Ind. Eng. Chem. Res. 1989, 28, 1020-1024
1020
quired. It is possible that cosolvents other than water and ethanol may be used provided they do not deactivate the exchange resin. There are two possible drawbacks to the use of exchange resins. Firstly, there may be a tendency for the resin to deactivate in the presence of the solvent power of supercritical fluids and cosolvents. However, this was not observed in the present work. Secondly, the resin could entrap other compounds from the fluid. This latter problem can be overcome by periodically flushing the resin bed with a neutral solvent or by loosely packing the resin. A logical extension of this work is in the application of anion-exchange resins to the removal of acidic components, such as fatty acids, rosin acids, and various acidic drugs, from supercritical fluids.
V. Conclusions
A novel supercritical fluid technique has been developed to isolate monocrotaline from a complex mixture. This two-stage process employs a cation-exchange resin in series with a supercritical extraction step and has been shown to yield almost pure monocrotaline. A further advantage of the exchange resin is that no pressure changes are employed in the supercritical extraction process. A major economic disadvantage of supercritical fluid extraction is therefore eliminated. Similar processes can also be de-
signed for other plant or biological materials. Literature Cited Dobbs, J . M.; Wong, J. M.; Lahiere, R. J.; Johnston, K. P. Modification of Supercritical Fluid Phase Behavior using Polar CoSolvents. Ind. Eng. Chem. Res. 1987, 26, 56-62. Gelbaum, L. T.; Gordon, M. M.; Miles, M.; Zalkow, L. H. Semisynthetic Pyrrolizidine Alkaloid Antitumor Agents. J . Org. Chem. 1982, 47, 2501-2504. Mattocks, A. R. Chemistry and Toxicology of Pyrrolizidine Alkaloids; Academic Press: Orlando, FL, 1986. Molyneaux, R. J.; Johnson, A. E.; Roitman, J . N.; Benson, M. E. Chemistry of Toxic Range Plants. Determination of Pyrrolizidine Alkaloid Content and Composition in Senecio Species by Nuclear Magnetic Resonance Spectroscopy. J . Agric. Food Chem. 1979, 27(3), 494-499. Schaeffer, S. T. Extraction and Isolation of Monocrotaline from Crotalaria spectabilis using Supercritical Fluids. Ph.D. Thesis, Georgia Institute of Technology, Atlanta, 1988. Schaeffer, S. T.; Zalkow, L. H.; Teja, A. S.Extraction of Monocrotaline from Crotalaria spectabilis using Supercritical Carbon Dioxide and Carbon Dioxide-Ethanol Mixtures. Biotechnol. Bioeng. 1988a, in press. Schaeffer. S. T.: Zalkow. L. H.: Teia. A. S. Suoercritical Extraction of Monocrotaline from Croia1a;iu spectabilis in the Cross-Over Region. AIChE J . 1988b, 34, 1740-1’742. Zosel, K. Process for the Decaffeination of Coffee. US Patent 4,260,639, 1981. Received for reuieu! November 8, 1988 Accepted April 4, 1989
Styrene/Ethylbenzene Separation Using Facilitated Transport through Perfluorosulfonate Ionomer Membranes Carl A. Koval,* Terry Spontarelli, and Richard D. Noblet Department of Chemistry a n d Biochemistry, Campus Box 215, University of Colorado, Boulder, Colorado 80309
Steady-state fluxes of styrene and ethylbenzene through perfluorosulfonate ionomer membranes exchanged with sodium and silver ions are reported. Due to the reversible formation of complexes with silver, the fluxes of styrene and ethylbenzene are enhanced when Na+ is replaced with Ag+. Since styrene forms a more stable complex, its flux is enhanced significantly more than that of ethylbenzene. This effect is investigated for different membrane thicknesses, membrane solvents, and permeate feed concentrations. Facilitation factors (Ag+ membrane flux/Na+ membrane flux) range from 50 to 590 for styrene and from 9 to 84 for ethylbenzene. Separation factors (styrene permeability/ethylbenzene permeability) are about 2 for Na+-exchanged membranes and range from 8 to 36 for Ag+-exchanged membranes. The data are analyzed qualitatively utilizing factorial analysis and quantitatively by comparison to the predictions of a mathematical model. Facilitated transport through liquid membranes, which relies on the reversible formation of a carrier permeate complex, is a potentially selective and efficient separation technique. The selectivity of a facilitated transport membrane (FTM) separation is mainly dependent on the selectivity of the carrier-permeate complexation reaction and the relative solubilities of the permeates in the membrane phase. The properties of the FTM support material can have large effects on the rate, selectivity, and stability of the separation. Membranes derived from ion-exchange materials have recently received considerable attention with respect to their structural, physical, and chemical properties (Elliott and Redepenning, 1984; Quezado et al., 1984; Szentirmay et al., 1986; Herrera and Yeager, 1987). The use of ionomer materials as a FTM support material *Address correspondence to this author. Also associated with the Department of Chemical Engineering, Campus Box 424.
