J. Phys. Chem. lW2, 86, 3651-3657
3651
Mechanism of Anion Pumping through a Synthetic Liquid Membrane' Lee A. Ulrlck,'b KeHh D. Lokkesmoe, and Maurlce M. Kreevoy' Chemical DpamicO Labuatqv, o e p e m n t of Chembby, University of Mhmsota, MinneepOH8, Minnesota 55455 (Received: November 5, 1981; I n Final F m : M y 10, 1982)
An anion, A-, is drawn across a suitable water-immiscible liquid membrane, against its concentration gradient,
by an accompanying proton, which is thereby moving from a solution of pH 6-8 to a more basic solution. The membrane was a phenyl ether solution of a C N secondary amine, B, supported on a thin film of porous plastic. The transfer is a pseudo-first-order process. The rate constant, k (cm-' 5-9, can be accounted for by two steps in series. One of these steps has a rate constant which is concentration independent but depends on the pumping rate. The other rate constant is independent of the pumping rate but depends linearly on (H+),(B),and inversely on the thickness of the membrane. (The hydrogen ion concentration of the loading aqueous phase is (H+); the overbar indicates the organic phase.) The form of this dependence identifies the major barriers to transfer as the semistagnant Nemst layer in the aqueous solution adjacent to the membrane on the leaching side, and the internal resistance to diffusion in the membrane itself. Aggregation of the ion pair may accelerate the latter process. Interfacial resistance was not observed. Some time ago Cussler and co-workers showed that a liquid membrane, supported on porous plastic, can be used to transfer an anion, A-, from one solution (the loading solution) to another (the stripping solution).24 The concept seems to have been introduced by Sollner and Shean, who used three bulk liquid phasesS6 A cation must accompany the anion, or else another anion must pass back, from the stripping solution to the loading solution. In the present work the accompanying cation was H+. The anions studied were methyl orange, 1, and picrate, 2. The 0-
1 2
membrane contained phenyl ether as solvent, and didodecylamine or Amberlite LA-28 as carrier for H+. The amine is designated B. The porous plastic support was either Celgard 2400, a polypropylene film, 2.5 X cm thick, or Gore-tex 0.02-pm expanded poly(tetrafluor0ethylene), 7.6 X 10" cm thick.' If the H+ concentration is much higher in the loading solution than in the stripping solution, A- is transferred, even though ita concentration is higher in the stripping solution than in the loading (1) (a) This work was supported by the National Science Foundation,
throughgrant CHE79-25990 to the University of Minnesota,by the North
Atlantic Treaty Organization, through a grant to the University of Minnesota, and by the Ventron Corp., now Thiokol/Ventron. (b) Formerly Hesledalen. (c) These pcmsibilities became apparent through the obervation of similar experiments by M. M. Kreevoy while he was a gueat of Dr. W. J. Albery, then at the Physical Chemistry Laboratory, Oxford. Profemor North and the Chemistry Department of Strathclyde University, Glaegow, provided generoue hospitality for another period during the progress of this work, and Dr. J. Hadgraft, of the Pharmacy Department, University of Nottingham, provided many useful insights and the facilitiee with which L.A.U. carried out the rotating membrane experiments. All of this is gratefully acknowledged. (2) Cuaeler, E. L. AZChE J. 1971, 17, 1300-3. (3) Hochhouser, A. M.; C d e r , E. L. AZChE Symp. - . Ser. 1976, No. 71, 136-42.
(4) Molnar, W.J.; Wang, C. P.; Evans, D. F.; Cusaler, E. L. J. Membr. Sci. 1978, 4, 129-36. (6)Sollner, K.; Shean, G. M. J. Am. Chem. SOC.1964, 86, 1901-2. (6) This ie a liquid mixture of secondary amines purchased from Rohm and Haas, with an average molecular weight around 360. It is more fully described in the Experimental Section. (7) Ce$ard is a registered trademark belonging to the Celaneae Corp. Gore-tex 18 a regwtered trademark belonging to W. L. Gore Aseociates, Inc.
