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Ind. Eng. Chem. Res. 1996, 35, 1090-1096
Evidence for Parallel Pathways in the Facilitated Transport of Alkenes through Ag+-Exchanged Nafion Films Roberto Rabago,† Debra L. Bryant,‡ Carl A. Koval,‡ and Richard D. Noble*,§ Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309-0215, and Department of Chemical Engineering, University of Colorado, Boulder, Colorado 80309-0424
Facilitated transmembrane fluxes for feed solutions containing 1,5-hexadiene, 1-hexene, and n-hexane are reported for hydrated Ag+-Nafion membranes that vary in thickness between 8 and 155 µm. Fluxes for n-hexane are virtually undetectable. Analysis of the fluxes for 1,5hexadiene and 1-hexene suggests that two transport pathways are operating in parallel. The fluxes associated with one pathway are inversely proportional to membrane thickness and lead to a limiting diene/monoene separation factor of 47. The fluxes associated with the second pathway are independent of membrane thickness and lead to a limiting separation factor of 100. The differences in the selecivity for the two pathways result in separation factors for the 8-155 µm membranes ranging from 50 to 70. Concentrations of solutes in the membranes under equilibrium and transport conditions and the rate of 1,5-hexadiene extraction from membranes as a function of time are determined and are used to infer properties associated with the two pathways. Introduction Perfluorinated ionomer membranes such as Nafion have numerous uses both in industrial chemical practice and in chemical research. Applications include the chlor-alkali process (Eisenberg and Yeager, 1982; Gronowski and Yeager, 1991), H2/O2 fuel cells (Eisenberg and Yeager, 1982; Poltarzewski et al., 1992; Springer et al., 1991), biomedical sensing (Malinski and Taha, 1992; Nagy et al., 1985), and other types of chemical sensors based on modified electrodes (Murray et al., 1987; Whiteley and Martin, 1987). Nafion has also been shown effective in chemically facilitated separations of molecules. Way and Noble have shown that contaminated natural gas can be purified using protonated ethylenediamine as a facilitated transport carrier (Way and Noble, 1989; Way et al., 1987). More recently, Koval et al. have shown that alkenes can be separated from similar compounds using a Nafion film in the Ag+ form (Koval and Spontarelli, 1988; Koval et al., 1989, 1992; Thoen et al., 1994). Separation factors of 100-1000 were obtained for separations of alkenes from saturated compounds where the separation factor for two components A and B is defined as
SAB )
JA [B]feed - [B]sweep JB [A]feed - [A]sweep
(1)
The additional observation that dienes could be effectively separated from monoenes was unexpected. Separation factors of 25-100 were reported for mixtures of 1,5-hexadiene and 1-hexene. Their work presented a semiquantitative sorption model to explain the unexpectedly high selectivities and required the second complexation available to the diene to control the concentration of alkenes in the membrane and hence * Author to whom correspondence is addressed. FAX: 303492-4341. E-mail:
[email protected]. † Current address: National Renewable Energy Laboratory, 1617 Cole Blvd., Golden, CO 80401. ‡ Department of Chemistry and Biochemistry. § Department of Chemical Engineering.
