Determination of Complex Formation Constants of Lipophilic Neutral

Debbie S. Silvester , Ewa Grygolowicz-Pawlak , Eric Bakker. Analytica Chimica Acta 2010 683 (1), ..... R. Daniel Johnson , Leonidas G. Bachas. Analyti...
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Anal. Chem. 1999, 71, 5279-5287

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Determination of Complex Formation Constants of Lipophilic Neutral Ionophores in Solvent Polymeric Membranes with Segmented Sandwich Membranes Yanming Mi and Eric Bakker*

Department of Chemistry, Auburn University, Auburn, Alabama 36849

A potentiometric method to determine ionophore complex formation constants in solvent polymeric membrane phases, proposed originally by Russian researchers, is critically evaluated and compared to other established methods. It requires membrane potential measurements on two-layer sandwich membranes, where only one side contains the ionophore. The resulting initial membrane potential reflects the ion activity ratio at both aqueous phase-membrane interfaces and can be conveniently used to calculate complex formation constants in situ. This method is potentially useful, since it does not require the use of a reference ion or second ionophore in the measurement. In this paper, the five ionophores valinomycin, BME-44, ETH 2120, tert-butylcalix[4]arene tetraethyl ester, and S,S′-methylenebis(diisobutyldithiocarbamate) are characterized in poly(vinyl chloride) (PVC) plasticized with dioctyl sebacate (DOS) and compared with other established methods. The resulting formation constants correspond well to literature values. The influence of varying membrane concentrations and different anionic site additives is studied and found to be relatively small. Experiments are also performed with and without lipophilic inert electrolytes and with ionophore-free sandwich membranes to illustrate the effect of ion pairing and the membrane internal diffusion potential on the response of such sandwich membranes. These experiments suggest that ions are completely associated in PVC-DOS membranes, but that such ion pairs are rather nonspecific. Diffusion potentials seem to play a minor role with these systems. The results are explained with theory. This work indicates that the characterization of electrically charged ionophores, anion-selective ionophores, and ionophores in membrane matrixes other than PVC plasticized with DOS may now be experimentally accessible.

Despite the wide use of lipophilic and chemically immobilized ionophores in chemical sensor applications,1 only a limited number of experimental techniques are available to assess the binding strengths of these highly selective molecular probes directly in (1) Bu ¨ hlmann, P.; Pretsch, E.; Bakker, E. Chem. Rev. 1998, 98, 1593. 10.1021/ac9905930 CCC: $18.00 Published on Web 10/15/1999

© 1999 American Chemical Society

the polymeric matrix of the sensor. Classical binding studies in protic solvents are usually not desired since binding constants significantly vary with different solvent environments, and ionophore binding is often weak in polar solutions.2-5 Moreover, many ionophores today are chemically immobilized onto polymeric supports6 or highly lipophilic,7 and new methods are required. In recent years, a new, interesting method has been proposed that makes use of unique binding characteristics of a series of H+-selective ionophores.8 It was shown with potentiometric selectivity studies9 and optical extraction experiments8,10 that they essentially do not complex alkali metals in poly(vinyl chloride) plasticized with dioctyl sebacate (PVC-DOS). Consequently, the competitive ion-exchange reaction between hydrogen ions and alkali metal ions could be followed optically with polymeric films spin coated on solid glass supports.11,12 It was shown that the corresponding ion-exchange equilibrium constant significantly changes if an additional alkali metal-selective ionophore is present in the polymeric film. This shift can be used to calculate effective complex formation constants. This technique was explored with a number of ionophores that were selective for alkali and alkaline earth metal ions8 and silver.13 This optical method was made more accessible to the general ion-selective electrode community by extending it to zero-current membrane potentials as the transduction mode.9,14 According to this potentiometric method, the membrane selectivity of hydrogen (2) Bliggensdorfer, R.; Suter, G.; Simon, W. Helv. Chim. Acta 1989, 72, 1164. (3) Frensdorff, H. K. J. Am. Chem. Soc. 1971, 93, 600. (4) Feinstein, M. B.; Felsenstein, H. Proc. Natl. Acad. Sci. U.S.A. 1971, 68, 2037. (5) Wipf, H.-K.; Pioda, L. A. R.; Stefanac, Z.; Simon, W. Helv. Chim. Acta 1968, 51, 377. (6) Brunink, J. A. J.; Lugtenberg, R. J. W.; Brzozka, Z.; Engbersen, J. F. J.; Reinhoudt, D. N. J. Electroanal. Chem. 1994, 378, 185. (7) Dinten, O.; Spichiger, U. E.; Chaniotakis, N.; Gehrig, P.; Rusterholz, B.; Morf, W. E.; Simon, W. Anal. Chem. 1991, 63, 596. (8) Bakker, E.; Willer, M.; Lerchi, M.; Seiler, K.; Pretsch, E. Anal. Chem. 1994, 66, 516. (9) Bakker, E.; Pretsch, E. Anal. Chem. 1998, 70, 295. (10) Bakker, E.; Lerchi, M.; Rosatzin, T.; Rusterholz, B.; Simon, W. Anal. Chim. Acta 1993, 278, 211. (11) Wang, K.; Seiler, K.; Morf, W. E.; Spichiger, U. E.; Simon, W.; Lindner, E.; Pungor, E. Anal. Sci. 1990, 6, 715. (12) Seiler, K.; Simon, W. Anal. Chim. Acta 1992, 266, 73. (13) Lerchi, M.; Reitter, E.; Simon, W.; Pretsch, E.; Chowdhury, D. A.; Kamata, S. Anal. Chem. 1994, 66, 1713. (14) Bakker, E.; Pretsch, E. J. Electrochem. Soc. 1997, 144, L125.

