Benzophenone as a Probe of Local Cosolvent Effects in Supercritical

854

Ind. Eng. Chem. Res. 1997, 36, 854-868

GENERAL RESEARCH Benzophenone as a Probe of Local Cosolvent Effects in Supercritical Ethane Barbara L. Knutson,† Steven R. Sherman,‡ Karen L. Bennett, Charles L. Liotta, and Charles A. Eckert* Schools of Chemical Engineering and Chemistry and Specialty Separations Center, Georgia Institute of Technology, Atlanta, Georgia 30332-0100

The n f π* shift of benzophenone has been used to quantify solute-cosolvent interactions in supercritical ethane. Dilute solutions of benzophenone in cosolvent/supercritical ethane mixtures were studied at 35 °C from 50 to 100 bar over a range of cosolvent concentrations. The following cosolvents were chosen for investigation on the basis of their varying abilities to interact with benzophenone: 2,2,2-trifluoroethanol, ethanol, chloroform, propionitrile, 1,2-dibromoethane, and 1,1,1-trichloroethane. In the supercritical systems investigated here, hydrogen bonding of protic cosolvents to the carbonyl oxygen of benzophenone is the primary mechanism of the n f π* shift. The results of this investigation are consistent with a chemical-physical interpretation of cosolvent effects in supercritical fluids in the presence of strong specific solute-cosolvent interactions. The experimental results for the ethane/TFE/benzophenone system were analyzed by using integral equations in order to study the assumptions of the chemical-physical model. This combination of spectroscopic data with radial distribution function models provides a powerful tool for understanding cosolvent effects. Introduction Promising applications of supercritical fluid (SCF) technology exist in a variety of fields, including the synthesis and purification of specialty chemicals and materials (Tilly et al., 1990; DeSimone et al., 1992; Eckert et al., 1992, 1993; Chaudhary et al., 1995) and environmental control (Dooley et al., 1987; Shaw et al., 1991). A flexible and predictive approach to SCF processing is necessary to implement significant advances in these technologies. The addition of cosolvents to SCFs is a powerful tool for the tuning of solvent properties (Johnston, 1994) and achieving this generalized approach. Cosolvents can affect significantly phase equilibria in SCFs. Typically cosolvents enhance solute solubilities by factors of 2-5 (Brennecke and Eckert, 1989; Ekart et al., 1993), but enhancements as high as 100-1000 have been reported (Dobbs and Johnston, 1987; Lemert and Johnston, 1991; Gurdial et al., 1993). Cosolvents have also been used to tune chemical reaction rates and selectivities in SCFs (Ellington et al., 1994). Several interrelated phenomena may contribute to the observed solubility increase of large solutes with the addition of cosolvent: specific solute-cosolvent interactions (Lemert and Johnston, 1987), an increase in solution bulk density with the addition of cosolvent (Ekart et al., 1993), and the effects of molecular asymmetry of solute/cosolvent/SCF solutions on the local solute environment (Pfund and Cochran, 1993; Tom and Debenedetti, 1993; Zhang et al., 1995). * Author to whom correspondence should be addressed. † Current address: Department of Chemical and Materials Engineering, University of Kentucky, Lexington, KY 405060046. ‡ Current address: E. I. Du Pont de Nemours Inc., Experimental Station, E336 149B, Wilmington, DE 19880-0336. S0888-5885(96)00080-2 CCC: $14.00

The effects of molecular asymmetry on solvation can be predicted in the absence of specific interactions and are not unique to near-critical solutions (Chialvo and Debenedetti, 1992; Phillips and Brennecke, 1993). For Lennard-Jones representations of typical solute-SCF systems, integral equation and molecular simulation results reveal significant short-ranged solvent enrichment around the dilute, large solute. The magnitude of this enhancement is dependent on the relative size and energy parameters of Lennard-Jones molecules (Tom and Debenedetti, 1993). With the addition of a cosolvent-like third component to the solute-solvent system, cosolvent composition enhancements in the vicinity of the dilute solute molecule are also observed (Pfund and Cochran, 1993; Zhang et al., 1995; Sherman and Eckert, 1995). These density and composition enhancements have also been inferred from thermodynamic and spectroscopic measurements (Kim and Johnston, 1987a,b; Yonker and Smith, 1988; Petsche and Debenedetti, 1989; Brennecke et al., 1990a,b; Knutson et al., 1992; Roberts et al., 1992) as well as from integral studies (Pfund et al., 1988; Wu et al., 1990; Tom and Debenedetti, 1993; Chialvo and Cummings, 1994). The differences in bulk and local environment may contribute to apparent cosolvent effects. Thermodynamic approaches suggest that solute/cosolvent hydrogen bonding also contributes significantly, although not exclusively, to cosolvent effects (Lemert and Johnston, 1987; Dobbs and Johnston, 1987; Walsh and Donohue, 1989; Ting et al., 1993). Charge-transfer complex formation, cosolvent/solute dipole-dipole alignment, and solvent electrostatic effects in non-hydrogen bonded systems have also been cited as sources of cosolvent effects (Ekart et al., 1993; Knutson, 1994). In addition, thermodynamic investigations have linked independent measures of solvent strength to cosolvent © 1997 American Chemical Society

Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 855

effects. For example, Ting et al. (1993) measured the solubility of naproxen in a series of cosolvent/SCF CO2 systems. The cosolvent effects on naproxen solubility were correlated with free energy relationships, which take into account hydrogen bond acidity/basicity and cosolvent polarity/polarizability effects. Spectroscopy allows the direct observation of these molecular-level events and thus is a particularly sensitive probe of the cosolvent environment of a solute. Density enhancements in SCF/dilute solute systems have been measured spectroscopically using probes of solvent environment whose spectral features are wellcharacterized in liquids (Kim and Johnston, 1987a; Kajimoto et al., 1988; Brennecke et al., 1990a,b; Sun et al., 1992). The strength and structure of specific interactions, primarily hydrogen bonding, has also been investigated in SCFs using solvatochromic and fluid structure probes (Fulton et al., 1991; Tomasko et al., 1993; Kazarian et al., 1993; Gupta et al., 1993; Bennett and Johnston, 1994). Several investigators have inferred the combined effects of specific interactions, solvent polarity/polarizability effects, and local composition on solvatochromic shifts in SCF solutions (Kim and Johnston, 1987b; Yonker and Smith, 1988). For instance, Bennett and Johnston (1994) used the n f π* transition of acetone and π f π* transition of benzophenone to probe the solute environment in SCF water and found persistence of hydrogen bond formation at 380 °C and densities as low as 0.1 g/cc. These results were consistent with both thermodynamic and computational studies. They suggested a significant connection between local environment effects and hydrogen bond formation. In this investigation, both the supercritical solvation structure and the solvatochromic behavior of benzophenone are used to examine the hydrogen bonding and electrostatic environment of this solute in various cosolvent/SCF ethane solutions. While the position of both the n f π* and π f π* absorption bands of benzophenone and other carbonyl compounds are sensitive to solvent environment, the n f π* transition was the focus of this study. In this excitation, one n-electron from the oxygen atom is promoted to an antibonding π* orbital delocalized over the carbonyl bond. Removal of this electron from the oxygen atom results in the contribution of the mesomeric structure C

O

⊕

Thus, the n f π* excitation results in a decrease of the dipole moment of the excited state relative to the ground state (Reichardt, 1988). With increasing solvent polarity, the relative stabilization of the ground state results in a blue shift of the n f π* transition. Further stabilization of the n f π* ground state can occur through hydrogen bonding of the carbonyl group with protic solvents. This interaction involves the stabilization of n-electrons of the oxygen atom. This bond is broken or severely weakened upon excitation; the energy of the molecule in the excited state is approximately equal the energy of the nonbonded excitedstate molecule. Therefore, the n f π* blue shift observed on going from nonpolar solvents to polar protic solvents comprises solvent polarity/polarizability and carbonyl/solvent hydrogen-bonding effects. For benzophenone, the magnitude of this shift in going from n-hexane to water is approximately -2200 cm-1 (Dilling, 1966; Fendler, 1975; Garcia and Redondo, 1987; Rei-

Table 1. Cosolvent Kamlet-Taft Parameters (Kamlet et al., 1983) cosolvent

π*

R

chloroform, CHCl3 1,2-dibromoethane, Br-CH2-CH2-Br ethanol, CH3-CH2-OH propionitrile, CH3-CH2-CtN 1,1,1-trichloroethane, CH3-CCl3 2,2,2-trifluoroethanol, CF3-CH2-OH

