Similarities and Differences between Liquid and Solid Ion Exchangers and Their Usefulness as Ion Specific Electrodes George Eisenman Department of Physiology, University of Chicago, Chicago, Ill. 60637 The principal features of the electrode potentials experimentally observed with solid and liquid ion exchange membranes are described and compared in relation to a general equation derived elsewhere by Sandblom, Eisenman, and Walker (7). This equation consists of three terms, the first of which is shared by solids and liquids. The remaining two terms are zero for a solid ion exchanger but depend on such properties of a liquid ion exchanger as the partition coefficients of the various species, their degree of dissociation, and their relative mobilities. The explicit expressions for the steady-state electrode potential of a completely dissociated liquid ion exchanger as well as for a strongly associated one are given and compared: the parameters determining ionic selectivity are discussed in relation to classical properties of weak electrolytes-e.g., dissociation constants, limiting equivalent conductances, transference numbers, and partition coefficients. Measurements of these parameters for a typical liquid ion exchanger (di-tethylhexyl phosphoric acid in wet n-amyl alcohol) are presented and compared with the electrode behavior theoretically expected for Na +-H mixtures. +
RECENTYEARS have seen an awakening interest in ion specific electrodes. From the establishment of the usefulness of such solid membranes as the now classical H+-selective glass electrode in the late thirties (2) and the development of glasses selective for univalent cations in the late fifties (3, 4, we have now progressed to the use of liquid membranes as electrodes for such divalent cations as Caz+ (5) and anions such as Clod- (6) (for the earlier history of liquid membranes see 7-12). All of the above electrodes are ion exchangers to which this paper will confine itself. However, ion exchangers are not the only kinds of ion specific electrodes. For example, the impregnated rubber electrodes of Pungor (13) and the solid state electrodes of Ross and Frant (14) are not simple ion exchange membranes although ion exchange processes are involved in their mechanism, The semiconducting glasses described by Hebert (15) should also be mentioned, as should ~~
(1) J. Sandblom, G. Eisenrnan, and J. L. Walker, Jr., J . Phys. Chem., 71, 3862 (1967). (2) M. Dole, “The Glass Electrode” Wiley, N . Y., 1941. (3) G . Eisenrnan, D. 0. Rudin, and J. U. Casby, Science, 126, 831 (1957). (4) G. Eisenman, Biophys. J . , 2, part 2, 259 (1962). (5) J. W. Ross, Jr., Science, 155, 1378 (1967). (6) J. W. Ross, Jr., Orion Research Inc., Bulletin 92-81. (7) F. G. Donnan and W. E. Garner, J . Chem. SOC.(London), 115, 1313 (1919). (8) M. Kahlweit, PpUgers Archic., 271, 139 (1960). (9) 0. D. Bonner and J. Lunney, J. Phys. Chem., 70,1140 (1966). (10) M. Dupeyrat,J. Chim. Phys., 61,306,323(1964). (11) G . M. Shean and K. Sollner, Ann. N. Y . Acud. Sci. 137, 759 ( 1966). (12) H . L. Rosano, P. Duby, and J. H. Schulman, J . Phys. Chem., 65, 1704 (1961). (13) E. Pungor, ANAL.CHEM., 39, (13) 28A (1967). (14) M. Frant and J. W. Ross, Science, 154, 1553 (1966); Orion Research Inc., Bulletin 94-09 and 94-16.
