Determination of Binary Diffusion Coefficients of Anisole, 2,4

Binary diffusion coefficients of anisole, 2,4-dimethylphenol, and nitrobenzene in supercritical carbon dioxide have been determined at 313, 323, and 3...
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Ind. Eng. Chem. Res. 2001, 40, 3711-3716

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Determination of Binary Diffusion Coefficients of Anisole, 2,4-Dimethylphenol, and Nitrobenzene in Supercritical Carbon Dioxide Luis M. Gonza´ lez, Julio L. Bueno, and Ignacio Medina* Departamento de Ingenierı´a Quı´mica y TMA, Universidad de Oviedo, 33071 Oviedo, Spain

Binary diffusion coefficients of anisole, 2,4-dimethylphenol, and nitrobenzene in supercritical carbon dioxide have been determined at 313, 323, and 333 K and at pressures between 15.0 and 35.0 MPa. Measurements have been obtained using the Taylor-Aris dispersion technique. The data have been correlated with temperature, pressure, density, and viscosity, and some general trends have been established. The applicability of several correlations to the experimental data was examined, and some correlations have shown that they are satisfactory for predicting diffusion coefficients. Introduction Over the past 2 decades supercritical fluids have received much attention because of their potential application in extraction processes (food processing, biochemical and pharmaceutical industries, etc.), in chemical fractionation, in chemical analysis (supercritical fluid chromatography), as reaction media, etc. Carbon dioxide has been the most supercritical fluid frequently used because of its desirable thermodynamic and transport properties.1,2 For the optimization of supercritical fluid extraction processes, the solubility and mass transfer in the critical region must be well understood. The lack of fundamental thermodynamic data required for process design and scale-up has hindered the development of the technology to a commercial level. There is a current need for rapid and simple methods of determination of solubility and mass-transfer coefficients in supercritical carbon dioxide. A considerable effort has been devoted to the measurement of solubility and transport properties data. Some reviews of high-pressure solubility data have been published by Fornari et al.3 and Dohrn and Brunner.4 Reliable data for transport properties such as binary diffusion coefficients are needed for the design of a separation process where mass transfer is involved as the dominant rate mechanism. Most of the available experimental data for the diffusion coefficients in supercritical carbon dioxide as well as other less commonly used solvents are summarized by Catchpole and King,5 Funazukuri and Wakao,6 and Sua´rez et al.7 In the pressure and temperature range where most supercritical extractions would be carried out, there are no general experimental values for mass-transfer coefficients. The binary diffusion coefficients in supercritical fluids can be measured by means of the solid dissolution technique, by photon correlation spectroscopy (PCS) or light scattering, by the nuclear magnetic resonance technique, and by means of the Taylor-Aris dispersion technique.8 The solid dissolution technique involves the use of a diffusion cell in which the pure solid material, * To whom correspondence should be addressed. Tel: 985103510.Fax: 985-103434.E-mail: [email protected].

compressed into tablet form, is allowed to dissolve and diffuse into the supercritical fluid. Measurements using photon correlation spectroscopy are based on determination of the width of the central or Rayleigh peak in the spectrum of scattered light. The nuclear magnetic resonance technique is confined to measurements of selfdiffusion coefficients. The Taylor-Aris dispersion technique is based on the dispersion of a solute in a fully developed laminar flow of the supercritical fluid through a tube of uniform diameter. The Taylor-Aris dispersion technique is particularly well suited for high-pressure applications, and the measurement of binary diffusion coefficients for supercritical fluids is most often carried out using this technique. It is the simplest and most accurate technique for binary diffusion coefficient measurements. The application of this technique has been demonstrated by a number of researchers. A comprehensive discussion of the experimental and theoretical problems encountered when applying the Taylor-Aris technique to the measurement of diffusion coefficients has been described by Levelt Sengers et al.9 In this work, the binary diffusion coefficients of anisole, 2,4-dimethylphenol, and nitrobenzene in supercritical carbon dioxide at 313, 323, and 333 K over the pressure range from 15.0 to 35.0 MPa were measured by the Taylor-Aris or capillary peak broadening technique. Conditions for the present diffusion measurements fall in the range of practical interest: 0.9 < Tr < 1.2 and Pr > 1. The dependence of temperature, pressure, density, and viscosity on the diffusion coefficient is discussed. The effect of molecular geometry was also investigated by observing the diffusion coefficients of solutes. Experimental Section The diffusion coefficients have been measured using the Taylor-Aris tracer response technique. Taylor10,11 showed that the dispersion of a pulse of a test substance in a fully developed laminar parabolic flow (Poiseuille flow) is due to the combined action of convection parallel to the axis and the molecular diffusion in the radial direction. The pulse of a solute, after a sufficient residence time, becomes normally distributed, and the