0888-5885/89/2628-1020$01.50/0
has been reported for the separation of gaseous mixtures such as C02/CH4 and ethylene/ethane (Way et al., 1987; LeBlanc et al., 1980). Ionomer membranes containing solvents display greater physical strength than liquid membranes immobilized on macroporous supports. They are more stable in the sense that the ionic carrier cannot be lost from the membrane if exchangeable ions are not present in the contacting phases. Also, since carrier solubility is dictated by ion-exchange site density and not by physical solubility limits, higher carrier loadings are possible. Fluxes of liquid-phase olefins such as 1-hexene and 1,5-hexadiene can be enhanced by a factor of over 400 when Na+ ions are replaced by olefin-complexing Ag+ ions in water-swollen Nafion membranes (Koval and Spontarelli, 1988). The reversible complexation of olefins by aqueous Ag+ is a well-known reaction (Beverwijk et al., 1970). The stability of the Ag+-olefin complex is dependent on electronic factors and on steric hindrance around the olefin 0 1989 American Chemical Society
Ind. Eng. Chem. Res., Vol. 28, No. 7, 1989 1021 Table I. High and Low Levels for a Four-Variable Factorial Experiment variable high low L Nafion 117 (200 pm) NE 111 (30 pm) S 50% ethanol H2O Na+ F Ag+ 0.1 mol L-' C 1.0 mol L-I
double bond. In principle, this effect allows the FTM separation of olefins that bind strongly to Ag+ from sterically hindered olefins and saturated hydrocarbons. p;9+ AQ'
carrier
+
R2C=CR2
permeate
e
I
R2CACRp
complex
Olefin separations by transition-metal-complexing agents have recently received considerable attention. This work has dealt mainly with the separation of C2-C5 gaseousphase olefins. Ethylene/ethane separations have been reported using aqueous silver nitrate supported by cellulose acetate membranes (Hughes et al., 1986; Teramoto et al., 1986) and sulfonated pol: (phenylene oxide) cation-exchange membranes (LeBlanc et al., 1980). Kawakami et al. (1987) have studied the permeation of ethylene and propylene through glass microfiber filters impregnated with poly(ethy1ene glycol) solutions of various transition metals. Solutions of cuprous diketonate have been used to separate Cz-C5 linear a-olefins from saturated hydrocarbons and sterically hindered olefin isomers (Ho et al., 1988). Herein we report the separation of styrene from ethylbenzene utilizing ionomer FTM's under a variety of experimental conditions. This separation is of commercial interest because most of the styrene used in the production of polystyrene is prepared by catalytic dehydrogenation of ethylbenzene. The reaction is endothermic and thereby equilibrium limited, even at elevated temperatures. Fluxes for styrene and ethylbenzene have been measured using different cations, membrane thicknesses, feed stream permeate concentrations, and membrane solvents. Due to the large number of measurements involved in this study, it is difficult to envision how all of the variables interact to affect overall flux and selectivity. We have used factorial analysis to gain a better understanding of the variable interactions and effects on the separation (Wilson, 1952). In a Y-type factorial experiment, each of the n variables is studied at two levels, high and low. In order to observe all of the possible high and low combinations, a four-variable experiment requires 16 (Z4)measurements. Table I lists the two levels of each of the variables we have studied for this system. We have also attempted to compare the results to predictions of mathematical models.
