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Ind. E n g . Chem. Res. 1991,30, 2470-2476
Symposium on Supercritical Fluids; Perrut, M., Ed.; 1988;pp 613-618. Coulson, J. M.; Richardson, J. F.; Sinnott, R. K. Chemical Engineering Vol. 6 Design; Pergamon Press: Oxford, 1983; pp 238-239. Daurelle, T.; Barth, D.; Perrut, M. Supercritical Fluid Extraction: Mass Transfer in a Counter Current Packed Column. In Proceedings of the International Symposium on Supercritical Fluids; Perrut, M., Ed.; 1988;pp 571-580. Debenedetti, P. G.; Reid, R. C. Binary Diffusion in Supercritical Fluids. In Supercritical Fluid Technology, Process Technology Proceedings; Penninger, J. M. L., Radosz, M., McHugh, M. A., Krukonis, V. J., Eds.; Elsevier: .Amsterdam, 1985; Vol. 3, pp 225-244. Debenedetti, P. G.; Reid, R. C. Diffusion and Mass Transfer in Supercritical Fluids. AIChE J. 1986,32 (12),2034-2046. de Haan, A. B. Supercritical Fluid Extraction of Liquid Hydrocarbon Mixtures. Ph.D. Dissertation, Delft University of Technology, 1991. de Haan, A. B.; de Graauw, J. Separation of Alkanes and Aromatics with Supercritical Carbon Dioxide. Sep. Sci. Technol. 1990,25 (13-151,1993-2006. Ender, U.;Peter, S. Verbesserung des Stoffaustausches bei der Uberkritischen Fluid-Extraktion durch Druckpulsation. Chem.-Ing.-Tech. 1989,61 (4),324-326. Evans, E. B. The Viscosities of Hydrocarbons, Part 1-111. J. Inst. Pet. Technol. 1938a,24, 38-53. Evans, E. B. The Viscosities of Hydrocarbons, Part VI1 and VIII. J. Inst. Pet. Technol. 1938b,24,537-553. Gasem, K. A. M.; Dickson, K. B.; Dulcamare, P. B.; Nagarajan, N.; Robinson Jr., R. L. Equilibrium Phase Compositions, Phase Densities and Interfacial Tensions for C02 + Hydrocarbon Systems. 5. C02 + Tetradecane. J. Chem. Eng. Data 1989,34(21, 191-195. Hufton, J. R.; Bravo, J. L.; Fair, J. R. Scale-up of Laboratory Data for Distillation Columns Containing Corrugated Metal-Type Structured Packing. Ind. Eng. Chem. Res. 1988,27,2096-2100. Jakob, H.; Seekamp, M.; Peter, S. Zum Stoffubergang beim Losen von Stoffen mit hoher Molmasse in uberkritischen Extractionsmitteln. Chem.-Ing.-Tech. 1987,59 (7),572-574. Lahiere, R. J.; Fair, J. R. Mass-Transfer Efficiencies of Column Contactors in Supercritical Extraction Service. Ind. Eng. Chem. Res. 1987,26,2086-2092. Lahiere, R.J.; Humphrey, J. L.; Fair, J. R. Mass Transfer in Countercurrent Supercritical Extraction. Sep. Sci. Technol. 1987,22 (2&3), 379-393.
Larian, M. G. Fundamentals of Chemical Engineering Operations; Constable and Company L T D London, 1959;pp 449-452. McGabe, W. L.; Smith, J. C.; Harriot, P. Unit Operations of Chemical Engineering, 4th ed.; McGraw-Hill: New York, 1985. Mizandjian, J. L.; Massie, J. F. Performance of a Packed Contactor in Supercritical COz Countercurrent Extraction. In Proceedings of the International Symposium on Supercritical Fluids; Perrut, M., Eds.; 1988;pp 661-667. Peter, S.; Jakob, H. Viscosity of Coexisting Phases a t Supercritical Fluid Extraction. In Proceedings of the International Symposium on Supercritical Fluids; Perrut, M., Ed.; 1988;pp 303-310. Peter, S.; Weidner, E.; Jakob, H. Die Viskositat koexistierender Phasen bei der uberkritischen Fluidextraktion. Chem.-hg.-Tech. 1987,59 (l),59-62. Pratt, H.R. C. Computation of Stagewise and Differential Contactors: Plug Flow. In Handbook of Solvent Extraction; Lo, T. C., Baird, M. H. I., Hanson, C., Eds.; Wiley: New York, 1983;pp 160-161. Rathkamp, P. J.; Bravo, J. L.; Fair, J. R. Evaluation of Packed Columns in Supercritical Extraction Processes. Solv. Extr. Ion Ex&. 1987,5 (3),367-391. Reid, R. C.;Prausnitz, J. M.; Poling, B. E. The Properties of Gases & Liquids, 4th ed.; McGraw-Hill: New York, 1987. Seibert, A. F.; Moosberg, D. G. Performance of Spray, Sieve Tray, and Packed Contactors for High Pressure Extraction. Sep. Sci. Technol. 1988,23(12&13), 2049-2063. Seibert, A. F.; Moosberg, D. G.; Bravo, J. L.; Johnston, K. P. Spray, Sieve Tray and Packed High Pressure Extraction ColumnsDesign and Analysis. In Proceedings of the International Symposium on Supercritical Fluids; Perrut, M., Ed.; 1988; pp 561-570. Sun, S. Tracer Diffusion in Dense Fluids up to the Supercritical Region. Dissertation, 1986;Available Univ. Microfilms Intl., Order No. DA8615303. Ulebin, S. A.; Makarushkin, V. I. Teploenergetika 1976,(6),65-69. Wells, P. A.; Foster, N. R. DIffusion in Supercritical Fluids. In Proceedings of the International Symposium on Supercritical Fluids; Perrut, M., Ed.; 1988; pp 319-326. Zarah, B. Y.; Luks, K. D.; Kohn, J. P. Phase Equilibria Behavior of Carbon Dioxide in Binary and Ternary Systems. J. Chem. Eng. Data 1974,19 (4),349-354. Received for review February 4, 1991 Revised manuscript received June 26, 1991 Accepted July 17,1991