0.58 0.75 0.54 0.71 0.49 0.73

0.44 0.00 0.83 0.00 0.00 1.51

chardt, 1988). The n f π* shift of benzophenone has been studied extensively and related to solvent characteristics (Brealey and Kasha, 1955; Becker, 1959; Ito et al., 1960). The n f π* transition of benzophenone was examined in several SCF ethane/cosolvent systems. In addition to having a moderate critical temperature and pressure (Tc ) 32.3 °C, Pc ) 48.8 bar), ethane cannot participate in specific interactions with either benzophenone or the cosolvents. In this way, benzophenone/cosolvent specific interactions were isolated from benzophenone/solvent and cosolvent/solvent interactions. The cosolvents listed in Table 1 were chosen on the basis of their ability to participate in specific and electrostatic interactions with benzophenone. Kamlet-Taft solvent parameters (Kamlet et al., 1983), which served as the basis of the cosolvent selection, are also given in Table 1. The cosolvents include chloroform (CHCl3), 1,2-dibromoethane (DBE), ethanol (ETOH), propionitrile (ETCN), 1,1,1-trichloroethane (TCE), and 2,2,2-trifluoroethanol (TFE). Because the stabilization of the n-electron ground state occurs through benzophenone/cosolvent hydrogen bonding or solvent polarity/polarizability effects, only the LSER parameters R and π* are relevant to this investigation. The solute benzophenone has a negligible hydrogen bond acidity, a large π* (1.50), and a solute β value of 0.50 (Abraham, 1993). The π* values of SCF ethane at 35 °C, measured by Smith and co-workers (1987), range from -0.5 to -0.2 and increase with pressure. Of the cosolvents in Table 1, TFE has the largest R and a high value of π*. Due to its negligible β value, TFE does not, in principle, self-associate significantly through hydrogen bonding. However, TFE self-association has been reported (Suresh et al., 1994). Therefore, free TFE molecules compete negligibly with benzophenone for uncomplexed TFE through hydrogen bonding, allowing the isolation of benzophenone/cosolvent effects. For these reasons, TFE was chosen as the primary cosolvent for this investigation. Ethanol is intermediate for hydrogen bond donation but has the ability to self-associate (β ) 0.77) through hydrogen bonding. The R value for chloroform was the lowest of those of the hydrogen-bonding solvents studied. ETCN and DBE have high π* values and negligible values of R; TCE has a lower π* and also a negligible R. According to these Kamlet-Taft parameters, any n f π* shift observed in going from pure ethane to ETCN, TCE, or DBE cosolvent systems would be due to solvent polarity/ polarizability effects. Cosolvents were chosen to delineate the relative contributions of solvent polarity/polarizability and hydrogen bonding on the n f π* transition. The effect of cosolvent concentration and proximity to solution criticality on the extent of solute/cosolvent interactions was inferred. A first-order thermodynamic model based on chemical-physical principles and available liquid data was then applied to this system. From these ap-

856 Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997

proximations, the n f π* shifts in these SCF/cosolvent systems were estimated for comparison with experiment. Another method is now available for studying the cosolvent effect which bridges the gap between the thermodynamic and spectroscopic measurementssradial distribution function studies (Reed and Gubbins, 1972; McQuarrie, 1976; Tom and Debenedetti, 1993). Integral equation theory has been used to study the microstructure and solvation characteristics of dilute supercritical mixtures and the effects of local density enhancement on the overall properties of the supercritical fluid. Munoz and Chimowitz (1992) studied the behavior of the chemical potential of a dilute solute in a near-critical fluid solvent with integral equations. Cochran and Lee (1989) have studied partial molar volumes of solutes in SCFs by this technique. Although most integral equation studies have examined only pure or binary systems, some researchers have already begun to examine ternary systems by integral equation methods. Pfund and Cochran (1993) developed a procedure to estimate the chemical potential of a solute in a supercritical solvent-cosolvent mixture which is based on scaled particle theory. Tanaka and Nakanishi (1994) examined the effects of a cosolvent on the solubility of a dilute solute in a SCF using integral equations. These researchers both examined the solubility characteristics of a dilute solute in a SCF solventcosolvent mixture. In order to examine the effects of the solvation structure around the solute benzophenone, the effects of local changes in density and composition as predicted by integral equation methods are compared to n f π* transitions of benzophenone in supercritical ethane with TFE as a cosolvent. Radial distribution functions for the ternary system of Lennard-Jones 12-6 potential molecules are calculated using the Ornstein-Zernike integral equations with the hypernetted chain closure rule at the experimental concentration and densities. Then, first-shell coordination numbers, local densities, and local mole fractions are calculated from the radial distribution functions. Changes in the first-shell coordination numbers, local density, and local composition are compared to changes in the wavenumber of the shift in order to gain an understanding of the solvation process in this SCF system. Although hydrogen bonding makes a significant contribution to the interaction between benzophenone and TFE, the solvation structure within liquids and supercritical fluids is generally dominated by repulsive and dispersive forces and can be modeled adequately using a simple Lennard-Jones model. In addition, the current methods for calculating radial distribution functions cannot accommodate highly directional intermolecular forces such as hydrogen bonding. As a result, only spherically symmetrical intermolecular potential models may be employed. Experimental Methods Materials. The cosolvents chloroform (99.9+%), 1,2dibromoethane (99+%), propionitrile (99+%), 1,1,1trichloroethane (99+%), and 2,2,2-trifluoroethanol (99+%) were obtained from Aldrich Chemical Co. and used as received. Benzophenone (99+%), dichloromethane (99.9%), and hexane (99+%) were also obtained from Aldrich and used as received. Dehydrated ethanol (99.95%) was purchased from Quantum Chemical Corporation and stored over molecular sieves. CP-grade ethane (99+%) was obtained from Matheson Gas Products.

Figure 1. Experimental apparatus for high-pressure UV absorption studies.

High-Pressure UV Absorption Experiment. UVvis absorption experiments were conducted in a doublebeam UV-vis spectrophotometer modified for highpressure applications. Details of this apparatus have been given previously (Tomasko, 1994; Knutson, 1994). For the purposes of this cosolvent investigation, a sampling valve (Valco Instruments Model C6UW) was added to the apparatus (Figure 1) to allow the direct introduction of cosolvent into the reference and sample cells. The benzophenone spectra were recorded as a function of increasing pressure at a constant concentration of benzophenone and cosolvent. A run of this experiment consisted of loading the sample cell with benzophenone, adding cosolvent to each cell while pressurizing the cells with ethane, and recording the benzophenone spectra at the desired pressure. The system pressure was increased further with the addition of pure ethane and the absorbance scan repeated. The zeroing and scanning procedures are described in detail elsewhere (Knutson, 1994). The spectra were obtained as a function of pressure from approximately 50 to 100 bar at 35 °C. All runs were performed at equal concentrations of benzophenone (0.00154 mol/L). Binary cosolvent/ethane mixture densities were calculated by multiplying the pure SCF ethane density by a ratio of cosolvent mixture density to the pure ethane density as determined from a Soave-Redlich-Kwong equation of state. Tc and Pc for each cosolvent were available in the literature (Reid et al., 1987; Suresh et al., 1994). For lack of further data, the binary interaction parameter (kij) was set to 0.1. Pure ethane densities were calculated using a modified Benedict-Webb-Rubin equation of state (Younglove and Ely, 1987). The benzophenone and cosolvent mole fractions were determined from the calculated mixture densities. Separate visual observations of cosolvent/SCF ethane phase equilibria for each cosolvent were made to ensure that all experiments were conducted in the one-phase region, as described by Ekart (1992). UV Absorption in Liquids. The benzophenone absorbance spectra were recorded with a Hitachi Model U-3110 Spectrophotometer in a series of binary TFE/ CH2Cl2 mixtures and in hexane. The absorbance maxima of the n f π* transition in pure TFE was not measured directly due to π f π* overlap. The transition maxima for these liquid systems were determined from the smoothed, curve-fit spectra manipulated with Spectra Calc software (Galactic Industry).

Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 857

Analysis of SCF Spectra. The shift of the n f π* transition was measured from its wavelength of maximum absorption. The smoothed data were corrected for the red shift of the π f π* transition, which often accompanied the blue shift of the n f π* transition. To resolve the tailing of the π f π* peak in the n f π* transition of interest, the tail of the π f π* transition was fit with an exponential curve in the region of 290300 nm (Becker, 1959; Balasubramanian and Rao, 1962). This exponential fit was then subtracted from the spectrum to determine the wavelength of maximum absorbance of the n f π* transition. The π f π* tail correction had little effect on the n f π* maximum in dilute cosolvent systems. However, in concentrated TFE systems (greater than 0.22 mol/L), the blue shift of the n f π* transitions was overpredicted by several nanometers due to interference from the π f π* transition. The uncertainty of the resulting n f π* transition maximum is estimated as (1.0 nm. Analysis of Benzophenone/TFE Interaction in SCFs Based on Liquid Data. The extent of benzophenone/TFE hydrogen bonding in SCFs was estimated from the benzophenone/TFE hydrogen-bonding equilibrium constant, Kc, measured in liquids. Singh and co-workers (1966) measured the equilibrium constant of benzophenone in a binary mixture of TFE and carbon tetrachloride (CCl4) at 25 °C (Kc ) 7.6 L/mol) by infrared spectroscopy. This equilibrium constant was adapted to SCFs through the definition of the “true” equilibrium constant, Ka

Ka )

aAD aAaD

(1)

where ai is the activity of species i. A, D, and AD refer to the hydrogen bond acceptor (benzophenone), the hydrogen bond donor (TFE), and the hydrogen-bonded complex, respectively. By definition, Ka is a function of temperature only. For this complex stoichiometry, equilibrium constants measured in gas and liquid phases are related to Ka by

φAD 1 Ka ) Ky ) φAφD P γAD (P - 1)(vAD - vA - vD) exp (2) Kx γ Aγ D RT

[

]

where φi and γi are the respective fugacity and activity coefficients of species i in the gas and liquid solution and vi is its molar volume. The Poynting term is generally negligible at low system pressures. Kx and Ky are the apparent hydrogen-bonding equilibrium constants defined in mole fraction units in the liquid and gas phase. Equilibrium constants in mole fraction units (Kx and Ky) and concentration units (Kc) are related by the solution density. The nonideality (Kγ ) (γAD/γAγD)) associated with the measurement of Kc (Singh et al., 1966) ranges from 0.9 to 1.2 according to regular solution theory calculations and varies with the estimation of the solubility parameter of the complex. Therefore, ideal chemical theory (Kγ ) 1) was assumed in further calculations. Kc was corrected to the SCF experimental temperature, 35 °C, using an enthalpy of complex formation determined by the method of Drago (Drago et al., 1971). TFE parameters existed for this four-parameter estimation technique. The two additional benzophenone parameters

Table 2. Structure and Estimated Critical Properties of Hydrogen Bond Donor, Hydrogen Bond Acceptor, and Complex

were determined from hydrogen bond enthalpies in benzophenone/tert-butyl alcohol and benzophenone/ chloroform systems (Balasubramanian and Rao, 1962). The value of ∆H calculated by this method was -4.6 kcal/mol, leading to an equilibrium constant of 5.9 L/mol at 35 °C. In mole fraction units, assuming the density of pure CCl4, Kx is equal to 61 at 35 °C. By the assumption of ideal chemical theory, this Kx is then equivalent to Ka at 35 °C. Physical contributions to nonideality in SCF solutions were estimated using the Soave-Redlich-Kwong equation of state. The fugacity coefficients of the hydrogenbonding complex (φAD) and of benzophenone (φD) were evaluated in their respective ternary solute/cosolvent/ SCF ethane solutions. In these dilute solute systems, φA was estimated for a binary TFE/SCF ethane system. Values for Tc, Pc, and ω for benzophenone and the benzophenone/TFE complex were calculated by group contribution methods (Reid et al., 1987) and are listed in Table 2. The model of this complex, shown in Table 2, attempts to account for the saturation of the hydrogen bond interaction. All binary interaction parameters (kijs) were set arbitrarily to 0.1 for lack of further data. Analysis of the concentration-dependent φAD and φD required iteration about the ratio of hydrogen-bonded benzophenone to free benzophenone. Integral Equation Theory and Implementation Various numerical methods for calculating radial distribution functions by integral equation methods have been developed for one, two, and three components (Lado, 1967; Baxter, 1968; Lowden and Chandler, 1973; Gillan, 1979; Labik et al., 1985; Lee, 1988; Wu et al., 1990). We have used a stepwise iterative technique that has been developed recently (Sherman and Eckert, 1995). The number of molecules of type j surrounding a solute molecule i within a radius R′ can be calculated by applying eq 3 to the calculated radial distribution functions. The first-shell coordination number of the solute is calculated by counting the number of molecules

858 Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997

∫0R′g∞ij(r) r2 dr

Nj ) 4πFj

(3)

of the solvent and cosolvent that fill the first solvation shell. Although the solvation shell is less well defined in a supercritical fluid than in a liquid, it provides a useful paradigm for understanding the arrangement of molecules in the solute’s local environment. For the purposes of this study, the first solvation shell is defined as the number of molecules of solvent and cosolvent that lie within a radius that extends to the first minimum in the radial distribution curves for the solvent-solute and the cosolvent-solute interactions. The excess number of molecules of type j surrounding a solute type i can be calculated by integrating the total correlation function

∫0∞[gij(r) - 1]r2 dr

excess ) 4πFj

(4)

where eq 4 gives the difference between the number of molecules of type j that surround a molecule of type i and the number of molecules that would be expected if the molecules were randomly distributed throughout the fluid (ideal-gas assumption). This integral has been used previously to demonstrate the phenomenon of clustering or local density enhancement in supercritical fluids (Wu et al., 1990). The local number density is defined as the density of a particular component within the local environment of a solute. This density is calculated by integrating eq 3 between rc and R′ and dividing by the enclosed volume

∫rR′gij(r) r2 dr R′ 4π∫r r2 dr

4πFi (Fij)local )

c

(5)

c

where rc is chosen to be the soft core radius of the solute which corresponds to the radius at which the radial distribution function for the solute-component interaction becomes nonzero. R′ designates the limit of the local region, and the choice of R′ is somewhat arbitrary. Mansoori and Ely (1985) have advocated that R′ be chosen so that

∫R∞[gij(r) - 1]r2 dr ) 0

4π

(6)

While eq 6 may work well for liquids where the solute solvation shells are well defined, it does not work well for calculating the local density around a supercritical solute because the solute radial distribution functions become increasingly long range. As a result, the definition of the local environment becomes less precise (Chialvo and Cummings, 1994). According to Tom and Debenedetti (1993) and Chialvo and Cummings (1994), 99% of the solute’s fugacity coefficient is determined by the local environment within the first two or three solvation shells, even at the critical point. In light of this fact, R′ should be chosen to extend no more than 3σsolvent to 5σsolvent. If there is more than one component in the local environment, then the local mole fractions of each component can be calculated from the local number densities. The three components in the system, ethane, TFE, and benzophenone, were modeled as Lennard-Jones

Figure 2. Comparison of the benzophenone/benzophenone radial distribution functions calculated using the HNC closure and the PY closure at the conditions T ) 308.15 K, F* ) 0.57, yTFE ) 2.71 × 10-2, and ybenz ) 1.24 × 10-4. Table 3. Lennard-Jones Parameters for the Ethane/TFE/ Benzophenone System interaction

ij σij (Å) σij/σ11 ij/k (K) ij/11

ethane-ethane ethane-TFE ethane-benzophenone TFE-TFE TFE-benzophenone benzophenone-benzophenone

11 12 13 22 23 33

4.242 4.500 5.411 4.759 5.670 6.580

1.000 1.061 1.276 1.122 1.337 1.551

233.1 295.3 282.2 374.2 484.3 626.7

1.000 1.267 1.640 1.605 2.078 2.689

molecules with the usual simple mixing rules

ij ) xiijj

(7)

σij ) 0.5(σii + σjj)

(8)

The Lennard-Jones parameters for the system are shown in Table 3. The parameters for benzophenone were calculated from critical property data given that the critical constants of a Lennard-Jones fluid in the PY approximation have been estimated to range from T*c ) 1.291, F* ) 0.27 to T* c ) 1.31, F* ) 0.28 (Tom and Debenedetti, 1993). While it is true that the actual intermolecular potentials for the three components are much more complicated, the Lennard-Jones model has been used successfully to model qualitatively the density enhancement and solubility properties of a supercritical solute (McGuigan and Monson, 1990; Tom and Debenedetti, 1993; Tanaka and Nakanishi, 1994). The Ornstein-Zernike equations were solved numerically by applying a modified direct iteration algorithm applied in a stepwise fashion (Sherman and Eckert, 1995). To calculate the radial distribution functions for this study, the grid spacing was defined to be ∆r ) 0.02σethane, and the number of grid points was set at 2048. The intermolecular potential was assumed to be equal to zero beyond r ) 40.96σethane. Radial distribution functions were generated for each of the densities and concentrations in Table 4 for the TFE cosolvent data. The HNC closure rule was chosen to model the system instead of the PY closure rule because the PY rule gave unrealistic radial distribution functions at the highest densities as shown in Figure 2. Although it is true that the PY closure models the critical properties of Lennard-Jones mixtures more accurately (McGuigan and Monson, 1990), the HNC

Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 859 Table 4. Benzophenone n f π* Transition Maximum in TFE/SCF Ethane at 35 °C TFE pressure density concentration (bar) (mol/L)

yTFE

ybenz

transition transition maximum maximum pressure density (nm) (cm-1) (bar) (mol/L)

yTFE

ybenz

transition transition maximum maximum (nm) (cm-1)