Experimental Method Materials. All chemicals were used as received. Styrene and ethylbenzene (99+ %) were obtained from Aldrich. The organic solvent used was 2,2,4-trimethylpentane (Aldrich, 99+%). Silver nitrate (EM Science) and sodium hydroxide (Baker) were reagent grade. The Nafion membranes used were of two types. Nafion 117 (hydrated thickness 200 pm) was obtained from Aldrich and an experimental Nafion material, NE 111 (30 pm thick), was provided by Dr. Louis L. Burton (Experimental Station, Central Research and Development, E. I. du Pont de Nemours & Co., Wilmington, DE). The membranes as received in the H+ form were converted to the Na+ form by gentle stirring in an aqueous solution of sodium hydroxide (1mol L-') for 24 h. Conversion to the Ag+ form
was accomplished by a similar treatment with a solution of silver nitrate. Flux Measurement. Flux measurements were made by using a two-compartment cell arranged vertically and separated by the membrane that was held in place with O-rings and a clamp. Both cell compartments were mechanically stirred and contained an organic solvent, 2,2,4-trimethylpentane (isooctane),that had been saturated with the membrane solvent (H20 or 50% ethanol). Isooctane was chosen as the organic solvent due to its low solubility in water and its noninterference with the GC analysis described below. The surface area of the membrane exposed to the solution was 1.8 cm2. The cell was assembled by filling the lower compartment with an equimolar solution of permeates until no air remained (20.8 cm3), clamping the membrane between the two compartments, and pipetting 20.00 cm3 of solvent into the upper compartment. Due to the low compressibility of liquids, it was assumed that the absence of air in the lower compartment would minimize the pressure gradient across the membrane. After the cell was assembled, aliquots (1pL) of the solution were removed from the upper compartment periodically with a syringe and analyzed for the permeates by gas chromatography. The gas chromatograph was a Hewlett-Packard 5890 with flame ionization detection, the column was a 25-m capillary (OV-1 stationary phase), and the injector and detector temperatures were both 250 "C. The styrene/ethylbenzene samples were separated isothermally at an oven temperature of 60 "C. Concentrations were determined by an internal standard (m-xylene) calibration. Determination of Permeate Concentrations in Nafion Membranes. Since both styrene and ethylbenzene absorb ultraviolet light, it is possible to measure their solubility in Nafion membranes spectroscopically. Due to the fact that the Nafion membrane environment is highly ionic and UV spectra are somewhat dependent on solvent polarity, calibration curves for both permeates dissolved in a polar solvent were needed. Ethanol (95%) was chosen as solvent because both styrene and ethylbenzene are soluble in it, allowing the preparation of a series of standards whose concentrations were accurately known. The ultraviolet spectra were measured by using a Hewlett-Packard 8451A diode array spectrophotometer. Absorbance maxima were found at 246 and 262 nm for styrene and ethylbenzene, respectively. Plots of absorbance versus concentration gave a molar absorptivity of 1.4 X lo4 L mol-' cm-l for styrene, while the ethylbenzene absorptivity was only 210 L mol-l cm-'. Spectroscopic measurements of solvated membranes showed them to be practically UV transparent in the Na+ form, but in the Ag+ form, they absorbed strongly below 300 nm. For this reason, it was not possible to measure permeate solubilities in the Ag+-exchanged membranes. The hydrated Nafion 117 and NE 111 Na+ form membranes were placed in 0.1 mol L-l solutions of the permeates in water-saturated isooctane for 24 h. The membranes were then washed with isooctane to remove permeate from the surface, and UV spectra were measured. Assuming a path length of 0.020 cm for Nafion 117 and 0.0030 cm for NE 111, the conand centration of styrene was determined to be 6 x 8X mol L-l for the two membranes. These calculated concentrations also assume that the molar absorptivity of styrene is the same in the membrane as in 95% ethanol. The ethylbenzene concentrations could not be determined due to its low molar absorptivity.
