Anal. Chem. 1980, 52, 1215-1218
may be possible to predict the extent of stacking of purines and pyrimidines in aqueous solutions from retention data. Futher work is now being carried out to examine these postulations.
ACKNOWLEDGMENT T h e authors thank Richard A. Hartwick and Malcolm McKeag for supplying retention data.
LITERATURE CITED (1) Hartwick, R. A.; Brown, P. R. J. Chromatogr. 1976, 726, 679. (2) Hartwick, R. A,; Assenza, S. P.; Brown, P. R. I n Advances in Chromatography", Zlatkis. A., et ai.. Eds.; University of Houston Press: Houston, Texas, 1979 (3) Anderson, F. S.; Murphy, R. C. J. Chromatogr. 1978, 127. 251. (4) Hoffman, N. E.; Liao, J. C. Anal. Chem. 1977 49, 2231. (5) Brown, P. R. J. Chromatogr. 1970, 52, 257. (6) Scholar, E. M.; Brown, P. R.; Parks R. E., Jr.; Cahbresi, P. Slood1973, 47, 927. (7) Brown P. R.: Parks, R. E.; Jr., Herod, J. Clin. Chem. 1973, 19, 919. ( 8 ) Hartwick, R. A,; Krstulovic, A. M.; Brown, P. R. J. Chromatogr. 1979, 786, 659. (9) Sentler, F. C.; Haliine, A. G.; Veening, H.; Dayton, D. A. Clin. Chem. 1976, 22, 1522. (IO) Orcutt, J. J.; Kozak, P. O., Jr.; Giilman, S. A,; Cummings, L. H. Ciin. Chem. 1977, 23, 599. (1 1) Krstulovic, A. M.; Hartwick, R. A,; Brown, P. R. Clin. Chim. Acta 1979, 97, 159. (12) Davis, G. E.; Suits, R. D.; Kuo, K. C.; Gehrke, C. W.; Waaikes, T. P.; Borek, E. Clin. Chem. 1977. 23, 1427. (13) Gehrke, C. W.; Kuo, K. C.; Davis, G. E.; Suits, R. D.; Waalkes, T. P.; Borek, E. J. Chromatogr. 1978, 150, 455. (14) Davis. G. E.; Gehrke, C. W.; Kuo, D. C.; A d s , T. F. J. Chromatoar. 1979, 173,381. (15) Brown, P. R.; Krstulovic, A. M.; Hartwick. R. A. J. Ciin. Chem. Biochem. IQ76 282 .- . -, 14 ., - -. (16) Krstuiovic, A. M.; Brown, P. R.; Rosie, D. M. Anal. Chem. 1977, 49, 2237. (17) Krstulovic, A. M.; Hartwick, R . A,; Brown, P. R.; Lohse, K. J. Chromatogr. 1978, 158, 365. (18) Bugge, C. I n "The Jerusalem Symposium on Quantum Chemistry and Biochemistry", Vol. IV; Israel Academy of Sciences and Humanities: Jerusalem, 1972; pp 194-195.