0888-5885/96/2635-1090$12.00/0
the resulting flux (Thoen et al., 1994). The model fit experimental data fairly well, yet left a number of questions unanswered. Specifically, the assumption was made that alkene concentrations in membranes under equilibrium conditions would be the same as those under transport conditions; clearly this was a simplification. Further, data from the previous work predicted without explanation that the facilitated flux through Nafion would be large in the limit of infinite membrane thickness. Probing these and other issues to more fully understand the facilitated transport behavior of alkenes in Nafion was the objective of this work. Experimental Section Membrane Casting and Preparation. The procedure for casting the Nafion membrane used in this study has been previously described (Rabago et al., 1994). Membrane thicknesses ranging from 8 to 155 µm were determined using an Ames Model 135 bench comparator (Waltham, MA) and are accurate to (1 µm. After casting, the membranes were removed from the casting dishes and boiled in concentrated HNO3 (37% w/w) for 1 h and then boiled in water for 1 h. The membranes were neutralized in 1.0 M NaOH for 30 min, washed thoroughly with water, and exchanged in 1.0 M AgNO3 (50-fold excess) for 30 min. After an additional water wash to remove excess AgNO3, the samples were then ready for transport or partitioning experiments. With the exception of the membranes for the water content experiments, all membranes described in this work were treated in the above fashion. Membrane Water Content. Water uptake into Nafion membranes under a variety of conditions was measured in the following way. Nafion 117 films (175 µm thickness) were purchased from Aldrich and boiled in concentrated HNO3 (37% w/w) for 1 h. Membrane samples were then either vacuum dried at 70°C for 1 h, boiled in HNO3 again for 1 h, or boiled in both HNO3 and water for 1 h each. The samples were then neutralized in 1.0 M NaOH for 1 h, washed thoroughly with water, and exchanged in 1.0 M AgNO3 for 1 h. The samples were then rinsed, gently blotted to remove © 1996 American Chemical Society
Ind. Eng. Chem. Res., Vol. 35, No. 4, 1996 1091 Table 1. Effects of Membrane Treatment on Alkene Flux and Separation Factor alkene fluxb × 109 (mol/cm2 s) membrane treatment vacuum dry + rehydration in water at 25°C vacuum dry + 1 h of HNO3 boil + rehydration vacuum dry + 1 h of HNO3 boil + 1 h of H2O boil
water
absorptiona 12% 21% 27%
(%)
1,5-hexadiene
1-hexene
separation factor (1,5-hex/1-hex)
12 16c 29
0.43 0.59c 0.65
28 27c 45
a Membrane material was 175 µm Nafion 117. Absorption values are given as water content in membrane (prior to alkene contact) as a percentage of the dry Ag+-form membrane mass (1200 g/equiv). b Feed solution was 0.5 M each of 1,5-hexadiene, 1-hexene, and n-hexane in isooctane. Membrane material was 20 µm cast Nafion. c Data from Thoen (1993).
surface water, and weighed. Dry membrane masses were obtained by weighing each after several hours of vacuum drying. Condensed-Phase Alkene Flux Measurements. Flux experiments were performed in a stirred two 2-compartment transport cell with the membrane mounted vertically between the feed and sweep reservoirs. The membrane area exposed to the feed and sweep solutions was 1.8 cm2. Permeation of each component was followed using gas chromatography as previously described (Koval et al., 1992). Feed concentrations of n-hexane, 1-hexene, and 1,5-hexadiene varied between 0.1 and 0.5 M, and the solvent was watersaturated 2,2,4-trimethylpentane (isooctane). Alkene Absorption into and Extraction from Nafion. Hydrated membranes (surface area 10.2 cm2) in the Ag+ form were contacted with mixtures of n-hexane, 1-hexene, and 1,5-hexadiene in isooctane and allowed to partition overnight. The samples were then rinsed in fresh isooctane and water and then extracted into fresh isooctane. To ensure complete extraction, the volume of extracting solvent was chosen for each experiment such that the maximum alkene concentration in the extracting solution would be less than 2 mM. Alkene concentrations were determined by the same GC method as for the flux measurements. Prior work has determined that this procedure will quantitatively extract alkenes from Ag+-form Nafion films into isooctane (Koval et al., 1992). To determine alkene content under transport conditions, the membrane was installed in a transport cell with feed and sweep solutions and run until a steadystate flux was obtained. Water was then added simultaneously to both cell compartments, displacing the feed and sweep solutions from the membrane surface. The membrane was then removed from the cell and extracted into isooctane as described above. Results and Discussion Membrane Water Content. The literature contains numerous suggestions that the amount of water that Nafion can absorb is dependent on membrane treatment procedures (Koval et al., 1992). Therefore, experiments were done to determine the effects of boiling the membranes in water on water absorption, alkene flux, and alkene separation factor. Due to the fact that a nitric acid boil is also frequently used as a cleaning step, the effects of this procedure were also examined. Results from the membrane treatment experiments are shown in Table 1. When a membrane is dehydrated by vacuum drying, the membrane shrinks and contains very little water. On subsequent immersion in water at 25 °C, the mass of water that the membrane can absorb is about 12% of the membrane’s dry mass. However, if the membrane is boiled in concentrated HNO3 after vacuum drying, the water content goes up to 21%. Finally, if the membrane is then boiled in
