I n d . Eng. Chem. Res. 1987,26, 1206-1213
1206
Temp. r i s i n g p e r i o d
Time (h)
Figure 12. Reaction profiles of the activated carbon impregnated with Ni, Rh, and Pt at 30 atm and 800 "C.
-
S%N i 1YOCa lOatm
latm
5% N i 10atm
(Figure 13) of the specimen after reaction. However, the better dispersion cannot be the whole explanation, because Mg salt was effective to retain better dispersion of nickel but was not able to promote the reaction as was Ca. The reason of the promotion of Ca is sought in this laboratory, and further results will be reported later. A gasification mechanism is being proposed in which carbon atoms are once dissolved in nickel and then gasified. On the basis of this hypothesis, one possible explanation is that Ca mediates a carbon-catalyst interaction so that carbon atoms become easier to separate from bulk carbon. In fact, there are several literatures which have suggested that in hydrogasification an interaction of a metallic catalyst with carbon is a crucial factor, rather than its ability to activate hydrogen (e.g., Otto and Shelef, 1977; Keep e t al., 1980; Holstein and Boudart, 1981; Baker and Sherwood, 1981). Based on the above data, i t is doubtless true that some calcium surface compounds do promote the hydrogasification of carbon that is catalyzed by iron-group metals. Application of this effect to gasification of coal or carbonaceous resources is still a t an infant stage, and much work is desired. But the observations described above should be of value for other reaction systems, such as those in a blast furnace or for carbon removal from a catalyst surface or a reactor wall as well.
Acknowledgment This study was supported by the Ministry of Education, Science, and Culture (Grant-in-Aid for Energy Research).
Literature Cited
Lc Figure 13. SEM photographs of the pitch coke gasified at 850 "C for 3 h with 5% Ni and 5% Ni-1% Ca catalysts. Different sections of an identical specimen are indicated by a and b.
metals, as stated in our preceding paper (Haga and Nishiyama, 1983b). In the present experiment, in which carbon conversions exceeded 7070, the nickel on the residues was more finely dispersed when promoted than unpromoted. One example is seen in the SEM photographs
Baker, R. T. K.; Sherwood, R. D. J. Catal. 1981,66,451. Blackwood, J. D.; McCarthy, D. J. Aust. J . Chem. 1966, 19, 797. Haga, T.; Nishiyama, Y. Carbon 1983a, 21,219.. Haga, T.; Nishiyama, Y. J . Catal. 1983b, 81, 239. Holstein, W. L.; Boudart, M. J . Catal. 1981, 72, 328. Keep, C. W.; Terry, S.; Wells, M. J . Catal. 1980, 66, 451. McKee, D. W. In Chemistry and Physics of Carbon; Walker, P. L., Ed.; Marcel Dekker: New York, 1981; Vol. 15, pp 1-118. Ono, T.; Haga, T.; Nishiyama, Y. Fuel ProcessinR Tmhnol. 1984,9, 265. Otto, K.; Shelef, M. Carbon 1977, 15, 317. Pullen, J. R. Catalytic Coal Gasification; I.E.A. Coal Research: London, 1984; ICTIS/TR26. Tomita, A.; Tamai, Y. J . Catal. 1972,27, 293. Zielke, C. W.; Gorin, E. Ind. Eng. Chem. 19.57,49, 396.
Received for review November 5, 1985 Accepted February 26, 1987
Molecular Interactions in Dilute Supercritical Fluid Solutions Sunwook Kim and Keith P. Johnston* Department of Chemical Engineering, University of Texas, Austin, Texas 78712
An indicator dye, phenol blue, has been used t o probe dispersion, induction, and dipole-dipole (orientation) and acid-base interactions in supercritical fluid ethylene, chlorotrifluoromethane, and fluoroform. Spectral shifts are compared for the dye in these supercritical fluid solvents vs. in conventional liquid solvents. T h e data are used t o predict the thermodynamic solvent effect on reaction rate constants and also t o determine the local solvent density around the dye, which is described theoretically. A number of recent review articles discuss the types of phase equilibria, e.g, solid-fluid and liquid-fluid equilibria which are relevant for supercritical fluid (SF)extraction (Paulaitis e t al., 1983; Johnston, 1984; McHugh, 1984).