10.1021/ie010102d CCC: $20.00 © 2001 American Chemical Society Published on Web 07/10/2001

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diffusion coefficient can be obtained from an analysis of the observed peak shape. The mathematical description of the concentration profile at the end of the column, in terms of a peak variance in units of length is

σ2 )

2D12L r02U0L + U0 24D12

(1)

where D12 is the infinite-dilution diffusivity of solute 1 in solvent 2, L is the dispersion tube length, U0 is the average velocity of the mobile phase, r0 is the dispersion tube inner radius, and σ2 is the variance of the curve in units of length. In chromatography the plate height H is defined by

H ) σ2/L

(2)

Substitution of eq 1 into eq 2 yields

D12 )

{ [ ( )] }

U0 r02 H ( H2 4 3

1/2

(3)

which provides values of D12 as a function of design parameters (r0 and L) and experimental data (U0 and σ2). A simple way to determine the variance σ2 and hence the plate height H is to measure the peak width at 0.607 times the peak height. The plate height can then be obtained from the following expression:

H ) U02W0.6072/4L

(4)

The mathematical model may be applied to coiled columns with only a few restrictions in the hydrodynamics and mass transfer throughout the column, which may be summarized in the adimensional condition

(De)(Sc)1/2 < 10

(5)

where De and Sc are the Dean and Schmidt numbers. The limitations of the Taylor dispersion method have been discussed by Liong et al.,8 Levelt-Sengers et al.,9 Roth,12 and Bueno et al.13 The experimental diffusion coefficients of anisole, 2,4dimethylphenol, and nitrobenzene in supercritical carbon dioxide were measured using a commercially available Hewlett-Packard G1205A supercritical fluid chromatograph (HP SFC). The HP SFC system consists of a pumping module, a column oven, a manual injection valve, a multiple-wavelength UV detector (MWD), a modifier pump, a mass flow sensor, an HP Vectra PC, and an HP printer.14 The HP SFC introduces the sample into the column through a heated manual injection valve. A Rheodyne model 7520 injector of ultralow dispersion with a 0.2 µL loop was used. Samples are injected as liquids at room temperature and looped directly into the supercritical stream. The oven module can accommodate capillary and standard HPLC columns. The oven has a temperature range from -80 to +450 °C. The oven module serves as a mainframe unit that integrates other parts of the HP SFC system. The HP SFC uses both gas- and liquid-phase detectors. In the present work, this unit uses a MWD.