water, the water absorption increases to 27%. The fact that the water content for PFSA membranes such as Nafion is highly dependent upon pretreatment procedures has been observed in other laboratories (Hinatsu et al., 1994). This effect has a great significance for alkene separations. After boiling only in HNO3, the water absorption and fluxes of both components increase. However, the separation factor remains the same, indicating that the membrane has swollen and become less resistive for both permeates equally. After boiling the membrane in water, water content and alkene fluxes increase once again. In this case, however, the increase in the diene flux is much larger than the increase in the monoene flux, resulting in an increased separation factor. The process of boiling the membrane in water allowed greater water loading into the membrane and also resulted in the membrane becoming more favorable to diene permeation, suggesting that the highly swollen membrane had an altered morphology. The observation of increased alkene flux with increased water content is consistent with a model of alkene transport, whereby the alkene moves between complexation sites which are closely associated with the polymer side chains (Rabago et al., 1994). The increased hydration may result in greater mobility of the side chains and hence easier movement of complexed alkene. Membrane Alkene Concentrations. Previous work reported values for equilibrium alkene concentrations in Ag+-form membranes which were later used for modeling studies (Thoen et al., 1994). This work assumed that the alkene concentrations in Ag+-form Nafion membranes would be the same under transport conditions as under equilibration conditions. Clearly, this assumption is an oversimplification. For the present work, a study of membrane alkene concentrations under equilibrium and transport conditions was done. Table 2 describes the results obtained. Alkene concentrations are described in terms of moles of alkene per mole of complexation sites in Nafion. Under equilibration conditions the membrane is allowed to absorb alkene from both surfaces for an extended period of time. Table 2 indicates that the absorption of either alkene is independent of membrane thickness when allowed to equilibrate, and the diene/monoene ratio is relatively constant at 13. If one assumes that the diene occupies two complexation sites, approximately 35% of the complexation sites in the membrane was complexed to alkene. This result is consistent with the previously cited report (Thoen et al., 1994). The observation of constant alkene absorption as the membrane thickness changes is what would be expected for equilibrated membranes. Alkene uptake is significantly different for membranes under steady-state transport conditions, as would be expected because only one surface of the membrane are in contact with the alkene-containing feed solution. Data for the 8 µm membrane is not
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Table 2. Alkene Absorption under Transport and Equilibrium Conditions membrane thickness (µm)
experimental conditions
mol of 1,5-hexadiene/ equiv of Nafion
mol 1-hexene/ equiv of Nafion
diene/ monoene
8 18 35 56 18 35 56 145
equilibriuma equilibrium equilibrium equilibrium transportb transport transport transport
0.18 0.16 0.16 0.19 0.13 0.11 0.090 0.10
0.013 0.012 0.013 0.016 0.0041 0.0051 0.0065 0.0085
14 13 13 12 33 21 14 12
a Contacting solutions were water-saturated isooctane containing 1,5-hexadiene (0.1 M) and 1-hexene (0.1 M). b Feed solutions were water-saturated isooctane containing 1,5-hexadiene (0.1 M) and 1-hexene (0.1 M). Receiving solutions were water-saturated isooctane.
Table 3. Alkene Flux through Membranes of Various Thicknesses and Using Different Feed Concentrations permeate flux × 109 (mol/cm2 s)
membrane thickness (µm)
alkene feed conc (M)b
1,5-hexadiene
1-hexene
8 18 18 18 35 56 135 155
0.1 0.02 0.1 0.5 0.1 0.1 0.1 0.1
31 6.5 17 33 11 8.0 5.7 4.8
0.62 0.081 0.29 0.72 0.17 0.12 0.084 0.070
n-hexane
alkene sep. factor 1,5-hex/1-hex
nda nd nd 0.02 nd nd nd nd
50 80 59 46 65 67 68 69
a nd ) not detectable. b The feed solution contained 1,5-hexadiene and 1-hexene at the specified concentration. Receiving solutions were water-saturated isooctane.