1215
(19) (a) Ts'o, P. 0. P. I n "Molecular Associations in Biology", Pullman, B., Ed., Academic Press: New York. 1968; p. 59. (b) Ts'o. P. 0. P. Ref. 19a, p 43. (20) Ts'o, P. 0. P.; Mekin, I.S.;Olsen, A. C:. J. Am. Chem. Soc. 1983, 85, 1289. (21) Ts'o, P. 0. P.; Chan, S. I.J. Am. Chem. SOC. 1964, 8 6 , 4176. Ts'o, P. 0. P. J . Chem. Soc. 1965, 87, (22) Schweizer, M. P.; Chan, S. I.; 5241. (23) Brown, A. D.; Schweizer, M. P.; Ts'o. P. 0. P. J. Am. Chem. Soc. 1967, 89,3612. (24) Solie, T. N.; Schellman, J. A. J. Mol. Bo/. 1986, 33, 61. (25) Ts'o, P. 0. P.; Kondo, N. S.; Robbins. R. K.; Broom, A. D. J. Am. Chem. SOC. 1889, 97, 5625. (26) Hanlon, S. Siochem. Siophys. Res. Commun. 1986, 23, 861. (27) Bloomfield, V. A.; Crothers, D. M.; Tinoco, I., Jr.; "Physical Chemistry of Nucleic Acids", Harper & Row: New York, 1974: p 53. (28) Hartwick, R. A.; Grill, C. M.; Brown, P. R. Anal. Chem. 1979, 57, 34. (29) "The Nucleic Acids", Vol. I , Chargeff, E., Davidson, J. N., Eds.; Academic Press: New York, 1955; p 81. (30) Hail. R. "The Modified Nucleosides in Nucleic Acids", Columbia University Press: New York, 1971. (31) Orlov, V. M.; Smirnov, A. N.; Yarshavsky, Y. M. Mol. Blol. 1976, 1 7 , 222.
(32) ibimfieid, V. A,; Crothers, D. M.; Tinoco, I., Jr.; 'Physical Chemistry of Nucleic Acids", Harper 8 Row: New York, 1974; p 76. (33) Bergmann, E. D.; Weiler-Feilchenfeld, H. In "PhysicoChemical Properties of Nucleic Acids", Duchesne, J., Ed.; Academic Press: New York, 1973. (34) Bergmann, E. D.; Weiler-Feilchenfeld, H. I n "The Jerusalem Symposium on Quantum Chemistry & Biochemistry", Vol. IV; Israel Academy of Sciences and Humanities: Jerusalem, 1972; pp 21-29. (35) Siifkin, M. A. I n "Physico-Chemical Properties of Nucleic Acids", Duchesne, J., Ed.; Academic Press: New York. 1973; pp 11-15. (36) Fell, A. F.; Plag, S. M.: Neil, J. M. J. Chromatogr. 1979, 186, 691. (37) Slifkin, M. A. I n "Physlco-Chemical Properties of Nucleic Acids", Duchesne, J., Ed.; Academic Press: New York. 1973; p 70. (38) Ludeman, H. D. Siophys. Structure Mechanism, 1975, 7(2), 121.
RECEIVED for review January 16, 1980. Accepted March 20, 1980. We gratefully acknowledge the support of the Public Health Services, Grant # 5R01 CA 17603 (P.R.B.) and Grant i f GM 20846 (E.G.). Presented at the ACS Award in Analytical Chemistry Symposium in honor of J. C. Giddings, Houston, Texas, March 1980.
Water Sorption and Cation-Exchange Selectivity of a Perfluorosulfonate Ion-Exchange Polymer A. Steck and H. L. Yeager" Department of Chemjstry, The University of Calgary, Calgary, Alberta T2N IN4, Canada
SelectivAy coefficient measurements for ion exchange in Nafion perfluorosulfonate polymer have been performed for alkall metal ions, alkaline earth ions, Ag', Ti', Co2+, and Zn2+ for as-recelved and expanded forms of the material. Water contents have also been determined as a function of counterlon. Results Indicate that the Increase In entropy when water Is released during exchange of hydrogen Ion for a metal ion is the controlling factor in determlning the magnitudes of selectivity coefficients. Alkali metal ion-hydrogen ion selectivity coefficients were also determined in methanol, and show little effect of the reduced solvent dielectric constant.