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ions relative to alkali metals will decrease as an alkali metalselective ionophore is present in the membrane. A careful analysis of the data reveals the binding constant of that ionophore in situ. Interestingly, the data obtained with this potentiometric method were identical to those from the corresponding optical method, even though the required relative concentration of ionic additives in the membrane is smaller in this case.8 This finding gave strong support for the already established notion that membrane internal diffusion potentials are only a small contribution to the overall membrane potential and can often be neglected.15 Still, the two mentioned methods have a number of significant drawbacks. First, it has not yet been explored whether these H+selective ionophores behave ideally in membrane matrixes other than PVC-DOS. This point is indeed problematic, since potentiometric studies on H+-selective membranes16 strongly suggest that the plasticizer DOS has significant cation-binding characteristics. Corresponding pH electrodes based on PVC membranes plasticized with o-nitrophenyl octyl ether (NPOE), for example, show much larger measuring ranges,16 indicating that this plasticizer stabilizes extracted alkali metal ions to a much smaller extent. Consequently, the H+ ionophore might more likely act as a chelator in the cation extraction process with such systems. Second, these experiments require careful pH control and need to be performed at sample pH values that will allow for a competitive ion extraction process between H+ and the ion of interest. A large number of ions are only soluble within a limited pH window, which limits the applicability of these methods. Sometimes measurements with H+ ionophores that have a smaller pKa value can be used to solve this problem,8 but this introduces additional complications to the measurement, including the accelerated acid decay of the incorporated tetraphenylborate derivative.17 Third, at this stage, the two-ionophore method is not adequate for anion-selective ionophores since the extraction equilibrium would be different and likely biased by significant ionpairing equilibria between the protonated, cationic H+ ionophore and the anionic ionophore-anion complex in the membrane. Also, electrically charged ionophores cannot be characterized with this method since they require other ionic site additives.18 Moreover, ion pairs between the protonated H+ ionophore and the uncomplexed, negatively charged ionophore would shift the relevant equilibria. An alternative method is therefore needed for these cases. The group of Koryta has used voltammetry at the interface of two immiscible electrolyte solutions to quantitate complex formation constants of ionophores.19 Girault has recently extended this approach to plasticized PVC membranes.20 This can in principle be done since the inner-phase boundary is kept invariant of the ionophore by using a nonpolarizable interface, for example, with tetrabutylammonium chloride in the inner electrolyte and tetrabutylammonium tetrakis(p-chlorophenyl)borate as inert lipophilic electrolyte in the membrane. The obtained complex formation constants for valinomycin in PVC-NPOE were, with log βKL ) (15) Bakker, E.; Bu ¨ hlmann, P.; Pretsch, E. Chem. Rev. 1997, 97, 3083. (16) Bakker, E.; Xu, A.; Pretsch, E. Anal. Chim. Acta 1994, 295, 253. (17) Rosatzin, T.; Bakker, E.; Suzuki, K.; Simon, W. Anal. Chim. Acta 1993, 280, 197. (18) Schaller, U.; Bakker, E.; Spichiger, U. E.; Pretsch, E. Anal. Chem. 1994, 66, 391. (19) Sabela, A.; Koryta, J.; Valent, O. J. Electroanal. Chem. 1986, 204, 267. (20) Lee, H. J.; Beriet, C.; Girault, H. H. J. Electroanal. Chem. 1998, 453, 211.

5280 Analytical Chemistry, Vol. 71, No. 23, December 1, 1999

Figure 1. Schematic representation of the two-layer sandwich method to determine complex formation constants in solvent polymeric membranes, shown for potassium ions. Individual membrane segments are separately conditioned and their membrane potentials confirmed to be equivalent before combining them to form the sandwich membrane. The resulting membrane potential reflects the organic ion activity ratio at both interfaces. The symbols L and Rindicate the ionophore and the anionic site additive. A square symbolizes the membrane phase.