0022-3654/82/2086-3651$01.25/0
solution, until (H+)'(A-)' is equal to (H+)2(A-)2.8 The subscripts 1 and 2 indicate the loading solution and the stripping solution, respectively. The quantities in parentheses should be activities, but in the present paper they will generally be approximated by concentrations. Since (H+)l can be made larger than (H+)2by many powers of 10, A- can be driven from a very dilute solution to one in which it is quite concentrated. In the present system, we find that the rate of this transfer is limited either by the rate of diffusion across the semistagnant Nernst layer in the aqueous solution on the loading side of the membrane or by the rate of diffusion through the membrane (the internal resistance) or by some combination of these two; interfacial resistanceg appears to be negligible. This is consistent with Cussler's previous conclusions.lo It permits the dependence of the transfer rate on the pumping rate, the membrane thickness, the concentration variables, and the identity of the anion to be rationalized. After a period of time the membranes stop functioning. The reason for this failure has been partially elucidated.
Experimental Section Methods. Equilibrium constants, KOa, for the extraction equilibria were measured in both ordinary and jacketed separatory funnels. Water at 25 "C was pumped through the jacket of the jacketed funnel to maintain that temperature in the contents of the funnel. The absorbance of 1or 2 was determined spectrophotometricallybefore and after equilibration with the organic phase. After equilibration the last traces of emulsified organic phase were removed from the aquesous solution, before measurement of ita absorbance, by paraffin shavings. The pH of the aqueous phase was controlled by an appropriate phosphate buffer and was checked with a glass electrode pH meter before and after equilibration with the organic phase. No significant change was observed. Room temperature was always between 20 and 25 "C, and there was no obvious difference between results obtained in the jacketed and unjacketed funnels. Membrane experiments were carried out in a modified dialysis cell, pattemed after one designed by Brandlein and Gregor," shown in Figure 1. Loading and stripping so(8) Thelander, P. F.; Hasledalen, L. A.; Kreevoy, M. M. J . Chem. Educ. 1980,57,609-11. (9) Albery, W . J.; Burke, J. F.; Leffler, E. B.; Hadgraft, J. J . Chem. Soc., Faraday Tram. 1 1976, 72, 1618-26. (10) Lee, K.-H.;Evans, D. F.; Cussler, E. L. MChE J. 1978,24, -8.
0 1982 American Chemical Society
Ulrlck et al.
3652 The Journal of Fhysical chemistry, Vole86, No. 18, 1982
flambraa rrsr"
I-,
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,
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Figure 1. Exploded, slmpllfied view of the working portion of the transfer cell. Inlet and outlet connections, and screws holding the apparatus together, have been omitted. Vexar ts a registered trademark of E. 1. du Pmt de " o u r s , Inc. Sofl sllicone rubber gaskets of 0.82mm thickness were used In 801118 experiments and bwdmsity polyethylene gaskets, 0.048 mm thlck, In others. There were corresponding differences In hydrodynamically limited rates but not in lnternaily llmlted rates.
