been written in a number of equivalent forms in eqs 13 and 23-25. Which of these should be used in a particular application will be determined by numerical considerations. For the finite difference results reported here, the form given in eq 23 is convenient since it involves only integrals over the volume of the ion atmosphere. This expression does not require the potential at the fixed charges to be evaluated, which in the TFD method requires the subtraction . ~addition ~ of a grid potential, or renormalization p r o c e d ~ r e . ~In to numerical considerations, the various forms represent different ways of assembling or charging up the system to its final state. The physical interpretations of eqs 13 and 24 have already been discussed. In eq 25 the potentials have been split up into their various contributions. The first term involves only the potentials arising from the colloid and the solvent (water) and thus gives the solvation energy of the colloid at zero ionic strength (see, for example, refs 3 and 43). The second term is the electrostatic work of placing the charged colloid in the already organized ion atmosphere, the third term is the electrostatic self-energy of ion atmosphere assembly, the fourth term is the entropy of ion organization, and the last term is the water chemical potential term. ~~~~
~~
~
~
(42) Chan, D. Y.;Mitchell, D. J. J. Colloid Inferface Sci. 1983, 95, 193. (43) Gilson, M. K.; Honig, B. Proteins 1988,4,7-18.
The second through fifth terms can also be thought of as the change in solvation energy of the colloid upon transferring it from pure water to a salt solution. The various interpretations of the energy density integral reiterate the point that there is a unique, unambiguous energy for any system modeled by the nonlinear PB equation, irrespective of the order or method of assembly of the components. The nonlinear PB equation may, however, be applied inconsistently, as in ionic solution theory, where one of the mobile ions is treated as fixed, Le., not subject to thermal averaging. On the other hand, in the applications of most interest to biophysics, surface chemistry, etc., it is not inconsistent to treat colloids, surfaces, membranes, polyelectrolytes, or macromolecules as fixed charged bodies with respect to the much smaller mobile ions.
Conclusions The method of variational calculus provides a simple way to obtain an expression for the total electrostatic free energy for any form of the PB equation. The expression involves what is termed here an energy density integral. Both the more familiar charging integral and the energy density integral can be applied to numerical solutions of the PB equation with equal accuracy, but, for the latter, the equation need only be solved once, resulting in a much greater computational efficiency. A consistent definition of the potential is given for the cell model, without which the charging and energy density integrals do not agree. The energy density integral involves the integral of the excess osmotic pressure of the ion atmosphere. The various forms of the PB equation which have been most widely discussed because of the availability of analytical solutions are shown to be special cases in which, which for a number of reasons, the osmotic term is not necessary. In general, however, this term cannot be neglected when calculating total energies for the nonlinear PB equation, and its importance is reemphasized here. Acknowledgment. We acknowledge helpful discussions with Hillary Rodman-Gilson and Michael Gilson. This work was supported by N I H Grants GM-30518 and GM-41371.
Nap)dha)ene/Trlethyllcrmine Exciplex and Pyrene Excimer Formation in Supercritical Fluid Solutions Joan F. Brennecke,+David L. Tomasko, Department of Chemical Engineering, University of Illinois, Urbana, Illinois 61801
and Charles A. Eckert* School of Chemical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0100 (Received: February 27, 1990)
Supercritical fluids (SCFs), especially mixed solvents or those with entrainers, exhibit specific interactions that make them a very powerful media for separations. It is important to understand microscopic interactions between solutes and entrainers, as well as between two solute molecules, to develop predictive thermodynamic models of supercritical solutions. We present new fluorescence spectroscopy results of exciplex and excimer formation in SCF solutions and describe special considerations required in the analysis. The results indicate a significant solvent effect on the photophysical kinetics and the presence of solute/solute interactions in very dilute SCF solutions.
Introduction Supercritical fluids (SCFs) exhibit a variety of properties that make them particularly attractive for separation processes and yet specially challenging to characterize. Specifically, S C F ~offer ‘Present address: Department of Chemical Engineering, University of Notre Dame, Notre Dame, IN 46556. * To whom correspondence should be addressed.
0022-3654/90/2094-1692$02.50/0
the advantages of both distillation and extraction, in that they separate compounds not only by differences in vapor pressure but also by specific interactions with well-chosen solvent components. Two of these specific interactions, entrainer effects and solutesolute synergism, have been the object of macroscopic experimental investigation with little corresponding success in model development. Entrainer effects, where a small amount (0.14%) of an additional component with some functionality increases the sol0 1990 American Chemical Society
The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 7693
Supercritical Fluid Solutions
>
t
1 I
I
0
E
-5000
J
u 5.01
/
i
--10000
-150001 Y 2*5 SOLVENT: PURE C o g
st
0.50
150
250
350
PRESSURE (BAR)
Fipre 1. Selectivity for acridine from a physical mixture of acridine and
anthracene using pure and entrainer modified supercritical C02 (Van Alsten, 1986).
DENSITY (gmol/cc) Figure 2. Partial molar volume at infinite dilution of naphthalene in supercritical ethylene at 12 "C.