Usually, the phase equilibrium data are correlated by using one or more adjustable binary interaction parameters, although some systems have been predicted by using pure-component properties (Johnston and Eckert, 1981;
0888-5885/87/2626-1206$01.50/00 1987 American Chemical Society
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 1207 Wong et al., 1985; Eckert et al., 1985). Predictive models could be improved if a better understanding of the strength of solute-solvent interactions in the SF state was available. For example, a derivative property, such as the partial molar volume of the solute a t infinite dilution, is related more directly to the attractive interaction constant than is a property such as composition or the fugacity coefficient (Eckert et al., 1986). Our contribution is to probe supercritical fluids at the molecular level using an indicator dye. This information is useful for understanding both macroscopic properties (for example, solubilities and selectivities in supercritical fluid solutions) and the thermodynamic solvent effect on rate constants of homogeneous reactions. It is ironic that the large growth in SF extraction at the Max-Planck Institute in Germany in the 1960s was the result of a serendipitous discovery of the solvent power of supercritical ethylene during the “Aufbau” reaction of triethylaluminum with ethylene (Zosel, 1978). The literature contains few examples where supercritical fluids have been used as media to modify or control reaction rate constants (Randall, 1982; Alexander and Paulaitis, 1984; Simmons and Mason, 1972). Liquid-phase reactions have been studied over wide pressure ranges, e.g., 1to >10 kbar, to determine the activation volume, which is the pressure derivative of the rate constant. These studies essentially ignore the highly compressible near-critical region where activation volumes may approach infinity, either positively or negatively as will be shown below. In the near-critical region, all of the density-dependent properties, such as the dielectric constant, refractive index, fugacity coefficient, and solubility parameter, are extremely strong functions of temperature and pressure. (This is the basis for SF extraction.) It will be demonstrated that this sensitivity could also be used advantageously in reaction processes. The density of CHF, will be varied to adjust the “solvent strength” to be equivalent to those of liquid fluorocarbons, hydrocarbons, ethers, aromatic hydrocarbons, acetates, and chloroform. These changes in the strength of a single SF solvent, which are accomplished by using modest adjustments in the temperature or pressure, are known to correspond to changes in certain reaction rate constants of several orders of magnitude. A dye, phenol blue, will be used as an indicator to determine the solvent strength of several supercritical fluid solvents as a function of temperature and pressure. The solvent affects the absorption wavelength of this dye markedly, a phenomenon called “solvatochromism”. The term solvent strength is very general and rather ambiguous. It has been quantified by the dipole moment, dielectric constant, refractive index, Hildebrand solubility parameter (Dack, 1976; Hildebrand and Scott, 1962), and in many other ways (Reichardt, 1979). For nonpolar molecules, solvent strength would refer to polarizability per volume. In this paper, solvent strength is defined as the transition energy, ET,of phenol blue in a solvent, which is simply equal to hc/X,, where A, is the wavelength of maximum absorption. Solvatochromic scales, based on the absorption wavelength, are used commonly to correlate and predict solubility phenomena, absorption maxima in IR, NMR, ESR, and UV-visible spectroscopy, solvent effects on reaction rate and equilibrium constants, free energies and enthalpies of acid-base complexes, retention indexes in chromatography, and finally, physiological and toxicological quantitative structure-activity relationships (Kamlet et al., 1984; Taft et al., 1985; Reichardt, 1979). Solvatochromic data are just beginning to become available for supercritical fluid solvents for limited pressure and tem-
Vacuum
8,
2~
i uv-VIS Spectrophotometer
Cylinder Syringe
A Thermostat
Figure 1. Apparatus for spectroscopic measurement of solvatochromism in supercritical fluids.