lutions were stored in glass reservoirs of about 100-cm3 capacity and pumped through the cell by a peristaltic pump (Gilson Minipuls 2 or Cole-Parmer Instrument Co. Masterflex) at rates up to 4 cm3 s-l. In all of the experiments described here, the pumping rates on the two sides of the membrane were the same. Masking experiments, conducted with masks cut 80 as to expose only part of the membrane surface, verified the uniformity of flow over the membrane surface. In all other experiments the full membrane surface was exposed. In two cells of the same design which were used, this area was 6.2 and 6.5 cm2. To demonstrate the ability of the device to pump Aagainst its own concentration differential, experiments were conducted in which the initial concentration of A- was much higher in the stripping solution than in the loading solution. Otherwise the initial concentrations of A- was the same in the loading and stripping reservoirs at the beginning of each experiment. Each membrane liquid was preequilibrated with an aqueous solution similar to the loading solution. In multiple-layer experiments and some one-layer experiments the membrane support was first placed in a filter flask and evacuated. Then the membrane liquid was dropped onto it, and the atmosphere readmitted, so that it would force the liquid into the pores of the support. In the case of multiple-layer experiments the membrane support was left covered with the membrane liquid, under atmospheric pressure, for periods up to 5 days, the required immersion period increasing with the membrane thickness. If this procedure was not followed, lower and irreproducible rates were observed, especially for three-layer and five-layer membranes. In all cases it was experimentally verified that the reported rates could not be further increased by lengthening the immersion period. The absorbance of A- was monitored in the loading reservoir, and sometimes in the stripping reservoir as well, by periodically withdrawing samples and measuring their absorbance in a Gilford-modified, Beckman DU spectrophotometer. In cases where both the loading and stripping reservoirs were monitored, the decrease in the one approximated the increase in the other, within 1% of the total absorbance, except when experiments with multiple (11) Brandlein, L.S.;M. S. Thesis, Columbia University, New York, NY, 1976, pp 16-20.
U
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2. Semipbts of the fraction of picrate untransferred as a function of thne,for a hydrodynamically limited experlment (lower curve) and for an internally limited experiment (upper curve). The dotdashed lines represent the initial slopes, assigned by inspection, from which k values were obtained. The solid line represents the prediction of eq 11, wlth c given a value of 5.3 x io-' cm s-' to optimize the fit to the experlmental points. The circles merely identify the points. They are not error circles.
layers of Celgard film were attempted. In experiments such as those described, the concentration of A- and, hence its absorbance, in the loading reservoir, are expected to decay exponentially, according to eq 1, which defines k." -ka=
In @,/At) (1) t u is the volume of each of the aqueous phases, which were equal in all of our experiments. The exposed area of the membrane is a. Other symbols have their usual significance. All kinetic results were summarized by values of k. In none of our experiments does eq 1actually describe the time dependence of A in full. Figure 2 shows two typical plots of log (AJA,) against t. The partial failure of eq 1 is due to the degradation of the membrane as each experiment proceeds, and is more fully dealt with in the Discussion section. Values of k were obtained from the initial slope of plots of log At or log (A,/Ao)against t. For many experiments, illustrated by the faster reaction shown in Figure 2, such a plot was linear over a sufficient range o f t that the evaluation of the initial slope did not make k significantly less reliable, but in slower experiments a significant uncertainty was introduced in this way. Materials. Methyl orange was obtained from Aldrich Chemical Co. and recrystalIized from water before use. Its visible spectrum in aqueous solution corresponded closely to that previously reported.13 Picric acid was obtained at various times from MCB Manufacturing Chemists, Inc., and Fisher Scientific Co. It was recrystallized from water before use and had a melting point of 121 OC;122.5 O C appears to be the best previously reported value.14 Its electronic spectrum also closely resembled that reported previ~usly.'~Phenyl ether was obtained at various times from Aldrich Chemical Co. and from Thiokol/Ventron Division, Alfa Products. It was distilled under reduced pressure before use, bp 90 OC/l.Otorr; 127 OC/lOtorr has been reported.16 This material had an infrared spectrum u
(12) Reference 9,eq 2 and 9,combined and integrated. (13) Fortune, W. G.; Mellon, M. G. J. Am. Chem. SOC.1938, 60, 2607-10. (14) Heilbron, I., et al. "Dictionary of Organic Compounds",4th ed.; Oxford University Press: New York, 1965; Vol. 5, p 2750. (15) Bortini, Fr. Z.Phys. Chem. 1914,87, 104-14.