ubility of a solid in an SCF, and solute-solute synergism, where the presence of an additional solute changes the solubility of both components, each introduce a third component to the system as well as different forces that cannot be accounted for with cubic equations of state. Since these appear to be molecular scale interactions, it would be useful to probe the environment around a solute and gain a better understanding of the microscopic interactions. In this paper we present the first application of a new technique to study SCF/entrainer systems. Fluorescence spectroscopy is used to study the exciplex formation between naphthalene (the solute) and triethylamine (the entrainer) in supercritical C 0 2 and the excimer formation of pyrene in S C F C02, C2H4,and CF,H as a means of estimating the importance of solute/solute interactions in highly asymmetric S C F solutions. In addition, we discuss the important considerations in the analysis of the spectra that are particular to highly compressible fluids. The relevance of this work is discussed in the following sections on entrainers, solvent aggregation about a solute, and solute/solute interactions. Entrainers. While specific interactions between a dilute solute and the SCF solvent itself can be important in enhancing solubilities (Brennecke and Eckert, 1989; Brennecke et al., 1990), this paper focuses on the specific interactions between a solute and an entrainer, as well as between two solute molecules, in S C F solutions. Both solubilities and selectivitiesof heavy organic solutes can be greatly enhanced by the addition of an entrainer, especially when the entrainer is selected to interact more strongly with one component of a solute mixture. The chemical basis of the solubility enhancement can be dipole/dipole, dipole/induced dipole, charge-transfer, or possibly hydrogen-bonding interactions. An example of improved selectivity (solubility of desired product/solubility of undesired components) with an entrainer is shown in Figure 1. Here the selectivity for acridine from a physical mixture of solid acridine and anthracene is increased significantly by adding 1% methanol to SCF carbon dioxide. The acridine should be highly interactive with the methanol through dipole interactions and hydrogen bonding, while the anthracene should be relatively unaffected. Thus, entrainers can improve separation selectivity while maintaining the sensitivity of the solubility to small changes in temperature and pressure, which has made S C F extraction such an attractive alternative to conventional separation methods. Unfortunately, current thermodynamic models are incapable of representing the phase behavior, especially in these systems designed to take advantage of strong specific interactions, without adding multiple adjustable parameters. As a result, microscopic information about specific chemical interactions in SCFs is very important in the modeling and prediction of S C F phase behavior. Local Densities. In addition to strong specific chemical interactions, high compressibilities, dramatically increasing solubilities, and mixtures of molecules of very different sizes and energies, the local molecular environment around a solute in a
SCF is believed to be complicated by the preferential aggregation, or clustering, of solvent molecules around the solute. There is significant evidence that this results in a local density that is 3-4 times that of the bulk, which is significantly greater than the local density increase around a solute in normal liquids. Moreover, the local composition around a solute may be dramatically enriched with the entrainer, especially in the region of high compressibility nearer the critical point (Kim and Johnston, 1987a, 1987b). In fact, in this region the local mole fraction of entrainer could be as high as 6 times that of the bulk. Evidence for high local densities or clustering includes the following: (1) Infinite dilution partial molar volumes of heavy organic solutes in SCFs that are negative and extremely large in magnitude (up to -20000 cm2/gmol) exist. See, for example, the B2- of naphthalene in SCF ethylene, just 3 OC from the critical temperature, in Figure 2 (Eckert et al., 1983, 1986b). These data suggest that the volume of the solution decreases dramatically when a solute molecule is added. (2) Wavelength shifts in the absorption spectrum of phenol blue in SCFs suggest the local density is greater than the bulk density, especially in the region of high compressibility (Kim and Johnston, 1987a, 1987b). ( 3 ) The Stokes shift and ratio of charge transfer to normal fluorescence of (N,N-dimethy1amino)benzonitrile in SCF CF3H could only be explained by an aggregation type model (Kajimoto et al., 1988). (4) Fluorescence intensity ratios and overall intensities of a variety of both nonpolar and polar solutes in S C F C 0 2 , C2H4, and CF3H indicate local densities as high as 3 or 4 times that of the bulk (Brennecke et al., 1990). ( 5 ) Molecular dynamics simulations of supercritical mixtures of neon and xenon distinctly show the clustering of solvents around the solute in the attractive case and a negative cluster or hole in the repulsive case (Petsche and Debenedetti, 1989). ( 6 ) Direct calculation of the pair correlation functions of supercritical fluid systems as asymmetric as naphthalene/C02 and pyrene/C02 indicate long-range correlations, which is consistent with the idea of clustering of the solvents around the solute (Cochran and Lee, 1989; Lee, 1989). The fluorescence spectroscopy results presented here and elsewhere (Brennecke and Eckert, 1988,1989; Brennecke et al., 1990) provide additional insight into the nature of the aggregation in SCFs. Unlike thermodynamic measurements, like the infinite dilution partial molar volumes, they provide microscopic measures of the intermolecular interactions. In contrast to other spectroscopic probes, the mechanisms of solvent influence on the fluorescence spectra are nearest neighbor, or first-shell, interactions so they record the environment in the immediate vicinity of the solute molecule. In addition, one can use fluorescence spectroscopy to look a t specific interactions in the form of excimers and exciplexes, as reported here. The combination of thermodynamic
7694
The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 10
I
-1,
NAPHTHALENE
W
z
0
/=
BENZOIC ACID
I-
o a
KURNIK AND REID, 1982
Figure 3. Synergistic solubility effect demonstrated for a physical mixture of naphthalene and benzoic acid in supercritical COz at 45 "C (Kurnik and Reid, 1982).
measurements, long- and short-range spectroscopic probes, and probes of specific chemical interactions gives a more complete picture of the intermolecular interactions on which to base phase equilibria model development. Solute/Solute Interactions. Despite dramatic enhancements, the solubilities of heavy organic solutes in SCFs are frequently still very low (less than 1 mol %), and solute/solute interactions are commonly eliminated from thermodynamic models. Unfortunately, these interactions may be very important. This was observed by Kurnik and Reid and Kwiatkowski and co-workers (Kurnik and Reid, 1982; Kwiatkowski et al., 1984) in the synergistic effects on the solubilitiesof mixed solutes. When a physical mixture of naphthalene and benzoic acid is extracted with S C F COz, the solubilities of both components is greater than the solubility of either pure component, as shown in Figure 3. This phenomenon occurs at concentrations as low as 10-2-10-3 mole fraction. Therefore, assuming "infinite dilution" of the solutes due to the low solubiljties may not be justified, and a better understanding of these solute/solute interactions may be very important for the prediction of S C F phase behavior. Experimental Section
The steady-state fluorescence measurements were made with a modular spectrometer assembly, composed mainly of Kratos optical components, and the spectra were detected with a Hamamatsu 1P-28 photomultiplier tube. The custom-built highpressure optical cell was equipped for 90' detection and had a 1.3-cm path length. More details of the spectrometer assembly, high-pressure assembly, temperature and pressure control, and procedure are given elsewhere (Brennecke and Ekkert, 1988, 1989; Brennecke et al., 1990). The SCFs used included Linde anaerobic grade carbon dioxide (99,99% purity, maximum O2 concentration of 10 ppm), Scott Specialty Gases CP grade ethylene (99.5% purity, guaranteed O2 concentration below 5 ppm), and fluoroform supplied by Du Pont (98% purity, passed through a series of two Alltech Oxy-traps to remove oxygen). The pyrene and naphthalene solutes were Aldrich 99+% purity and they were used without further purification. The triethylamine was Aldrich 99+%, Gold Label, and this was used also without further purification.