The HP SFC uses an electrothermally cooled reciprocating pump to supply supercritical fluids to the system. Electrothermal cooling provides clean, selfcontained, quiet, and reliable operation. The pump has feedback control, which compensates for fluid compressibility, minimizes pressure ripple, and provides for more reproducible results. In addition, the use of a reciprocating pump eliminates the inconvenience associated with refilling syringe pumps. The variable restrictor is a programmable, backpressure control device located inside the pump module. The variable restrictor consists of a pressure transducer and nozzle, which opens and closes accordingly, releasing a mobile phase to control pressure. Flow rate and column outlet pressure are independently controlled by the system. The SFC ChemStation consists of a PC and HP SFC software. The SFC ChemStation enables instrument control and data handling on a Microsoft Windows based platform. The mass flow sensor is a device located inside the pumping module. The solutes used during this study, anisole, 2,4dimethylphenol, and nitrobenzene, were obtained from Merck (synthesis grade). 2,4-Dimethylphenol had a minimum purity of 98%, and anisole and nitrobenzene had a minimum purity of 99%. The chemicals were used without further purification. The carbon dioxide supplied by Air Liquide had a minimum purity of 99.998%. Compression of the carbon dioxide is accomplished by pumping it as a liquid from a standard cylinder with a siphon. After pressurization the CO2 is heated to the desired temperature in the oven, is passed through the column and detector, and exits through the variable restrictor as a gas. A diffusion column, consisting of an entirely empty coiled (coil diameter 0.26 m) stainless steel tubing of 0.762 mm i.d. × 30.48 m, is kept at constant temperature in the oven. Once both temperature and pressure have reached the desired levels, the flow system is allowed to equilibrate for 1-2 h. After thermal and hydrodynamic equilibrium is established, small amounts (0.2 µL) of the pure liquid solute are introduced by means of the manual injection valve, as a pulse into the CO2 stream at the column inlet. Injection of sample solutions then follows at intervals of 12-15 min, with the time between two subsequent injections chosen to prevent any overlapping of the solute peaks. The solute concentration profile leaving the capillary column was monitored by the MWD. The wavelength of the UV detector varied depending on the solute used. The wavelengths were 241, 243, and 245 nm for anisole and 2,4-dimethylphenol and 340, 345, and 350 nm for nitrobenzene. Fortunately, no tailing was observed, and the peaks were symmetrical in all of the runs. The reproducibility of the measured diffusivities is normally 2% (absolute average deviation) or better for a total of 5-10 injections. The retention time of the injected liquid pulse is about 2 h. The reproducibility of experimental conditions in the supercritical region is excellent and, thus, the experimental apparatus and procedure are considered to be capable of generating accurate diffusion data. Results and Discussion The diffusion coefficients of benzene in supercritical carbon dioxide at different conditions of pressure and temperature were measured and compared with those obtained by other authors to verify the applicability of

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Figure 1. Chemical structures of anisole, 2,4-dimethylphenol, and nitrobenzene. Table 1. Experimental Diffusion Coefficients D12 (in m2 s-1) for Anisole, 2,4-Dimethylphenol, and Nitrobenzene in Supercritical CO2 D12 × 109 T (K)

P (MPa)

anisole

2,4-dimethylphenol

nitrobenzene

313 313 313 313 313 323 323 323 323 323 333 333 333 333 333

15 20 25 30 35 15 20 25 30 35 15 20 25 30 35

11.78 10.15 9.24 8.70 8.23 13.17 11.30 10.33 9.54 8.93 14.97 13.27 11.76 10.83 10.16

9.64 8.89 8.32 7.81 7.50 11.36 10.19 9.28 8.61 8.34 12.95 11.85 10.84 10.00 9.56

10.66 9.77 8.95 8.37 7.98 12.70 11.00 10.22 9.33 8.86 13.97 12.51 11.55 10.60 10.06

the method. Our data were in good agreement with those of Swaid and Schneider15 and Lauer et al.,16 all of them systematically lower than the values published by Sassiat et al.17 at 40 °C. The obtained data were compared in a figure in a previous work.13 Also, Levelt Sengers et al.9 illustrated in a figure all of the data for the diffusion coefficient of benzene in CO2 as a function of density. Our data agree quite well with those obtained by several authors. Only the data obtained by Sassiat et al.17 are consistently higher. The experimentally determined diffusion coefficients for anisole, 2,4-dimethylphenol, and nitrobenzene in supercritical carbon dioxide, together with the temperatures and pressures at which the results were obtained, are presented in Table 1. Chemical structures of anisole, 2,4-dimethylphenol, and nitrobenzene are shown in Figure 1. Even though the three solutes have different structures, it is possible to order diffusivities at the same conditions as follows: D12(anisole) > D12(nitrobenzene) > D12(2,4-dimethylphenol). The diffusion coefficient of anisole is about 1.04 times larger than that of nitrobenzene and about 1.12 times larger than that of 2,4dimethylphenol at the same conditions. The values of diffusion coefficients depend on a number of factors: the density and viscosity of the solvent, the size and shape of the solute, and the interactions between solute and solvent. The observed values for the three solutes can be explained in terms of the size, shape, and polarity of the solutes. These factors operate in opposite directions, and the results justify which factors are more important. The anisole molecule is the smallest of the three solutes, followed by 2,4-dimethylphenol and nitrobenzene. The diffusion coefficients of anisole are very close to those of nitrobenzene though the molar masses of these compounds are clearly different (108.14 and 123.11 g mol-1, respectively). According to polarity, the diffusion coefficients should keep the same order: anisole followed by 2,4dimethylphenol and nitrobenzene. The nitrobenzene