We report here the results of further studies of the ionexchange properties of Nafion (DuPont), a perfluorosulfonate cation-exchange polymer. This material is produced mainly for membrane applications in which chemical inertness and low electrical resistance are important considerations. These applications include the electrolytic production of chlorine0003-2700/80/0352-12 15$01.OO/O
caustic ( I , 2 ) and solid polymer electrolyte fuel cells ( 3 ) . Nafion is a n uncross-linked high molecular weight polymer with an ion-clustered morphology ( 4 ) . This structure produces interesting differences in the diffusional behavior of ions in this material compared to conventional cross-linked sulfonate ion-exchange resins (5, 6). Unusual differences are also seen for cation-exchange selectivities. Nafion exhibits a spread in selectivity coefficients for the exchange of alkali metal ions with hydrogen ion which is about three times larger than for 16% divinylbenzene cross-linked Dowex 50 sulfonate resin (7).Also, the ion clusters appear to produce a more uniform exchange site environment, as inferred from the lack of dependence of selectivity coefficients for alkali metal ions on the ionic fraction of sites occupied by the metal ion. This is probably due to the dynamic nature of these ion clusters, as seen in the large changes in water content of the polymer as a function of counterion (7). For the current studies, we report measurements involving the alkali metal ions and alkaline earth ions, as well as Ag+, T1+,Co'+, and Zn2+as representatives of cations with less ideal 0 1980 American Chemical Society
1216
ANALYTICAL CHEMISTRY, VOL. 5 2 , NO. 8, JULY 1980
hydration properties, for comparison. Ndion has been shown to irreversibly sorb increased solvent when heated in water (8). The ion exchange selectivities and water contents of this expanded form of the polymer were also measured for various univalent and divalent cations. Finally, the ion-exchange isotherms for alkali metal ion-hydrogen ion exchange in anhydrous methanol were measured. Nafion shows greatly increased swelling in this and other alcohols (6, 81, and these measurements were performed to test the influence of swelling and reduced solvent dielectric constant on selectivity properties.
Table I. Selectivity Coefficients and Water Contents in Nafion 120 mol H,O/mol
so
ion H' Li' Na' K+ Rb' Cs' Tl+ Ag+ Mgz+ Caz+ SIz+ Ba2+ Coz+ ZnZ+
EXPERIMENTAL Materials. Nafion 120 membrane (Plastics Dept., DuPont, Wilmington, Del. 19898) with a nominal exchange capacity and thickness of 0.83 mequiv/g dry H-form polymer and 0.025 cm, respectively, was used in all experiments. Reagent grade alkali metal and alkaline earth chlorides, silver nitrate, thallium(1) chloride, cobalt chloride, and zinc chloride were used as received. The purification of methanol has been described previously ( 5 ) . Anhydrous 0.01 M HC1 solutions in methanol were produced by bubbling high purity HC1 into purified methanol followed by dilution to the proper concentration. Procedure. Standard HCl ("OB for Ag+ and TI+ experiments) and metal salt solutions were prepared. The concentrations of salt solutions were determined by column ion exchange for hydrogen ion followed by titration. The pretreatment of membrane samples as well as the experimental procedure for the measurement of selectivity coefficients for univalent ions has been described previously (7). These experiments use membrane equilibrating solutions of 0.01 M ionic strength and membrane samples of 4 cm2in area. The same general procedure was used for experiments involving divalent ion-hydrogen ion exchange. However, in these cases it is necessary to use larger membrane pieces, 16 cm2,in order to obtain accurate hydrogen ion contents. To maintain solution volumes at practical levels, a higher ionic strength of 0.1 M was used for the equilibrating solutions. Each membrane sample was equilibrated for 36 h at 25 or 40 f 0.01 "C with mechanical shaking. The membrane was then removed and carefully blotted with paper tissue before rinsing with distilled water. (This procedure is necessary because the relative proportions of counterions in the membrane can change if adhering electrolyte solution is diluted when the ion-exchange process involves ions of different charge type (9).) Then the membrane was washed repeatedly with distilled water and immersed in 2 M NaCl solution. The released hydrogen ion was determined by titration. Aliquots of equilibrating solution were also titrated for hydrogen ion. Selectivity coefficients were calculated from the results of the hydrogen ion-divalent ion-exchange experiments using the equation:
where XB,XArepresents equivalent ionic fraction of the ions in the membrane and C represents solution molarity. Single ion activity coefficients, 7, were calculated using the extended Debye-Huckel equation and Kielland's individual ion size parameters. As before, activity corrections were not applied to univalentunivalent ion selectivity coefficients (7). Samples of H-form Nafion 120 were boiled in water (96 OC) for 5 h in order to produce expanded form membranes. We have found that after less than 3 h of boiling a t this temperature, the membrane reaches a constant value of water sorption which remains unchanged after 4 weeks of equilibration in water at 25 "C. Ion-exchangeexperiments were performed with these samples using procedures identical t o those already described. Water to exchange site mole ratios were determined by weight loss measurements after heating samples in various ionic forms. Temperatures of 12C-160 "C for 15 h under vacuum were sufficient to completely dry samples with univalent counterions, but temperatures of up to 180 "C were necessary for divalent ion forms. Completeness of drying was checked using infrared spectroscopy. The number of exchange sites in each membrane sample was
25°C
40°C
0.57gb 1.22' 3.97b 6.26b 9.11b 6.12
0.555 1.31 9.04b
1.07'
2.30 3.60 4.23 5.55 1.24 0.97
2.36 5.27
3-
25 "C (E)'
25°C
25 " C (E)'
0.586
16.7' 14.3b 11.9'
22.3 22.3 18.4 13.3
1.18
3.48 4.71 7.06 3.83 0.90 2.15 2.87 3.79
12.2 13.9 12.9 12.3
4.61
11.6
11.3 11.7 17.6 19.8 17.5 16.9 14.9
13.7
20.0
14.1
19.9
8.gb
7.7; 6.6 8.0
' Expanded form, produced by heating in water.
11.8
Ref.
7. determined beforehand by titration. In order to determine whether the measured ion-exchange capacity of Nafion 120 depends on the counterion, a single membrane sample was successively placed in the H+, Na', Cs+, Mg2+,and Ca2+forms, and analyses were performed for each counterion after desorption. Analyses for Na+ and Cs+were performed by radioisotope dilution methods and Mg2+ and Ca2+were titrated with EDTA. No difference in the measured capacity could be found within experimental error. Water contents for boiled membranes were measured after exchange at 25 "C from H-form to the appropriate counterion form. Measurements of selectivity coefficients for alkali metal ionhydrogen ion exchange were performed in similar fashion to those in aqueous solution (7). Membranes in alkali metal ion or H-forms were equilibrated with several portions of anhydrous methanol over a period of several days before exchange experiments were performed in order to remove last traces of water.
RESULTS AND DISCUSSION Selectivity coefficients for metal ion-hydrogen ion exchange for as-received and expanded forms of Nafion 120 are listed in Table I. For some ions, the results of measurements at 40 "C for the as-received material are also listed. These values were obtained by the measurement of selectivity coefficients a t several equivalent fractions of metal ion in the polymer and determination of the value a t equivalent fraction = 0.5 by interpolation. In general, this yields a good approximation to the result obtained by integration over all equivalent fractions in the ion-exchanger phase (10). This is particularly valid for Ndion, because in this and previous studies we have found that selectivity coefficients have much less dependence on equivalent fraction of metal ion than for divinylbenzene cross-linked polystyrene sulfonates (7). Estimated relative standard deviations for the selectivity coefficients in Table I are 1.5% and 2.5% for univalent ion and divalent ion values, respectively. Molar ratios of water to exchange site for both forms of Nafion 120 are also listed in Table I as a function of exchanged metal ion. As seen from Table I and Ref. 11 and 12, Nafion shows much greater selectivity differences among alkali metal ions than polystyrene sulfonate resins of 4, 8, or 16% divinylbenzene cross-linking, whereas for alkaline earth ions the selectivity coefficients are very similar to a 4% DVB resin and smaller than those of 8 or 16% cross-linking. Selectivity coefficients of Ag+, T1+,Co2+,and Zn2+for Nafion are all lower than those for the conventional sulfonate resins of any cross-linking, probably indicating that for this perfluorinated polymer with no aromatic content, nonelectrostatic interac-