Naphthalene/Triethylamine Exciplex Formation Amines can quench the normal fluorescence of aromatic hydrocarbons by forming fluorescent exciplexes, which result in the appearance of a red-shifted broad, structureless band (Mataga et al., 1966a-c; Potashnik et al., 1971; Davidson et al., 1975, 1977; Basu, 1978; Tavares, 1980; Purkayastha and Basu, 1982; Karpurkayastha and Basu, 1982; Castella et al., 1986). In particular, triethylamine effectively quenches the fluorescence of naphthalene solutions in liquid cyclohexane (Van and Hammond, 1978). Triethylamine is also known to fluoresce efficiently (Freeman et
Brennecke et al. al., 1971), but the excitation wavelength used here (265 nm) is sufficiently removed from the absorption maximum of this amine. When placed in a supercritical fluid solvent, the naphthalene and triethylamine represent the "solute" and the "entrainer", respectively, and the exciplex formation can be a measure of the interaction between the solute and entrainer in the highly compressible S C F region. Results. The normal fluorescence and exciplex formation were recorded for 1 x mole fraction naphthalene (corresponding to approximately 6 X 10-5-2 X lo4 M) and three concentrations of triethylamine (0.06, 0.14, and 0.27 mol %, which correspond to approximately 0.005-0.05 M) in S C F C 0 2 at 35 and 50 OC and pressures from 74 to 140 bar. The critical point of C 0 2 is 3 1 "C and 73.9 bar; all experiments were removed sufficiently from the scaling region, yet some were within the area believed to experience the dramatically increased local densities or clustering. Care was taken to remain within the one-phase region. The experiments consisted of scans at several pressures along a given isotherm, at constant solute mole fraction, and constant entrainer mole fraction. As the pressure decreased, the density also decreased, which lowered the molar concentration of all the components. At 35 OC, nearer the critical point of CO,, the ratio of exciplex to normal fluorescence increases dramatically at higher pressures and falls off rapidly at low pressures when plotted versus entrainer molarity a t all three triethylamine mole fractions. This is in striking contrast to the data at 50 OC, just 19 'C above the critical temperature, where the exciplex/normal fluorescence ratio increases almost linearly with triethylamine concentration. Clearly, proximity to the critical point has a profound effect on the exciplex formation. Discussion. A mechanism proposed for the fluorescence in dilute naphthalene solutions with triethylamine in S C F C 0 2 is (Van and Hammond, 1978) A*
kl --*
A
+ hvA
(1)
ki
A*-A A*
+Q
-
(2)
k3
(AQ)*
k-3
+ Q + hVAQ (AQ)* 2 A + Q
(AQ)*
k4
+
A
(3)
(4)
(5) Rare Analysis. In the thermodynamic framework of transition state theory (Evans and Polanyi, 1935) A + B z TS products (6)
-
the rate will be a function of pressure, given by 8 In k / d P = A v * / R T
(7)
where Av* is the activation volume, given by the difference in partial molar volumes of the transition state and the substrate: However, the above equations are valid only if the rate expressions are written with pressure-independent concentration units (Eckert, 1972; Grieger, 1970). Therefore, the common practice of analyzing the exciplex formation in terms of molar concentrations is inappropriate in this situation because the molarity changes with pressure. If molarity were used, eq 7 would have to be corrected with a term including the compressibility of the SCF. Using the pressure-independent units of mole fraction, the rate expressions are essentially equivalent to standard molar expressions, except the concentration units are mole fraction and the units of the rate constants are s-]. Assuming steady-state fluorescence, the concentration of exciplex is x,q. =
k3XA*XQ
k-3
+ k4 + k5
(9)
The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 7695
Supercritical Fluid Solutions 50
I/ :::::I Pressure (bor)l
Preos;lg,bor)
TRIETHYLAMINE NAPHTHALENE
TRIETHYLAMINE/NAPHTHALENE EXCIPLEX IN SCF COz
. p="
112.4 103.4 106.9
30-
92.7
- e .
97.9
\
s
-e
20-
84.8
93.8
80.7
89.6 83.8 78.6
76.5 75.0
10-
74.8
o i . . : .
0.000
I
o.ob1
.
,
L
,
,
9
7
,
.
$
r
.
0.0
'
T%EHYLAMINE CONC. (mot f r a c t i o n )
0.003
0.002
0.001
TRIETHYLAMINE CONC. (mol f r a c t i o n )
Figure 4. Ratio of normal fluorescence area of naphthalene without and with triethylamine in S C F C 0 2 at 35 OC.
1
TRIETHYLAMINE/NAPHTHALENE EXCIPLEX IN SCF Con
,/$
103.4
100
84.8 92.7
2-
80.7
76.5 75.8 74.8
a
73.8
-
80 0
i Y 11
+I
-
I E x p e r i m e n t a l Values ) \ T = 35 C
-
2 -c 40.-
v
-
0 1 ,
I
.
1
o.oo1
1
I
I
I
0.002
I
I
I
I
,
0.003
I
0
TRIETHYLAMINE NAPHTHALENE EXCIPLEX IN &F COz
-
601
0.ow
0.003
Figure 6. Ratio of exciplex to normal fluorescence for triethylamine/ naphthalene in S C F C 0 2 at 5 0 OC.
1
139.6 118,9
0.002
-
I 'I
,
I
'1
d
,I
TRIETHYLAMINE CONC. (mol f r a c t i o n )
Figure 5. Ratio of exciplex to normal fluorescence for triethylamine/ naphthalene in S C F C 0 2 at 35 OC.
The ratios of the quantum yield of the normal fluorescence without triethylamine to the quantum yield with triethylamine is given by k3(k4 + kS)xQ *PIAo - I + (10) (ki + k2Hk-3 + k4 + ks) *fA
--
and the ratio of quantum yield of the exciplex fluorescence to normal fluorescence is
These equations require that the solvent densities of the two experiments in the ratio be the same. The relative quantum yields of the normal and exciplex fluorescence were determined by the area underneath the peaks, without any correction for the photomultiplier tube response or variation in transmission efficiencies. Therefore, at a given solvent density and solute mole fraction (1 X mole fraction in these experiments) a ratio of the areas plotted as a function of triethylamine mole fraction should yield a straight line, the slope of which corresponds to the ratio of rate constants in eqs 10 and 1 1. The ratio of normal fluorescence area without and with triethylamine at 35 OC is shown in Figure 4 for several different solvent densities. The lines are linear least-squares fits a t each density. The slopes, corresponding to the ratio of rate constants in eq 10, decrease by a factor of almost 7 with a decrease in pressure from 140 to 74 bar (which corresponds to a decrease in density from about 0.018 to 0.007 mol/cm3). The ratios of exciplex to normal fluorescence areas at several pressures are shown in Figures 5 and 6 at 35 and 50 OC, respectively. The linear least-squares fits represent adequately the data at each pressure, but the slopes are again strong functions of that pressure. Therefore, the ratio of reaction rate constants in eq 11 also changes with the pressure or solvent density. Note that at 35 O C (just 4 OC above the critical temperature) the slope decreases rapidly at high densities, levels off, and then falls rapidly again at pressures
Figure 7. Pressure dependence of the rate constant for exciplex formation numerically determined from the slopes in Figure 4. The line connects experimental points.
very near the critical pressure. This is in striking contrast to the same plot at 50 "C. Reaction 3 is likely to be the most sensitive to pressure and may be responsible for the interesting decrease in the slopes of Figures 4-6. It is the only bimolecular reaction, so the difference of partial molar volumes (eq 8) may be significant. Clearly, there may also exist a difference in partial molar volumes for the other reactions but we shall concentrate our efforts on reaction 3, since its reaction rate constant is likely to change more dramatically with pressure. According to eq 7, the pressure dependence of k3 should be related to the difference of the partial molar volumes of the transition state and the reactants. Unfortunately, these data do not give the pressure dependence of k3 but rather that of the entire ratio in eq IO or 11. However, with the assumption that only k3 depends on pressure, the natural logarithm of the slopes in Figures 4-6 is just the logarithm of k3 plus a constant. Therefore, d In (slopes from Figure 4)ldP should be proportional to -Au'. The quantity d(1n k3 C,)/dP was determined numerically from the values in Figure 4 and is plotted as a function of pressure in Figure 7 for 35 O C . Similarly, d In ( k , + C 2 ) / d Pwas determined numerically from Figures 5 and 6 and is plotted as a function of pressure in Figure 8 for 35 and 50 OC. Notice the sharp peak in the experimental values of d In kJdP at 35 OC, which is in the highly compressible region nearer the critical point. Partial Molar Volumes. To estimate the behavior of a In k3/dP, one must calculate the partial molar volumes of the reactants and transition-state complex. In fact, in the context of transition-state theory, reaction 3 is
+
A*
+Q
-
-
( A Q ~ (AQ)*
(12)
so Ad = B(transition-state complex) - B(excited-state naphthalene) - D(triethy1amine). We used the Peng-Robinson equation to estimate the equation of state contribution to the partial molar volumes. Since the
7696 The Journal of Physical Chemistry, Vol. 94, No. 19, 1990
Brennecke et al.