included because the time required to remove the membrane from the transport cell is roughly the same as the time required to load or extract such a thin membrane. As shown in Table 2, the 1,5-hexadiene concentration under transport conditions is slightly more than half the value obtained under equilibration conditions. Similarly, the concentration of 1-hexene under transport condition for thick membranes is slightly over half the equilibrated value. However, for thin membranes the transport concentrations for 1-hexene are smaller, therefore, the ratio of diene to monoene under transport conditions is different from the equilibration values, especially for the thinner membranes. The significance of this trend is discussed later in the paper. Alkene Fluxes as a Function of Membrane Thickness. A series of alkene flux experiments using membranes of different thicknesses was performed. Membranes for this series were all boiled both in HNO3 and in water. The results are shown in Table 3 and Figure 1 depicts the data in Table 3 (0.1 M feed solutions) as alkene flux as a function of (membrane thickness)-1. Two observations are immediately apparent. The first is that the slopes are linear, which is what would be expected for a diffusion-limited process. However, the fact that both permeates have rather large y-intercepts is at first glance rather troubling because the y-intercept indicates the expected flux at infinite membrane thickness. A similar observation was reported in a previous study, but no comment was made regarding the positions of the lines (Thoen et al., 1994). For most membrane processes, the total membrane resistance increases with thickness and an intercept near zero is expected for a plot of flux vs (membrane thickness)-1. Based on Figure 1, the fluxes at infinite thickness for 1,5-hexadiene and 1-hexene are 4.1 × 10-9 and 0.041 × 10-9 mol cm-2 s-1, respectively. These values are not only nonzero but constitute most of the flux for the thickest membranes in Table 3. One possible explanation for this effect is that there may exist in Nafion a transport path or mechanism for alkene movement that is independent of membrane thickness over the range
Figure 1. Plot of alkene flux vs (membrane thickness)-1. The alkene feed concentration is 0.1 M for each component. Filled circles represent 1,5-hexadiene flux; open circles represent 1-hexene flux.
of thicknesses studied here. Additionally, because the slopes in Figure 1 are nonzero, there must be a second transport path that is a function of membrane thickness. In order to discuss the existence of two alkene transport paths through Nafion in a quantitative manner, the membrane was modeled as two transport pathways operating in parallel. One pathway was assumed to result in alkene fluxes, Jv, that were proportional to the concentration driving force within the membrane, ∆C, and a mass-transfer coefficient, k, as predicted from Fick’s law, i.e., Jv ) kv∆C. The masstransfer coefficient for this pathway was assumed to vary with membrane thickness, L, in the usual way; e.g., kv ) Deff/L where Deff is the effective diffusion coefficient for the solute in the membrane. The flux for the other pathway, Jc, is assumed to be independent of membrane thickness. The observed alkene flux is simply the sum provided by both pathways,
Jobsd ) Jv + Jc ) kv∆C + Jc
(2)
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Figure 2. Plot of the reciprocal of the alkene flux attributed to the thickness dependent pathway vs membrane thickness. The alkene feed concentration is 0.1 M for each component. Filled circles represent 1,5-hexadiene flux; open circles represent 1-hexene flux.
Figure 3. Separation factor for 1,5-hexadiene flux/1-hexene as a function of membrane thickness. The alkene feed concentration is 0.1 M for each component.
The concentration dependence of Jc will be discussed later in the text. The concentration driving force, ∆C, within the membrane can be estimated by assuming that Cx)L ) 0, which is resonable given that the alkene concentrations in the sweep solutions remained very low throughout the transport experiments. Values of Cx)0 for 1,5-hexadiene and 1-hexene were determined by equilibrating Ag+-Nafion membranes with the feed solution, as described below. Nafion membranes in the Ag+ form that are not hydrated absorb only very small amounts of alkene even after days of contact and exhibit virtually zero fluxes in transport experiments. For this reason, concentrations of alkenes within the membrane are calculated based on the volume of absorbed water. Previous experiments with the type of transport cells used in this study show that the rate of alkene transport from the feed solution to the membrane surface far exceeds the rate of transport through