Figure 2. Binary diffusion coefficients of anisole in supercritical carbon dioxide as a function of pressure.

molecule has the advantage of a more compact shape. Anisole showed the highest value of diffusivity because it has the lowest molar mass and polarity. Nitrobenzene diffuses better than 2,4-dimethylphenol because its more compact shape has more influence than the lower polarity and molar mass of 2,4-dimethylphenol. The binary diffusion coefficients of the three solutes in supercritical carbon dioxide were determined as a function of pressure and temperature. As expected, the general trend observed is that the diffusion coefficient decreases with increasing pressure, with this influence varying with temperature. With decreasing temperature, diffusion becomes less pressure-dependent. In all cases, the influence of pressure on the diffusion coefficients was less significant at higher pressures, as is illustrated for anisole in Figure 2. Similar behavior was found for 2,4-dimethylphenol and nitrobenzene. Figure 2 makes it clear that the pressure dependence is predominantly the result of changes in density, and this effect is more pronounced at higher temperatures. The binary diffusion coefficients of the systems investigated decrease by about 25-30% for pressure rising from 15.0 to 35.0 MPa. The temperature dependence of the diffusion coefficient at constant pressure may be illlustrated as, by way of example, is shown for 2,4-dimethylphenol in Figure 3. Similar behavior was observed for anisole and nitrobenzene. Figure 3 shows a marked increase in the diffusion coefficient as the temperature is increased isobarically. In addition, the results indicate that the dependence of the diffusion coefficient on temperature decreased as the pressure was increased. An increase in the diffusion coefficient of 25-35% is observed over a 20 K temperature range. The diffusion coefficients have been determined over a considerable range of density from 609 to 936 kg m-3. The density dependence of the diffusion coefficients in supercritical carbon dioxide is clearly shown in Figure 4, where the diffusivity values of nitrobenzene are plotted as a function of supercritical carbon dioxide density. The density dependence is similar to that found by other works using a variety of supercritical fluids as solvents. As was expected, a high dependence on carbon dioxide density is observed. As the density of the solvent increases, the diffusion coefficient decreases. It was also observed that the decrease in diffusivity with respect

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Figure 3. Binary diffusion coefficients of 2,4-dimethylphenol in supercritical carbon dioxide as a function of temperature.

Figure 4. Influence of the density of supercritical carbon dioxide on the diffusion coefficient of nitrobenzene.

to increasing fluid density was linear. The decrease of diffusivity with increasing carbon dioxide density is due to the increased collision and the reduced mean free path of the solutes. The densities of supercritical carbon dioxide were calculated from the IUPAC equation of state given by Angus et al.,18 which is accepted as one of the most adequate equations of state for carbon dioxide. The binary diffusion coefficients in supercritical carbon dioxide are plotted as a function of reciprocal carbon dioxide viscosity. The viscosity of supercritical carbon dioxide was taken from Stephan and Lucas.19 In this work, the viscosity of carbon dioxide varied between 47.6 and 102.3 µN s m-1. The trend observed is that the diffusion coefficient decreases with increasing solvent viscosity. Figure 5 shows the variation of the diffusion coefficient for anisole. Within the limits of experimental error, the data yielded a straight line with a small positive intercept. Similar behavior was observed for all of the systems investigated. The results obtained are consistent with the trends found by previous researchers.11,20 The observed diffusion coefficients were used to evaluate the applicability of several empirical equations.

Figure 5. Influence of the viscosity of supercritical carbon dioxide on the diffusion coefficient of anisole.