TABLE I: Parameters for the Peng-Robinson Equation compd T., K P,,bar acentric factor co20 304.2 74 0.225 535 31 0.329 triethylamineb naphthaleneb 748 41 0.302 complexb 803 17 0.472
Q 1
a
2-
--
"Reid et al. (1987). bTc and P, calculated by Lyderson's method (Reid et al., 1977). Acentric factor calculated by the method of Lee and Kesler (Reid et al., 1987).
\
TRIETHYLAMINE/NAPHTHALENE EXCIPLEX IN SCF CO2
,
U
'
Experimental Values
35 C I
c1
Y
v
c 1-
TABLE 11: Parameters for Calculating the Electrostriction Contribution to the Activation Volume
u'
4
I
I
I
0
C
50
lo8 x molec solute
u. D
radius, cm
3.07
triethylamine/naphthalene complex
0.66 0.0 1 1.1
triethylamine naphthalene
01
I
I
I
80
60
PR
3.46
I
I
E'&
UR
,
I
E''y ba r)I
I
I
4
160
'O
Figure 8. Pressure dependence of the rate constant for exciplex formation numerically determined from the slopes in Figures 5 and 6. The line
excited state of naphthalene is nonpolar, the partial molar volume of ground-state naphthalene should be a good estimate. Although there are only a few partial molar volume measurements in SCFs available, naphthalene in S C F COz is one of them (Ziger, 1983; Eckert et al., 1986b). Therefore, the binary interaction parameter for naphthalene/COz in the Peng-Robinson equation was regressed from actual partial molar volume data. The interaction parameter for triethylamine/C02 was assumed to be the same as that regressed from trihexylamine/C02 liquid/SCF data (Schmitt and Reid, 1988) since there were no data available for triethylamine. The interaction parameter for the transition-state complex/C02 was assumed to be the same as that used for triethylamine/CO,. The critical properties and acentric factors of C 0 2 and triethylamine are available in the literature (Reid et al., 1987). The critical properties and acentric factor of naphthalene and the transition-state complex were estimated with Lyderson's method and the method of Lee and Kesler (Reid et al., 1977; Reid et al., 1987). Since there are no appropriate methods available, the boiling temperature of the naphthalene/triethylaminecomplex was estimated as 100 OC above that of naphthalene. The parameters used in the Peng-Robinson equation are shown in Table I. There is an additional contribution to the partial molar volumes from electrostriction. This is particularly important for the exciplex, which has an estimated dipole moment of 11.1 D (Van
connects experimental points.
and Hammond, 1978). The partial molar volume due to electrostriction is given by
where t is the dielectric constant of the solvent and r is the radius of the cavity about the dipole. The dipole moment of triethylamine is 0.66 D, and the first excited state of naphthalene is an essentially nonpolar 'Lb (Birks, 1970). Molar volumes were used to estimate the cavity radius. The dielectric constant was assumed to follow the Clausius-Mosotti function, and the value of the constant was obtained from the literature (Johnston and Cole, 1962). A summary of the constants used to calculate the electrostriction contribution to the partial molar volumes are listed in Table 11. All of the estimates of the contributions to the partial molar volumes are shown in Table 111. The electrostriction is overwhelming and causes the activation volumes to be large and negative, especially in the compressible region at 35 OC. Since d In k3/aP is the negative of the activation volume, the partial molar volume calculations predict a large positive peak in a In k3/aP in the region of highest compressibility, as shown in Figure
TABLE 111: Activation VoluW of Napbtbalene/Trietbylamine Complex Formation eq of state hEA h p h k"mcx EA pressure, psi 35 OC 2025 105 79 515 -1.8 -2.7 1725 78 39 521 -4.3 1500 510 31 -30 1345 464 -47 -142 -1 1.3 1230 -338 -1 79 -15.5 344 -714 -413 1 I70 48 -77.2 -789 1130 -42.6 -1435 -632 -2212 -29.5 1 IO9 -1321 -2855 -4866 -24.9 -1823 1100 -4899 1086 -21.5 -445 1 -4985 -6639 1070 -4956 -14.9 -3776 -3420
electrostriction L*h
&Oill*l~X
activation vol
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
-347 -531 -845 -2236 -3068 -15314 -8450 -5850 -4940 -4264 -2964
-14 -124 -332 -1572 -2192 -14062 -68 15 -3857 -3059 -1446 -709
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
-580 -816 -1 144 -1 542 -2189 -2161 -2489 -2990 -2595 -2241 -1890
-219 -390 -640 -954 - 1494 -2161 -2489 -2193 -1912 -1 728 -1603
50 OC
2300 2060 1880 1750 1630 1550 I475 1420 1360 1300 1215 Oln units of cm3/mol.
65 22 -42 -1 28 -277 -450 -689 -878 -1007 -101 1 -903
25 -35 -122 -238 -434 -655 -938 -I 135 -1239 -1210 -1071
448 409 334 214 -27 -343 -818 -1231 -1576 -1719 -1696
-2.9 -4.1 -5.8 -7.8 -1 1.0 -14.8 -16.7 -15.1 -13.1 -1 1.3 -9.5
Supercritical Fluid Solutions
The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 7697 0.44
,
EXCIPLEX IN SCF CO2 v 0 12000
, , Colculoted volues
1
NAPHTHALENE/TRIETHYLAMlNE IN SCF CO2
NAPHTHALENE/TRIETHYLAMINE
O
.I
00.40 + Q
/
o,-/oo@*
T = 35 T, = 31
LT t k
in z
0.36
z E
J
4AAWO.00 mol% TEA **t** 0.06 mok TEA ppppLl0.14 mob TEA QCQS90.27 mob TEA
i 0.32
0.000
0.005
0.020
0.015
0.010
BULK DENSITY ( g m o l / c c )
Figure 9. Negative of the activation volume calculated from the sum of the contributions from the Peng-Robinson equation of state and eq 13. The line connects calculated points.