the membrane. Therefore, it can be assumed that values of Cx)0 for alkenes are approximately equal to the equilibrium values. Values of Cx)0 calculated using the average of the equilibrium values reported in Table 2 are 5.2 × 10-4 mol cm-3 for 1,5-hexadiene and 4.2 × 10-5 mol cm-3 for 1-hexene when the contacting solution was 0.1 M in each component. These concentration values are smaller than values reported previously (Thoen et al., 1994) because the membranes used in the earlier studies absorbed less water. As shown in Table 2, the amount of alkene absorbed for equilibrated membranes is not dependent on the membrane thickness; therefore, ∆C for the experiments depicted in Figure 1 is 5.2 × 10-4 mol cm-3 for 1,5-hexadiene and 4.2 × 10-5 mol cm-3 for 1-hexene. It is important to recognize that this calculation assumes that all of the alkenes that absorb into the membrane are available for transport via the thickness-dependent pathway. Values of Jc for 1,5-hexadiene and 1-hexene are readily extracted from the intercepts of the plots in Figure 1 and are equal to 4.1 × 10-9 and 4.1 × 10-11 mol cm-2 s-1, respectively. Values of Jv for the various membranes are then calculated (Jv ) Jobsd - Jc) for the two solutes and different membrane thicknesses. Plots of Jv-1, which is equal to (1/Deff∆C)L, versus membrane thickness are depicted in Figure 2. These plots are linear with intercepts near the origin, which is exactly
what would be expected for a membrane with a single transport pathway that operates through Fickian-like diffusion. Plotting the data as in Figure 2 also avoids the compression of the data for the thicker membranes which occurs in Figure 1. These figures provide strong evidence to support the idea that there are two separate alkene transport pathways in Nafion that are very different from each other in character. From the slopes of the plots in Figure 2 and using the values of ∆C estimated earlier, values of Deff for 1,5-hexadiene and 1-hexene can be calculated and are found to be 4.1 × 10-8 and 1.1 × 10-8 cm2 s-1, respectively. The fact that the diffusion coefficient for 1,5-hexadiene is greater than the value for 1-hexene, i.e., that the selectivities observed cannot be soley attributed to differences in the solubility of the two components in the membrane, is consistent with our earlier papers on these types of separations (Thoen et al., 1994). Additional evidence for the two-pathway model is obtained by plotting the data in Table 3 as separation factor vs membrane thickness for the 0.1 M feed solutions (Figure 3). As membrane thickness increases, the flux contribution from the thickness-dependent pathway will fall to zero. Therefore, the theoretical separation factor at infinite membrane thickness is given by the ratio of the y-intercepts in Figure 1. This ratio is 100; therefore, as the membrane thickness increases, the separation factor should approach 100. As is apparent from Figure 3, the separation factor does in fact increase with membrane thickness. For singlepathway, diffusion-limited facilitated transport membrane processes, no dependence of separation factor on membrane thickness should be observed. Alkene Extraction Rate. Alkene extraction from Ag+-Nafion was studied in an attempt to better understand alkene partitioning into Nafion under transport conditions. Facilitated transport through Ag+Nafion can be viewed as a three-step process. The first step involves the alkene partitioning into the membrane from the feed phase, the second involves complexation and diffusion within the polymer matrix, and the third involves the alkene exiting the membrane and entering the sweep phase. The previous discussion described Ag+-Nafion as a parallel pathway medium, with the flux through one of the paths independent of thickness. The thickness-independent path must involve a step
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Figure 4. Amount of 1-hexene extracted from a 180 µm Nafion membrane into isooctane divided by the total amount extracted vs time. Prior to extraction, the membrane was equilibrated with a solution that was 0.1 M in 1-hexene (open circles) and a solution that was 0.5 M in 1-hexene and 0.1 M in 1,5-hexadiene (filled circles). The sloped solid line represents linear regression of the single-component data between 2200 and 4800 s.
Figure 5. Amount of 1,5-hexadiene extracted from a 180 µm Nafion membrane into isooctane divided by the total amount extracted vs time. Prior to extraction, the membrane was equilibrated with a solution that was 0.1 M in 1,5-hexadiene (open circles) and a solution that was 0.1 M in 1,5-hexadiene and 0.5 M in 1-hexene (filled circles). The sloped solid line represents linear regression of the single-omponent data between 300 and 800 s.