The Journal of Physlcal Chemlstry, Vol. 86, No. 78, 7982 3653
Anion Pumping through a Synthetic Llquld Membrane I
I
I
I
I
I
I
I
25 20
t
I
I
I
I
I
I
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4
5
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Flgue 3. Test of eq 3 for plcrate, wlth dldodecylamlne (open circles) and LA-2 (filled drcles); v/P had a value of 2 throughout. The lines shown were forced through the origin and gbe values of 1.45 x 10" Some of the ab(dkkdecylamlne) and 6.26 X 10'' (LA-2 for K,. so a more convenient sorbances were too hlgh for easy "ent, absorbance was measured In a cell of 0.100cm path length and muitlplled by 10 for use In this figure and calculation.
identical with that reported.17 Didodecylamine was a gift of Armack Co. It was recrystallized from ethanol before use and had a melting point of 42-48 "C; 55-56 "C has been reported.'* The infrared and NMR spectra of this material had the expected general appearance, but the apparent molecular weight determined by titration was 394 instead of 353. Apparently it is contaminated with a hydrocarbon-like impurity, which lowers and broadens its melting point. In all of the work described in the rest of this paper its theoretical molecular weight was used. This would make the KO,,values too large by 1070,but the D' values would be unaffected, since the errors would cancel in eq 5. Amberlite LA-2 is a mixture of variously branched secondary amines. It was obtained from the Rohm and Hass Co. and was used as supplied. It was found by acid-base titration to have an equivalent weight of 360. It therefore averages about 24 carbons, which would have an equivalent weight of 353. In calculating the concentrations of LA-2, in both equilibrium and kinetic experiments, we used a molecular weight of 360. Sodium hydroxide and KH2P04 were purchased from various sources and were of AR grade.lg They were used as supplied. Celgard 2400 film was purchased from the Celanese PlasticsCo. and 0.02-pm Gore-tex film was purchased from W. L. Gore and Associates, Inc. Electron micrographs reveal that the Celgard material is a continuous film, with elongated pores, -0.1 pm long by -0.02 pm wide. These pores tend to be grouped, with areas of unbroken surface between groups of pores.20 The Gore-tex material resembles a random mat of fibers, and the 0.02-pm "pore size" refers to the maximum size of particles which it will pass.21 The thicknesses of the two films were determined with micrometer calipers. They were 2.5 X cm for the Celgard film and 7.6 X lC3cm for the Gore-tex film,fairly
-
(16) Schorigin, P. Ber. 1923,56, 176-86. (17) Sadtler Standard Spectra, Standard Grating Spectrum no. 28330K. (18) Wojcik, B.; Adkine, H. J . Am. Chem. Soe. 1934, 56, 2119-24. (19) " w e n t Chemicals";American Chemical Society Washington, D.C. 1974. (20) Celanese Plastics Co. "Celgard MicroporousPolypropylene Film, Technical Bulletin", undated, p 5. (21) W. L. Gore and Associates, Inc. "Gore-Tex Expanded PTFE", 1978, p 7.
Flgure 4. Test of eq 3 for methyl orange, with didodecylamlne (open circles) LA-2 (filled circles); the aqueous and organic volumes were equal throughout. Some of the absorbance were too hlgh for easy measurement, so a more convenient absorbance was measwed in a cell of 0.100Gm path length and muttlplled by 10 for use In this flgure and celarlatlm. A sbpe and a cocrespondlngKua value, 1.74 X lo'', were obtained from the dllute-solution data for didodecylamlne, as shown. For LA-2 it was assumed that the ratio of KO,, values generated by the two amines would be the same as that generated by the same two amlnes wlth picrate. This assumptlon leads to a value of 7.5 x io0 for KO/, with LA-2 and methyl orange. These two values lead to the slopes shown as solM Ilnes.
TABLE I: Kola Values anion
base
10-'OK, laa
2 2 1 1
didodecylamine LA-2 didodecylamine LA-2
14.5 6.26 1.74 0.75
N o uncertainties are cited with the KO/!values because the systematic errors, due t o uncertainties in the base compositions and the methods by which the values for methyl orange were obtained ( - 30%), are much larger than the uncertainty which would be inferred from the scatter (-10%). Three figures are cited to permit the reader t o make calculations consistent with ours.
uniform from one sample to another.