perature ranges (Hyatt, 1984; Sigman et al., 1985). Precise ETdata are reported below for phenol blue over a wide range of pressures and temperatures in several SF solvents. Phenol blue was chosen because it has been characterized thoroughly, both experimentally (Reichardt, 1979; Figueras, 1971; Kolling and Goodnight, 1973) and theoretically (McRae, 1957; Figueras, 1971) in a large number of liquid solvents. In addition, it is sufficiently soluble such that spectral measurements can be performed in ethylene at a reduced density as low as 0.85 at 25 “C. The ET data are used to predict solvent effects on certain reaction rate constants, as has been done for many reactions in numerous liquid solvents (Reichardt, 1979; Dack, 1976). This approach is useful, given the lack of rate constant data in SF solvents and the simplicity and accuracy of the spectroscopic technique. The ET data are also used to determine the local density of a SF solvent in the vicinity of the solute and, finally, to probe hydrogen bonding for CHF,. Experimental Section Phenol blue (N,N-dimethylindoaniline,Aldrich >97 YO) was purified by recrystallization and chromatographic separation (Kolling and Goodnight, 1973). The purity was checked by its melting point (161-162 “C) and its absorption maximum in acetone (582 nm) and in CCll (565 nm). The dye was of chromatographic purity, as determined by thin-layer chromatography on silica gel. The supercritical solvents, CzH4 (AIRCO, >99.8% ), ClCF, (Linde UCON 13, >99%), and CHF3 (Linde Halocarbon 23, >98%), were used as received. The volume of the cylindrical high-pressure cell is 14 cm3, and the pressure and temperature ranges are 0-6000 psi and -30 to 250 “C, respectively (see Figure 1). The inside diameter is 1.75 cm, and the wall thickness is 1.67 cm. Because of the large 6-cm path length of the cell, the spectral shift can be measured for concentrations as low as lo* M at 0.1 AU (absorbance units). Each 1-cm-thick by 2.5-cm-diameter sapphire window is flat to one wavelength of yellow light, and the optical axis is perpendicular to the face. A Teflon O-ring is inserted between the window and a flat surface on the 316 stainless steel vessel. The cell is thermostated by using a l/*-in. copper heat exchange coil that, is jacketed with Fiberglas insulation. The temperature was indicated and controlled to k O . 1 OC with a platinum resistance thermometer which extended 1-mm inside the inner surface of the cell. The pressure was adjusted, using a 100-cm3 Ruska syringe
1208 Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987
pump, and was measured within f0.1% with a 710A Heise digital pressure gauge which is traceable to an NBS standard. The pressure varied less than 0.15 bar (2 psi) during a spectral scan. The wavelength accuracy was i0.2 nm for the Cary 17 spectrophotometer. The cell was loaded with g of phenol blue, evacuated, and pressurized with the solvent. A spectrum was obtained a t a given pressure after the temperature and absorbance equilibrated. The absorption band was scanned over a range of 450-600 nm 2-3 times to obtain an average A., The reproducibility in A, was f0.2 nm which corresponds to a precision in ET of *0.02 kcal/mol. The data acquisition is rapid for this in situ technique, as an isotherm consisting of six data points at various pressures could be measured in several hours. The density of ClCF, and CHF, was measured by using a Mettler/Paar DMA512 digital densitometer. The pressure and temperature control was the same as above. The densitometer was calibrated by using C02 and water (Eckert et al., 1986). The reproducibility in density was i10* mol/cm3. The density of these gases had been measured previously over a limited range (Hou and Martin, 1959; Hori et al., 1981; Michels et al., 1966). The new and old data agreed within *0.5%.
Excited
0-
N
State
0
W*(CH,),
State n-Hexane
Methanol
= 5 5 0 nm
A m a ~
Am*, =
608nm
Figure 2. Transition energy (ET)for the phenol blue.
A-A*
6
56
dT
absorption band of
55
;0 1 Y I-
Y
v
W
2
54
c Y
1
Results and Discussion Solvent Strength and Its Effect on Rate Constants. Transition-state theory may be used to bridge the gap between thermodynamics and kinetics, as it is assumed that the transition state, M, is in equilibrium with the reactants. For the elementary reaction A + B -+M product
Figure 3. Transition energy (ET)and isothermal compressibility vs. density for phenol blue in ethylene: (0)25 "C,(A) 10 "C,( - - - ) calculated EoT.