ANALYTICAL CHEMISTRY, VOL. 52, NO. 8, JULY 1980
tions between counterions and the polymer matrix are reduced to a minimum. All selectivity coefficients are smaller for the expanded form of Nafion, but the spread in alkali metal ion values remains larger than for polystyrene sulfonate resins. The water to exchange site mole ratios also show different trends for various counterions compared to conventional sulfonate resins. For cations with large free energies of hydration, such as hydrogen ion and all of the alkaline earth ions, water contents are similar to resins of 4% cross-linking. However, the value for cesium ion is closer to that of a 16% DVB resin, 5 . 7 , than for the 4 % DVB material, 19.0 (11). Values in Table I for the other alkali metal ions vary smoothly between these extremes. The water contents for the expanded form of Nafion are much higher as expected, but all trends remain the same. Now though, the water content of the cesium ion form is more like that for an 8% DVB resin, 8.8 (11). The water contents for sulfonate resins show greater changes from Mg2+to Ba2+forms than Nafion values, unlike the alkali metal ions (11, 12). Boyd (13) has discussed the nature of ion-exchange reactions between hydrogen ion and these metal ions, in polystyrenesulfonate resins of various cross-linkings, in terms of the measured enthalpy, entropy, and volume changes of the ion-exchange reactions. Enthalpy and entropy changes are both small and negative for alkali metal ion exchange in lightly cross-linked resins. No indication of ion pairing is seen, and these changes are likely due to differences in ionic hydration in the solution phase for the exchanging ions. For resins of higher cross-linking (and lower water content) electrostatic interactions increase and solvent separated ion pairs appear to form. This results in increasingly negative values for the enthalpy and entropy of exchange and improved selectivities for alkali metal ions. T h e magnitudes of selectivity coefficients for divalentunivalent cation-exchange reactions for polystyrenesulfonate exchangers are generally controlled by positive entropies of exchange; a large factor in this entropy change is the increase in solution entropy when a divalent cation is replaced by two univalent cations which have much smaller hydration entropies (13-15). Changes in resin water content are relatively larger than for the exchange of univalent ions (11, 12), probably because of the formation of solvent-separated and contact ion pairs (13). This release of water from the exchanger phase will also cause a positive entropy change to the system, as will the statistical entropy increase when divalent counterions distribute among twice as many univalent exchange sites ( 1 4 , 16). Enthalpies of exchange also tend to be positive, owing to the increased energy required to dehydrate a divalent cation as it enters the resin phase. It is expected that Nafion would differ in a t least two respects from polystyrenesulfonate resins in its properties as an ion exchanger. First, the perfluorinated backbone should yield a much lower charge density on the sulfonate exchange sites, reducing the extent of electrostatic interactions and minimizing the formation of even solvent-separated ion pairs. Indeed, Nafion in the hydrogen ion form has been shown to be an effective “superacid” solid catalyst for a wide variety of organic reactions (17, 18). Also, although Nafion is structured in that the sulfonates group into ion clusters, the polymer presumably contains no formal chemical cross-links. Thus Nafion has a more dynamic morphology, and the water content of the material is more dependent on the hydration energy of the counterion than for polystyrenesulfonate resins. In the latter case, large amounts of interstitial water are present for low cross-linkings which, as Reichenberg concludes (IO),have the effect of “diluting” ion-exchange selectivities to reduce selectivity differences among ions. For higher cross-linkings, the rigid three-dimensional matrix forces
2.5 2.0
t1
1217
d .