Figure 10. Ratio of intensity of the first peak to the fourth peak in the naphthalene spectrum for naphthalene in SCF C02 at 35 O C . 0.40 >
9, for both 35 and 50 OC. This is in remarkable agreement with the experimental observations in Figures 7 and 8. Therefore, the unusual behavior of the exciplex formation is due to a large extent to the electrostriction of the dielectric solvent medium about the exciplex. The estimates of the partial molar volumes of the solutes in S C F C 0 2 are very rough becuase of the following: (1) The Peng-Robinson equation has limited accuracy in predicting partial molar volumes in the SC region, especially with estimated binary interaction parameters. (2) The value of the Clausius-Mosotti function is a zeroth-order approximation and most likely to give some error when the density is changing dramatically. (3) The bulk dielectric constant of COzis used; however, the local influence of triethylamine on the dielectric constant is likely to be significant. Despite these limitations, the remarkable qualitative agreement with the experimental data suggests that taking the pressure effect on the reaction rate is not only appropriate but also necessary when looking a t reactions in highly compressible SCFs. Intensity Ratios. While we have shown that solute/entrainer exciplex formation needs to be analyzed in terms of the solvent effect on the photophysical kinetics, domination of the overall intensity of the normal and exciplex formation by electrostriction seriously hampers the investigation of the specifics of the interactions between the solute and the entrainer. Fortunately, there is another measure of the strength of intermolecular interactions in the fluorescence spectrum of several nonfunctional polycyclic aromatics (Kalyanasundaram and Thomas, 1977; Dong and Winnik, 1982, 1984). The first peak in the spectrum is very solvent sensitive. The first transition is forbidden by symmetry arguments; however, it has been found that the stronger the interactions between the solute and its environment, the more the symmetry is disrupted and allows that transition to take place with higher intensity. For more discussion see Brennecke et al. (1990). Therefore, the ratio of the height of the first peak to the height of a more stable fourth peak in naphthalene is plotted in Figures 10 and 1 1 a t 35 and 50 OC,respectively, for four triethylamine concentrations, ranging from 0.0 to 0.27 mol %. Both solvent and triethylamine would be expected to affect the 11/14ratio. In fact, the dramatically decreasing bulk solvent density is the likely cause of the lower Z1/14values at lower bulk densities (Brennecke et al., 1990). At 35 "C, the ratio increases with increased triethylamine mole fraction at all bulk densities, even though the bulk concentration (moles/liter) of triethylamine goes down with the decreasing bulk density. The net effect is that a t lower bulk densities, nearer the critical point, the presence of triethylamine may contribute a greater fraction of the interactions that disrupt the symmetry and allow the transition to take place. Conversely, at 50 OC the presence of more triethylamine does not seem to have a significant effect on the ratio. In principle, a semiquantitative calculation of the local entrainer concentration could be made by determining 1,/14 in pure triethylamine, but amines are efficient quenchers, meaning that liquid-phase ex-
NAPHTHALENE/TRIETHYLAMINE IN SCF C o p
0.06 m o k TEA LlM570.14 m o b TEA -0.27 m o k TEA
1 1 -
0.28
!
0.000
.
r
.
,
0.008
.
,
,
BULK DENSITY (gmol/cc)
o.o\
6
Figure 11. Ratio of intensity of the first peak to the fourth peak in the naphthalene spectrum for naphthalene in SCF C02 at 50 O C .
periments cannot provide this information. Regardless, these data are entirely consistent with previous suggestions (Van Alsten, 1986; Kim and Johnston, 1987a, 1987b; Walsh et al., 1987) that the local composition is enriched with the entrainer, especially in the region where the compressibility is high, near the critical point. Therefore, the dramatic changes in the exciplex formation are largely due to the kinetic solvent effects from electrostriction of the solvent about the highly polar excited-state complex. However, the intensity ratios indicate an increased enhancement from the triethylamine at 35 OC and very little influence a t 50 OC. This is in agreement with the idea of strong specific interactions between the solute and the entrainer that cause the local environment to be enriched with the entrainer. Unfortunately, solubility data are not available for naphthalene/triethylamine/C02. Since the fluorescence spectra predict an enhanced solute/entrainer interaction with the triethylamine present, it would be interesting to see if there is any solubility enhancement in the ternary system.
Excimers Even in liquid solutions, as the concentration of pyrene is increased, the normal fluorescence quantum efficiency decreases, with the corresponding formation of a broad structureless band at longer wavelengths. Extensive studies revealed this to be an excited 1:l dimer of pyrene in a planar arrangement (Birks, 1968, 1970,1975; Birks et al., 1963a, 1963b, 1964a, 1964h 1964c, 1968, 1971; Birks and Christophorou, 1962a, 1962b, 1963a, 1963b, 1964). Although other polycyclic aromatic hydrocarbons form excimers, the particularly high excimer quantum efficiency of pyrene makes it an ideal probe of solute/solute interactions in SCFs. While excimers are not dimers in the sense of a groundstate complex, their existence does indicate that there is sufficient interaction in the approximately 10% lifetime of the excited state (Turro, 1978) to form the excited-state complex.
7698 The Journal of Physical Chemistry, Vol. 94, No. 19, 1990
1
PYRENE IN ETHYLENE T=ll C P=53 BAR
1,
1
Brennecke et al. 0.60
!
m 0.50
t -
2
y z = 5.5 x 10-6
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z 0.40 0
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o
dL 0.30 0.20
'
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I
356.0
406.0
456.0
506.0
WAVELENGTH (NM)
550.0
Figure 12. Fluorescence spectra of pyrene in SCF ethylene at 1 1
o.oiz
o.oi4
o.ois
o.oia
o.oLo
DENSITY (gmol/cc)
I
Figure 13. Fraction of pyrene molecules fluorescing as excimers in SCF C 0 2a t 35 OC. OC.