Results Figure 1 contains typical data for the concentration of
1022 Ind. Eng. Chem. Res., Vol. 28, No. 7 , 1989 Table 11. Fluxes of Styrene and Ethylbenzene through Na+- and Ag+-Exchanged Nafion Membranes exptl styrene fluxb ethylbenzene fluxb conditions" Ag+ Nat Na+ Ag+ Nafion 117, 1.1 x 10-11 1.1 x 10-9 3.3 x 10-12 6.0 x 10-11 HZO, 1.0 6.1 X Nafion 117, 1.6 X 3.2 X 4.4 x 10-l2 HzO, 0.1 Nafion 117, 2.1 X 9.4 X 1.2 X 1.1 X lo4 50% ethanol, 1.0 Nafion 117, 4.3 X lo-" 2.2 X 2.4 X lo-" 2.2 X 50% ethanol, 0.1 NE 111, HzO, 6.4 X 3.8 X 2.5 X lo-'* 2.1 X
Time, sec X I O 3 Figure 1. Facilitated transport of styrene and ethylbenzene across Nafion 117 water-swollen membranes. Ordinate is the concentration of permeate determined in the upper compartment of the transport cell. Open and filled triangles: ethylbenzene through Na+- and Ag+-exchanged membranes, respectively. Open and filled circles: styrene through Na+- and Ag+-exchanged membranes, respectively. Solid lines represent linear regression. Feed concentrations are 0.1 mol L-I.
styrene and ethylbenzene in the upper compartment of the cell as a function of time. The membrane used in the two transport experiments depicted in the figure was waterswollen Nafion 117 exchanged with either Na+ or Ag+ ions. The lower compartment of the cell was 0.1 mol L-' in the two permeates. Several features are readily apparent. The concentration of permeates in the upper compartment was never zero immediately after the cell was assembled ( t = 0). This was due to slight contamination of the membrane surfaces and upper cell compartment with the feed solution during assembly. Normally, corrections are made for this error, but since the data are more easily viewed with the curves separated, it was left uncorrected. For the Na+exchanged membrane, the concentrations remain low for many hours, indicating that permeation of both styrene and ethylbenzene is extremely slow. Replacement of the Na+ ions by Ag+ ions has only a small effect on the rate of transport of ethylbenzene. In contrast, after about 2 h, the concentration of styrene in the upstream compartment increases dramatically, indicating the Ag+ ion enhances the flux of this permeate through the membrane. The 2-h transient period, which occurs for both Na+ and Ag+ membranes, is the time required to reach a steadystate flux across the membrane and depends on both membrane thickness and mobility of the permeating species. Data obtained using NE 111 membranes were similar to Figure 1 except that the transient period is much shorter due to the difference in thickness. Linear regions of the concentration versus time plots are indicative of a constant flux of the permeates through the membranes that can be calculated from the slopes. In the case of styrene through Ag+-exchanged membranes, only the data obtained well after the transient period were used. In the cases where a transient period was not obvious, all of the data were used even though some transient period undoubtedly existed. This procedure may cause a slight underestimation of the fluxes. In all of the conditions investigated, the fluxes through the Na+-exchanged membranes contain more random error than the fluxes obtained through Ag+-exchanged membranes. Table I1 contains calculated fluxes for all of the possible combinations of experimental conditions listed in Table I. Fluxes for styrene range from 6.1 X to 4.3 x mol cm-* s-l, while those for ethylbenzene range from 3.2
1.0 NE 111, H,O, 0.1 NE 111, 50% ethanol, 1.0 NE 111, 50% ethanol, 0.1
2.5 x
1.9 x lo-"
3.8 x
6.3 x
1.4 X lo-''
4.3
X
lo-'
7.1 X lo-" 5.4
2.1 X lo-"
7.4
X
lo-'
8.7
X lo-''
X
5.6 X
Membrane material, membrane solvent, permeate feed concentration in mol L-I. Units of mol cm+ s-l.