K* = YM[MI/(YA[AlYB[BI) (1) The rate constant is proportional to the concentration of M so that k = K(~BT/~)K*YAYB/YM (2) The pressure derivative of the Gibbs energy of activation gives the activation volume, which is equivalent to the change in the rate constant with respect to pressure -(dAG*/aP), = RT(a In kx/dP)T = -Aut (3) where kx is the concentration-independent reaction rate constant and the activation volume, A u t , is given by Au* = DM - UA - DB (4) High-pressure studies in the range 1-10 kbar have been performed for liquid-phase reactions to determine activation volumes which are a tool to determine reaction mechanisms (Thies, 1978; Eckert et al., 1974). These studies have essentially ignored the highly compressible region. Simmons and Mason (1972) observed an abrupt decrease in Aut near the critical conditions for the cyclic dimerization of C2F3C1. It is due to the large negative partial molar volume of the dimer in the transition state. At 120 "C, the rate constant doubled for a pressure increase from 43 to 53 bar. Alexander and Paulaitis (1984) measured activation volumes as low as -500 cm3/mol for the DielsAlder cycloaddition of isoprene and maleic anhydride in C02. The rate constant increased about 60% for a change in pressure of several bar. Figure 2 depicts the effect of the solvent on the transition energy, ET, for the visible ir-x* absorption band of phenol blue. The dipole moment of the excited state is about 2.5 D greater than that of the ground state (Reichardt, 1979). As a result, the energy of the excited state is stabilized more than that of the ground state by in-
duction, dipole-dipole forces (orientation), and specific interactions such as hydrogen bonding. Therefore, the transition energy decreases as the strength of the solvent increases (red shift). Because of this large change in the dipole moment on transition, phenol blue is an extremely sensitive probe of solvent strength. For phenol blue, E T is 51.96 kcal/mol in n-hexane and 47.03 kcal/mol in methanol, which corresponds to a shift in A, of 58 nm. The experimental technique is highly sensitive, as A, can be measured to f0.2 nm, which corresponds to an accuracy in E T of f0.02 kcal/mol. The transition energy, ET, of phenol blue in ethylene is plotted vs. density in Figure 3 at 10 and 25 "C (see also Table 11). At low density, e.g., 6.6 mol/L (p, = 0.85), the excited state is stabilized only to a small degree such that E T is relatively large and A ,, is 520.0 nm. At higher densities, the increased stabilization of the excited state lowers E,; thus, A,, shifts to longer wavelengths (red shift). This is due to the higher polarizability/volume of the solvent, which increases the strength of the induction forces. This will also increase the strength of the dispersion forces if there is a significant difference in the polarizabilities of the ground and excited states of phenol blue, information which is presently unavailable. A t constant density, ET is relatively insensitive to temperature, as is evident from the data a t 10 and 25 "C. It is extremely sensitive to pressure in the highly compressible critical region, as is the density. These results demonstrate the key advantage of SF solvents compared ko ordinary liquid solvents. For liquid solvents, the density and E T are relatively insensitive to temperature and pressure. In order to adjust ET, it is necessary to change the solvent or to add a cosolvent. However, E T of a single SF solvent may be altered over a wide range with modest changes in temperature and/or pressure. While this effect is significant for ethylene, it
-
53
0 E
10
15
DENSITY (MOL/L)
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 1209 54.8
n
56 n
54.4
5
d
5
4
0 Y
54
0
-i 54.0
Y
u
W
I-
W
52
53.6
IO
9
12
11
DENSITY (YOL/L)
50
Figure 4. Transition energy (ET) vs. density for phenol blue in CF3Cl: (0) 30 "C, (- -) calculated pp
-
SF Solvents with n -Hexane at 8,
25 40 25
T, P, bar 1.056 1.037
1700 1300 1
P,
p , g/c3
33.8 33.2
0.57 1.95 0.66
cm3)1/2 a / v 7.0 0.052 6.9 0.051 7.3 0.057
Table 11. Wavelength of Absorption Maximum (Amas) of Phenol Blue in Ethylene
nm, at 25 " C 520.0 522.8 529.9 525.7 530.4 527.4 531.6
,A,,
,A,,
P, bar 65.9 70.9 81.1 101.3 181.9
10 OC
P, bar 202.7 253.4 304.0 354.7
10 O C 535.7 536.8 537.9 539.0
nm, at 25 "C 533.6 536.0 536.5
Table 111. Wavelength of Absorption Maximum (Amm) of Phenol Blue in CF&l at 30 "C
P, bar 60.8 81.1 101.3
15
nm 522.9 524.6 526.1
hllax,
P, bar 202.7 304.0
Figure 5. Transition energy (ET) vs. density for phenol blue in 3.5 "C, (A)26 "C, ( 0 )30 OC, (X) 40 OC, (- - -) calculated CHF,: (0) FTbased on the bulk density, -) corrected ElT based on the local density. (-e
(Cd/
T,OC
10
DENSITY (MOL/L)
Table I. Comparison of Constant ET
solvent C2Hd CF3Cl n-CeH,,
5
nm 529.1 531.5
LaX,