Extraction of Lysozyme Using Reversed Micellar Solution: Distribution Equilibrium and Extraction Rates Takumi Kinugasa, Shin-Ichiro Tanahashi, and Hiroshi Takeuchi* Department of Chemical Engineering, Nagoya University, Chikusa-ku, Nagoya, 464-01, Japan
Studies were made of the extraction of lysozyme from aqueous KCl media with an isooctane solution containing Aerosol OT (AOT). The distribution equilibrium of the protein between the aqueous and the organic phases was explained in terms of two effects: an electrostatic interaction between the charged proteins and AOT headgroups, and a size exclusion effect due to water pool of the reverse micelles. The amount of water solubilized into the surfactant solution was correlated with both concentrations of the salt and AOT. It was found that the micellar solution saturated with proteins has a limiting content that depends on only water content of the organic phase. Furthermore, rates of both the forward and backward extraction of lysozyme were examined in a stirred transfer cell. In the stripping of the protein from the micellar solution, it was found that there is a dominant resistance to leave it at the oil-water interface.
Introduction With progress in genetic engineering and cell fusion techniques, new synthesis methods of proteins have been established. However, the development of efficient methods for recovery or concentration of proteins and other biproducts from fermentation broths and cell culture media is crucial for an advance in biotechnology. Various forms of chromatography and electrophoresis are usefully
applied to purification of high-value pharmaceuticalsbut are expensive and difficult to scale beyond laboratory size. Usual solvent extraction can be applied to large-scale processes for separation of organic acids and amino acids; however, its application for proteins is not suitable because of denaturation in organic solvents. Most recently, a novel extraction technique using reverse micelles has been reported by Luisi et al. (1979) as an
0888-588519112630-2470$02.50/0 0 1991 American Chemical Society
Ind. Eng. Chem. Res., Vol. 30, No. 11, 1991 2471 alternative procedure. A reverse micelle is an associated colloid of amphiphilic surfactants; the hydrophilic headgroups are located in the interior of the aggregate, whereas the hydrophobic tales extend to an organic solvent. An inner core of water in reverse micelle is surrounded by surfactant molecules and shielded from organic solvent; therefore, bioproducts can be extracted into the core water without denaturation. Goklen and Hatton (1987) attempted a separation of a ternary protein mixture using a mixer-settler cascade. Dekker et ai. (1986,1989) examined a continuous extraction operation of a-amylase and proposed a mathematical model for the extraction. Dahuron and Cussler (1988) discussed the transfer rate of proteins by using a microporous hollow-fiber contactor. Moreover, the application of a reversed micellar liquid membrane has been demonstrated by Luisi et al. (Luisi et al., 1979; Luisi, 1985), Armstrong and Li (1988), and Kuboi et al. (1990). However, the mechanism of extraction and stripping (back extraction) of proteins in reversed micellar extraction systems is still obscure because of the complication of the solubilization characteristics of water and proteins in a surfactant system. In this study the distribution equilibrium (partitioning) of proteins into a reversed micellar solution was examined for lysozyme, a low molecular weight protein, using an anionic surfactant with pH conditions below its isoelectric point. Solubilization of water in the surfactant system was also studied along with the size of the reverse micelle. Furthermore, the kinetics of solubilization of lysozyme in the micellar extraction system was discussed on the basis of both the extraction and stripping rates. Experimental Section Distribution Equilibrium. Sodium