310
ANALYTICAL CHEMISTRY
the bilayer lipid membranes (and thicker solvent phases) which, when treated with depsipeptide (16, 17) and macrolide (18) antibiotics, become highly specific electrodes for K+ and Rb+. A classical ion exchange is unlikely to be the basis of the electrode properties in the latter systems because the few ion exchange groups of these molecules are expected to be undissociated at neutral pH, and a coordination-complexing reaction is more likely. ELECTRODE POTENTIAL OF SOLID ION EXCHANGERS
Because the electrode potential of a typical solid ion exchanger, the glass electrode, has been extensively characterized elsewhere (19, 20), only those properties will be described which are necessary as a basis for comparison with the less familiar liquid ion exchangers, noting that other solid ion exchangers have also been well described (21-24). A desirable characteristic of any practical electrode is that its response faithfully reflect at all times the activity of the ion of interest in the solutions to which the electrode is exposed. Such behavior is observed for solid ion exchangers for which a steady potential is usually established within a few minutes after a step change in ionic activity [see for example Figure 5-1 of Reference (20) and the careful discussion of transient phenomena by Rechnitz (2511. Indeed, a step response is expected from theory for a solid ion exchanger if its chemical properties are spatially uniform and temporally invariant (26), but is not expected for a solid ion exchanger whose immediate surface properties differ from those of the bulk (27) nor for a liquid ion exchanger, even if its chemical properties are constant (1, 28), with the exception of certain special (15) N . C. Hebert, Analytical Division, Summer Symposium, Clarernont, Calif., 1967. (16) A. A. Lev and E. P. Buzhinsky, Cyfologiu (U.S.S.R.), 9, 106 (1967). (17) P. Mueller and D. 0. Rudin, Biophys. Biochem. Res. Comm., 26, 398 (1967). (18) Z . Stefanac and W. Simon, Microchem. J., 12, 125 (1967). (19) G. Eisenrnan, “Advances in Analytical Chemistry and Instrumentation, 4“ (C. N . Reilley, Ed.), Wiley-Interscience, N. Y., (1965), 215 (reprinted in G. Eisenman, R. Bates, G. Mattock and S. M. Friedman, “The Glass Electrode,” Wiley-Interscience, N . Y. (1966)). (20) G . Eisenman, Ed., “Glass Electrodes for Hydrogen and Other Cations: Principles and Practice, M. Dekker, N. Y., (1967). (21) K. Sollner,J. Phys. Chem., 53,1211, 1226 (1949). (22) C. E. Marshall, J. Phys. Chem., 48, 67 (1944). (23) G. N. Ling, chapter 10 of Ref. (20). (24) A. H. Truesdell and C. L. Christ, chapter 1 1 of Ref. (20). (25) G . A. Rechnitz, Analytical Division, Summer Symposium, . Clarernont, Calif., (1967): (26) F. Conti and G. Eisenman, Biophvs. J., 5,247 (1965). (27j G . Eisenrnan, “The Ion Exchange Characteristics of the Hydrated Surface of Na+ Selective Glass Electrodes,” in “Symposium on Microelectrodes,” M. Lavallee, Ed., Wiley-Interscience, in press (1967). (28) J. Sandblom and G . Eisenrnan, Biophys. J . , 7, 217 (1967), particularly pp 231-232.
cases which will be discussed later. However, it should be noted that a step response is expected both for solid exchangers having heterogeneous chemical properties and for liquid exchangers, when one is dealing with a step change in concentration of an ion to which the electrode is sufficiently selective that other ions can be neglected. The relative sensitivity of glass electrodes to various cations has been described (3) in terms of the parameter K12Po' of Equation 1 for Vo(t), the difference of electric potential between solutions (') (") on the two sides of the glass membrane at any time t subsequent to the brief transient mentioned above:
The parameters n and K I ~ ~are " 'empirical constants characteristic of each glass composition for a given pair of cations 1 and 2; and a1 and a2 are the activities of species 1 and 2 in the solutions signified by the (') and ("). Equation 1 has been tested extensively for a variety of cation-hydrogen mixtures [cf.pp 231-248 of (19) and pp 211-218 of (2911. On the other hand, in mixtures of many univalent cations at constant pH, n = 1 so that Equation 1 reduces to the simplified form: N
i-1
valid for mixtures of Ncations (19). The selectivity for various cations is defined by the parameter KlgPo'of Equations l and 2, and typical values relative to K+ have been summarized for aluminosilicate glass electrodes in Figure 9-7 of (20), which illustrates that solid ion exchangers are highly selective for univalent cations but considerably less so for divalent cations. This limitation is not due to poor ion exchange affinities for divalent US. monovalent cations, because aluminosilicate ion exchangers have quite respectable selectivities for divalent relative to monovalent cations (30). Rather, from the considerations noted below, the limitation appears to be the result of a low mobility of divalent cations within the solid exchanger; it is the circumvention of this limitation by using a liquid which appears to offer the prime advantage of liquid ion exchangers over solids. Parameters Involved in Membrane Potential Selectivity,
It has been possible to deduce theoretically by integrating the Nernst-Planck flux equations for an ion exchanger (26,29,31) that the potential selectivity constant KifPotof Equation 2 is simply the product of the equilibrium constant Kij of the ion exchange reaction
J+ (aqueous)
+ I+ (membrane) e J+ (membrane)
+ I+ (aqueous),
(3)
and the mobility ratio uj/ut of the ions within the membrane. Thus : (4)
(29) B. P. Nicolsky, M. M. Schultz, A. A. Belijustin, and A. A. Lev, chapter 6 of Ref. (20). (30) A. H. Truesdell and C. L. Christ, Chapter 1 1 of Ref. (20), pp 318-319. (31) G. Karreman and G. Eisenrnan, BUN. Math. Bioplzys., 24, 413 (1962).