Results In a solvent as nonpolar as phenyl ether it was assumed that almost all ions would be present as neutral aggregates-ion pairs or higher aggregates. Tetrabutylammonium picrate has a dissociation constant of 1.7 X lo-" at 35 "C in phenyl ether; the dielectric constant of phenyl eter is 3.6 at that temperature.= Accordingly, the mass action expression for the extraction of our anions was formulated as shown in eq 2. The overbar indicates a
property of the organic phase. In terms of absorbances, A, this can be reformulated as shown in eq 3. The sub(3) script, i, indicates a value before equilibration. Unsubscripted values were obtained after equilibration. In (22) Nauwelaers, F.;Hellemam, L.; Persoom, A. J . Phys. Chem. 1976, 80,767-75.
3854
The JOWM~of phvsicel Chemisby, Vol. 86, No. 18, 1982
Uirick et al.
TABLE 11: Hydrodynamically Limited ka/v as a
TABLE 111: Internally Limiteda ka/v as a Function of
Function of Initial (A-Y
Initial (A-)
l@ka/v, 1 0 5 ( ~ - )M, 0.65 1.2
S-
1.0 1.0
1 0 5 ( ~1,- M 2.4 5.3
l@ka/u, anion
S- I
1.2 1.0
These experiments were performed with methyl orange, using the soft rubber gaskets, at a pumping rate of 0.33 cm3 s-I, a pH of 6.2, and a didodecylamine concentration of 0.02 M. Under these conditions eq 5 gives a value of 1 . 3 X s-’ for k,a/u.
practice, since (H+)was controlled by a buffer and B was always in very large excess over A- neither (H+) nor (B) was much changed by the equilibration. If u / B is held constant, eq 3 predicts that (H+)(B)Ashould be a linear function of Ai - A, with zero intercept and slope of u / (DK,,& Figure 3 shows that eq 3 successfully accounts for all of the results on the extraction of picrate, by either amine. Methyl orange appears to behave nonideally, with either amine, a t higher concentrations of BH+A- in the phenyl ether. The dilute-solution didodecylamine data appear to define a slope and, thereby a Kolavalue. It was then assumed that the two Kolavalues for methyl orange would have the same ratio as those for picrate. As shown in figure 4, the data are consistent with this hypothesis. The resulting values of Kolaare shown in Table I. The data for methyl orange, particularly with didodecylamine and higher (BH+A-), are also badly scattered. Both the nonideality and the scatter are thought to be due to aggregation beyond ion pairs in the organic solutions. Such aggregation would be favored both by the ionic head groups and by the well-known tendency of azobenzene derivatives to stack.23 In other media the stacking phenomenon has been reported to be both time and surface area dependent, and might well contribute an element of irreproducibility . Membrane experiments defined two extreme categories, with a broad crossover region between them. Low solutiqn pumping rates, a low loading solution pH, and a high (B) tended to produce results of the first category. In this category kl was strongly dependent on the pumping rate, but independent of (H+),, (B), and the nature of the membrane. These conditions will be described as hydrodynamically limited, for reasons that will become clear. High loading solution pumpkg rates, a relatively high loading solution pH, and low (B) tended to produce results in the second category. Under these conditions kl was invariant under changes in pumping rate, but directly proportional to (B) and (H+)l,and inversely proportional to 1, the thickness of the organic membrane. Such conditions are designated “internally limited”. Experiments under hydronamically limited conditions gave linear plots of log (Ao/At) or log A, as a function of t for 1-2 h (at least 50% decrease in A,, as shown in Figure 2). Then, over a fairly short period of time, the transfer process stopped. The values of k were obtained from such plots by inspection.% These values of k were invariant under changea in the initial (A-), and replicate experiments gave values generally differing by less than 10%. Table I1 shows a typical set of such results. Experiments under internally limited conditions gave plots of log A, vs. t for which the slope became increasingly negative for the first several hours of operation; that is, (23) DeVylder, M.; DeKeukelaire, D. Bull. SOC.Chim. Belg. 1978,87, 9-13. (24) Weston, R. E., Jr.; Schwarz, H. A. ‘Chemical Kinetics”;Prentice-Hall; Englewood Cliffs, NJ, 1972; pp 7-11.