bis(2-ethylhexyl) sulfosuccinate (Aerosol OT or AOT) as an anionic surfactant was obtained from Nacalai Tesque Inc. and used without further purification. An organic solution was prepared by dissolving AOT in 2,2,4-trimethylpentane (isooctate) of commercial GR grade. An aqueous protein solution was prepared by dissolving an appropriate amount of lysozyme in distilled water containing potassium chloride for the adjustment of its ionic strength. The aqueous solution was further adjusted to a desired pH by the direct addition of 0.1 M HC1 or 0.1 M KOH. The protein used in this study was lysozyme from chicken egg white (molecular weight Mp = 14300, isoelectric point PI=11)obtained from Sigma Chemical Co. Ltd. In some experiments, we also used a-chymotrypsin (M,= 25310, p l = 8.1-8.6) and ribonuclease A (M,= 13680, p l = 9.6) from bovine pancreas. In the distribution measurements, equal volumes (10 mL) of the organic and aqueous solutions were placed in a flask and shaken for 120 min by use of a shaker in a water bath at 298 K. After reaching equilibrium, the two phases were separated on a centrifuge, and the protein content of each phase was then determined by spectrophotometry at 280 nm using a Shimadzu UV-160 instrument. Percent extraction of proteins, E, and its distribution ratio between the phases, m, were calculated from
E = CoVo(l~)/Cw,iVw,i m = Co/Cw
(1)
(2)
where Cw and Co are the protein contents of the aqueous and organic phase, respectively; Vw and Vo are the volume of each phase; the subscript i refers to the initial aqueous feed.
Q
silicone
9 detector
Figure 1. Details of transfer cell used in the present study (unit: mm). B, the interface between reversed micellar (upper) phase and aqueous (lower) phase; P, constant flow pump.
Water content of the organic phase was determined by Karl Fischer titration, and the molar ratio of the water to the surfactant, Wo, was then obtained as wo = [H,OI/[AOTl (3) where [ ] represent the molar concentration of species in the brackets. Extraction Rate Measurements. Extraction and stripping of lysozyme were carried out with AOT/isooctane micellar solution at 298 K, using a stirred transfer cell made of glass; the geometry is shown in Figure 1. The stirrer for aqueous and organic phases comprised two impellers with two flat blades, mounted on a shaft driven by an electric motor. Equal volumes (20 mL) of the micellar solution and aqueous feed were put in the upper and lower section of the cell, respectively, the two phases being stirred at a speed of 1.3-6.6 s-l under conditions of no ripple at the interface. The aqueous solution was drawn from a sampling port located at the lower section of the cell by a constant flow pump, and then returned to a position at an adequate depth from the liquid-liquid interface via a UV spectrophotometric detector (Shimadzu SPD-7A),whereby the time course of protein content was obtained from a change in the absorbance. Aqueous feed pH was adjusted to a desired value by use of a phosphate or borate buffer. In the forward extraction runs, we used the micellar solution obtained in contact with a KC1 solution having the same composition as the aqueous feed without lysozyme. The micellar solution for the back extraction was laden with the protein in advance. Rates of the extraction and the stripping were calculated from J = (Vw/A)* (dCw/dt),where the plus and minus signs give the backward rate, JB,and the forward one, JF,respectively; A is the interfacial area between the two phases, 9.7 cm2 and t is the contact time. In all the experiments the concentration change of the protein was linear with the contact time over 15-30 min. Light Scattering Measurements. A liquid sample of a reversed micellar solution of AOT in isooctane was obtained through a membrane filter (pore size 0.45 bm). Size distribution of the reverse micelles was determined on a dynamic light scattering photometer with the light source of an argon ion laser, UNION GIKEN DLS-700. The
2472 Ind. Eng. Chem. Res., Vol. 30, No. 11, 1991
08
0
02
04
06
08
10
12
”
CKCII Ckmd/m?
Figure 2. Effect of aqueous concentration of KCl on the extraction of lysozyme at pH 6.3. [AOT] = 0.01 ( O ) ,0.05 (A),and 0.10 (0)M.
0
0.2
(dl
0.4 0.6 0 8 [KCII Ckmol/m’l
10
median diameter of the number distribution obtained was used for analysis of the mean diameter.