Figure 1. Diagram of chamber in which membrane potentials of liquid ion exchangers were studied (36) (1) Represents a 1.5 inch thick Lucite rod in which a hole of 1-cm diameter (2) was drilled and which had the various outlets indicated for changing aqueous solutions. Two such chambers were carried on a machined key way so they could be moved sideways. Interposed between the two Lucite chambers which carried the aqueous solutions was a Lucite disk of various dimensions (3) which contained the liquid exchanger. The liquid exchanger was retained within the Lucite disk by polyethylene millipore guard filters (4) which were filled with aqueous solutions; and the entire assembly was retained by pressure from neoprene O-rings (5). The chamber also had inlets and outlets for convenient changing of the membrane phase. The normal diameter of the membrane hole was 1 cm and the normal thickness of the membrane was also 1 cm although this could be varied as desired. A variety of reference and specific ion electrodes could be inserted through the openings indicated in the top of the chamber
for an ideal ion exchange membrane. This result shows how diffusion-migration processes in the interior of glass and equilibrium processes at its phase boundaries contribute jointly to the origin of the glass electrode potential. An experimental analysis has recently been carried out for the thickly hydrated surface of NAS 27-4 glass, a typical Kf electrode, with the finding that the tenfold selectivity observed for Kf relative to Na+ as an electrode is the result of a hundredfold ion exchanger preference for K+ over Na+ opposed by a 10-fold lower mobility of K+ than that of Na+ (32). Reference (32) also demonstrated that Ca2+had a very low mobility in the hydrated glass surface, an observation which is in accord with the generally poor mobility of divalent cations in zeolites (33, 34) as well as in dry glass (35), and which suggests that this is the cause of the poor electrode selectivity of such solid ion exchangers for divalent cations. It therefore appears that the principal restriction to be overcome, when trying to devise electrodes selective for ions other than those of Groups Ia and Ib using solid ion exchangers, is the tendency for decreases in mobility to offset any increases in ion exchange affinity for multivalent (or large) ions in solids. It is precisely in this respect that liquid ion exchangers offer theoretical advantages over solids, as will be seen in the following portion of this paper. ELECTRODE POTENTIAL OF LIQUID EXCHANGERS Methods. The membrane potential of liquid ion exchangers were characterized using the chamber illustrated in Figure 1. The membrane consists of a liquid ion exchanger interposed between two aqueous solutions from which it is separated by polyethylene millipore filters (0.13 mm thick) filled with aqueous solution. To study the (32) (33) (34) (35) (36)
G. Eisenman, Chapter 5 of Ref. (20). W. Peria, Bull. Am. Phys. SOC.,3, 230 (1958). R . M. Barrer, Proc. Brit. Ceram. Soc., 1, 145 (1964). R. H. Dorernus, chapter 4 of Ref. (20). G . Eisenman and J. L. Walker, Jr., unpublished results, 1967. VOL. 40, NO. 2, FEBRUARY 1968
31 1
mV
- 2.0
0
2 .o
4.0
-2.0
- Log
Q
0
2.0
4.0
cat
O H No Ca