Results and Discussion. The purpose of this study is to show the importance of solute/solute interactions in S C F mixtures. Indeed, we observe the formation of pyrene excimers even at extremely low concentrations in SCF COz, CzH4, and CF3H; Figure 12 shows the spectra of pyrene in S C F C 0 2 at two concentrations. At a mole fraction of just 5.5 X lod significant excimer formation takes place, even at high pressures away from the critical point. This mole fraction corresponds to approximately M solution. To obtain a similar level of excimer a 5 X M solution formation in liquid cyclohexane requires a 2 X (Birks, 1970). One would expect the excimer formation to be controlled by diffusion. According to the Einstein-Smoluchowski diffusion theory, the rate should be proportional to the diffusion coefficient, or inversely proportional to the solvent viscosities (Birks, 1970). This has been confirmed for pyrene in liquids at high pressures (Forster et a]., 1963). However, the viscosity of cyclohexane at room temperature is 0.88 CP(Reid et al., 1977) and the viscosity of SCF COz at 150 bar and 35 OC is 0.074 CP(Lamb et al., 1989). Thus, this could account for a 12-fold increase in excimer formation but not the &fold increase observed. It would appear that solute/solute interactions are even more pronounced in asymmetric S C F solutions than in normal liquids. The solute/solute interactions are important because a large fraction of the solute molecules fluoresce as excimers. In fact, assuming equivalent quantum efficiencies of the normal and excimer fluorescence (Birks, 1970) leads to an estimate of about 50% of the solute molecules fluorescing as excimers in a solution a t a mole fraction of just 8 X lod, as shown in Figure 13. Note the increase in the excimer formation at the low bulk densities, which are nearer the critical point. This is most likely due to the dramatically increased diffusivity in the immediate vicinity of the critical point (Lauer et al., 1983; Baker et al., 1984; Lamb et al., 1989) and not to any additional increase in solute/solute interactions. However, the large fraction of molecules fluorescing as excimers strongly suggests that the common practice of neglecting solute/solute interactions in models of SCF phase equilibria when the solute concentration is below 1-2 mol % is unsubstantiated and that our concept of infinite dilution in SCFs may need to be reevaluated. Summary
In summary, we have presented a method to investigate entrainer/solute interactions in supercritical fluids, shown how intensity ratios can be used as measures of the strength of solute/entrainer interactions, and shown the important factors in the analysis of the normal and exciplex intensity data. While each of these factors important to the intensity data can be accounted for in the analysis, each adds additional uncertainty to the interpretation. Therefore, future studies should look carefully at well-characterized systems, whose spectra will not be so strongly influenced by electrostriction. In addition, excimer fluorescence can be used to investigate solute/solute interaction and shows that
these interactions are especially pronounced, even in very dilute S C F solutions, and need to be taken into account in any thermodynamic model of supercritical phase behavior. These fluorescence spectroscopy results are unique in providing information on the short-range and specific chemical interactions in SCF solutions. They complement the solvatochromic shift data, partial molar volume measurements, solubility measurements, calculations of the pair correlation functions, and computer simulations of other researchers to provide a more complete understanding of the molecular interactions in supercritical fluid solutions for the development of more accurate phase equilibria models. Acknowledgment. We gratefully acknowledge funding support for this work from the U S . Environmental Protection Agency, through the Advance Environmental Control Technology Research Center at the University of Illinois, supported under Cooperative Agreement CR-806819, from the U.S. Department of Energy under Grants DE-FG22-88PC88922 and DE-FG22-84x70801, from the Hazardous Waste Research Information Center of the State of Illinois under Grant SENR H W R 89-062, and from the National Science Foundation and E. I. Du Pont de Nemours Co. for fellowship support. We are grateful to the Du Pont Co. also for furnishing the fluoroform used. In addition, we acknowledge the very helpful advice of Dr. Curt Frank, Department of Chemical Engineering, Stanford University, and thank Julie Peshkin, who obtained a significant portion of the fluorescence spectroscopy data presented here. Literature Cited Baker, E. S.; Brown, D. R.; Jonas, J. Self-Diffusion in Compressed Supercritical Ethylene. J . Phys. Chem. 1984, 88, 5425. Basu, S.Exciplex-Aromatic Complex Formation. J. Photochem. 1978,9, 539. Birks, J. B. The Pyrene Excimer. Acta Phys. Pol. 1968, 34, 603. Birks, J. B. Photophysics of Aromatic Molecules; Wiley-Interscience: New York, 1970. Birks, J. B . Excimers. Rep. Prog. Phys. 1975, 38, 903. Birks, J. B.; Alwattar, A. J. H.; Lumb, M. D. Influence of Environment on the Radiative and Radiationless Transition Rates of the Pyrene Excimer. Chem. Phys. Lett. 1971, 2, 89. Birks, J. B.; Appleyar, J. H.; Pope, R. The Photo-dimers of Anthracene, Tetracene and Pentacene. Photochem. Phorobiol. 1%3a, 2, 493. Birks, J. B.; Braga, C. L.;Lumb, M. D. Excimer Fluorescence. VI. Benzene, Toluene, P-xylene and Mesitylene. Proc. R. Soc. A 1965, 282, 83. Birks, J. B.; Christophorou, L. G. Excimer Fluorescence of Aromatic Hydrocarbons in Solution. Nature 1962a, 194, 442. Birks, J. B.; Christophorou, L. G. Resonance Interactions of Fluorescent Organic Molecules in Solution. Nature 39628, 196, 33. Birks, J. B.; Christophorou, L.G. Excimer Fluorescence Spectra of Pyrene Derivatives. Spectrochim. Acta 1963a, 19, 401. Birks, J. B.; Christophorou, L. G. Excimer Fluorescence. 1. Solution Spectra of 1:2-benzanthracene Derivatives. Proc. R . Soc. A 196%. 274, 552. Birks, J. B.; Christophorou, L.G. Excimer Fluorescence. IV. Solution Spectra of Polycyclic Hydrocarbons. Proc. R. SOC.A 1964, 277, 571.
. . .-. . . - . . Supercritical Fluid bolutlons Birks, J. 9.;Dyson, D. J.; King, T. A. Excimer Fluorescence. 111. Lifetime Studies of 1:2-benzanthracene Derivatives in Solution. Proc. R. SOC.A 1964r. 277, 270. Birks, J. B.; Dyson, D. J.; Munro, I. H. Excimer Fluorcscence. 11. Lifetime Studies of Pyrene Solutions. Proc. R . Soe. A 1%3b, 275, 575. Birks, J. 9.;Lumb, M. D.; Munro, 1. H. Excimer Fluorescence. V. Influence of Solvent Viscosity and Temperature. Proc. R . SOC.A 1964b, 280, 289. Birks, J. B.; Lumb, M. D.; Munro, I. H. Temperature Studies of the Fluorescence of Pyrene Solutions. Acta Phys. Pol. 19&, 26, 379. Birks, J. 9.;Srinivasan, 9. N.; McGlynn, S.P. The Luminescence of Pyrene in Viscous Solutions. J . Mol. Specrrosc. 1968, 27, 266. Brennecke, J. F.; Eckert, C. A. Molecular Interactions from Fluorescence Spectroscopy. Proceedings of The International Symposium on Supercritical Fluids; Nice, France, Oct 1988. Brennecke, J. F.; Eckert, C. A. Fluorescence Spectroscopy Studies of Intermolecular Interactions in Supercritical Fluids. ACS Symp. Ser. 1989,406, 14. Brennecke, J. F.; Tomasko, D. L.; Peshkin, J.; Eckert, C. A. Fluorescence Spectroscopy Studies of Dilute Supercritical Solutions. Ind. Eng. Chem. Res., in press. Brignole, E. A.; Andersen, P. M.; Fredenslund, A. Supercritical Fluid Extraction of Alcohols from Water. Ind. Eng. Chem. Res. 1987, 26, 254. Castella, M.; Tramer, A.; Piuzzi, F. Isomeric Forms of Aromatic Hydrocarbon-Aromatic Amine Complexes. Chem. Phys. Letr. 1986,129(2), 112. Cochran, H. D.; Lee,L. L. Solvation Structure in Supercritical Fluid Mixtures Based on Molecular Distribution Functions. ACS Symp. Ser. 1989,406, 27. Davidson, R. S.;Lewis, A.; Whelan, T. D. Excited Complex Formation Between Aromatic Hydrocarbons and Heterocyclic Compounds. J . Chem. Soc., Chem. Commun. 