The diffusion coefficients in supercritical fluids exhibit a stronger temperature dependence that is predicted according to the hard-sphere theories. This suggests a hydrodynamic description. In a hydrodynamic approach, the Stokes-Einstein expression is used as a starting point, and a plot of D12 vs η-1 should yield a straight line through the origin. Figure 5 shows the anisolecarbon dioxide system plotted in this manner. The line has small but finite intercepts, indicating deviation from strictly hydrodynamic behavior. It is of interest to investigate the behavior of the quantity ηD12T-1 (Debenedetti and Reid21). This quantity does not change significantly over the range of conditions tested, and this fact can be used to extrapolate experimental data. The mean of experimental values is 1.641 × 10-2 for anisole, 1.457 × 10-2 for 2,4-dimethylphenol, and 1.586 × 10-2 for nitrobenzene. Hydrodynamic behavior is approached at high enough viscosities. Empirical correlations, such as those by Wilke and Chang,22 Scheibel,23 and Reddy and Doraiswamy,24 were derived from the Stokes-Einstein expression. In all cases, the correlations overestimated observed diffusion coefficients. The Wilke-Chang equation performed significantly better than the other equations tested. The absolute average deviation of these equations was 10.1% for the Wilke-Chang equation, 23.1% for the Scheibel equation, and 45.4% for the Reddy-Doraiswamy equation. Sassiat et al.17 pointed out that the Wilke-Chang equation was good for predicting diffusion coefficients in supercritical carbon dioxide over a certain range of density (higher than 600 kg m-3). If the constant value in the Wilke-Chang equation, 7.4 × 10-15, is modified, as is suggested by Sassiat, by 8.6 × 10-15, this equation leads to higher diffusion coefficients, and the absolute average deviation of this equation increases (11.7%). The overestimation of the diffusion coefficients by these correlations is due to the inability to accurately describe the role of the viscosity in the diffusion process. Another model was developed by Hayduk and Minhas.25 These authors proposed a correlation based on the interaction between the solvent viscosity and the solute molar volume. This equation was tested with the observed diffusion values, and the deviations, still overpredicted values, were higher than those obtained by using the Wilke-Chang equation. The absolute average deviation of this equation was 24.9%.

Ind. Eng. Chem. Res., Vol. 40, No. 16, 2001 3715 Table 2. Absolute Average Deviations for Different Equations of the Three Solutes in Supercritical CO2 equation

anisole

2,4-dimethylphenol

nitrobenzene

Wilke-Chang22 Scheibel23 Reddy-Doraiswamy24 Hayduck-Minhas25 Chen et al.31 Eaton-Akgerman32 He-Yu33 Liu et al.34

9.15 22.86 41.75 23.57 25.29 10.02 3.97 33.82

15.25 29.30 53.92 31.58 17.13 11.25 7.32 31.06

5.82 17.18 40.46 19.52 22.82 14.81 5.10 28.81

The rough-hard-sphere theory assumes that molecular interactions involve collisions between only two molecules at any one time. A much simpler form of this theory was adopted by Dymond,26 and Chen27 suggested a new form to describe the diffusion coefficients. Excellent correlations between experimental and predicted values were obtained by Matthews and Akgerman,28 Liong et al.,29 and Funazukuri et al.,30 using the model proposed by Dymond as a starting point. The structure of the molecule has an important effect on diffusion in a supercritical solvent. In this case, the molar volume of the solute is used to characterize its size instead of the molecular weight. A good correlation was observed for the three solutes studied with an average deviation of 21.8% if the equation suggested by Chen et al.31 was used. The absolute average deviation obtained was significantly different from the Wilke-Chang equation, and the free volume diffusion model was less successful in correlating the experimental data. Eaton and Akgerman32 have obtained a predictive equation, based on the rough-hard-sphere theory. The predictions are excellent, with an average absolute error of 12.03%. The results indicate that the predictions are slightly higher than the experimental values. New correlations have been proposed for predicting the diffusion coefficients of solutes in supercritical solvents in recent years. On the basis of the hard-sphere theory, He and Yu33 developed a new correlation to estimate the binary diffusion coefficients of liquid and solid solutes in supercritical solvents. This correlation shows a 5.5% difference when compared with the experimental results. Liu et al.34 proposed two correlation models involving only one binary parameter. This correlation performs worse than the He-Yu correlation, and the difference is large. It exhibits an absolute average deviation of 31.2%. As a result of the limited amount of diffusivity data, a detailed analysis of these correlations could not be undertaken. Table 2 contains the absolute average deviations for all of the equations or models used to predict the diffusion coefficient values for the three solutes used in this work. Acknowledgment The financial support for this work by the DGE of Spain by means of project 98-PB97/1273 is gratefully acknowledged. Nomenclature D12 ) molecular diffusion coefficient, m2 s-1 De ) Dean number H ) height equivalent to a theoretical plate, m L ) diffusion tube length, m P ) pressure, MPa