Figure 2. Electrode potentials of “wet” n-amyl alcohol containing the indicated percentages of bis-2-ethyl hexyl phosphoric acid (36) “Instantaneous” potential values were measured for 1.0-cm thick membranes, as described in the text. The solid diagonal lines indicate the theoretical Nernst slopes of 59 mV for monovalent cations, while the dashed line is drawn with a 29.5 mV Nernst slope for divalent cations “instantaneous” potentials referred to in the theoretical section below, a relatively thick liquid-exchanger phase was used (1.0 cm as routine, but membranes whose thickness varied from 0.5 to 5.0 cm gave the same results). With such a thickness, the membrane potential was found to reach a steady value within several minutes after changing solutions and to remain constant thereafter for a sufficiently long period to be measured easily and reproducibly (36). Whenever a drifting potential was encountered, most often in dilute solutions, the “instantaneous” value was estimated by repeatedly renewing the solutions and, occasionally, the membrane. Aqueous solutions were prepared as the chlorides at neutral pH using analytical grade reagents and were saturated with the solvent used for the membrane. The liquid cation ex-
3 12
ANALYTICAL CHEMISTRY
changer was usually bis-Zethyl hexyl phosphoric acid (obtained from Union Carbide; unpurified, and abbreviated hereafter in the figures as “H Bis” or as “DZEHP”) in various straight chain alcohols (obtained from Baker Co. ; analyzed). The potential differences between the two aqueous phases were measured, as routine, with saturated KC1-Calomel half cells, as well as with AgCl electrodes and the appropriate cation-selective glass electrodes, thereby giving a simultaneous measurement of the ionic activities in the aqueous solutions. Experimental Observations. Figures 2, 3, 5 present typical electrode potentials for “wet” n-amyl alcohol containing the indicated percentages by volume of bis-2-ethyl hexyl phosphoric acid. The liquid exchanger was pre-equilibrated with aqueous 1O-W HC1, which was held constant as the
mV
A OY.
0.1% 0
1.0% 1O.OY.
Figure 3. Electrode potentials of “wet” n-amyl alcohol containing the indicated percentages of bis-2-ethyl hexyl phosphoric acid Data of Figure 2 are replotted for ease of comparison with the data in n-decyl alcohol to be presented in Figure 6
16C
+
mV
8C
0
- 80
- Log C,,,(RHS) Figure 4. Membrane potentials of “wet’ n-decanol containing 10 % bis-2-ethyl hexyl phosphoric acid (36) Illustrates particularly clearly that the selectivity between two ions of the same valence is independent of the absolute solution concentration (cf. the 144-mV potential difference between 1.ON NaCl and 1.ON HCI, in good agreement with the 142 m V observed between 0.1N NaCl and 0.1N HCI)
reference solution on one side of the membrane. The composition of the other aqueous phase was varied; the cation activity is indicated on the abscissa. For the pure solvent (labelled “0%” at the upper left of Figure 2 and indicated by open triangles in Figure 3), a region of Nernstian response to H+ and Na+ is seen for the most dilute solutions, but there is no such response to Ca2+. The effects of adding a liquid ion exchanger to the solvent are illustrated in the remainder of Figures 2 and 3. With increasing H Bis concentration, the cation response becomes increasingly pronounced, as can be seen by comparison with the theoretical slopes. However, even with as much as 10%-
-160
- 2.0
2.o
0
-Log
4 .O
‘]cat O H
0l.i
*No
A K
*Rb
ACs
Figure 5. Electrode response to the indicated alkali metal cations of wet n-amyl alcohol containing 10 bis2-ethyl hexyl phosphoric acid (36)
Le., 0.3%-H Bis, deviations from the Nernst slope are apparent at the higher solution concentrations and are most severe for Na+. It should also be apparent that the H+ to Na+ selectivity (as judged by comparison of the potentials in the most dilute solutions where deviations from Nernst-slope are smallest) is essentially unaffected by changing the concentration of the liquid exchanger. This effect contrasts with those of ion VOL. 40,
NO. 2, FEBRUARY 1968
313
mV
A
OY. 0.1 Y.