/ 0
2
1 4
1
! I ’ 1 1 6
8
10
12
A H P O E X c H ,M O L / E Q U I V
Figure 1. Logarithm of selectivity coefficients vs change in water content for Nafion 120. 0, 0 ,alkali metals; 0 ,. , alkaline earth ions; A, A,Ag’; V,V,TI’. Open symbols, asreceived form; closed symbols, expanded form
counterions, especially polyvalent ones, to partially dehydrate in order to enter the exchanger phase. The changes in water contents of Nafion for the various counterions in Table I do in fact correlate well with the respective differences in their free energies of hydration (19). (For divalent ions, one half of the free energy of hydration should be used for comparison, in accordance with the stoichiometry of the ion-exchange reaction.) Both of these factors would result in lowered enthalpies of ion-exchange reactions for Nafion. The selectivity coefficient values at 40 “C appear to confirm that these equilibrium constants have small heats of reaction. This was also seen in the lack of temperature dependence for the chromatographic separations of the alkali metal ions and the alkaline earth ions (7). Small enthalpies of reaction are easily hidden by experimental error in the measurement of the temperature dependence of selectivity coefficients however. Also, since the water content of Nafion is temperature dependent, the system changes between the two temperatures. Therefore, calorimetric measurements of heats of exchange would be needed in order to confirm that enthalpy changes are minimal. It does appear, however, that increased heats of reaction over those of conventional sulfonate resins cannot account for the wide spread in selectivity coefficients for the alkali metal ions for Nafion. The more important factor here appears to be the positive entropy of reaction when hydrogen ion is replaced by a metal ion in the polymer phase. This exchange is always accompanied by release of water and some polymer contraction, both of which are entropy-producing processes (14,ZO). Release of water from ionic crystalline hydrates is accompanied by entropy increases of about 40 J mol-’ K-I (21,22). Although magnitudes of this level are not expected for Nafion, the large changes in water content would be a compensating factor. If it is assumed that enthalpies of ion exchange are minimal for Nafion, and that the major source of entropy change is water release from the polymer, then a relationship should exist between the logarithm of selectivity coefficient and the amount of water released per mole of exchanged counterions. This is shown in Figure 1,where In K is plotted vs. the change in water content for alkali ions and alkaline earth ions in both as-received and expanded forms of Nafion. Silver ion and thallium ion have been included in the plots for the univalent ions. The lines are least-squares fits, excluding the latter two ions. The linearity of these relationships and the similarity of slopes of alkali metal and alkaline earth ion plots for the as-received and expanded forms of Nafion suggest that for each morphology a constant increment in entropy is gained
1218
ANALYTICAL CHEMISTRY, VOL. 52, NO. 8, JULY 1980
I7L
I
16
14 16
, 110,
I
IOC
1
7
2c
6 7 5 0.0
0.2
0.4
0.6
0.8
1.0
0
1_
-
-
'I---
IONIC FRACTION OF M+
Figure 2. Water content of Nafion 120 in H+ form as a function of ionic fraction of metal ion. 0, Na'; 0, Cs'
per released water molecule. The slopes of these lines for as-received Nafion yield values of 0.90 and 0.94 k J mol-' at 25 OC for the alkali metal and alkaline earth ions, respectively. Corresponding values for the expanded form are 0.53 and 0.40 k J mol-l. These values along with the amount of released water can account for the magnitudes of the selectivity coefficients, even though they are only a small fraction of the entropy increase for the release of water from ionic crystalline hydrates. T h e results for the expanded form of Nafion indicate that the ion clusters present a more aqueous-like