r0 ) internal radius of the diffusion tube, m Sc ) Schmidt number T ) absolute temperature, K U0 ) average linear velocity of the carrier fluid, m s-1 W0.607 ) peak width at 0.607 times the peak height, m Greek Letters η ) solvent viscosity, kg m-1 s-1 F ) solvent density, kg m-3 σ2 ) total peak variance, m2

Literature Cited (1) Teja, A. S.; Eckert, C. A. Commentary on Supercritical Fluids: Research and Applications. Ind. Eng. Chem. Res. 2000, 39, 4442. (2) Perrut, M. Supercritical Fluid Applications: Industrial Developments and Economic Issues. Ind. Eng. Chem. Res. 2000, 39, 4531. (3) Fornari, R.; Alessi, P.; Kikic, I. High-Pressure Fluid Phase Equilibria: Experimental Methods and Systems Investigated (1978-1987). Fluid Phase Equilib. 1990, 57, 1. (4) Dohrn, R.; Brunner, G. High-Pressure Fluid-Phase Equilibria: Experimental Methods and Systems Investigated (19881993). Fluid Phase Equilib. 1995, 106, 213. (5) Catchpole, O. J.; King, M. B. Measurement and Correlation of Binary Diffusion Coefficients in Near Critical Fluids. Ind. Eng. Chem. Res. 1994, 33, 1828. (6) Funazukuri, T.; Wakao, N. Application of the Rough Hard Sphere Model to Binary Diffusion Coefficients of Organic Compounds in Dense CO2. Kagaku Kogaku Ronbunshu 1995, 21, 204. (7) Sua´rez, J. J.; Medina, I.; Bueno, J. L. Diffusion Coefficients in Supercritical Fluids: Available Data and Graphical Correlations. Fluid Phase Equilib. 1998, 153, 167. (8) Liong, K. K.; Wells, P. A.; Foster, N. R. Diffusion in Supercritical Fluids. J. Supercrit. Fluids 1991, 4, 91. (9) Levelt Sengers, J. M. H.; Deiters, U. K.; Klask, U.; Swidersky, P.; Schneider, G. M. Application of the Taylor Dispersion Method in Supercritical Fluids. Int. J. Thermophys. 1993, 14, 893. (10) Taylor, G. Dispersion of a Solute Matter in Solvent Flowing Slowly through a Tube. Proc. R. Soc. London 1953, A219, 186. (11) Sua´rez, J. J.; Bueno, J. L.; Medina, I. Determination of Binary Diffusion Coefficients of Benzene and Derivatives in Supercritical Carbon Dioxide. Chem. Eng. Sci. 1993, 48, 2419. (12) Roth, M. Diffusion and Thermodynamic Measurements by Supercritical Fluid Chromatography. J. Microcolumn Sep. 1991, 3, 173. (13) Bueno, J. L.; Sua´rez, J. J.; Dizy, J.; Medina, I. Infinite Dilution Diffusion Coefficients: Benzene Derivatives as Solutes in Supercritical Carbon Dioxide. J. Chem. Eng. Data 1993, 38, 344. (14) Medina, I.; Bueno, J. L. Solubilities of 2-Nitroanisole and 3-Phenyl-1-propanol in Supercritical Carbon Dioxide. J. Chem. Eng. Data 2000, 45, 298. (15) Swaid, I.; Schneider, G. M. Determination of Binary Diffusion Coefficients of Benzene and Some Alkylbenzenes in Supercritical CO2 Between 308 and 328 K in the Pressure Range 80 to 160 bar with Supercritical Fluid Chromatography. Ber. Bunsen-Ges. Phys. Chem. 1979, 83, 969. (16) Lauer, H. H.; McManigill, D.; Board, R. D. Mobile-Phase Transport Properties of Liquefied Gases Near-Critical and Supercritical Fluid Chromatography. Anal. Chem. 1983, 55, 1370. (17) Sassiat, P. R.; Mourier, P.; Caude, M. H.; Rosset, R. H. Measurement of Diffusion Coefficients in Supercritical Carbon Dioxide and Correlation with the Equation of Wilke and Chang. Anal. Chem. 1987, 59, 1164. (18) Angus, S.; Amstrong, B.; de Reuck, K. M. IUPAC International Thermodynamic Tables of the Fluid State. Carbon Dioxide, Pergamon Press: Oxford, 1976. (19) Stephan, K.; Lucas, K. Viscosity of Dense Fluids; Plenum Press: New York, 1979. (20) Wells, T.; Foster, N. R.; Chaplin, R. P. Diffusion of Phenylacetic Acid and Vanillin in Supercritical Carbon Dioxide. Ind. Eng. Chem. Res. 1992, 31, 927. (21) Debenedetti, P. G.; Reid, R. C. Diffusion and Mass Transfer in Supercritical Fluids. AIChE J. 1986, 32, 2034.