Results and Discussion Distribution Equilibrium of Lysozyme: Effect of Ionic Strength and pH on Extraction. Figure 2 shows the effect of the salt concentration, [KCl], on the extraction of lysozyme in three reversed micellar solutions with different AOT concentrations, [AOT], wherein the protein content of the aqueous feed was 1g/L. The solubilization characteristics were sensitive to [KCl] over a narrow range; the extraction of the protein was lowered as [KCl] increased. Such behavior can be explained in terms of two effects due to a change in thickness of the electric double layer, as have been pointed out by many investigators. One is a “size exclusion effect”. The electric double layer adjacent to the hydrophilic headgroups of the surfactant is thinned with an increase in the ionic strength, and hence the electrostatic repulsion force between the neighboring headgroups is reduced. This contribution gives rise to the formation of smaller reverse micelles in the organic phase and is likely to provide the exclusion effect in response to the size of protein molecule. The other is due to electrostatic attractions between the charged groups of the protein and the polar heads of the surfactant in a reverse micelle. Thus, with increasing ionic strength, the extent of the extraction of lysozyme was lowered. Similar behavior was also found in the extraction of a-chymotrypsin and ribonuclease A, although these data are not given here. To confirm the size exclusion effect, we here consider the size of molecule of these proteins. A Stokes diameter of proteins can be obtained from the partial specific volume by use of the friction factor (Takagi et al., 1976); it was found that these values are 3.8, 4.6, and 3.3 nm for lysozyme, a-chymotrypsin, and ribonuclease A, respectively. In Figure 3, the diameter of the reverse micelle into which one molecule of each protein was entrapped is compared with the mean diameter obtained by use of the dynamic light scattering photometer, whereby the length of AOT molecule was assumed to be 1.1 nm according to Wong et al. (1977). The present results for the micelle size are comparable to the literature values by photon correlation spectroscopy (Zulauf and Eicke, 1979), ultracentrifugation (Levashov et al., 1982; Zampieri et al., 1986), and small-angle neutron scattering (Kotlarchyk et al., 1982; Caselli et al., 1988). The results for the lysozyme extraction can be obviously explained by the size effect. However, the percent extraction for either a-chymotrypsin or ribonuclease A was low even when the micelle size was larger than these protein molecules. This implies that the electrostatic interactions have a significant effect in the extraction of a-chymotrypsin and ribonuclease A compared with lysozyme.
”
0
0.1
0.3
0.2
CAOT 1 Ckmol/m31
lbl
Figure 3. Plots of mean diameters of reverse micelles against (a) KC1 concentration and (b) AOT concentration. Dashed lines represent the diameter of the reverse micelle into which one molecule of each protein was entrapped: 1, lysozyme; 2, a-chymotrypsin; 3, ribonuclease A. 10 08
m
06
Y
w 04 02 0
2
4
6 8 pH C-1
1 0 1 2
Figure 4. Effect of solution pH on the extraction of lysozyme. M; [AOT] = 0.05 M. [KCI] = 0.1 ( O ) , 0.5 (A),and 1.0 (0)
The effect of aqueous feed pH on the extraction of lysozyme is shown in Figure 4. In the case of low KC1 concentration, the extraction changed drastically at a pH value adjacent to the p l of the protein. When the aqueous feed has a value of pH above its pl, the electrostatic repulsions between the negative charges of the protein and polar groups of AOT act as a suppression in the extraction. A t high KC1 concentration, a lower pH value was required for the extraction because of weak electrostatic attractions. However, further decrease in the pH caused a reduction of the extraction. This may be due to the formation of aggregates from lysozyme and AOT molecules at the oilwater interface. Although lysozyme is not denatured by acids, it is considered that too strong attractions between the protein and AOT molecules are liable to form insoluble aggregates. Effect of Water Content on the Solubilization of Proteins. Figure 5 shows the effects of the salt and surfactant concentrations on the solubilization of water in AOT/isooctane solutions with and without proteins. The
Ind. Eng. Chem. Res., Vol. 30, No. 11, 1991 2473 10
10 , I
A 10'
.10
P
E
P
Y
$10
1oO
10"
CKCll
Ckmol/m'l
10
1fl
io-'
IO-^
loo
'.01 C,
10'
1 oz
Ckglm'l
Figure 7. Extraction equilibria of lysozyme as a plot of the protein content of the micellar solution, Co, against that of the aqueous solution, Cw. The aqueous feeds were with 0.1-25 g/L lysozyme a t pH 6.6-7.0.
-:calc. line 1 oo
l(r'
[KCII
It.)
calclin
Ckmol/m33
Figure 5. Effect of salt concentration on the water content of AOT/isooctane solution (a) in the absence of proteins and (b) in the presence of proteins. 1,lysozyme; 2, a-chymotrypsin; 3, ribonuclease A. calc line
-:
m I Y
10'
L -' 1u' Id
P
lU1 IO
lo-z
loo
CHz03 tkmd/m'I ~
2
4
6
8
1012
pH c-3
Figure 6. Effect of solution pH on the water content of the organic phase containing the proteins. K e y are the same as thoee in Figure 5b.