16, very high in comparison to 9.3 in PVC-DOS obtained with the two-ionophore methods mentioned above.9 It must be pointed out that voltammetry is an intrinsically kinetic method. A larger number of systematic errors may be present than with potentiometric or solvent extraction techniques. Moreover, no experiments have yet been reported with PVC-DOS, which is the matrix so widely used with potentiometric and optical sensors. In a recent short review, Mikhelson pointed out a different method to determine complex formation constants in the membrane phase.21 The technique has so far been described together with Stefanova and Mokrov in Russian journals only22-24 and is therefore not accessible to most researchers in other countries. This method effectively uncouples both phase boundary potentials from each other by inducing a well-defined initial ion concentration profile in the membrane. This is accomplished by using two membrane segments, each having a different composition, that are combined to form a nonuniform sandwich membrane (see Figure 1). The field is only now in a position to critically evaluate this technique and to compare the results with the two-ionophore system mentioned above. This paper attempts to accomplish this task and to introduce this segmented sandwich membrane technique to the larger scientific community. For this purpose, five already well-characterized lipophilic neutral cation-selective ionophores (see Figure 2) in PVC-DOS membranes are here evaluated. THEORY With ordinary ion-selective electrode membranes, the membrane potential is essentially independent of the incorporated (21) Mikhelson, K. N. Sens. Actuators B 1994, 18-19, 31. (22) Mikhelson, K. N.; Grekovich, A. L.; Materova, E. A. Elektrokhimiya 1982, 18, 1237. (23) Mokrov, S. B.; Stefanova, O. K. Elektrokhimiya 1985, 21, 540. (24) Morkov, S. B.; Stefanova, O. K.; Materova, E. A.; Ivanova, E. E. Vestn. Leningrad Univ. 1984, 16, 41.

Figure 2. Chemical structures of the ionophores characterized in this paper.

ionophore if no interferences are observed. This can be illustrated by describing the well-known membrane potential EM as a function of the potentials at the two membrane-aqueous phase boundaries as follows:

EM )

aI(aq)′ aI(org)′′ RT ln zIF aI(org)′ aI(aq)′′

In the case where the two contacting aqueous solutions are identical and no concentration polarizations exist within the membrane and the Nernst diffusion layers, the membrane potential should be zero on the basis of eq 1. For a properly conditioned and ideally functioning membrane where no interference from other ions is observed, eq 1 reduces to the Nernst equation, where the membrane potential is independent of the membrane composition. On one hand, this is a clear practical advantage as symmetric changes in the membrane compositions at both interfaces have negligible effect on the sensor response. However, such measurement configurations will make it impossible to reveal binding characteristics of the ionophore. Therefore, both phase boundary potentials must be effectively uncoupled from each other to make such a measurement possible. The method discussed in this paper makes use of a two-layer sandwich membrane, which is freshly prepared and assembled just prior to measurement. The compositions of both segments are essentially identical, but only one side contains an ionophore. At that side, the uncomplexed ion concentration aI(org)′ shown in eq 1 will be significantly decreased relative to aI(org)′′ owing to the strong complexation between the extracted cation, which is ion-paired with incorporated ionic site additives, and the ionophore. For a two-layer sandwich membrane that contacts two aqueous samples of equal composition without interferences, aI(aq)′ is equal to aI(aq)′′ and eq 1 simplifies to

EM )

RT aI(org)′′ ln zI F aI(org)′

(2)

(1)

where a prime (′) indicates the ion activities aI at the samplemembrane interface and a double prime (′′) at the inner electrolytemembrane interface. The respective phases are indicated in parentheses, and R, T, and F are the gas constant, the absolute temperature, and the Faraday constant, respectively. The ion I carries a charge of zI. In principle, the membrane potential may also be influenced by a membrane internal diffusion potential, which may originate in ion mobility differences in the membrane, given that substantial ion fluxes are encountered.25,26 There are still ongoing discussions about the relevance of the diffusion potential in many cases.27,28 Very close correlations of the extraction behavior of ion-selective membranes and the corresponding zero-current membrane potential have however suggested that the diffusion potential is a minor contribution to the overall potential and that it can often be neglected.9,29,30 Of course, situations might exist where the diffusion potential will not be negligibly small, but in many circumstances, neglecting it may be warranted to simplify the theoretical treatment. (25) Meyer, K. H.; Sievers, J.-F. Helv. Chim. Acta 1936, 19, 649. (26) Theorell, T. Proc. Soc. Exp. Biol. Med. 1935, 33, 282. (27) Mikhelson, K. N.; Lewenstam, A. Sens. Actuators B 1998, 48, 344. (28) Mi, Y.; Green, C.; Bakker, E. Anal. Chem. 1998, 70, 5252. (29) Bakker, E.; Na¨gele, M.; Schaller, U.; Pretsch, E. Electroanalysis 1995, 7, 817. (30) Rakhmanko, E. M.; Yegorov, V. V.; Gulevich, A. L.; Lushchik, Y. F. Sel. Electrode Rev. 1991, 13, 5.