1975,6, 203. Davidson, R. S.;Lewis, A.; Whelan, T. D. Excited Complex Formation Between Heterocyclic Compounds and Aromatic Hydrocarbons and Amines. J. Chem. Soc., Perkin Trans. 2 1977, 10, 1280. Dong, D. C.; Winnik, M. A. The Py Scale of Solvent Polarities. Solvent Effects on the Vibronic Fine Structure of Pyrene Fluorescence and Empirical Correlations with & and Y Values. Photochem. Photobiol. 1982, 35, 17. Dong, D. C.; Winnik, M. A. The Py Scale of Solvent Polarities. Can. J. Chem. 1984, 62, 2560. Eckert, C. A. High Pressure Kinetics in Solution. Annu. Rev. Phys. Chem. 1972, 23, 239. Eckert, C. A.; Van Alsten, J. G.;Stoicos, T. Supercritical Fluid Processing. Enuiron. Sci. Technol. 19860, 20, 319. Eckert, C. A.; Ziger, D. H.; Johnston, K. P.; Ellison, T. K. The Use of Partial Molal Volume Data to Evaluate Equations of State for Supercritical Fluid Mixtures. Fluid Phase Equilib. 1983, 14, 167. Eckert, C. A.; Ziger, D. H.; Johnston, K. P.; Kim, S.Solute Partial Molal Volumes in Supercritical Fluids. J . Phys. Chem. 1984, 90, 2738. Ely, J. F.; Baker, J. K. A Review of Supercritical Fluid Extraction. NBS Tech. Note (US.)1983, 1070. Evans, M. G.;Polanyi, M. Some Applicationsof the Transition State Method to the Calculation of Reaction Velocities, Especially in Solution. Trans. Faraday SOC.1935, 31, 875. Forster, Th.; Leiber, C. 0.;Seidel, H. P.; Weller, A. Der Konzentrationsumschlag der Fluoreszenz in Losung bei hoheren Drucken. Z . Phys. Chem. (Munich) 1963, 39, 265. Freeman, C. G.; McEwan, M. J.; Claridge, R. F. C.; Phillips, L. F. Fluorescence of Aliphatic Amines. Chem. Phys. Letr. 1971, 8(1), 77. Grieger, R. A. High-PressureKinetic Studies of Diels-Alder Reactions. Ph.D. Thesis, University of Illinois, Urbana, IL, 1970. Johnston, D. R.; Cole, R. H. Dielectric Constants of Imperfect Gases. 11. Carbon Dioxide and Ethylene. J . Chem. Phys. 1962, 36, 318. Kajimoto, 0.;Futakami, M.; Kobayashi. T.; Yamasaki, K. Charge-Transfer-State Formation in Supercritical Fluid: (N,N-Dimethylamino) benzonitrile in CF3H. J . Phys. Chem. 1988, 92, 1347. Kalyanasundaram, K.; Thomas, J. K. Environmental Effects on Vibronic Band Intensities in Pyrene Monomer Fluorescence and Their Application in Studies of Micellar Systems. J . Am. Chem. SOC.1977, 99, 2039. Karpurkayastha, A.; Basu, S. Specific & Non-specific Solvent Effects on Exciplex Emission from Hydrocarbon-Tritertiary Amine Systems. Ind. J. Chem. 1982, 2 l A , 663.
The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 7699 Kim, S.; Johnston, K. P. Clustering in Supercritical Fluid Mixtures. AIChE J , 1987r. 33( IO), 1603. Kim, S.;Johnston, K. P. Molecular Interactions in Dilute Supercritical Fluid Solutions. Ind. Eng. Chem. Res. 1987b, 26, 1206. Kurnik, R. T.; Reid, R. C. Solubility of Solid Mixtures in Supercritical Fluids. Fluid Phase Equil. 1982, 8, 93. Kwiatkowski, J.; Lisicki, Z.; Majewski, W. An Experimental Method for es of Solids in Supercritical Fluids. Ber. Bunsen-Ges. Phys. Chem. 1984,88 865. Lamb, D. M.; Adamy, S.T.; Woo, K. W.; Jonas, J. Transport and Relaxation of Naphthalene in Supercritical Fluids. J. Phys. Chem. 1989, 93, 5002. Larson, K. A.; King, M.L. Evaluation of Supercritical Fluid Extraction in the Pharmaceutical Industry. Biorechnol. Prog. 1986, 2(2), 73. Lauer, H. H.; McManigill, D.; Board, R. D. Mobile-Phase Transport Prop erties of Liquified Gases in Near-Critical and Supercritical Fluid Chromatography. Anal. Chem. 1983,55, 1370. Lee, L., personal communication, 1989. Mataga, N.; Ezumi, K.; Okada, T. Temperature Effects on Charge Transfer Fluorescence Spectra and Mechanisms of Charge Transfer Interactions in the Excited Electronic State. Mol. Phys. 1966a, 10, 201. Mataga, N.; Okada, T.; Ezumi, K. Fluorescence of Pyrene-N,N-dimethylaniline Complex in Non-polar Solvent. Mol. Phys. 1 9 6 6 ~10, 203. Mataga, N.; Okada, T.; Yamamoto, N. Solvent Effects on Charge-transfer Spectra with Implications for the Electron-transferReaction in the Excited State. Bull. Chem. SOC.Jpn. 1966b, 39, 2562. McHugh, M. A.; Krukonis, V. K. Supercritical Fluid Extraction: Principles and Practice; Butterworths: Boston, 1986. Paulaitis, M. E.; Krukonis, V. J.; Kurnik, R. T.; Reid, R. C. Supercritical Fluid Extraction. Rev. Chem. Eng. 1982, 1(2), 179. Peng, D.-Y.; Robinson, D. 9. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 1976, I5(1), 59. Petsche, I. 9.; Debenedetti, P. G.Solute-Solvent Interactions in Infinitely Dilute Supercritical Mixtures: A Molecular Dynamics Investigation. Submitted to J . Chem. Phys. Potashnik, R.; Goldschmidt, C. R.; Ottolenghi, M. Absorption Spectra of Exciplexes. J . Chem. Phys. 1971, 55( 1 l), 5344. Purkayastha, A. K.; Basu, S.Some Notes on Exciplex Emission from Aromatic Hydrocarbon-Aromatic Tritertiaryamine. Ind. J . Phys. 1982, 56B, 375. Reichenberg, D. The Viscosities of Gases at High Pressures. NPL Rep. Chem. 38; National Physical Laboratory: Teddington, England, Aug (1975). Reid, R. C.; Prausnitz, J. M.; Poling, 9. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1987. Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties of Gases and Liquids, 3rd ed.; McGraw-Hill: New York, 1977. Rizvi, S.S. H.; Benado, A. L.; Zollweg, J. A,; Daniels, J. A. Supercritical Fluids Extraction: Fundamental Principles and Modeling Methods. Food Technol. 1986, 40(6), 55. Saad, H.; Gulari, E. Diffusion of Liquid Hydrocarbons in Supercritical C 0 2 by Photon CorrelationSpectroscopy. Ber. Bunsen-Ges. Phys. Chem. I%, 88, 834. Saad, H.; Gulari, E. Diffusion of Carbon Dioxide in Heptane. J. Phys. Chem. 1984b, 88, 136. Schmitt, W. J.; Reid, R. C. The Solubility of Paraffinic Hydrocarbons and Their Derivatives in Supercritical Carbon Dioxide. Chem. Eng. Commun. 1988, 64, 155. Stephan, K.; Lucas, K. Viscosity of Dense Fluids. Plenum Press: New York, 1979; p 75. Swaid, I.; Schneider, G.M. Determination of Binary Diffusion Coefficients of the Benzene and Some Alkylbenzenes in Supercritical C 0 2 between 308 and 328 K in the Pressure Range 80 to 160 bar with Supercritical Fluid Chromatography (SFC). Ber. Bunsen-Ges. Phys. Chem. 1979,83,969. Tavares, M. A. F. On the Intermolecular Interaction in r-exciplexes of Aromatic Hydrocarbons with Amines. J . Chem. Phys. 1980, 72(1), 43. Tsekhanskaya, Y. V. Diffusion in the System pNitrophenol-Water in the Critical Region. Russ. J . Phys. Chem. 1968, 42, 532. Tsekhanskaya, Y. V. Diffusion of Naphthalene in Carbon Dioxide Near the Liquid-Gas Critical Point. Russ. J . Phys. Chem. 1971, 45, 744. Turro, N. J. Modern Molecular Phorophysics: Benjamin/Cummings: Menlo Park, CA, 1978. Van, S.-P.; Hammond, G.S.Amine Quenching of Aromatic Fluorescence and Fluorescent Exciplexes. J . Am. Chem. SOC.1978, 100(12), 3895.