would be even more substantial for more polar solvents, for which changes in the density promote pronounced changes in the dielectric constant. The ETof CF3C1is shown in Figure 4 at 30 OC (see also Table 111). The behavior resembles that of ethylene, although the density range is much narrower. In Table I, SF ethylene and CF3C1are compared with liquid n-hexane a t a reduced temperature near 1.05. For each fluid, the pressure and density are chosen to match the ET values for C2H4 and CF3C1with the value for nhexane. Many investigators have implied that the solvent strength of a SF approaches that of a liquid as the densities become equal. This concept is incorrect, as is evident from the data for CF3Cl and n-hexane. The polarizabilities per molecule for ethylene and CF3C1 are less than that of n-hexane, as is the solvent strength at a given number or molar density. Instead, the solvent strengths of these nonpolar fluids are described more realistically by the Hildebrand solubility parameter, polarizability per volume, a/V, or the E T value. Notice that each of these properties is roughly constant for the three fluids listed in Table I. Extremely high pressures in excess of a kilobar are required to compress C2H4and CF3C1to attain values of ET, 6, or a/V that are comparable with that of n-hexane. Therefore, at typical SF extraction conditions, e.g., 200 bar, ethylene is a significantly weaker solvent than hydrocarbon liquids. The results are presented for phenol blue in CHF3 over a wide range in temperature and density in Figure 5 (see
Table IV. Wavelength of Absorption Maximum (Amas) of Phenol Blue in CHFS
P, bar 50.5 80.4 100.4 201.0 301.6
3.5 "C 564.1 565.2 565.8 567.5 568.9
Amax, nm, at 26 "C 30 "C 555.1 545.3 558.5 557.1 560.0 558.4 561.8 560.8 564.2 562.5
40 O C 541.3 553.1 556.7 559.6 561.4
also Table IV). At 40 "C, the value of E T in SF CHF3 is comparable to that in liquid n-hexane or isooctane a t 9 mol/L, CS2at 16 mol/L, and CC14 at 17 mol/L. Although CHF3 is less polarizable than both C2H4 and CF3C1, it is a stronger solvent due to its large dipole moment and to hydrogen bonding. Solvatochromic scales are often quantitative indicators of the solvent effect on rate constants for a variety of types of reaction mechanisms. Reichardt (1979, 1983) reviewed the interrelations of numerous solvatochromic scales with each other and with the rate constants for a variety of well-characterized reactions. The "ET(30)"scale (Dimroth et al., 1963; Dimroth and Reichardt, 1969), which uses pyridinium N-phenolatebetaine as an indicator dye, is much more effective than the Kirkwood dielectric factor (Reichardt, 1979) for correlating solvent effects on the rate constant of the Menschutkin reaction of triethylamine and ethyl iodide. The high-pressure ET(30) data of Tamura et al. (1973a,b) have been correlated linearly with the logarithm of Menschutkin reaction rate constants in the liquid phase. The ET(30) scale was correlated linearly with the rate constant for the thermal racemization of chiral allyl p-tolyl sulfoxide (Reichardt, 1979, r = 0.976). Since the dipole moment of the transition state is less than that of the reactant, the rate of racemization decelerates significantly as the solvent strength is increased. The iZ for the pyridine-catalyzed ionic decomposition of t-butyl peroxyformate has been correlated with the T* scale of Kamlet, Taft, and co-workers (1977,1981,19831,which is based on solvent effects on electronic transitions of a series of nitro aromatics. This reaction can be correlated with E T for phenol blue (Kamlet et al., 1979; Kolling, 1981). It is an example of a unimolecular dissociation into two ionic species. In the Menschutkin reaction of tripropylamine and methyl iodide, the transition state [(H,C3)3N6+...CH3...16-]*
1210 Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987
where kT is the isothermal compressibility of the pure solvent. Partial molar volumes of solutes in SF solvents are highly negative in the near-supercritical region due to the large compressibility. The activation volume is obtained by substitution of eq 6 into eq 4, where the aP/an, factor is divided into a repulsive and an attractive term to give
li'
Y
10-91
1
,
100
200
300
400
PRESSURE (BAR)
Figure 6. Predicted rate constant for the Menschutkin reaction of tripropylamine and methyl iodide in ethylene a t 25 "C using eq 5 . Table V. Prediction of the Activation Volume of the Menschutkin Reaction between Tripropylamine and Methvl Iodide in SuDercritical Ethylene at 25 "C 66 AV*,cm3/mol -5000
80 -1000
100 -560
250
300
350
-220
-150
-80