0
I
.or*
IO.OY*
Figure 6. Electrode potentials of “wet” n-decyl alcohol containing the indicated percentages of bis-2-ethyl hexyl phosphoric acid (36) Solid diagonal lines indicate the theoretical Nernst slopes for monovalent cations of 59 mV exchanger concentration on the selectivity for Ca2+ relative to H+ and Na+, which increase markedly with increasing concentration of the liquid exchanger. Over the region of Nernst response, the selectivity between the monovalent cations H+ and Na+ is not a function of the solution concentration, as is seen particularly clearly in Figure 4; but the selectivity of the divalent cation Ca*+relative to the monovalent cations can also be seen to increase as the concentrations in the aqueous solutions decrease, as expected from the differences in Nernst slopes. Both the effects of exchanger concentration and solution concentration on the behavior of ions of different valence are to be anticipated from the law of mass action for an ion exchanger because the lower the concentration of the aqueous relative to the membrane phase, the more preferred is the cation of higher charge. The response to the other Group Ia cations is illustrated in Figure 5 , from which it appears that the electrode response is generally sigmoidal, with a central Nernstian region from which deviations occur at high and low concentrations. Presumably, the deviations at high concentration are due to incomplete co-ion exclusion, while the deviations at low concentration result from dissolving of the liquid exchanger. While H+is preferred to the Group Ia cations with n-amyl alcohol as the solvent, there appears to be relatively little selectivity among the cations themselves. The principal differences among cations are in their relative deviations from the Nernst slope. This behavior is typical of alcohols. The effects of varying the solvent are illustrated in Figures 6 and 7. Comparison of Figure 6 and Figure 3 shows that the electrode behavior is similar in alcohols regardless of chain length. The most salient difference on increasing the chain length is a shift of the region of Nernst response for Na+ toward the higher, and away from the lower, concentrations. Even more striking effects are seen with nonalcoholic solvents. For example, Beutner long ago 314
ANALYTICAL CHEMISTRY
showed that if the solvent is made basic instead of acidice.g., aniline instead of alcohol-the membrane becomes anion-selective instead of cation-selective (37). Even with less extreme changes, interesting effects are seen. Thus, pronounced selectivity differences among the Group Ia cations appear if the solvent is nitrobenzene (38, 39), as is illustrated in Figure 7. THEORETICAL EXPECTATIONS FOR LIQUID ION EXCHANGERS Vo(t),the electrode potential of an ion exchange membrane, whether the membrane is solid or liquid, at any time, t , has been shown by Sandblom, Eisenman, and Walker ( I ) to be given by :
where zf is the valence of the iih counterion species, ai’ and ai“ are its activities in the solutions ( I ) and ( ’ I ) on each side of the membrane, u iis its mobility within the membrane, and k r is a constant characteristic of its difference of standard chemical potentials in the membrane us. water [cf. Equations 10 and 11
of(0l. Equation 5 can be seen to contain, in addition to the first term which is similar to that of solid ion exchange membranes (cf, Equation 2), two additional terms whose values depend (37) R. Beutner, “Phys. Chem. of Living Tissues and Life Processes,” Williams and Wilkens Co., Baltimore, Md. 1944. (38) W. J. V. Osterhout, Cold Spring Harbor Symposium 8, 51 (1940).
(39) M.Dupeyrat, Chim. Phys., 61, 323 (1964).
+
varies between 0 for complete dissociation and uscs/(uscs uicl)for strong association.
+ 100
I
rnV
Limiting Case of Negligible Mobility of the Site Species. When the mobility of the site species is negligible compared to that of the counterion species, J,*and t are zero for all times. Equation 5, therefore, reduces to its first term. This is the proper limit in this situation, which corresponds to that of a solid ion exchange membrane in which the sites are essentially fixed in space [cf. Equation 38 of (26)]. The ratio kj/ki of Equation 5 corresponds formally to the ion exchange equilibrium constant K i j of Equation 4. All noceI properties of liquid ion exchange membranes are therefore contained solely in the terms f 1 andf 2. Limiting Case of Complete Dissociation. Because t is zero in this limit,fl is zero regardless of time. Moreover, both in the steady-state and also immediately subsequent to a step change in solution conditions J,* is zero; so that fZ is zero in these situations. Therefore, the “instantaneous” as well as the steady-state electrode potential is given by the first term of Equation 5 :
0
- 100
-2.0
2 .o
0
-Log Ct,
(9)