2 2 2
1 0 5 ( ~ - ) ,105ha/u, 1 0 5 ( A - ) , 105ka/u, M s-’ anion M S- ’ 1.43 7.01 57.4
5.1b 5.Eib 4.gb
1 1 1
1.92 4.03 8.63
3.8‘ 5.7‘ 7.6‘
Under these conditions k,a/v is - 8 0 X s-l. These experiments were performed with 0.030 M LA-2 and a loading pH of 7.88, at a pumping rate of 2.5 cm3 s-I, using the 0.048-mm polyethylene gaskets, These experiments were performed with 0 . 0 9 8 M LA-2 and a loading pH of 7.88, at a pumping rate of 2.6 cm3 s - I , using the 0.048-mm gaskets. a
ov 0.0
I
0.5 10-1i-’,
I
I
1.0
1.5
1
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Flgure 5. Relation between k and membrane thickness,‘i. Picrate ion, Goretex support, 0.030 M LA-2 as the proton carrier, a loading pH of 7.88, thin polyethylene gaskets, and a pumping rate of 2.7 cm3 s-‘ were used. The nearly straight cwve represents eq 4 and 5, with 6.26 X 10” for KO, (Figure 3), 9.5 X lo3 cm s-’ fork, (Figure l l ) , and 1.9 X lo-’ ctn’s-’ for 6’, the latter being adjusted to fit this data and that in Figwe 6. The circles are not error circles. They merely identii the points.
the apparent value of k increased. Then, as with hydrodynamically limited experiments, transfer stopped. For many of these experiments a plot of A, itself against t was linear for a considerable period at the beginning of the experiment. Experiments in the crossover region gave intermediate results. For all of these experiments k values were generally obtained from the initial slopes either of plots of log A, against t or of plots of A, against t, and this procedure increased the uncertainty in k somewhat. A theory developed in the Discussion section gives an integrated rate law for experiments in the second catergory, and this is shown to fit the data over most of the course of such an experiment, yielding k values in substantial agreement with those obtained from the initial slope. Table III shows typical sets of such results, both for picrate and for methyl orange. For picrate at all amine concentrations and for methyl orange at low amine concentrations k is invariant under initial (A-) changes, but for methyl orange at higher amine concentrations there is a distinct drift toward higher values of k as the initial (A-) increases. This is assumed to be related to the nonideal behavior shown in Figure 4, as discussed below, and the transfer process is regarded as first order in (A-) in all subsequent quantitative analyses of data. Figures 5-11 show k as a function of pumping rate, loading pH, organic amine concentration, and membrane thickness, in various combinations of polymer support and A-. Changes in membrane thickness were achieved by using multiple support films. Only the Gore-tex film could
Anion Pumping through a Synthetic Liquid Membrane
l
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o
The Journal of Physical Chemistry, Vol. 86, No. 18, 1982 3655
1
t
5.0
(L), n
i 0.9
Figure 6. Variation of k with amine concentrallon for picrate ion. LA-2 was the base, with Gore-tex support, thin polyethylene gaskets, and a pumping rate of 2.8 cm3 s-l. The solid curve represents eq 4 and 5 with 6.26 X 10" for K, (Figure 3), 1.0 X lo-* cm s-' fork, (Figure 111, and 1.9 X lo-' cm2s-l for 6',the latter being adjusted to ftt this data and that in Figure 5. The pH was 7.88. The circles are not error circles. They merely identify the experimental points.
Figure 8. Relatbn between k and amine concentration for picrate bn. LA-2 was the base, with Celgard support, soft rubber gaskets, and a pumping rate of 2.5 om3 s-'. The solid curve represents eq 4 and 5 with 6.26 X 10'' for K ,a (Figure_3), 3.36 X s-' for k , (Figure l l ) , and 9.8 X lo8 cm8 5-l for D'(Figure 7).
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