Table 111. Facilitation and Separation Factors for Styrene and Ethvlbenzene facilitation factorb separation factor' ethylexotl conditions" styrene benzene Nat Ag+ Nafion 117, HzO, 1.0 100 18 3.3 18 1.9 36 Nafion 117, HzO,0.1 260 14 1.8 8.5 Nafion 117, 50% ethanol, 1.0 45 9.2 Nafion 117, 50% ethanol, 0.1 1.8 10 51 9.2 NE 111, H20, 1.0 2.6 18 590 84 NE 111, HzO, 0.1 170 7.6 1.5 33 NE 111, 50% ethanol, 1.0 2.0 8.0 310 76 NE 111, 50% ethanol, 0.1 2.4 13 350 64
'Membrane material, membrane solvent, permeate feed concentration in mol L-l. bRatio of the permeate flux for the Ag+- to the Na+-exchanged membrane. "Ratio of the styrene to the ethylbenzene permeabilities. x to 5.4 x In all cases, the flux of styrene exceeded that of ethylbenzene. Discussion Separation Factors. One purpose of these experiments is to determine the conditions that give the highest styrene flux without sacrificing selectivity. Table I11 shows the separation factor of styrene over ethylbenzene for each experiment. For Na+-exchanged membranes, the separation factors were about 2, which reflects a slightly greater solubility of styrene in the membrane solvents. Separation factors ranging from 10 to 36 are achieved with Ag+ membranes. In general, lower permeate feed concentrations result in better separations since carrier facilitation, rather than diffusive flux, is the predominant transport mechanism at low feed concentration. Comparison of Tables I1 and 111 shows that higher separation factors are obtained with water as the membrane solvent, but the overall flux is greater for the 50% ethanol membranes. Although ethanol is slightly more viscous than water and membranes solvated with 50% ethanol are 20% thicker, the higher solubilities of styrene and ethylbenzene in ethanol result in higher fluxes. Since the solubilities in pure water membranes are much lower than the carrier concentration, it was hoped that a 50% ethanol/ water membrane solvent would increase the fluxes without decreasing the separation factor. Fluxes did increase by over a factor of 10; however, the separation factor
Ind. Eng. Chem. Res., Vol. 28, No. 7 , 1989 1023 '"
I
-1
'O;
1
- - 10
i"
1
m $ & a s y o 2 ~ A s q L 0
Factor
b0
Figure 2. Primary effects and interactions of four variables on the membrane separation factor for styrene over ethylbenzene. Variables: membrane thickness, L; feed concentration of permeates, C; solubility of permeates in the membrane phase, S; facilitated transport of permeates, F.
decreased by a factor of 2, which would indicate that the permeate solubility was increased to the point of carrier saturation. Since only 50% ethanol and pure water were used as solvents, it is possible that a lower ethanol percentage could increase the permeate flux without saturating the carrier. Factorial Analysis. In order to better understand how the selectivity of the separation is effected by the four variables under study, the data were analyzed by a factorial method (Wilson, 1952). The 16 separation factors listed in Table I11 correspond to the 16 possible high and low combinations of the four variables listed in Table I. The primary effect of each variable on the response (separation factor) is calculated from 2"
EwviRi i=l '- -
effect, = 2n/2 where n is the total number of variables studied, wVjis the weighting factor of the variable of interest for experiment i (+1for high; -1 for low), and Riis the measured response for experiment i. First-, second-, and third-order interactions of the variables are calculated in a similar manner. The results of this analysis are shown in Figure 2, which is a plot of the effects and interactions of the four variables on the separation factor. In general, the factors to the right side of the plot cause an increase in the response, those on the left have an inverse effect, and those near the middle have little effect. As expected, substitution of Na+ by Ag+ ion has the greatest positive effect on the separation factor, while increasing the permeate solubility in the membrane phase has the greatest negative effect due to carrier saturation. However, as mentioned earlier, further solubility studies at lower ethanol percentages may in fact give higher fluxes without degrading the separation. The two other variables, membrane thickness and permeate feed concentration, seem to have little effect on the separation factor, at least over the range that was studied. In the case of membrane thickness, this indicates that the membrane transport is not limited by the rate of the complexation reaction. For both membrane thicknesses used, the reaction times must be very rapid compared to the diffusion times, causing the flux ratios to remain the same. Explanation of the interaction of the variables is more difficult. On the negative side of the plot, the factors SF