Figure 7. Effect of solvent on liquid exchanger electrode specificity The membrane is nitrobenzene containing 5 oleic acid (40). The points indicate the observed potentials at neutral pH. Note the large selectivity differences among the alkali cations. These are essentially independent of whether the added exchanger is a carboxylic sulfonic or phosphoric acid (40). Interestingly, the solid curves are drawn according to Equation l but the deviation from the Nernst behavior at the lowest cation concentrations is presumably the result of the dissolving of the sites rather than due to the effects of other cations because at neutral pH the H+effect is far too small to account for this deviation
which can be seen to be the proper limit by comparison with the steady state Equation 35 of (41). Limiting Case of Strong Association. For this case, and restricting the number of counterion species to two, Sandblom, Eisenman, and Walker (I) have shown that Equation 5 becomes :
on the particular characteristics of the liquid exchanger. are two integrals across the thickness of These terms, f land fz, the membrane from 0 to d :
both “instantaneously” and in the steady-state, with:
in which the subscripts s refer to the dissociated site species and the subscripts is refer to the undissociated ion pairs. Thus, us is the mobility of the dissociated site species; uts is the mobility of the undissociated ion pair; K i is the dissociation constant of this pair; and cis, c., and cs are the concentrations of undissociated pairs, dissociated counterions, and dissociated sites within the membrane. Js* in fzis the total flux of sites (regardless of whether in a dissociated or undissociated state); while the parameter t infl: t =
The electrode potential of a liquid ion exchange membrane with strong association can be seen to consist of two logarithmic terms, whose relative contributions are governed by the parameter T . The Parameters Controlling Electrode Specificity. Restricting ourselves to 25” C and to two permeant monovalent cation species, 1 and 2, Equations 9 and 10 simplify to:
uscs
(8)
(40) G. Eisenman and G. K. Larson, unpublished results, 1967.
(41) F. Conti and G. Eisenman, Biophys. J., 6, 227 (1966). VOL 40, NO. 2, FEBRUARY 1968
31 5
for complete dissociation, and
u2 US - -f- = UI US
+
-
A2.9"
Azo
Also
AI"
+ + As"
ASo
(17)
The product k2Kl/klK2of Equation 13 is according to Equation 15:
Alternatively, Equation 18 has been shown ( I ) to be identical to the equilibrium constant K ~ z : for strong association, respectively. The explicit similarities and differencesbetween solid and liquid exchangers are given by the comparison of Equation 2 with Equations 9a and loa. From Equations 9a and loa, the electrode potential of liquid exchangers is seen to be describable either (for complete dissociation) as a single logarithmic term containing the weighted sum of counterion activities in the aqueous solutions, or (in the case of strong association) as a sum of two such logarithmic terms. The value of 7,which lies between 0 to 1, depending on the properties of the solvent and of the ion exchanger, determines the relative importance of the two logarithmic terms of Equation loa. Each logarithmic term is similar in form to Equation 2 which is characteristic of solid ion exchangers. The weighing factors determining the relative effects of various counterions on the electrode potential are given by the quantities in square brackets in Equations 9a and 1Oa :
[I$ . z]
[" .
~ l s
2+ (aqueous)
+ 1 s (membrane) e 1+ (aqueous)
+ 2 s (membrane)
(20)
Equations 9a and 10a can now be rewritten in terms of classically measurable quantities as:
for Equation (9a)
for the first term of Equation loa,
(13)
51for the second term of Equation (loa)
(14)
kl Kz
For a given pair of counterions, each of these terms should be a constant, related to the properties of the solvent and the ion exchanger as described below. Let us now examine the physical meaning of the weighing factors 12, 13, and 14. The ratio k2/k1,which appears in all these, is by definition the ratio of the distribution coefficientsof the (dissociated) counterions in the solvent at infinite dilution [cf.Equations 9 and 10 of ( I ) ] . This ratio equals the square of the ratio of the limiting values at infinite dilution of the distribution coefficients of the salts of any common anion X- between the pure solvent and water [cf. (42) as discussed on p 3869 of ( I ) ] .
The mobility ratio of the counterion species u2/u1in Equation 12 is simply the ratio of the limiting single-ion conductances X 2 O / X l 0 : u1
X1"
(16)
while the mobility ratio (uz+us)/(ul+us) in Equation 13 is simply the ratio of the limiting equivalent conductances of the 2 and 1 forms of the ion exchanger: (42) T. Shedlovsky and H. H. Uhlig, J. Gen. Physio/., 17, 563 (1933-34).
3 16
for the ion exchange reaction:
ANALYTICAL CHEMISTRY
Also, if K1