is much more polar than the reactants; thus, A G * and In kx are extremely sensitive functions of the solvent strength. In fact, k x increases by 5 orders of magnitude as the solvent is changed from n-hexane to nitromethane, due to the increased stability of the transition state relative to that of the reactants (Lassau and Jungers, 1968). This effect resembles solvatochromism in which the more polar state in an electronic transition is stabilized to a greater extent than the less polar one. Therefore, it is not surprising that the two phenomena are correlated. The E, of phenol blue in non-hydrogen-bonding solvents has been related linearly to the logarithm of the rate constant of the reaction of tripropylamine and methyl iodide (Lassau and Jungers, 1968),with a correlation coefficient of 0.98 where In kx = -2.822ET + 134.56 (5) The ET data for phenol blue will be used to predict the rate constant of the Menschutkin reaction of tripropylamine and methyl iodide in supercritical ethylene. To our knowledge, this reaction rate has not been measured in this solvent. Since ethylene does not form hydrogen bonds, eq 5 is applicable based on the results of non-hydrogenbonding liquids. The prediction of eq 5 is shown in Figure 6. Although ethylene is nonpolar, the prediction indicates that the rate constant should increase 2 orders of magnitude as the density is increased from 6.6 to 15.9 mol/L. This can be attributed to an increase in the number of induced dipoles in the solvent shell about the solute as the density increases. The activation volume (see eq 3) is a large negative number in the critical region where ethylene is highly compressible, as shown in Table V. For example, kx increases about 300% for a pressure increase of 65-75 bar. At 25 "C and 350 bar, Au* is only moderately negative, Le., -80 cm3/mol, compared with a value of -65 cm3/mol in liquid CC1, at 30 "C. It is negative due to bond formation between the two reactants in the transition state. The large magnitude of the activation volumes in Table V is the result of the large magnitude of the ut's (see eq 4). The partial molar volume of a solute infinitely dilute in a supercritical fluid was investigated recently, both experimentally and theoretically (Eckert et al., 1981, 1983, 1986). Thermodynamically, uZmis the product of two factors
u," = ukTn(aP/dn2G,v,,,
(6)
For a reaction of the form given in eq 1,the repulsive term in parentheses is clearly negative due to bond formation between the reactants. The attractive term is more difficult to evaluate. If the attractive interaction with the highly polar transition state exceeds that with both reactants combined, then the attractive contribution decreases &*. The magnitude of the activation volume may be large in the near-supercritical region due to large compressibility, even if it is only on the order of h30 cm3/mol in a liquid solvent. In many of the above examples taken from the literature, the rate constant has been related to an ET scale by ln k x = -aET + b (8) where a and b are empirical constants. By use of eq 3 and 8, the activation volume may be expressed as Av* = +aRT(aET/ap),pkT
(9)
For the system shown in Figure 6, the factor (dET/ap), is relatively constant compared to pkT, especially in the highly compressible region. The value of (aET/ap), is comparable to that of liquids. Since ( d E T / a p ) T is negative, the activation volume is negative and reaches a minimum at the same density as that where the compressibility reaches a maximum. The unusually large negative activation volumes in ethylene in the critical region are due to the large compressibility. Compression of a Supercritical Fluid about a Solute. Several reviews discuss theories of solvatochromism for the electronic absorption spectra of a dissolved molecule (Robertson and King, 1961; Basu, 1962; Mataga and Kubota, 1970; Amos and Burrows, 1973; Kampas, 1974). The theory, which has been applied only to liquids, will be extended to include compressible supercritical fluids. The local density of the solvent about the dye will be calculated by using statistical mechanics. It will be shown that the local density is a direct function of the partial molar volume of the solute, u2, which is largely negative in compressible supercritical fluids. Local densities will be estimated from the solvatochromic data which are consistent with the theory. Using second-order quantum mechanical perturbation theory, McRae (1957) (see also Mataga and Kubota, 1970) related the intrinsic solvent strength, Et, to the bulk solvent properties by 2n2 + 1
n2 + 2
where n is the refractive index and D is the dielectric constant. The constants, A , B, and C, are functions of the properties of dye such as the dipole moment and oscillator strength of the ground and excited states and the cavity radius. Although the theory treats the solvent as a homogeneous polarizable dielectric, it has been used successfully for phenol blue in 21 non-hydrogen-bonded solvents (McRae, 1957). The E$ was calculated by using eq 10 and with values of D and n which were obtained as follows. The dielectric