that is slower than the diffusion rate. This transportlimiting step is unlikely to be due to the initial partitioning of alkene into the membrane because in that case both transport paths would be affected, resulting in a total membrane flux that would be constant for all thicknesses. More likely, the transport-limiting step for the thickness-independent pathway is the rate of alkene exiting the membrane. To test this hypothesis, an experiment was done to determine the rate of alkene extraction from a membrane. In a series of experiments, a 180 µm Ag+-form membrane with a surface area of 10.2 cm2 on each side was initially equilibrated with a solution containing alkenes and then extracted into a large volume of isooctane. The equilibration solutions were 0.1 M 1,5hexadiene, 0.1 M 1-hexene, and a mixture containing 0.1 M hexadiene and 0.5 M 1-hexene. A higher concentration of 1-hexene in the mixture was used so that appreciable amounts of both alkenes would be absorbed into the membrane. Aliquots were removed periodically to determine the amount extracted as a function of time. The extraction data for 1-hexene and 1,5-hexadiene, which have been normalized to the total amount of alkene extracted for each run in order to facilitate comparisons, are depicted in Figures 4 and 5, respectively. For all of the extraction vs time experiments, including replicates not shown in Figures 4 and 5, several qualitative features are readily observed. First, for either single component of mixed alkene equilibration solutions, the overall time required to extract 1-hexene is 2-3 times longer than that to extract 1,5hexadiene. Second, the kinetics of the extraction process are biphasic. For the extraction of 1-hexene, the rate of extraction is rapid and changes with time, prior to about 1500 s. Between roughly 2200 and 4800 s, a linear region is observed, indicating that the rate of extraction is constant. The kinetic behavior for 1,5hexadiene is similar except that the early, rapid portion occurs prior to about 500 s while a linear portion is observed between 300 and 1000 s. For both alkenes, the shape and time scale of the extraction curve are nearly identical for membranes that contain a single component or a mixture. In the case of 1-hexene, this
is true even though the total amount extracted using the mixed equilibration solution is roughly 1/4 the amount extracted from the single-component equilibration solution. In an earlier paper, an equation was presented that describes the expected behavior for extraction of a solute in a membrane by a purely diffusive pathway with no kinetic limitations at the interfaces (Rabago et al., 1994). In this equation,
Mt/M0 ) 1 - (8/π2) exp(-π2Defft/L2)
(3)
where Mt is the amount of solute extracted at time t and M0 is the initial amount in the membrane. The extraction data in Figures 4 and 5 at early times appear to have this functional form, but the curves are complicated by the subsequent linear regions. If one assumes that the linear extraction regions can be attributed to the thickness-independent pathway and that this process has contributed to loss of alkenes from the time the membranes were placed in the extraction solution (t ) 0), it is reasonable to extrapolate the linear portions to obtain the amount of alkene extracted by this pathway. As indicated by the lines through the data in Figures 4 and 5, a linear region was chosen for the extraction experiments involving single component equilibration solutions. These lines were used to determine M0, the total amount of alkene leaving the membrane by the diffusive pathway, and to correct the early time data for amounts of alkene lost due to the thickness independent process and thereby obtain values of Mt. The early time data for extraction of 1-hexene and 1,5-hexadiene were then fit to eq 2 as shown in Figure 6. The slope of the plots in Figure 6 are equal to -π2Deff/ L2, which provides an estimate of Deff for 1-hexene and 1,5-hexadiene which do not depend on the concentration of alkene in the membrane. Using the known membrane thickness, 180 µm, values of Deff ) 5.4 × 10-8 and 3.4 × 10-7 cm2 s-1 are obtained for 1-hexene and 1,5hexadiene, respectively. The value of Deff for 1,5hexadiene obtained from Figure 6 appears to differ significantly from the value calculated using the data
Ind. Eng. Chem. Res., Vol. 35, No. 4, 1996 1095
Figure 6. Plots representing the fit of the early portions of the single-component extraction data from Figures 4 and 5 using eq 2. The data were corrected for extraction via the thicknessindependent pathway (see text).