0 0 0 0 0

1.91E-0.4a 1.82E-04 1.71E-04 1.62E-04 1.54E-04

347.0 347.0 346.4 345.6 345.2

28 820 28 820 28 870 28 940 28 970

64.1 71.1 82.8 98.9

10.5 11.0 11.5 12.0

0 0 0 0

1.47E-04 1.41E-04 1.34E-04 1.28E-04

345.0 345.0 346.4 346.0

28 990 28 990 28 870 28 900

7.5 7.9 8.2 8.3 9.1

1.49E-03 1.42E-03 1.38E-03 1.35E-03 1.23E-03

2.04E-04 1.95E-04 1.89E-04 1.86E-04 1.69E-04

332.8 334.0 335.0 335.0 344.0

30 050 29 940 29 820 29 850 29 070

55.7 59.0 71.2 83.0 99.5

9.6 10.1 11.0 11.5 12.0

1.17E-03 1.11E-03 1.02E-03 9.74E-04 9.34E-04

1.61E-04 1.53E-04 1.40E-04 1.34E-04 1.28E-04

344.0 344.0 344.4 344.8 345.2

29 070 29 070 29 040 29 000 28 970

51.7 51.9 52.0 52.1 52.3 53.0

7.4 7.5 7.5 7.8 8.0 8.6

3.01E-03 3.04E-03 2.98E-03 2.87E-03 2.80E-03 2.62E-03

2.09E-04 2.04E-04 2.06E-04 1.97E-04 1.92E-04 1.80E-04

333.4 333.0 334.0 333.6 334.4 334.0

29 990 30 030 29 940 29 980 29 900 29 940

55.8 63.8 71.0 81.4 98.8

9.5 10.5 11.0 11.5 12.0

2.36E-03 2.14E-03 2.05E-03 1.96E-03 1.87E-03

1.62E-04 1.47E-04 1.40E-04 1.35E-04 1.29E-04

334.6 335.0 342.6 341.8 344.8

29 890 29 850 29 190 29 260 29 000

0.034 mol/L

52.1 52.9 53.0 54.0 55.9

8.4 9.0 9.1 9.4 9.8

4.00E-03 3.74E-03 3.71E-03 3.58E-03 3.44E-03

1.83E-04 1.71E-04 1.70E-04 1.64E-04 1.57E-04

333.2 334.2 333.4 332.8 332.8

30 010 29 920 29 990 30 050 30 050

58.6 64.1 71.0 83.2 99.2

9.8 10.2 10.7 11.1 12.0

3.30E-03 3.16E-03 3.04E-03 2.91E-03 2.80E-03

1.51E-04 1.45E-04 1.39E-04 1.33E-04 1.28E-04

334.0 333.8 335.2 336.2 334.2

29 940 29 960 29 830 29 740 29 920

0.045 mol/L

51.6 51.8 52.1 52.4 53.9

8.1 8.3 8.7 9.0 9.6

5.51E-03 5.41E-03 5.15E-03 5.00E-03 4.68E-03

1.89E-04 1.86E-04 1.77E-04 1.72E-04 1.61E-04

331.2 330.0 333.4 334.8 334.6

30 190 30 300 29 990 29 870 29 890

56.1 58.7 70.9 82.4 99.1

10.0 10.3 11.1 11.6 12.1

4.51E-03 4.37E-03 4.04E-03 3.88E-03 3.72E-03

1.57E-04 1.50E-04 1.39E-04 1.33E-04 1.28E-04

334.4 333.0 334.4 333.0 334.8

29 900 30 030 29 900 30 030 29 870

0.11 mol/L

51.8 52.1 52.4 52.9 53.9 56.0

9.2 9.5 9.7 9.9 10.1 10.4

1.21E-02 1.19E-02 1.16E-02 1.13E-02 1.11E-02 1.08E-02

1.67E-04 1.63E-04 1.59E-04 1.55E-04 1.52E-04 1.49E-04

330.4 330.6 329.8 328.6 331.2 331.2

30 270 30 250 30 320 30 430 30 190 30 190

58.9 63.9 71.1 83.1 99.3

10.6 11.0 11.3 11.7 12.2

1.06E-02 1.03E-02 9.94E-03 9.58E-03 9.23E-03

1.45E-04 1.41E-04 1.36E-04 1.32E-04 1.27E-04

331.4 330.0 329.8 331.2 329.0

30 180 30 300 30 320 30 190 30 400

0.22 mol/L

51.5 51.8 52.4 52.8 54.0

9.8 10.1 10.4 10.6 10.8

2.30E-02 2.22E-02 2.15E-02 2.12E-02 2.08E-02

1.58E-04 1.52E-04 1.48E-04 1.46E-04 1.42E-04

327.8 329.4 330.4 329.2 329.4

30 510 30 360 30 270 30 380 30 360

58.6 63.9 83.1 99.4

11.1 11.3 11.9 12.3

2.02E-02 1.99E-02 1.88E-02 1.83E-02

1.39E-04 1.36E-04 1.29E-04 1.25E-04

330.4 330.6 328.8 329.4

30 270 30 250 30 410 30 360

0.34 mol/L

51.7 51.9 52.2 52.4 52.6 54.0

10.5 10.6 10.8 11.0 11.1 11.3

3.22E-02 3.17E-02 3.11E-02 3.05E-02 3.04E-02 2.98E-02

1.47E-04 1.45E-04 1.42E-04 1.39E-04 1.39E-04 1.37E-04

328.6 328.8 329.8 329.8 329.8 330.4

30 430 30 410 30 320 30 320 30 320 30 270

56.1 59.1 64.0 71.3 83.1 99.2

11.4 11.5 11.6 11.8 12.1 12.4

2.96E-02 2.93E-02 2.90E-02 2.85E-02 2.78E-02 2.71E-02

1.35E-04 1.34E-04 1.33E-04 1.30E-04 1.27E-04 1.24E-04

328.8 329.0 330.2 329.4 329.6 330.4

30 410 30 400 30 280 30 360 30 340 30 270

pure ethane

52.4 52.8 54.1 55.8 59.1

8.1 8.5 9.0 9.5 10.0

0.011 mol/L

51.8 51.9 52.1 52.3 53.9

0.022 mol/L

a

1.91E-04 represents 1.91 × 10-4.

closure rule was chosen to model all for the data so that model results would be consistent. While the first-shell solvation radius is easily defined for a supercritical solvent/solute system, it is more ambiguous for a supercritical ternary system because the radius of the solvent and cosolvent solvation shells are different lengths unless the solvent and the cosolvent are the same size. For the purposes of this study, first-shell coordination numbers for the solute were calculated at each experimental condition by applying eq 5 and integrating to a radius extending to the first minimum in the radial distribution functions for the solvent/solute and cosolvent/solute interactions. The total first-shell coordination numbers were calculated by adding the number of solvent and cosolvent molecules in the first solvation shell. The local mole fractions were calculated by dividing the local density of cosolvent in the first solvation shell by the total local density in the first solvation shell. Although the local environment of the solute extends to at least three solvation shells (Tom and Debenedetti, 1993), this study will examine only the first solvation shell in order to examine more closely the assumptions of the proposed chemical-physical model.

Results and Discussion Spectroscopic Results. The investigation of the benzophenone n f π* transition allows us to examine both solvent polarity/polarizability effects and hydrogen bonding in near-critical systems. The concomitant red shift of the π f π* transition was not investigated due to differences in the absorption intensities of the transitions. As shown by the spectrum of benzophenone in hexane (Figure 3), the absorption intensity of the n f π* transition is much less than that of the corresponding π f π* transition. The reproducibility of the spectra suggests that the addition of cosolvent through the sample loop is a valid technique of generating pressurized cosolvent mixtures. The order in which the cells were filled did not affect the results, meaning that equal volumes of cosolvent were delivered to each cell. The validity of this technique is also supported by the clear trend of increasing n f π* blue shift with increasing cosolvent concentration for all cosolvent concentrations studied, until a maximum shift was obtained. In Table 4, the energy of the benzophenone n f π* transition is given as a function of TFE cosolvent concentration in TFE/SCF ethane systems at 35.0 °C.

860 Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997

Figure 3. Absorption spectrum of benzophenone in hexane. Figure 5. Benzophenone n f π* transition maximum in TFE/ SCF ethane at 35 °C as a function of yTFE. The curves represent constant densities 8.5, 9.1, 9.6, 10.1, and 11.0 mol/L.

Figure 4. Benzophenone n f π* transition maximum in TFE/ SCF ethane at 35 °C as a function of density.