and CF appear. These two interactions are similar since S and C, solubility and feed concentration, both result in an increase of the amount of permeate in the membrane. Even though facilitated transport has the highest positive effect on the separation factor, a large increase in the solubility of the permeate, which is undesirable (ethylbenzene), can override the facilitation effect and decrease the selectivity of the separation. Interactions of the second and third order are possible but unlikely and even more difficult to envision. Due to the limitations of this study (only two levels being used for each variable), it is difficult to draw the line between the real effects and sampling error. More information could be gained by this method if the variables were studied over three or four different levels, but in the case of a four-variable experiment, that would involve 81 or 256 measurements, respectively. Model Comparison. From the data collected thus far, it is not possible to unambiguously describe the molecular processes responsible for facilitated transport in this system. For example, the observed flux enhancement could be due to a mobile carrier-permeate complex or to a "hopping" mechanism in which permeate molecules exchange between immobile Ag+ ions. If a mobile Ag(olefin)+ complex is responsible for the facilitation effect, Noble et al. (1986) has shown that the facilitation factor, assuming reaction equilibrium and no mass transport resistance at the membrane interfaces, should be aKD 1 + KD
F=l+-
where the dimensionless equilibrium constant, KD, is equal to the equilibrium constant for the complexation reaction, Keg,multiplied by the concentration of permeate in the membrane phase. The a term is related to the ratio of the mobility of the complex to that of the permeate: ~complex[carrierI,o~l CY=
Dpermeate[~ermeatelz=~
(3)
By use of the data from Figure 1and the above equations, diffusion coefficients for the free and complexed styrene in the membrane can be calculated. For the calculation of K,, Kegfor styrene is 18.2 L mol-l in aqueous solution (Beverwijk et al., 1970). The styrene solubility in a Na+-exchanged membrane contacted with a 0.1 mol L-' feed solution was found to be 6 X mol L-I. This yields a KD value for styrene of 0.1 in water-swollen Nafion 117. Substituting this KD and the measured facilitation factor of 260 into eq 2 gives an cy value of 2800. The denominator in eq 3 can be calculated from the permeate flux through the Na+ membrane and the membrane thickness using Fick's first law, D,,,[permeate],,o = L(Jpemmte).Using the Na+ flux for styrene of 6.1 X mol cm-2 and a thickness for water-swollen Nafion 117 of 200 bm gives a value of 1.2 X mol cm-I s-l. This implies that the diffusion coefficient of uncomplexed styrene is 2 x 10" cm2 s-l. For the numerator in eq 3, a value of 5 mol L-I for [ ~ a r r i e r ] ,is~ a typical carrier concentration for 1100 g/ equiv of Nafion. The diffusion coefficient of the complex can then be calculated by substitution as 7 X cm2 s-l. These diffusion coefficients are much smaller than typical solution values (10-5-10-6 cm2 s-l) but are comparable to values for ionic species in Nafion (10-7-10-12) (Elliott and Redepenning, 1984). The calculations above are based on the applicability of a facilitated transport model derived for liquid membranes. While the calculated diffusion coefficients are reasonable, the molecular processes occurring within Nafion membranes are likely to be quite different from those
1024 Ind. Eng. Chem. Res., Vol. 28, No. 7, 1989
observed in solution. The microstructure of perfluorosulfonate ionomers has been studied by X-ray scattering techniques and is thought to consist of ionic cluster regions 4-5 nm in diameter surrounded by a fluorocarbon polymer phase (Eisenberg and Yeager, 1982). Diffusion of permeates and complexes must occur through the ionic regions which contain the majority of absorbed water. The flux data in Table IT seem to indicate a significant difference in the diffusion process occurring in the two membrane types used in this study even though their equivalent weights are the same (1100 g/equiv). Macroscopically, the Nafion 117 membranes are about 7 times thicker than NE 111, but comparison of the fluxes for the Ag+-exchanged membranes shows only a factor of 4 difference. In the case of the Na+-exchanged membranes, fluxes through NE 111 membranes were usually lower than through the thicker Nafion 117 membranes. Some of these observations can be explained by differences in solvent content since Nafion 117 retains almost twice as much water as NE 111, but there may also be structural differences that are contributing to the effect. In order to better understand facilitated transport through ionomer membranes, reliable techniques must be developed to observe the relevant properties within the membrane environment. We are currently investigating spectroscopic and electrochemical methods that can be applied to property measurement in Nafion membranes.