in Figure 2, 4.1 × 10-8 cm2 s-1. However, the latter value was calculated by using the absorption data in Table 2 for membranes that were fully equilibrated with diene and by assuming that all of the diene present in the membrane was available to establish the concentration gradient experienced by the thickness-dependent pathway. As shown in Table 2, the average amount of diene in the membranes under transport conditions is only about 65% of the average amount under equilibrium conditions. Furthermore, the data in Figure 5 suggest that only about 50% of the diene is available to this pathway. If a value of ∆C used to calculate Deff for 1,5-hexadiene from Jv is 5.2 × 10-4 × 0.65 × 0.50 ) 1.7 × 10-4 mol cm-3 (instead of 5.2 × 10-4 mol cm-3), Deff is calculated to be 1.2 × 10-7 cm2 s-1, which is in better agreement with the value obtained from the early time data in Figure 5. This agreement also supports the hypothesis that initial extraction of 1,5-hexadiene observed in Figure 5 is occurring by the same pathway responsible for the thickness dependent values of Jv in Figure 2. The ratio of the diffusion coefficients obtained for the two alkenes from Figure 6, which is 6.3 (1,5-hexadiene/ 1-hexene), is in reasonably good agreement with the ideal separation factor of 4.3 (calculated from singlecomponent transport experiments) for these two species reported earlier (Thoen et al., 1994) for 25 µm Nafion membranes. This agreement would be expected if a majority of the flux were through the thickness-dependent pathway, which is the case as shown in Figure 1, and if the absorption of these two alkenes were the same from single-component solutions. In fact, single-component isotherms for 1,5-hexadiene and 1-hexene are nearly identical at these concentrations (Thoen, 1993). The slopes of the linear portions of extraction curves like those shown in Figures 4 and 5 are more difficult to analyze quantitatively than are the early time data. Due to the overall curvature in the extraction plots and the inherent noise in the data, assignment of the linear regions is somewhat arbitrary. Therefore, using the slopes to calculate extraction rates for the thicknessindependent pathway is not highly accurate. Nevertheless, values obtained by this procedure are consistent with the information about the thickness-independent pathway obtained from the transport data. For example, values of the extraction rate for 1,5-hexadiene obtained from linear portions of experiments including those in Figure 5 fell in the range of (1-5) × 10-9 mol cm-2 s-1 per surface. The thickness-independent trans-
port flux, Jc, from the Y-intercept in Figure 1 is 4.1 × 10-9 mol cm-2 s-1. Extraction rate by the thickness-independent pathway appears to follow zero-order kinetics. However, the slopes of linear portions of extraction curves appear to scale linearly with the amount of alkene initially present in the membrane. Clearly, further research is necessary to better understand the nature of the two transport pathways and to develop a physical picture of them. Separation Factor vs Membrane Thickness. Reconciling the absorption results in Table 2 with the transport data in Table 3 seems troublesome, because while the diene/monoene ratio in the membrane under transport conditions decreases with membrane thickness, the separation factor increases. The dual-path transport model is partially consistent with these results. For the thickest membranes studied, where most of the flux occurs via the thickness-independent pathway, separation factors of nearly 70 are observed. Furthermore, the ratio of Jc values obtained by extrapolating the lines in Figure 1 predicts a separation factor of 100 for infinitely thick membranes. Since the diene/ monoene concentration ratio is only 12 for thick membranes and since the data in Figure 4 suggest that Jc is concentration independent, much of the selectivity associated with this path must be due to some ratelimiting kinetic factor which is considerably different for dienes and monoenes. Separation factors observed for thin membranes, where most of the flux occurs by the thickness-dependent pathway, should be sensitive to membrane concentration. The limiting separation factor for this pathway is 47, obtained from the ratio of Jv values from Figure 2, which is close to the separation factor of 50 observed for the 8 µm membrane. Nevertheless, the unusually low 1-hexene concentrations (and high diene/monoene ratios) observed for thin membranes under transport conditions remain unexplained. Conclusions The fact that hydrated PFSA polymers such as Nafion contain domains with dramatically different properties (fluorocarbon polymer vs ionic aqueous solution) leads to a variety of unusual phenomena associated with the transport of solutes. For the process of facilitated transport of alkenes by Ag(I) ion, the data and analysis presented in this paper demonstrate that two transport pathways operate in parallel. One pathway is diffusive in nature and responds to changes in membrane thickness and solute concentration in the expected ways. The other pathway results in membrane fluxes that are thickness-independent and possibly independent of the solute concentration in the membrane. The two pathways exhibit different selectivities for dienes vs monoenes resulting in separation factors for these compounds which are dependent on membrane thickness. Acknowledgment R.R. was supported by a fellowship from the Ford Foundation. This research was supported by grants from the National Science Foundation (CTS-9315090) and Chevron Research and Technology Co. Abbreviations and Symbols Jobsd ) observed alkene flux (mol cm-2 s-1) Jv ) portion of the alkene flux that varies with membrane thickness (mol cm-2 s-1)
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Jc ) portion of the alkene flux that is independent of membrane thickness (mol cm-2 s-1) k ) alkene mass-transfer coefficient (cm s-1) D ) diffusion coefficient (cm2 s-1) ∆C ) concentration gradient within the membrane (mol cm-3) L ) membrane thickness (cm or µm) Mt ) amount of alkene extracted from the membrane at time t (mol) M0 ) amount of alkene contained in the membrane initially (mol) SAB ) separation factor of components A and B, defined in eq 1
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Received for review June 1, 1995 Accepted November 22, 1995X IE9503306
X Abstract published in Advance ACS Abstracts, February 15, 1996.