water content decreased with an increase in [KCl], slightly depending on [AOT]. Such behavior is responsible for the change in the micelle size, as illustrated in Figure 3a. I t should be noted that there is no significant difference in the water contents of the reversed micellar solutions with and without the proteins. Furthermore, Figure 6 shows the effect of pH value of the aqueous solution to be solubilized on the water content, indicating that Wo is independent of the pH. Consequently the water solubilization data are correlated by
Wo = 9.8[AOT]o.'2[KC1]-'".34 (4) as illustrated with the solid lines in Figures 5 and 6. Figure 7 shows the equilibrium relation in lysozyme contents between the aqueous and organic phases, Cw and Co, where the initial protein contents of the aqueous feed ranged from 0.1 to 25 g/L. With increasing initial content, the organic phase in equilibrium with the aqueous phase increased in the protein content, and then went through a maximum value. At higher [KCl], however, the distribution ratio of lysozyme decreased with an increase in Cw
Figure 8. Relationship between lysozyme content and water content of the reversed micellar solution. Keys are the same aa those in Figure 7. Dashed lines represent the water content calculated from eq 4.
even in the region below the maximal content. In the case of larger Cw,it was liable to form aggregates consisting of lysozyme and AOT molecules at the oil-water interface. This leads to lowering of [AOT], and hence the value of Wo decreases. Here, we consider how water content of the reversed micellar solution affects the protein extraction. Figure 8 shows a plot of CO vs [H20] from the results illustrated in Figure 7, where the dashed lines represent the calculated values from eq 4. With increasing value of Cw in Figure 7, the organic phase increased in Co up to a limiting value on the dashed line for each constant [H20] as shown in Figure 8. However, further increase in Cw permitted it to behave two different ways in response to the salt concentration, given by the solid and dash-dotted lines. In the case of higher [KCl] (lines 1-4,6, and 7), after reaching each limiting content, the value of COdecreased with [H20] on the solid line in Figure 8, whereby a decrease in [H20] may be caused from the lowering of [AOT] due to the formation of the aggregates as mentioned above. For the aqueous feeds with low [KCl] (lines 5 and 8 for 0.1 M), the value of Co increased and went through a maximum on the dash-dotted line in Figure 8 with variation of [H20]; the maximal content was about twice as high as the lim-
2474 Ind. Eng. Chem. Res., Vol. 30, No. 11, 1991 r 1 1
I
- 1 1 1 1 1
1OD
/
i
10'
N Cl/sl
Figure 9. Effect of stirring speed on individual mass-transfer coefficient in the absence of AOT. kw,I is for iodine transfer from the aqueous to isooctane phase; kOAeis !or acetic acid transfer from the organic to aqueous phase.
iting value. This implies that a reverse micelle formed under the present experimental conditions can contain two molecules of lysozyme from having the diameter of about 10 nm (see Figure 3a). Rates of Extraction and Stripping of Lysozyme. In the extraction of proteins with reversed micellar solution, diffusion resistances through both aqueous and organic boundary films are crucial because of the comparatively large size of protein molecules. In addition, the solubilization kinetics at the oil-water interface might become a serious problem. Thus it is necessary to know the individual mass-transfer coefficient in the transfer cell. In the present study, the aqueous film mass-transfer coefficient, kw, for lysozyme was evaluated on the basis of kws, obtained for the transfer of iodine from the aqueous to isooctane phase containing AOT. We determined the rate of I2 extraction by measuring the absorbance change in the organic phase at 520 nm. The organic transfer coefficient, ko, for the reversed micelle with lysozyme was evaluated from the value of kObc for the transfer of acetic acid from the isooctane solution with and without AOT to aqueous phase. In this transfer experiment, the concentration of acetic acid in the organic phase was determined by titration with a sodium hydroxide solution. The detailed procedure for determining kw,I and ko,Ac is available elsewhere (Takahashi et al., 1988). The values of kw and kok thus obtained in the absence of AOT are plottetin Figure 9 against the stirring speed, N , wherein the solid lines represent the following equations:
According to many previous studies (for example, Mayers, 1961; Komasawa et al., 1980; Asai et al., 1983; Takahashi and Takeuchi, 1984; Imai and Furusaki, 1987), mass-transfer coefficients in stirred transfer cells are in direct proportion to the 0.5-0.8 power of agitation speed; thus, the present results agree with the previous correlations. Table I shows the effect of AOT concentration on both the values of kw and kobc at the stirring speed of 3.8 s?, indicating that the individual coefficient slightly decreases with an increase in (AOT]. Such reduction of the masstransfer coefficient in the presence of AOT as a surfactant may be attributed to two effects: one is an interfacial resistance as a diffusion barrier due to the adsorption of AOT molecules at the oil-water interface and the other is a suppression of the renewal of the fluid element at the interface or of convective actions through the fluid boundary film. However, it is very difficult to discriminate between these effects. Thus, assuming that the AOT