The intensity corresponding to these maxima, as well as the shape of the n f π* peak, remained relatively constant with pressure over the course of each constant concentration run. However, the intensity of n f π* transition approximately doubled on going from pure SCF ethane to SCF ethane doped with 0.34 mol/L of TFE. The sensitivity of the n f π* transition to TFE cosolvent concentration is shown as a function of system density in Figure 4. A maximum shift of approximately 17 nm (or 1530 cm-1) was measured in going from pure SCF ethane to TFE cosolvent/SCF ethane systems. The n f π* transition in SCF ethane was relatively constant (ν ) 28 910 cm-1) over the range of densities investigated here. The slight decrease of the blue shift observed at near-critical densities may correspond to the decreasing π* of ethane observed by Smith and coworkers (1987). A maximum in the shift was observed for the three greatest TFE concentrations, 0.11, 0.22, and 0.34 mol/L. In these runs, the n f π* transition maxima were approximately equal and showed only a slight density dependence. This suggests that the benzophenone/TFE interactions responsible for the shift were saturated at TFE concentrations greater than 0.11 mol/L. At TFE concentrations of 0.034 and 0.045 mol/ L, the n f π* transitions are also density independent. However, the proximity of these shifts to pure ethane data suggests that specific benzophenone/TFE interactions are not saturated. When the concentration of TFE is decreased further to 0.011 and 0.022 mol/L, the transition maxima decrease with increasing solution density. The final n f π* transition maxima at these low TFE concentrations approach that of the pure ethane system. In these runs, the interactions responsible for the shift in the n f π* transition are more prevalent in the lower density region, closer to the critical density.

In Figure 5, the n f π* transition maxima are plotted as a function of TFE mole fraction. In systems of dilute TFE (yTFE < 0.005), the transition maximum at a given mole fraction are larger at lower densities. Approximating the critical properties of these dilute mixtures from that of pure ethane (Fc ) 6.74 mol/L), this increased shift at low densities corresponds to increased benzophenone/TFE interactions in the near critical region. This result is consistent with a benzophenone environment enhanced in TFE. The molecular asymmetry of solute/cosolvent/SCF solutions may contribute to this enhancement through local density or local composition enhancements in the vicinity of the solute molecule. These effects are not readily distinguishable, as both mechanisms act simultaneously to increase the local cosolvent concentration (Ellington et al., 1994). The unusual transition density dependence in the dilute cosolvent regime suggests that local environment enhancements, which increase the encounters of cosolvent and solute, may affect the extent of intermolecular interactions. The intermolecular interactions measured in TFE cosolvent systems include contributions from solvent polarity/polarizability effects and benzophenone/cosolvent hydrogen bonding. In order to examine the extent of these interactions independently, the n f π* transition of benzophenone was measured in the other cosolvent/SCF ethane systems. These data are given in Table 5. In Figure 6, the transition maxima are plotted with increasing system density for pure ethane and ethane/cosolvent mixtures of chloroform, propionitrile, DBE, TCE, ethanol, and TFE. The cosolvent concentrations corresponding to Figure 6 are 0.21 mol/L chloroform, 0.20 mol/L DBE, 0.29 mol/L ethanol, 0.24 mol/L propionitrile, 0.17 mol/L TCE, and 0.22 mol/L TFE. The observed transition maxima can be explained in terms of cosolvent Kamlet-Taft parameters. Of the cosolvents investigated, TFE has the largest hydrogen bond acidity and also has a considerable π* value. Thus, the n f π* transition of benzophenone shows the largest blue shift from pure ethane in this cosolvent system. The specific TFE/benzophenone interactions are approximately saturated at the cosolvent concentration (0.22 mol/L). For several of the remaining cosolvents, the benzophenone cosolvent interactions do not appear to be saturated, as shown by their increased blue shift at lower system densities. Ethanol has an ability to hydrogen bond with benzophenone intermediate to that of TFE and chloroform, resulting in an intermediate blue shift. This observation does not take into account

Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 861 Table 5. Benzophenone n f π* Transition Maximum in Cosolvent/SCF Ethane at 35 °C cosolvent, concentration (mol/L)

pressure density (bar) (mol/L)

yTFE

ybenz

transition transition maximum maximum pressure density (nm) (cm-1) (bar) (mol/L)

yTFE

ybenz

transition transition maximum maximum (nm) (cm-1)