environment to sorbed water which results in smaller entropy increments upon release, even though the amount of water released per equivalent of exchanged ions is generally larger for the expanded form. An implication of this approach is that the water content of mixed counterion forms of Nafion should be the weighted average of the water contents of the pure ion forms. In Figure 2 this is shown to be essentially correct for the sodium ion and cesium ion forms in as-received Nafion, where the water content as a function of metal ion fraction is plotted for exchange with hydrogen ion. We conclude that entropy changes associated with changes in Nafion's water content are responsible for the excellent spread in selectivities for alkali metal ion exchange with hydrogen ion. For divalent ions, the low basicity of exchange sites, along with the much larger enthalpies of hydration with these cations, couple to lower water changes and largely remove this effect. This results in selectivity coefficients which are very similar to 4 % divinylbenzene polystyrenesulfonate. Ion-exchange selectivity isotherms for alkali metal ionhydrogen ion exchange in methanol are shown in Figure 3. T h e isotherms of K', Rb+, and Cs+ exchange show large positive slopes. The exchange for these ions is accompanied by volume decreases of up to 40%, and the resulting change in cluster environment may be responsible for an increased preference for the metal ion. These curves were integrated to provide overall selectivity coefficients. The results are: Li+, 0.443; Na+, 0.680; K+, 4.68; Rb', 7.17; and Cs+, 9.61; with an estimated relative standard deviation of 3% in each case. These values are similar to the aqueous results, and do not indicate increased electrostatic interactions due to the lower dielectric constant of methanol. In contrast, selectivity coefficients of hydrogen ion exchange in 8% divinylbenzene polystyrenesulfonate for methanol are: Li', 0.335; Na+, 3.23;
. 3031307. Yeo, R. S . ; McBreen, J. J. Electrochem. SOC. 1979, 126, 1682-87. Yeo, R. S.; Eisenberg. A. J. Appl. Polym. Sei. 1977, 2 1 , 875-96. Lopez, M.; Kipling, 8.: Yeager, H. L. Anal. Chem. 1977, 49, 629-32. Yeager, H. L.; Kipling, B. J. Phys. Chem. 1979, 8 3 , 1836-39. Yeager, H. L.; Steck, A. Anal. Chem. 1979, 5 1 , 862-65. Grot, W. G. F.; Munn, G. E.; Walmsley, P. N. "Perfluorinated Ion Exchange Membranes", presented at 141st National Meeting, The Electrochemical Society, Houston, Texas, May 7-1 1, 1972. Bonner, 0. D.; Livingston, F. L. J. Phys. Chem. 1958, 6 0 , 530-32. Reichenberg, D.I n "Ion Exchange", Marinsky, J. A,, Ed.; Marcel Dekker: New York, 1966; Vol. I,Chapter 7. Bonner, 0.D. J. Phys. Chem. 1955, 5 9 , 719-21. Bonner, 0 . D.; Smith, L. L. J. Phys. Chem. 1956, 6 1 , 326-29. Boyd, G . E. I n "Charged Gels and Membranes", SBldgny, E., Ed.; D. Reidel: Dordrecht, Holland, 1976; Volume I, pp 73-89. Boyd, G. E.; Vaslow, F.; Lindenbaum, S. J. Phys. Chem. 1987, 71, 2214-19. Rieman, W.; Walton, H. F. "Ion Exchange in Analytical Chemistry"; Pergamon: New York, 1970; Chapter 3. Cruickshank, E. H.; Meares, P. Trans. Faraday Soc. 1957, 53, 1289-98. Olah, G. A.: Kaspi, J.; Bukala, J. J. Org. Chem. 1977, 42, 4187-91. Obh, G. A.; Prakash, G. K. S.; Sommer, J. Science 1979, 206. 13-20. Franks, F. "Water, A Comprehensive Treatise"; Plenum: New York. 1973; Volume 3, Chapter 1. Gamaiinda, I.; Schioemer, L. A.; Sherry, H. S.;Walton, H. F. J. Phys. Chem. 1987, 71. 1622-28. Moore. W. J. "Phvsical Chemistw", 4th ed.; Prentice-Hall: Enqlewood Cliffs, N.J., 1972;Chapter 3. Latimer, W. M. "Oxidation Potentials"; Prentice-Hall: Englewood Cliffs, N.J.. 1952: ~. rD 364. Fesher. R. G.; Strobel, H. A. J. Phys. Chem. 1963, 67, 2562-68. Eisenman. G. Siophys. J. 1962, 2. Part 2, 259
RECEIVED for review January 21, 1980. Accepted March 24, 1980. This work was supported by the Natural Sciences and Engineering Research Council of Canada and by the University of Calgary.