Table I. Effect of AOT Concentration on Individual Mass-Transfer Coefficients, kw,,* and k o ~Obtained ~ , at the Stirring Speed of 3.8 s-' [AOT], kmol/m3 kwJl, m/s k o ~lob ~ , m/s 1.29 2.71 0 1.26 2.62 0.01 1.10 2.43 0.05 2.24 0.10 0.895 "Initial concentrations: CwJz = 2.8 X lo-' M for aqueous feed and Co, = 0.12 M for organic feed. Distribution Coefficients of iodine and acetic acid between isooctane and water: m12 = 46.2 and mAe = 0.0108,respectively. Table 11. Effect of Solution pH and Initial Content of Lysozyme on Rates of Forward and Back Extraction at the Stirring Speed of 3.8 s-' ([AOT] = 0.05 M) (a) Forward Extraction Rate, Jp DO-' ka/(m2 s)l; lKCll = 0.25 M CW,ir k / m 3 DH 0.18 0.35 0.68 6.08 14.1 4.7 3.59 6.9 3.80 8.26 14.8 14.2 9.1 3.15 7.50 10.0 0.163 1.41 5.87 (b) Back Extraction Rate, J B [ lo-' kg/(m* e)]; [KCl] = 0.84 M Cn;.k d m 3 PH 0.24 0.46 0.85 11.3 2.10 4.05 8.41 5.59 13.1 11.8 2.50 12.2 2.16 5.55 14.3
concentration dependence of the mass-transfer coefficient has no relation to the agitation speed, we can correct eqs 5.1 and 5.2 with the extent of the reduction, obtained from the results in Table I. The experimental results for the extraction and stripping of lysozyme are given in Table 11. The forward extraction rate was independent of the solution pH in the range of 4-9; however, the rate sharply decreased at pH above 10. The stripping rate in the back extraction increased with pH. Here we evaluated the individual mass-transfer coefficient for lysozyme, kw and ko, from eq 5 with an assumption that the mass-transfer coefficient is proportional to the 2 / 3 power of the diffusion coefficient. This evaluation is explained in detail in the Appendix, together with the estimation of diffusion coefficients. In the micellar extraction system the total resistance in the protein transfer could be expressed as the s u m of two resistances through the aqueous and organic boundary films. Thus, if the resistance in the solubilization is ignored, the overall transfer coefficients in the lysozyme extraction can be given by the following equations: 1/Kw = l / k w + l / ( m k o ) (6.1) l/Ko = m / k w l / k o (6.2)
+
The extraction and stripping rates, JFand JB,are expressed in terms of the respective overall coefficients as J F = Kw(CW- C d m ) (7.1) J B = Ko(Co - mCw) (7.2) Now, considering the initial conditions of the present experiments, Co = 0 in eq 7.1 for the extraction runs and Cw = 0 in eq 7.2 for the stripping; thus we can obtain the values of Kw and KO based on each initial rate. Figures 10 and 11 show the comparisons between the experimental results and the calculated values for Kw and KO, respectively. For the forward extraction, a close agreement is found between (Kw)d and ( K w )=~ J~F / C W ~ in the pH range of 4-9. This suggests that the solubili-
Ind. Eng. Chem. Res., Vol. 30, No. 11, 1991 2475 io+
iL 107
10s
10'6
w-' (KwL
tmkl
Figure 10. Comparison of overall aqueous phase transfer coefficients for the forward extraction. (Kw)d is the calculated value from eq 6.1, and (Kw)obthe observed value based on the initial rate. 10"
following results were obtained. 1. The distribution equilibrium of the protein was explained in terms of an electrostatic interaction and a size exclusion effect. These contributions depend on the concentration of KCl and pH in the aqueous solution. 2. The water content of the micellar solution was correlated with the ionic strength and AOT concentration, irrespective of the presence of proteins. The maximum concentration of proteins solubilized in the micellar solution was dependent upon only the water content. 3. The forward extraction rate of lysozyme in the reversed micellar solution at pH values below its p l was controlled only by the diffusion through the boundary films. In the stripping for the back transfer of the protein from the micellar solution, there was a dominant resistance to leave it at the oil-water interface. Acknowledgment
This work was supported by a Grant-in-Aid for Scientific Research (No. 01550730) from the Ministry of Education, Science and Culture of Japan. We thank Dr. Toyoko Imae, Faculty of Science of Nagoya University, for the use of the dynamic light scattering photometer. Appendix. Evaluation of Individual Mass-Transfer Coefficient With an assumption that the mass-transfer coefficient is in direct proportion to the 2/3 power of the diffusion coefficient, D, the aqueous film mass-transfer coefficient for lysozyme, kw, was evaluated from the following relation with kW,12for iodine
n
VI
I
E
Y
3 10-6 h 0
kw/kw,I, = (Dp/D1J2/' = (1.27 X 10-1°/1.25
10-5
lmlsl
X
10-9)2/3= 0.218 (A.l)
where Dp of lysozyme was corrected from the value a t 20 "C, 1.11 X 1@l0m2/s (Imahori and Yamakawa, 19841, using the Stokes-Einstein equation (eq A.3), and DI, of iodine is from Reddy and Doraiswamy (1967). The diffusion coefficient of acetic acid in isooctane can be predicted from the Wilke-Chang equation (1955)
Figure 11. Comparison of overall organic phase transfer coefficients for the back extraction. (KO)&is the calculated value from eq 6.2, and ( K o )the ~ ~observed one based on the initial rate.