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 1211 constant of C2H, was calculated by using a dielectric virial equation (Johnston and Cole, 1962; Bose and Cole, 1971). It was obtained from the literature for CF3Cl (Makita et al., 1977) and also for CHF, (Franck, 1981). The refractive indexes of the three fluids were calculated by using the Lorentz-Lorentz virial equation along with the necessary constants which have been published (St-Rnaud and Bose, 1978; Sutter and Cole, 1970; Rathjen and Straub, 1977). The EoT will be used as a basis in order to determine the local density of the solvent about the solute, which is a strong function of the compressibility. The local density of water about an ion was described by Wood et al. (1981) in the critical region using a modified Born equation. At 17.7 MPa (P, = 0.803) and 327 OC ( T , = 0.927), the density of water is 0.64 g/cm3 ( p , = 1.99). For dilute solutions, the local density of water increases from 0.64 to 0.9 g/cm3 as the distance from an ion decreases from infinity to 0.2 nm, since the compressibility islarge a t these conditions. At 0.9 g/cm3, the pressure of water is 280 MPa. This effect of the compressibility on the local density of a solvent is also substantial for the data in Figure 3. The local density behavior will be described by using distribution function theories. The number of i molecules surrounding a j molecule within a spherical shell of radius rIjis given by (Hill, 1956)
where ri; is a radius of a sphere within which the local composition is present. Therefore, the average local density within this sphere is pi) =
-S vi;
riJ
0
gij(r) dr
where Vijis the volume of a sphere with radius ri, and the superscript 1 means local. In Figure 3, consider the physical meaning of points A and B. In a fixed volume, V . . the number of solvent molecules about the solute a t p iX’ is given by eq 11. At the same value of ET, point B represents the density which is calculated for a homogeneous liquid (see eq 10). Since the distribution of solvent molecules is uniform at point B, gi;(r)equals one, and the number of solvent molecules in Vi; a t point B is
N 1,1 .= PiBVij
(13)
We choose to define the local density by equating eq 11 and 13 so that the number of solvent molecules in a fixed volume, V,, is equal a t A and B; thus, = -Jri’gij(r) PiA pi
dr
vi; 0
Therefore the density at B is the local density around the solute molecule when the bulk density is p k For example, a bulk density of 6.5 mol/L (point A) corresponds to a local density in the solvent cage of 10 mol/L (point B). This approach is essentially equivalent to the local composition concept which has been used widely (Mansoori and Ely, 1985). The difference between the local and bulk densities increases as the compressibility of the solvent increases. By use of e q 12, the difference between the local and bulk densities can be written as p.1- p, = pi lr”[gi;(r) - 11 dr
vij 0
If rij is chosen such that the integration of gij(r)- 1 from infinity equals zero, a more useful form of eq 15 may
rij to
pi/
- p i = PiJm[gi;(r) Vij
0
- 11 dr
Kirkwood and Buff (1951) formulated expressions for the isothermal compressibilities and the partial molar volumes of mixtures as
and
CpiIBIij
ui =
CPjPklBljk
(18)
j k
where IBlij is the cofactor of Bij in the determinant JBIand Bij is expressed by
Bij = Pi&j + PiPjJ[gij(r) - 11 d r
(19)
where 6ij is the Kronecker delta. By use of eq 6, 17, and 18,
For a binary mixture at infinite dilution, eq 20 reduces to
Nij(ri,)= p i ~ r z J g i j (drr )
Pi
be expressed as (Mansoori and Ely, 1985)
At infinite dilution, gT1(r) and p are pure solvent properties; thus,
By use of eq 6,16, and 22, the density difference may be expressed as a function of the isothermal compressibility and uZm
Based on previous results (Eckert et al., 1983), it is reasonable to assume that Dzm =
UkT
+b
(24)
By use of eq 23 and 24, the final result is (Pi2
- P ) / P = a’kT + b’
(25)
where a’ and b’ are functions of temperature and Vlz. The local density, plJ, was approximated as a function of density using the experimental ET and EoT as explained above using Figure 3. The result of this procedure, which is shown in Figure 7, is consistent with the theoretical expression given in eq 25 with a correlation coefficient of 0.989. Solvatochromism in Hydrogen-Bonded Systems. It has been shown for liquid solvents that solvatochromic measurements may be used to characterize hydrogen bonding qualitatively (Figueras, 1971; Kolling, 1973). In the future, it would be useful to apply quantitative theories for hydrogen bonding (Trotter, 1966; Ben-Naim, 1972; Rao, 1981; Rossky and Pettitt, 1982) to supercritical fluid mixtures. In the excited state, the carbonyl oxygen in phenol blue becomes electron rich and the terminal nitrogen becomes electron poor (see Figure l). Therefore, a hydrogen-bond donor would stabilize the excited state
1212 Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 0.6
a
\
a
0.4
I
v
0.2
20
kT x
40
60
l o 2 (BAR-')
Figure 7. Local density of ethylene about phenol blue vs. hT at 25 O C .