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Van Alsten, J. G. Structural and Functional Effects in Solutions with Pure and Entrainer-Doped Supercritical Solvents. Ph.D. Thesis, University of Illinois, 1986. Walsh, J. M.; Ikonomou, G.D.; Donohue, M. D. SupercriticalPhase Behavior: The Entrainer Effect. Fluid Phase Equilib. 1987, 33, 295.
Williams, D. F. Extraction with Supercritical Gases. Chem. Eng. Sci. 1981, 36, 1769. Ziger, D . H. Solid-Supercritical Fluid Equilibrium: Experimental and Theoretical Studies of Partial Molar Volumes and Solubilities. Ph.D. Thesis, University of Illinois, Urbana, IL, 1983.
Excess Partial Molar Free Energies and Entroples In Aqueous tert-Butyl Alcohol Solutions at 25 O C Yoshikata Koga,* William W. Y. Siu,t and Terrance Y. H. Wong Department of Chemistry, The University of British Columbia. Vancouver, B.C., Canada V6T 1Y6 (Received: March 12. 1990)
The total vapor pressures of tert-butyl alcohol (TBA)-water mixtures were measured at closely spaced mole fractions. The excess partial molar free energies for 25.00 OC, GmE(i)(i = TBA or H 2 0 ) were calculated by the Boissonnas method. In the range where the Boissonnas method is not appropriate, the Guggenheim expression for the excess integral molar free energy, GmE,was used to analyze the data. The excess partial molar enthalpies, HmE(i)(i = TBA or H20), at 25.00 OC were calculated from the data of the previous calorimetric works from this laboratory. The excess partial molar entropies, SmE(i) (i = TBA or H20),were then calculated. These data show that there are changes in the mixing scheme, or the ‘structure” of these solutions, at about xB= 0.045 and xB= 0.62. (xBis the mole fraction of TBA in the liquid phase.) The first crossover is associated with an anomaly in the quantities that are proportional to the third derivative of the free energy, while the second is accompanied by an anomaly in the fourth derivative. We suggest that the first crossover is the transition of a short to intermediate range order, while the latter is a transition of more subtle nature.
1. Introduction Thermodynamic studies on alcohol-water mixtures have been active for a long time and comprehensive review articles are available.’q2 The existing data on the measured enthalpies of mixing that cover the entire concentration range are all essentially the integral enthalpies except for a single work on methanol and ethanol aqueous solutions in which the excess partial molar enthalpies were r e p ~ r t e d .The ~ latter work has escaped the attention of the review articles, however. The integral enthalpies of mixing provide only indirect information on the solute-solvent and the solute-solute interactions. It is the partial molar enthalpies of each component that provide direct information, particularly in such grossly nonideal solutions as the alcohol-water mixtures. In principle, the partial molar enthalpies can be obtained by differentiating the integral enthalpies. In practice, however, the existing integral enthalpies were not generally measured for sufficiently close-spaced mole fractions to withstand differentiation without losing accuracy. Thus, the values of the partial molar enthalpies of mixing have not been readily available for most aqueous solutions of alcohols. We have been filling this gap by directly measuring the excess partial molar enthalpies of aqueous solutions.eE In particular, the excess partial molar enthalpies of tert-butyl alcohol (TBA), HmE(TBA),4*6 and those of H 2 0 , HmE(HzO),’ in TBA-H20 mixtures were measured accurately. The results have provided more direct information than hitherto available about the solute-solvent and the solutesolute interactions in terms of enthalpy. Thus, a deeper insight into the scheme of mixing in this system was gained.6*8 Now that the accurate values of HmE(i)(throughout this paper, i stands for TBA or H20)are available for closely spaced mole fractions, the values of the excess partial molar free energies are required to calculate the excess partial molar entropies and thus to understand the mode of mixing in terms of entropy. Kenttamaa et a1.k data9 on the partial vapor pressures can be used to calculate ‘To whom correspondence should be addressed. ‘Present address: Department of Pharmacology,The University of British Columbia.
0022-3654/90/2094-7700$02.50/0
the excess partial molar free energies GmE(i)(i = TBA or H20). However, their data points are only a few for the entire concentration range. In a previous paper,’ we made an attempt to fit the Guggenheim expression of the form GmE = XB(1 - xB)xaj(2xB - l y j=O
(1)
to the data of the excess integral free energy, GmE. Such data have been compiled by Westmeier.lo We had wished to differentiate eq 1 algebraically to calculate the excess partial free energies. (xBis the mole fraction of TBA.) The fit appeared to be adequate judging from the value of the total square deviation with six terms for the nine data points. However, the attempt itself at describing the TBA-H20 system by a single equation of the type (1) was not appropriate.’ The chemical potentials, ~ T B A and p H I 0 ,calculated from the fit suggested a phase separation in the range, 0.1 < xB < 0.4, which does not occur in reality. Obviously a subtle curvature of the fit in this range is not correct. After all, the philosophy behind using eq 1 is that the system can be described as a deviation from a regular solution. The TBAH 2 0 system is qualitatively different from a regular solution. Thus, an accurate measurement of the partial molar free energies of this solution is warranted. The present paper reports the results of such measurements. The total vapor pressures of (1) Franks, F.; Ives, D. J. G.0.Reo. 1966, 20, 1. (2) Franks, F.; Desnoyers, J. E. In Warer Science Review, Franks, F., Ed.; Cambridge University Press: Cambridge, U.K., 1985; Vol. 1, p 171.
(3) Bertrand, G. L.; Millero, F. J.; Wu, C.-H.; Hepler, L. G. J. Phys. Chem. 1966, 70, 699. (4) Koga, Y. Can. J . Chem. 1986,64, 206. ( 5 ) Koga, Y . J . Chem. Thermodyn. 1987, 19, 571. (6) Koga, Y. Can. J . Chem. 1988, 66, 1187. (7) Koga, Y . Can. J. Chem. 1988, 66, 3171. (8) Siu, W.; Koga, Y.Can. J . Chem. 1989, 67, 671. (9) Kenttamaa, J.; Tommila, E.; Martti, M. Ann. Acad. Sci. Fenn. A 2 1959, 93, 2. (IO) Westmeier, S . Chem. Techno/. 1977, 29, 218.
0 1990 American Chemical Society