zation resistance of lysozyme at the interface is of no significancecompared with the diffusion resistance. Above pH 10, however, the value of (Kw)obwas smaller than the calculated value from eq 6.1; therefore, the solubilization rate of lysozyme is slow compared with the diffusion through the boundary films. In contrast to Figure 10 for the forward extraction, Figure 11 implies that the backward extraction is controlled by an interfacial process: there is a dominant resistance in the process that the lysozyme leaves the micellar phase to the aqueous stripping solution. From the above discussion, a conclusion can be drawn that in the extraction process of lysozyme using reverse micelles the stripping from the extract is of significance. The results obtained in the present study may be useful for elucidating the solubilization mechanism of proteins in reversed micellar solutions. Presently further research is being undertaken in our laboratory by using a liquid membrane to quantify the solubilization kinetics. Conclusion The extraction of lysozyme with reversed micellar solution was studied in the AOT/isooctane system, and the
where 71 is the viscosity, Vl is the partial molar volume of solute at its boiling point, M is the molecular weight, d) is the association parameter, and Tis the temperature; the subscripts 1 and 2 refer to the solute and solvent, respectively. Equation A.2 gives a value of 2.52 X lo* m2/s as DAefor acetic acid, which is dimerized in isooctane (Reid et al., 1987). For the reverse micelle entrapped protein in an apolar solvent, we assumed that the micelle has the same size as that without protein; the diffusion coefficient can be then estimated from the Stokes-Einstein equation: 012
= k T/(3Td112)
(A.3)
where k is the Boltzmann constant and dl is the effective diameter of the micelle. By using the micelle size of 7.4 nm in isooctane, eq A.3 gives a value of 1.16 X m2/s as Dpmfor the reversed micelle with lysozyme under experimental conditions of the back extraction. The organic-phase mass-transfer coefficient for the reverse micelle, ko, can be related with ko,Acas ko/koAAc= (DP,/DA,)~/~ =
(1.16 X 10-1°/2.52
X
10-9)2/3= 0.128 (A.4)
Ind. Eng. Chem. Res. 1991,30, 2476-2482
2476
Combining eqs A.l and A.4 with eqs 5.1 and 5.2, respectively, and further taking into account the effect of the presence of AOT, we obtained the individual masstransfer coefficient for the extraction of lysozyme in the reversed micellar solution containing AOT of 0.05 M as kw = 8.70 X 10-7(0.853)No.83 (A.5) ko = 1.33 X 10-s(0.893)No'65
(A.6)
where the two multipliers in the parentheses, 0.853 and 0.893, represent the extent of the reduction of kw and ko, respectively, due to the presence of AOT (see Table I). Registry No. AOT, 577-11-7; isooctane, 540-84-1; lysozyme, 9001-63-2.
Literature Cited Armstrong, D. W.; Li, W. Highly Selective Protein Separations with Reversed Micellar Liquid Membranes. Anal. Chem. 1988, 60, 86-88. Asai, S.; Hatanaka, J.; Uekawa, Y. Liquid-Liquid Mass Transfer in an Agitated Vessel with a Flat Interface. J . Chem. Eng. Jpn. 1983, 16, 463-469. Caselli, M.; Maestro, M.; Morea, G. A Simplified Model for Protein Inclusion in Reverse Micelles SANS Measurements as a Control Test. Biotechnol. Prog. 1988, 4, 102-106. Dahuron, L.; Cussler, E. L. Protein Extractions with Hollow Fibers. AIChE J . 1988,34, 130-136. Dekker, M.; Van't Riet, K.; Weijers, S. R.; Baltusaen, J. W. A,; Laane, C.; Bijsterbosch, B. H. Enzyme Recovery by Liquid-Liquid Extraction Using Reversed Micelles. Chem. Eng. J . 1986,33, B2733. Dekker, M.; Van't Riet, K.; Bijsterbosch, B. H.; Wolbert, R. B. G.; Hilhorst, R. Modeling and Optimization of the Reversed Micellar Extraction of a-Amylase. AIChE J . 1989, 35, 321-324. Goklen, K. E.; Hatton, T. A. Liquid-Liquid Extraction of Low Molecular-Weight Proteins by Selective Solubilization in Reversed Micelles. Sep. Sci. Technol. 1987, 22, 831-841. Imahori, K.; Yamakawa, T. Seikagaku Jiten (Encyclopedia of Biochemistry);Tokyo Kagaku Dojin: Tokyo, 1984; p 1333. Imai, M.; Furusaki, S. Extraction Rate of Lanthanum by D2EHPA. Kagaku Kogaku Ronbunshu 1987, 13, 355-362. Komasawa, I.; Otake, T.; Yamada, A. Diffusional Resistance in Extraction Rate of Copper with Hydroxyoxime Extractant. J . Chem. Eng. Jpn. 1980, 13, 209-213.