Acknowledgment This research is supported by the NSF under Grant CBT-8604518. Acknowledgment is also made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this work. We thank J. J. Pellegrino (NBS, Boulder, CO) and L. L. Burton (DuPont, Wilmington, DE) for providing samples of the Nafion membranes and R. Barkely (CU) for assistance with the gas chromatography measurements.
Nomenclature C = concentration of permeate in the feed solution [ ~ a r r i e r ] ,=~ total concentration of carrier in the membrane [permeate],,,, = concentration of permeate in the membrane at the feed side D i= diffusion coefficient of species i in the membrane FTM = facilitated transport membrane F = facilitation factor, ratio of flux with carrier present to flux without K D = dimensionless equilibrium constant K,, = equilibrium constant L = membrane thickness
n = number of variables studied in factorial analysis R, = measured response for experiment i S = .olubility of permeate in the membrane phase t - cime U J " , ~ = weighting factor of a variable for experiment i Greek Letter u
= dimensionless factor related to the ratio of complex mobility to permeate mobility
Literature Cited Beverwijk, C. D. M.; Van Der Kerk, G. J. M.; Leusink, A. J.; Noltes, J. G. Organosilver Chemistry. Organometal. Chem. Reu. A 1970, 5, 215. Eisenberg, A., Yeager, H. L., Eds. Perfluorinated Ionomer Membranes; ACS Symposium Series 180 American Chemical Society: Washington, DC, 1982. Elliott, C. M.; Redepenning, J. G. Aqueous and Non-aqueous Electrochemistry in Thick-film Nafion/Mercury Modified Electrodes. J . Electroanal. Chem. 1984, 181, 137. Herrera, A.; Yeager, H. L. Halide and Sulfate Ion Diffusion in Nafon Membranes. J . Electrochem. SOC.1987, 134, 2446. Ho, W. S. Winston; Doyle, G.; Savage, D. W.; Pruett, R. L. Olefin Separations via Complexation with Cuprous Diketonate. Ind. Eng. Chem. Res. 1988, 27, 334. Hughes, R. D.; Mahoney, J. A.; Steigelmann, E. F. Recent Deuelopments in Separation Science; CRC Press: Boca Raton, FL, 1986. Kawakami, M.; Tateishi, M.; Iwamoto, M.; Kagawa, S. Selective Permeation of Ethylene and Propylene Through Rh3+-Polyethylene Glycol Liquid Membranes. J. Membr. Sci. 1987,30, 105. Koval, C. A,; Spontarelli, T. Condensed Phase Facilitated Transport of Olefins through an Ion Exchange Membrane. J . Am. Chem. Soc. 1988, 110, 293. LeBlanc, 0. H.; Ward, W. J.; Matson, S. L.; Kimura, S. G. Facilitated Transport in Ion-exchange Membranes. J . Membr. Sci. 1980,6, 339. Noble, R. D.; Way, J. D.; Powers, L. A. Effect of External Mass Transfer Resistance on Facilitated Transport. Ind. Eng. Chem. Fundam. 1986,25,450. Quezado, S.; Kwak, J. C. T.; Falk, M. An Infrared Study of Water-ion Interactions in Perfluorosulfonate (Nafion) Membranes. Can. J . Chem. 1984, 62, 958. Szentirmay, M. N.; Campbell, L. F.; Martin, C . R. Silane Coupling Agents for Attaching Nafion to Glass and Silica. Anal. Chem. 1986, 58, 661.
Teramoto, M.; Matsuyama, H.; Yamashiro, T.; Katayama, Y. Separation of Ethylene from Ethane by Supported Liquid Membranes Containing Silver Nitrate as a Carrier. J . Chem. Eng. Jpn. 1986, 19, 419. Way, J. D.; Noble, R. D.; Reed, D. L.; Ginley, G. M.; Baker, L. A. Facilitated Transport of COP in Ion Exchange Membranes. AIChE J . 1987, 33, 480. Wilson, E. B. An Introduction to Scientific Research; McGraw-Hill: New York, 1952.
Receiued for reuiew September 23, 1988 Accepted April 25, 1989