ethanol, 0.058

51.6 51.9 52.1 52.4 53.1

8.4 8.7 8.9 9.2 9.4

6.91E-03 6.71E-03 6.56E-03 6.32E-03 6.20E-03

1.83E-04 1.77E-04 1.73E-04 1.67E-04 1.64E-04

342.6 342.4 343.4 343.6 344.8

29 190 29 210 29 120 29 100 29 000

54.0 56.0 58.9 64.5

9.7 10.0 10.4 10.8

6.03E-03 5.80E-03 5.62E-03 5.39E-03

1.59E-04 1.53E-04 1.49E-04 1.43E-04

344.8 345.2 343.0 344.8

29 000 28 970 29 150 29 000

ethanol, 0.15

51.6 51.7 51.9 52.2 52.2 52.9

9.3 9.4 9.6 9.9 9.9 10.1

1.56E-02 1.54E-02 1.51E-02 1.47E-02 1.47E-02 1.44E-02

1.65E-04 1.63E-04 1.60E-04 1.56E-04 1.55E-04 1.52E-04

344.0 344.8 344.8 343.6 344.4 344.2

29 070 29 000 29 000 29 100 29 040 29 050

54.0 55.8 58.7 64.1 71.1 99.3

10.4 10.6 10.8 11.1 11.4 12.2

1.40E-02 1.38E-02 1.35E-02 1.31E-02 1.28E-02 1.19E-02

1.49E-04 1.46E-04 1.43E-04 1.39E-04 1.35E-04 1.26E-04

343.0 344.8 344.8 344.6 345.2 345.6

29 150 29 000 29 000 29 020 28 970 28 940

ethanol, 0.29

52.1 52.2 52.7 52.9 53.9 55.8

10.7 10.8 11.0 11.0 11.2 11.3

2.72E-0.2 2.69E-02 2.66E-02 2.65E-02 2.61E-02 2.58E-02

1.44E-04 1.42E-04 1.41E-04 1.40E-04 1.38E-04 1.37E-04

333.6 342.8 341.8 342.8 341.8 343.2

29 980 29 170 29 260 29 170 29 260 29 140

59.0 64.1 71.0 83.0 99.2

11.4 11.6 11.8 12.1 12.4

2.56E-02 2.52E-02 2.47E-02 2.41E-02 2.34E-02

1.35E-04 1.33E-04 1.31E-04 1.27E-04 1.24E-04

341.8 344.0 343.0 345.2 345.2

29 260 29 070 29 150 28 970 28 970

ethanol, 0.44

51.8 52.0 52.2 53.0 53.8

11.0 11.1 11.3 11.7 11.7

5.21E-02 5.13E-02 4.99E-02 4.75E-02 4.61E-02

1.84E-04 1.81E-04 1.76E-04 1.68E-04 1.63E-04

335.8 334.4 336.6 334.6 337.2

29 780 29 900 29 710 29 890 29 660

56.4 59.1 70.5 85.6 98.5

11.8 11.9 12.1 12.4 12.6

4.38E-02 4.25E-02 3.94E-02 3.74E-02 3.63E-02

1.54E-04 1.50E-04 1.39E-04 1.32E-04 1.28E-04

343.6 344.4 343.8 344.0 344.2

29 100 29 040 29 090 29 070 29 050

chloroform, 0.21

51.6 52.0 52.3 59.7

9.6 9.8 10.0 10.9

2.21E-02 2.16E-02 2.12E-02 1.94E-02

1.60E-04 1.57E-04 1.54E-04 1.41E-04

342.6 343.8 343.8 342.8

29 190 29 090 29 090 29 170

64.4 70.9 82.9 98.3

11.2 11.5 11.8 12.2

1.90E-02 1.86E-02 1.80E-02 1.74E-02

1.38E-04 1.35E-04 1.30E-04 1.26E-04

344.2 343.0 343.0 344.0

29 050 29 150 29 150 29 070

chloroform, 0.32

53.3 54.6 55.8 58.9

10.9 11.0 11.1 11.2

2.93E-02 2.89E-02 2.87E-02 2.84E-02

1.41E-04 1.40E-04 1.39E-04 1.37E-04

343.0 341.4 342.6 344.8

29 150 29 290 29 190 29 000

64.1 70.8 82.1 97.7

11.4 11.7 12.0 12.3

2.79E-02 2.74E-02 2.67E-02 2.59E-02

1.35E-04 1.32E-04 1.29E-04 1.25E-04

344.8 344.4 344.0 345.0

29 000 29 040 29 070 28 990

propionitrile, 0.24

51.8 54.6 56.3 59.0

8.4 9.8 10.0 10.3

2.83E-02 2.44E-02 2.39E-02 2.31E-02

1.83E-04 1.57E-04 1.54E-04 1.49E-04

341.2 344.0 342.4 344.4

29 310 29 070 29 210 29 040

64.1 82.9 100.0

10.7 11.6 12.1

2.22E-02 1.44E-04 2.06E-02 1.33E-04 1.97E-02 1.28E-04

344.0 342.8 342.6

29 070 29 170 29 190

1,1,1-trichloroethane, 0.17

51.4 51.9 52.0 52.8 53.8

9.6 10.1 10.0 10.5 10.7

1.78E-02 1.69E-02 1.70E-02 1.62E-02 1.60E-02

1.61E-04 1.53E-04 1.54E-04 1.47E-04 1.45E-04

343.8 344.4 343.8 344.0 344.6

29 090 29 040 29 090 29 070 29 020

55.8 59.0 63.8 83.2 99.6

10.8 11.0 11.2 11.9 12.3

1.58E-02 1.55E-02 1.52E-02 1.44E-02 1.39E-02

1.43E-04 1.40E-04 1.37E-04 1.30E-04 1.26E-04

343.8 343.2 3433.6 344.0 344.0

29 090 29 140 29 100 29 070 29 070

1,2-dibromoethane, 0.20

51.5 52.2 52.6 53.4 54.2

10.5 11.3 11.3 11.5 11.6

1.87E-02 1.75E-02 1.74E-02 1.72E-02 1.70E-02

1.46E-04 1.37E-04 1.36E-04 1.33E-04 1.33E-04

342.4 344.6 344.0 344.8 344.6

29 210 29 020 29 070 29 000 29 020

55.9 59.0 64.0 83.6 98.8

11.7 11.7 11.8 12.3 12.6

1.69E-02 1.68E-02 1.67E-02 1.61E-02 1.57E-02

1.32E-04 1.31E-04 1.30E-04 1.26E-04 1.23E-04

345.0 345.8 345.2 345.2 345.8

28 990 28 920 28 970 28 970 28 920

a

6.91E-03 represents 6.91 × 10-3.

compete with benzophenone/ethanol hydrogen bonding and reduce the extent of cosolvent/solute interactions. Chloroform, with a large π* and a weaker ability to act as a hydrogen bond acid than ethanol or TFE, is less able to stabilize the ground state n-electron through specific interactions.

Figure 6. Benzophenone n f π* transition maximum in cosolvent/SCF ethane at 35 °C. The cosolvent concentrations represented here are 0.21 mol/L CHCl3, 0.20 mol/L DBE, 0.29 mol/L ETOH, 0.24 mol/L ETCN, 0.17 mol/L TCE, and 0.22 mol/L TFE.

the difference in concentration of the cosolvent systems shown in Figure 6 or the ability of ethanol to selfassociate. With a solvent β value of 0.77, ethanol has a higher hydrogen bond basicity than benzophenone (β(solute) ) 0.50). Therefore, ethanol self-association will

As suggested in Table 1, the blue shifts in DBE or TCE cosolvent systems are due primarily to polarity/ polarizability interactions with benzophenone. The density-dependent blue shift in DBE/SCF ethane is markedly smaller than that observed in systems with significant hydrogen-bonding potential. The blue shift in TCE cosolvent, which has a smaller π* value than DBE, is slight and approximately constant with density. Similarly, in the case of propionitrile cosolvent, the shift is not a strong function of density. However, the shift in the propionitrile cosolvent is greater than in the DBE/ SCF ethane systems at the cosolvent concentrations studied here. This is consistent with the large π* value of propionitrile and the strong propionitrile/benzophenone interactions, possibly due to dipole-dipole alignment, as observed by Becker (1959). No significant

862 Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997

Figure 8. Shift in benzophenone n f π* transition maximum in binary TFE/CH2Cl2 mixtures as a function of local mole fraction. This shift is given relative to the transition maximum in pure CH2Cl2 (29 240 cm-1).

these random and nonrandom contributions by Figure 7. Schematic of local mole fraction model.

correlation exists between the n f π* transition and the cosolvent R and π* at experimental compositions. These collective qualitative arguments suggest that hydrogen bonding is the primary means of benzophenone ground state n-electron stabilization in the SCF ethane/TFE systems, with increased hydrogen bonding in the near-critical region. This is in good agreement with an FTIR investigation of hydrogen bonding in triethylamine/methanol/SCF SF6, where the number of hydrogen-bonding encounters was found to increase in the near-critical region and was attributed to solutesolute clustering (Gupta et al., 1993). On the basis of the dominant contribution of hydrogen bonding to the observed n f π* transition, a simple chemical-physical thermodynamic model was applied to predict the shifts in TFE/SCF ethane systems from liquid data. Prediction of n f π* Shift in SCFs Using Liquid Data and a Simple Model. The local benzophenone cosolvent concentration in liquids and SCFs was approximated from the principles of chemical association and liquid-phase data for benzophenone/TFE complexation. Assuming that the shifts of the n f π* transition in both liquids and SCFs are a similar function of this solvent environment, the shifts in SCFs were predicted from liquid data. To a first-order approximation, the concept of a local mole fraction shown in Figure 7 describes the local benzophenone environment in liquids and SCFs on the basis of the fraction of hydrogenbonded to nonbonded molecules f, the coordination number c, and the bulk mole fraction of the hydrogenbonding solvent xbulk. This local mole fraction, x*, is defined as the number of cosolvent molecules (molecule D) in the first solvation shell about the probe molecule (molecule A) divided by the total number of molecules in this solvation shell. The total number of molecules in this first solvation shell corresponds to a phasedependent coordination number. In this model, a distribution of solvent molecules in proportion to their bulk composition fills the first solvation cell about the benzophenone molecule (molecule A). The exception to this random filling of the solvation sites occurs in the position occupied by a D molecule due to a 1:1 A-D complex. Thus, the apparent mole fraction of cosolvent in (c - 1) + (1 - f) sites is equal to the bulk mole fraction of cosolvent. An additional contribution to the number density occurs from the nonrandom fraction of A molecules which are involved in a hydrogen bond. The local mole fraction of solvent D around solute A, x*, is defined in terms of

x* )

xD,bulk(c - f) + f c

(9)

This analysis applies only to dilute solute solutions, when solute/solute interactions are negligible. In SCFs, x* has been calculated at each pressure measurement in TFE cosolvents from the fraction of hydrogen-bonded benzophenone molecules. The extent of benzophenone/TFE hydrogen bonding in the SCF system was determined from Ka at 35 °C, the system pressure, and solution nonideality term (as described in the previous section):

φAφD yAD ) Ka y P yD φAD A

(10)

The coordination number in SCFs is the average of a fluctuating nearest-neighbor solvent shell. The value of 16 was determined from the integral equation results for Lennard-Jones molecules in the ternary benzophenone/TFE cosolvent/ethane system. On the basis of these purely physical results, minimal variation in the number of molecules in the solvation shell was observed for these Lennard-Jones molecules over the range of densities and cosolvent concentrations investigated here. In liquids, x* was determined from benzophenone absorbence spectra in a series of binary TFE/CH2Cl2 mixtures using Kc (Singh et al., 1966). A coordination number of 18 was used to describe this liquid phase. In Figure 8, the benzophenone n f π* shifts, relative to the pure “inert” CH2Cl2 solvent, are plotted as a function of x* for these binary mixtures. Notice that the behavior of this shift in liquids suggests a saturation of the interaction at x* greater than approximately 0.15. Also, the n f π* transition maximum determined in these binary solutions at “saturation” is approximately equal to the n f π* transition maximum measured at the highest TFE concentrations in SCF ethane. The “relative” n f π* shift in liquids and SCFs was assumed to be equal for equivalent values of x*. For this purpose, a curve was fit to the plot of ∆νLIQ versus x*. A scaling factor was used to account for the difference in maximum shifts observed in the TFE/SCF ethane system and the TFE/CH2Cl2 system. The benzophenone n f π* shift in SCFs was estimated from the liquid shift at an equal value of x* and scaled by

∆νSCF ) ∆νLIQ(f(x*))

[

νTFE in C2H6 - νC2H6

]