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(22) Wilke, C. R.; Chang, P. Correlation of Diffusion Coefficients in Dilute Solutions. AIChE J. 1955, 1, 264. (23) Scheibel, E. G. Liquid Diffusivities. Ind. Eng. Chem. 1954, 46, 2007. (24) Reddy, K. A.; Doraiswamy, L. K. Estimating Liquid Diffusivity. Ind. Eng. Chem. Fundam. 1967, 6, 77. (25) Hayduck, W.; Minhas, B. S. Correlations for Prediction of Molecular Diffusivities in Liquids. Can. J. Chem. Eng. 1982, 60, 295. (26) Dymond, J. H. Corrected Enskog Theory and the Transport Coefficients of Liquids. J. Chem. Phys. 1974, 60, 969. (27) Chen, S. H. A Rough-Hard-Sphere Theory for Diffusion in Supercritical Carbon Dioxide. Chem. Eng. Sci. 1983, 38, 655. (28) Matthews, M. A.; Akgerman, A. Diffusion Coefficients for Binary Alkane Mixtures to 573 K and 3.5 MPa. AIChE J. 1987, 33, 881. (29) Liong, K. K.; Wells, P. A.; Foster, N. R. Diffusion Coefficients of Long-Chain Esters in Supercritical Carbon Dioxide. Ind. Eng. Chem. Res. 1991, 30, 1329.

(30) Funazukuri, T.; Ishiwata, Y.; Wakao, N. Predictive Correlation for Binary Diffusion Coefficients in Dense Carbon Dioxide. AIChE J. 1992, 38, 1761. (31) Chen, S. H.; Davis, H. T.; Evans, D. F. Tracer Diffusion in Polyatomic Liquids. III. J. Chem. Phys. 1982, 77, 2540. (32) Eaton, A. P.; Akgerman, A. Infinite-Dilution Coefficients in Supercritical Fluids. Ind. Eng. Chem. Res. 1997, 36, 923. (33) He, C. H.; Yu, Y. S. Estimation of Infinite Diffusion Coefficients in Supercritical Fluids. Ind. Eng. Chem. Res. 1997, 36, 4430. (34) Liu, H.; Silva, C. M.; Macedo, E. A. New Equations for Tracer Diffusion Coefficients of Solutes in Supercritical and Liquid Solvents Based on the Lennard-Jones Fluid Model. Ind. Eng. Chem. Res. 1997, 36, 246.

Received for review February 5, 2001 Revised manuscript received May 16, 2001 Accepted May 17, 2001 IE010102D