Kotlarchyk, M.; Chen, S. H.;Huang, J. S. Temperature Dependence of Size and Polydispersity in a Three-Component Microemuleion by Small-Angle Neutron Scattering. J. Phys. Chem. 1982, 86, 3273-3276. Kuboi, R.; Hashimoto, K.; Komasawa, I. Separation of Proteins with Reverse Micellar Liquid Membranes. Kagaku Kogaku Ronbunshu 1990, 16, 335-342. Levashov. A. V.: Khmelnitskv. Y. L.: Klvachko. N. L.: Chernvak. V. Y.; Makinek; K. Enzymes Entrapped into Reversed Micelles in Organic Solvents: Sedimentation Analysis of the Protein-Aerosol OT-H20-Octane System. J . Colloid Interface Sci. 1982, 88, 444-457. Luisi, P. L. Enzymes Hosted in Reverse Micelles in Hydrocarbon Solution. Angew. Chem., Int. Ed. Engl. 1985,24, 439-450. Luisi, P. L.; Bonner, F. J.; Pellegrini, A.; Wiget, P.; Wolf, R. Micellar Solubilization of Proteins in Aprotic Solvents and Their Spectroscopic Characterisation. Helv. Chim. Acta 1979,62,740-753. Mayers, G. R. A. The Correlation of Individual Film Coefficient of Mass Transfer in a Stirred Cell. Chem. Eng. Sci. 1961,16,69-75. Reddy, K. A,; Doraiswamy, L. K. Estimating Liquid Diffusivity. Ind. Eng. Chem. Fundam. 1967,6, 77-79. Reid, R. C.; Prausnitz, J. M.; Poling, B. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1987; p 598. Takagi, T.; Yanagi, S. Bunshiryo Sokutei (Measurement of Molecular Weight). Tanpakushitsu no Kagaku: I (Chemistry of Proteins: 4; Yamakawa, T., Imahori, K., Eds.; Tokyo Kagaku Dojin: Tokyo, 1976. Takahashi, K.; Takeuchi, H. Rates of Copper Extraction by LIX65N. Kagaku Kogaku Ronbunshu 1984,10,409-414. Takahashi, K.; Kato, M.; Hirayama, K.; Takeuchi, H. Simultaneous Determination of Water and Oil Phase Mass Transfer Coefficients in Liquid-Liquid Extraction. Kagaku Kogaku Ronbunshu 1985, 11,110-112. Wilke, C. R.; Chang, P. Correlation of Diffusion Coefficients in Dilute Solution. AIChE J . 1955, 1, 264-270. Wong, M.; Thomas, J. K.; Nowak, T. Structure and State of H 2 0 in Reversed Micelles, 3. J . Am. Chem. SOC.1977, 99, 4730-4736. Zampieri, G. G.; Jackle, H.; Luisi, P. L. Determination of the Structural Parameters of Reverse Micelles after Uptake of Proteins. J . Phys. Chem. 1986, 90,1849-1853. Zulauf, M.; Eicke, H. F. Inverted Micelles and Microemulsions in the Ternary System H20/Aerosol-OT/Isooctane as Studied by P h e ton Correlation Spectroscopy. J . Phys. Chem. 1979,83,480-486. Received for review July 5, 1990 Revised manuscript received March 26, 1991 Accepted June 17,1991
GENERALRESEARCH Solubility of Cholesterol in Supercritical Carbon Dioxide S.L. J i m m y Yun,K. Keat Liong, Gurdev S.Gurdial, a n d Neil R.Foster* School of Chemical Engineering and Industrial Chemistry, University of New South Wales, P.O.Box I, K e nsingt on 2033, A us t ra lia
The solubility of cholesterol in supercritical carbon dioxide was measured in the temperature range 40-60 "C and at pressures between 100 and 250 bar. The experimentally determined solubility data was correlated using two density-based correlations and a semiempirical correlation based on both the van der Waals equation of state and regular solution theory. Introduction The advantages of utilizing solvents above their critical points to perform extractions have been well documented (Williams, 1981; Paulaitis et al., 1982; Eckert et al., 1986). These advantages include the ability to vary the solvent
density through changes in the system pressure and/or temperature. This means that small changes in extraction conditions are often all that is required to achieve complex separations. Carbon dioxide is a promising solvent for supercritical
08~8-5885/91/2630-2476$02.50/0 0 1991 American Chemical Society