νTFE in CH2Cl2 - νCH2Cl2

(11)

where ∆νSCF and ∆νLIQ are the respective shifts in SCF

Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 863 Table 6. Comparison of Experimental and Estimated Values of the Benzophenone n f π* Transition Maximum in Cosolvent/SCF Ethane bulk TFE pressure density y(complex)/ concentration (bar) (mol/L) y(benz)

x*

predicted exptl bulk maximum maximum pressure density y(complex)/ -1 -1 (cm ) (cm ) (bar) (mol/L) y(benz)

x*

predicted exptl maximum maximum -1 (cm ) (cm-1)

pure ethane

52.4 52.8 54.1 55.8 59.1

8.1 8.5 9.0 9.5 10.0

0.00 0.00 0.00 0.00 0.00

0.000 0.000 0.000 0.000 0.000

28 910 28 910 28 910 28 910 28 910

28 820 28 820 28 870 28 940 28 970

64.1 71.1 82.8 98.9

10.5 11.0 11.5 12.0

0.00 0.00 0.00 0.00

0.000 0.000 0.000 0.000

28 910 28 910 28 910 28 910

28 990 28 990 28 870 28 900

0.011 mol/L

51.8 51.9 52.1 52.3 53.9

7.5 7.9 8.2 8.3 9.1

0.78 0.73 0.69 0.67 0.58

0.029 0.028 0.027 0.026 0.024

29 400 29 380 29 370 29 360 29 320

30 050 29 940 29 820 29 850 29 330

55.7 59.0 71.2 83.0 99.5

9.6 10.1 11.0 11.5 12.0

0.53 0.48 0.43 0.41 0.40

0.023 0.021 0.020 0.019 0.019

29 300 29 280 29 250 29 240 29 240

29 070 29 070 29 040 29 000 28 970

0.022 mol/L

51.7 51.9 52.0 52.1 52.3 53.0

7.4 7.5 7.5 7.8 8.0 8.6

1.56 1.51 1.54 1.45 1.39 1.27

0.041 0.040 0.041 0.040 0.039 0.037

29 580 29 570 29 570 29 560 29 550 29 530

29 990 30 030 29 940 29 980 29 900 29 940

55.8 63.8 71.0 81.4 98.8

9.5 10.5 11.0 11.5 12.0

1.07 0.91 0.85 0.82 0.81

0.035 0.032 0.031 0.030 0.030

29 480 29 440 29 430 29 420 29 410

29 890 29 850 29 190 29 260 29 000

0.034 mol/L

52.1 52.9 53.0 54.0 55.9

8.4 9.0 9.1 9.4 9.8

1.99 1.79 1.77 1.66 1.54

0.045 0.044 0.043 0.042 0.041

29 640 29 610 29 610 29 600 29 580

30 010 29 920 29 990 30 050 30 050

58.6 64.1 71.0 83.2 99.2

9.8 10.2 10.7 11.1 12.0

1.43 1.33 1.26 1.21 1.20

0.040 0.039 0.038 0.037 0.037

29 560 29 550 29 530 29 520 29 520

29 940 29 960 29 830 29 740 29 920

0.045 mol/L

51.6 51.8 52.1 52.4 53.9

8.1 8.3 8.7 9.0 9.6

2.74 2.68 2.49 2.39 2.13

0.051 0.051 0.050 0.049 0.047

29 710 29 710 29 690 29 680 29 660

30 190 30 300 29 990 29 870 29 890

56.1 58.7 70.9 82.4 99.1

10.0 10.3 11.1 11.6 12.1

1.99 1.88 1.67 1.60 1.59

0.046 0.045 0.043 0.042 0.042

29 640 29 630 29 600 29 590 29 590

29 900 30 030 29 900 30 030 29 870

0.11 mol/L

51.8 52.1 52.4 52.9 53.9 56.0

9.2 9.5 9.7 9.9 10.1 10.4

5.30 5.17 5.01 4.85 4.67 4.52

0.064 0.064 0.063 0.063 0.062 0.061

29 870 29 870 29 860 29 850 29 850 29 840

30 270 30 250 30 320 30 430 30 190 30 190

58.9 63.9 71.1 83.1 99.3

10.6 11.0 11.3 11.7 12.2

4.29 4.11 3.97 3.86 3.82

0.061 0.060 0.059 0.059 0.058

29 830 29 820 29 820 29 810 29 800

30 180 30 300 30 320 30 190 30 400

0.22 mol/L

51.5 51.8 52.4 52.8 54.0

9.8 10.1 10.4 10.6 10.8

8.91 8.53 8.30 8.15 7.92

0.078 0.077 0.076 0.076 0.075

30 020 30 010 30 000 30 000 29 990

30 510 30 360 30 270 30 380 30 360

58.6 63.9 83.1 99.4

11.1 11.3 11.9 12.3

7.59 7.45 7.17 7.22

0.074 0.074 0.073 0.072

29 980 29 980 29 970 29 960

30 270 30 250 30 410 30 360

0.34 mol/L

51.7 51.9 52.2 52.4 52.6 54.0

10.5 10.6 10.8 11.0 11.1 11.3

11.35 11.20 11.00 10.76 10.67 10.47

0.088 0.087 0.087 0.086 0.086 0.085

30 110 30 110 30 100 30 100 30 100 30 090

30 430 30 410 30 320 30 320 30 320 30 270

56.1 59.1 64.0 71.3 83.1 99.2

11.4 11.5 11.6 11.8 12.1 12.4

10.42 10.22 10.16 10.07 10.05 10.18

0.085 0.085 0.084 0.084 0.083 0.082

30 090 30 080 30 080 30 080 30 070 30 070

30 410 30 400 30 280 30 360 30 340 30 270

and liquids, determined at equivalent values of x*. The numerator of eq 11 is the average maximum shift in the TFE/SCF ethane system (1490 cm-1), while the denominator is the maximum shift in the liquid TFE/ CH2Cl2 system (1160 cm-1). The shift in the SCF system is referenced to the transition maxima in pure SCF ethane (28 910 cm-1), which was assumed to be constant over the pressures investigated here. Table 6 compares the n f π* transition maxima estimated by this analysis with those measured in the benzophenone/TFE/SCF ethane system. For each spectroscopic measurement, the ratio of complexed to uncomplexed benzophenone and the resulting x* are also listed. These estimated and experimentally determined shifts are compared as a function of density for several TFE concentrations (0.011, 0.045, and 0.34 mol/L) in Figure 9. Other than the assumptions listed above, no adjustable parameters were used in the estimation of these shifts. This simple model is able to describe qualitatively the cosolvent concentration dependence of the n f π* shift, particularly in the case of the intermediate (0.034 mol/L) and high (0.22 mol/L) TFE concentration runs. A more stringent test of the model is its ability to capture the density-dependent behavior at the low TFE concentration (0.011 mol/L). Although

the estimated values at this TFE concentration fall within the experimental range, the model underpredicts the n f π* transition maxima at low densities and overpredicts this value at high system densities. The ratio of complexed to uncomplexed benzophenone molecules is sensitive to the model of the hydrogenbonded TFE/benzophenone species, as well as the evaluation of the “true” hydrogen-bonding equilibrium constant. The values of the estimated shifts, and not the observed trends in density and concentration, are affected by these parameters. Also, this model uses bulk TFE concentrations in calculation of both the system nonideality as well as the number density of cosolvent around the probe molecule. Therefore, this model does not account directly for local density and composition enhancements observed in near critical solutions. It relies purely on the strength of the hydrogen-bonding interaction to explain the nonrandom distribution of cosolvent molecules around benzophenone. The cosolvent environment, as inferred from these spectroscopic measurements, also affects solubilities of solutes in SCFs, particularly in systems of strong solute/ cosolvent interactions. The qualitative agreement of the model and spectroscopic data suggests the possibility of relating the local solvent environment, such as that

864 Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997

Figure 9. Experimental and estimated benzophenone n f π* transition maximum in TFE/SCF ethane at 35 °C as a function of local mole fraction. The experimental transition maxima are given for systems of 0.011 (b), 0.045 (2), and 0.34 mol/L (9) TFE. The lines represent the corresponding estimated shifts at the same conditions.

Figure 10. Radial distribution functions calculated for the ethane/ TFE/benzophenone system at T ) 308.15 K, F* ) 0.34, yTFE ) 1.49 × 10-3, and ybenz ) 2.04 × 10-4 using the HNC closure rule.

measured by x*, to observed cosolvent effects. The validity of this technique could be determined by correlating cosolvent effects on the solubility of benzophenone with x*. Many equilibrium constants for benzophenone with potential cosolvents are available in the literature. A high correlation would suggest the ability to predict cosolvent effects from knowledge of equilibrium constants of the solute/cosolvent interactions in liquid systems and chemical-physical arguments. Integral Equation Results. Radial distribution functions were calculated for all of the data shown for TFE in Table 4. As an example, the radial distribution functions calculated for the lowest density point in the 0.011 mol/L TFE data subset are shown in Figure 10. The distance to the first peak for each interaction occurs in order of the σijs. The first solvent/solute peak occurs at R′ ) 1.41σethane and has a value of 4.19. The solute/ solute peak is the largest one, and this occurs at R′ ) 1.72σethane and has a value of 7.30. The solvent/solute, cosolvent/solute, and solute/solute radial distribution functions show that the mixture is near the critical point

Figure 11. Radial distribution functions calculated for the ethane/ TFE/benzophenone system at T ) 308.15 K, F* ) 0.55, yTFE ) 9.34 × 10-4, and ybenz ) 1.28 × 10-4 using the HNC closure rule.