via interaction with the oxygen atom (red shift) and destabilize it (blue shift) via interaction with the terminal nitrogen. The previous solvatochromic shift data for phenol blue indicate that hydrogen-bond donors interact strongly with the carbonyl oxygen, although a discrete hydrogen bond is not formed. The specific solvent strength is defined here as an approximate quantity that describes the strength of forces in addition to dispersion, orientation, and induction so that ET(exptl) = ETo ETs where ETo is the intrinsic solvent strength described by eq 10. For phenol blue, the specific solvent strengths are 6.3, and 1.6 kcal/mol for the solvents m-cresol (a strong Lewis acid) and methanol. The ETSis zero for the nonacidic solvents C2H4and CF,Cl. The experimental E T data for phenol blue in CHF, deviate from the calculated ETo because of clustering due to nonspecific forces as well as hydrogen bonding. A t densities greater than 15 mol/L where the solvent is incompressible, the nonpolar forces are not expected to cause clustering, based on the ETdata for ethylene and CF3C1. A t these conditions, the deviation between ET(exptl) and ET', which is 1.3 kcal/mol, is expected to be due to hydrogen bonding. In comparison, the ETSis 1.9 kcal/mol for liquid chloroform (Kolling et al., 1973). The local densities obtained for fluoroform (see Figure 5) were correlated against the compressibility using eq 25. The correlation was linear ( r = 0.995), as was the case for ethylene as shown in Figure 7. The slope, a', was 210% larger than the value for ethylene due to the stronger attractive forces, e.g., hydrogen bonding. Since little is known about hydrogen bonding in supercritical fluid solutions, an attempt has been made to estimate the specific solvent strength as a function of pressure. The first step was to correct the ETo to include the effect of nonpolar forces on clustering (see Figure 5). This was accomplished using the ethylene data along with corresponding states theory as described elsewhere (Kim, 1986). The difference between ET(exptl) and the corrected E T is relatively constant over a wide range in density. Although it appears that the hydrogen-bonding strength becomes fairly saturated at a relatively low density, a great deal of further experimental and theoretical work is required to understand the behavior more quantitatively.
+
Conclusions Solvatochromic shift data have been shown to provide a sensitive indication of the structure and solvent strength of SF solvents. The ET scale for phenol blue is particularly useful, as this dye is sufficiently soluble in nonpolar SF solvents. Extremely high pressures in excess of a kilobar are required to compress C2H, and CF&l sufficiently to attain an ET, 6, or N I V which is comparable to that of
n-hexane at ambient temperatures. The ET os the hydrogen-bond donor, CHF3, is comparable to that of liquid n-hexane a t 9 mol/L, CS2 at 16 mol/L, and CCl, a t 17 mol/L. Therefore, the solvent strength of a single SF solvent may be varied significantly by using only modest changes in temperature or pressure. The ET data were used to predict that the activation volume is -5000 cm3/mol for the Menschutkin reaction of tripropylamine and methyl iodide in ethylene at 25 "C and 65.9 bar. This large negative value is due to the large compressibility in the critical region. These results suggest that certain rate constants may be altered markedly in SF solvents, using only modest changes in temperature and pressure. The spectroscopic data indicate that the SF solvent clusters about the solute such that the local density exceeds the bulk density. The ratio of the local density to the bulk density is related linearly to the isothermal compressibility, kT, as was shown both experimentally and theoretically. The spectral data indicate the solvent strength and structure in a more fundametnal and direct manner than solution thermodynamic data, such as solubility data. This spectroscopic information will be extremely useful for extending the understanding of SF extraction to include polar solutes, solvents, and/or cosolvents. It will also be a useful basis for future attempts to quantify the relationship between specific interactions in the SF phase and the resulting selectivity of SF solvents.
Acknowledgment This material is based on work supported by the National Science Foundation under Grant CPE-8306327. Any opinions, findings, and conclusions or recommendations expressed in this publication do not necessarily reflect the views of the National Science Foundation. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this work. Further support is acknowledged from the Dow Chemical Foundation and the Separations Research Program at the University of Texas.
Nomenclature B,J = defined by eq 20 c = speed of light D = dielectric constant E - solvatochromic transition energy for phenol blue E$ 2 intrinsic solvent strength defined by eq 10 ET = specific solvent strength E ~ ( 3 0= ) solvatochromic scale based on pyridinium N phenolate betaine dye h = Planck's constant g, = radial distribution function kB = Boltzmann constant kT = isothermal compressibility, bar-' k x = reaction rate constant, s-l M = transition state P, = reduced pressure (P/P,) T , = reduced temperature ( T / T , ) u = molar volume, cm3/mol VI, = coordination volume with radius rlJ D, = partial molar volume of component i Greek Symbols a = polarizability e = energy parameter K = transmission coefficient X = wavelength, nm T* = solvatochromic scale based on a series of nitro aromatics = size parameter Au* = activation volume p = density
Ind. Eng. Chem. Res., Vol. 26,No. 6,1987 1213 6 = solubility parameter, ( c a l / ~ m ~ ) ' / ~ Y~ = activity coefficient of component A Subscripts
i, j , 1, 2 = component designation r = reduced value Superscripts 1 = local value m = infinite dilution Registry No. Phenol blue, 2150-58-5;methyl iodide, 74-88-4; tripropylamine, 102-69-2.
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