since the radial distribution functions are long range and approach the gij(r) ) 1.0 line asymptotically from above. In Figure 11 the radial distribution functions are shown for the highest density point in the 0.011 mol/L data subset. This point is further from the critical point of the mixture and shows more liquid-like radial distribution functions. The peak heights are much lower for the solvent/solute, cosolvent/solute, and solute/solute interactions, and the radial distribution functions show more definition of the second solvation shell around the solute. The examples shown in Figures 10 and 11 are characteristic of all of the radial distribution functions calculated at the lowest and highest densities for the entire data set. The ethane/TFE/benzophenone mixture, like virtually all ternary supercritical mixtures of industrial interest, can be described as an attractive mixture characterized by a density enhancement around the solute near the critical point (Wu et al., 1990). This is demonstrated by counting the number of molecules around the solute by integrating eq 4 from 0 to ∞. Figure 12 shows the excess number of molecules that result from such a calculation for the lowest density point in the 0.011 mol/L TFE data subset. The ordinate represents the total number of ethane molecules and the number of molecules in excess of what would be expected if the solvent were randomly distributed throughout the fluid as a function of radius. While the total number of molecules increase to infinity with increasing radius, the total excess number of solvent molecules levels out to a maximum value of 17.5 solvent molecules for this particular system and set of experimental conditions. The excess number of cosolvent molecules around the solute shows similar though less pronounced behavior because of the lower concentration of the cosolvent in the mixture. To test the assumption of a constant coordination number, first-shell coordination numbers were calculated for the entire data set. Calculated first-shell coordination numbers (Figure 13) are not constant and appear to be a linear function of the fluid density. The abrupt changes in the coordination number between 7 and 8 mol/L and between 10 and 11 mol/L are not a result of any physical forces but rather the discrete nature of the calculations. The radial distribution

Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 865

Figure 12. Total number and excess number of solvent molecules surrounding a solute molecule for the ethane/TFE/benzophenone system at T ) 308.15 K, F* ) 0.34, yTFE ) 1.49 × 10-3, and ybenz ) 2.04 × 10-4.

Figure 14. Comparison of the measured n f π* transition to the first solvation shell local density around the solute benzophenone for the data subset with no cosolvent shown in Table 4.

Figure 15. Calculated local cosolvent composition enhancement in the first solvation shell of benzophenone as a function of density. Figure 13. First solvation shell coordination number of the solute benzophenone as a function of fluid bulk density.

functions are calculated at discrete points only, and the coordination number must be calculated from a numerical integration of the data. As can be seen in Figure 12, the total number of molecules changes very rapidly for small changes in radius, especially within the region of the first solvation shell. The resolution of the coordination number calculation could be improved by decreasing the grid spacing. The first-shell coordination numbers appear to range between 15 and 18 molecules at the densities studied, where 18 is the number of molecules expected in the first solvation shell for this solute in liquid ethane. Although the coordination number increases with increasing fluid density as does the local density, the density increase does not correspond to any real change in the shift of the solute as can be seen in Figure 14. The points in the figure show the total local density around the solute for ethane/benzophenone in the absence of any cosolvent versus the shift. The error bars in the figure show the estimated error in the wavenumbers for the n f π* shift measurements. Since the shift does not change in response to changes in the local

density due to the proximity of the critical point or to increases in the overall fluid density, the shift changes seen in the solvent/cosolvent/solute mixture must be related to changes in the local cosolvent density or composition. The calculated local mole fractions of cosolvent within the first solvation shell around the solute were compared to the bulk mole fractions of the cosolvent in the supercritical fluid (Figure 15). The ratio of the local to bulk mole fractions of the cosolvent referred to in the figure as the cosolvent composition enhancement is related to the fluid density with the highest compositional enhancements occurring closest to the critical point of the mixture (the lowest fluid densities). The compositional enhancements are modest with the highest enhancements of about 36%. The local mole fractions of the cosolvent within the first solvation shell are compared to the measured n f π* shift of the solute in Figure 16. The shift appears very sensitive to local composition in the very dilute range but almost insensitive above about 1%. This figure, along with Figure 14, suggests that local density enhancements and local composition enhancements alone are not enough to account for the changes in the solute shift. Another factor unaccounted for by the Lennard-Jones model must be responsible for the be-

866 Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997

of interaction (such as hydrogen bonding) between the cosolvent and the solute must be responsible. The chemical-physical model may be improved by using a nonconstant coordination number and by using local instead of bulk mole fractions for the system’s components. The relatively poorer performance of the model at lower cosolvent concentrations versus higher solvent concentrations must be less related to the mixture’s physical behavior near the critical point and more related to the characterization of the specific cosolvent/solute interactions. Acknowledgment

Figure 16. Measured n f π* transition versus the calculated local composition of the cosolvent in the first solvation shell of benzophenone.

havior of the shift in Figure 16. This could well be saturation of the hydrogen bond between the TFE and the benzophenone, unaccounted for by a Lennard-Jones potential. Conclusions Benzophenone is a sensitive probe of solvent environment. The n f π* shift was as great as 1530 cm-1 in going from pure SCF ethane to SCF ethane with more than 1 mol % TFE. These shifts have been interpreted in terms of hydrogen bonding in the SCF and the effect on the local environment around the probe molecule. The n f π* shift was also measured for several other cosolvents, and the results were analyzed in terms of the Kamlet-Taft solvatochromic parameters R and π*. The spectroscopic results for hydrogen bonding in the SCF ethane/TFE systems are rationalized with a simple chemical-physical solution model. The major simplifying assumptions were that local mole fraction in the first solvation shell around a benzophenone molecule was perturbed by a single hydrogen bond, with the equilibrium constant found from liquid data, that the coordination number in the SCF was constant, and that the Soave-Redlich-Kwong equation of state accounted for the physical contributions to system nonideality. The satisfactory agreement of model and data demonstrates the potential of using spectroscopic methods in conjunction with thermodynamic models. The assumptions of the chemical-physical model proposed for predicting the n f π* shift of benzophenone in a supercritical solvent/cosolvent mixture of ethane and benzophenone were examined by integral equation methods. The coordination number is not quite constant but varies with density with the maximum value being about 18 for the solute in liquid ethane. The density and local compositional enhancements predicted by the radial distribution functions could not account for the increase in the shift at lower densities and the relatively constant shift at higher densities. It was suggested that hydrogen bonding between the cosolvent and the solute is the primary means of benzophenone ground state n-electron stabilization in the supercritical ethane/TFE/benzophenone system on the basis of spectroscopic arguments. The results of the integral equation analysis suggest that dispersion forces alone in Lennard-Jones fluids are insufficient for causing the behavior of the measured shifts; some other kind

The authors gratefully acknowledge funding support for this work from the U.S. Department of Energy under Grant DE-FG22-91PC91287 as well as support from the E.I. Du Pont de Nemours Co. Additionally, we thank Alison Williams and Wendy Windsor for their work on this project. Nomenclature ai ) activity of species i c ) coordination number cij ) direct correlation function f ) fraction of hydrogen-bonded solute molecules gij(r) ) radial distribution function gij∞(r) ) radial distribution function of infinitely dilute solute hij ) total correlation function HNC ) hypernetted chain closure rule kij ) binary interaction parameter k ) Boltzmann’s constant Ka ) true equilibrium constant Kc ) equilibrium constant in concentration units (L/mol) Kx ) liquid phase equilibrium constant in mole fraction units Ky ) gas phase equilibrium constant in mole fraction units Kγ ) ratio of physical nonidealities Nj ) number of molecules of type j O.Z. ) Ornstein-Zernike P ) system pressure PY ) Percus-Yevick closure rule r ) radius rc ) soft core radius R ) gas constant R′ ) radius of local region T ) system temperature T* ) normalized temperature [(kT)/solvent] v ) molar volume x* ) local mole fraction xi, yi ) mole fraction of species i Greek Letters R ) Kamlet-Taft hydrogen bond acidity parameter β ) Kamlet-Taft hydrogen bond basicity parameter ij ) Lennard-Jones energy parameter γij ) indirect correlation function γi ) activity coefficient of species i φi ) fugacity coefficient of species i µi ) dipole moment of species i ∆νi ) change in transition maximum (cm-1) in phase i νi ) transition maximum (cm-1) in solution i π* ) Kamlet-Taft polarity/polarizability parameter Fi ) number density [molecules/Å3] 3 F* i ) normalized number density [Fi/σsolvent] Flocal ) local density σij ) Lennard-Jones radius parameter ω ) acentric factor

Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 867 Subscripts A ) hydrogen bond acceptor AD ) hydrogen bonded complex c ) critical point D ) hydrogen bond donor LIQ ) liquid phase SCF ) supercritical fluid phase

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Resubmitted for review February 6, 1996 Revised manuscript received February 6, 1996 Accepted February 16, 1996X IE9600809

X Abstract published in Advance ACS Abstracts, December 15, 1996.