This relationship can be more explicitly related to the formation constant of the ion-ionophore complex by considering two separate cases, one where ion pairing is significant and the other where it is not. In the past, most theoretical treatments have neglected ion pairing in the organic phase,15 noting that such ion pairs are ideally nonspecific and their strength is therefore within the same order of magnitude for different ions or complexes. Nonetheless, ion pairing will always be strong in nonpolar organic phases,31 and it is important to offer a treatment for both cases.17 Determining Formation Constants without Considering Ion Pairing in the Membrane. If ion pairing is neglected, all ions are assumed to be in the dissociated form or complexed to the ionophore. For a membrane segment without incorporated ionophore, the ion activity is given by the charge balance condition in that membrane segment:

aI ) γIRT/zI

(3)

where γI is the activity coefficient for the ion I and RT is the concentration of the lipophilic ionic site additives. The phase notations (org) are omitted from here on since all species discussed are in the organic phase. For a membrane segment with an incorporated ionophore L, complexes may form with the stability constant βILn, where n is the complex stoichiometry: (31) Verpoorte, E.; Chan, A.; Harrison, D. J. Electroanalysis 1993, 5, 845.

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5281

βILn ) aILn/aIcLn

(4)

It is here assumed that activity coefficients for neutral species are unity. The charge balance can be written as

RT/zI ) cI +

∑c n

(5)

ILn

Combination of eqs 4 and 5, with aI ) γIcI, gives

aI )

γIRT zI

{

∑

1+

}

βILncLn γILn

n

-1

(6)

where the concentration of free ionophore cL is given by

cL ) LT -

∑ (nc n

ILn)

(7)

The symbol LT is the total concentration of ionophore in the membrane segment. In many cases, it can be assumed that only one complex stoichiometry n is relevant and that the complexes are sufficiently strong so that the concentration of uncomplexed ions is much smaller than that of the complexes. If this is the case, eq 6 is rewritten as

aI )

γILnRT

(8)

zIβILn(LT - nRT/zI)n

The membrane potential for a two-segment membrane, with only the segment in contact with the sample having an incorporated ionophore, can be described by inserting eqs 3 and 8 into eq 2:

EM )

(

)

γIn nRT RT β L ln zIF γILn ILn T zI

n

(

) ( )

nRT zI

-n

exp

EMzIF RT

Analytical Chemistry, Vol. 71, No. 23, December 1, 1999

(11)

If a two-layer membrane would contain different concentrations of ionic site additives in each segment, but no ionophore, aI would be equal to aR for electroneutrality reasons if the extracted ion is monovalent. For strong ion pairs, the membrane potential is then described by

EM )

RT cIR′′ ln 2F cIR′

(12)

The membrane potential is expected to show an apparent halfNernstian slope with respect to the ionic additive concentration in the membrane segment facing the inner electrolyte if the other segment is kept indifferent and no interferences are observed from other sample ions. The slope for this experiment would be Nernstian if no ion pairing would be present. This indicates that this could be used as an experimental technique to evaluate the extent of ion pair formation in solvent polymeric membranes. If an ionophore is present in the membrane, the electrically charged complexes may ion pair with the ionic site additives according to the following equilibrium constant:

KILnRzI ) cILnRzI/aILnaRzI

(13)

For simplicity reasons, it is again assumed that the extracted ions are monovalent and that ion-ionophore complexes are sufficiently strong that the concentration of uncomplexed ions (paired with ionic sites) is negligible relative to that of the complexed ions. In that case, eq 13 reduces to

aILn ) xcILnR/KILnR

(10)

This relationship allows for the convenient determination of formation constants of ion-ionophore complexes within the membrane phase on the basis of transient membrane potential measurements on two-layer sandwich membranes if ion pairing can be neglected. Determining Formation Constants by Considering Ion Pairing in the Membrane. For nonpolar membrane phases, as most often encountered with potentiometric membrane electrodes, ion pairing cannot be neglected.31 Unfortunately, reliable ion pair formation data are still not available for the matrixes of interest 5282

KIRzI ) cIRzI/aIaRzI

(9)

If both membrane segments have the same ionic strength, it is convenient to assume that the activity coefficients for the complexed and uncomplexed ions are approximately equal. In that case, they can be omitted and the complex formation constant is related to the membrane potential as follows:

βILn ) LT -

in chemical sensors.32 One can assume that most of the extracted ions are strongly ion paired with the lipophilic ionic site additive. Although the strength of the ion pair will be inversely dependent on the effective ionic radii of both ions, large changes from one extracted ion to another are ordinarily not expected because the lipophilic ionic sites are typically large tetraphenylborate or tetraalkylammonium derivatives, which lack structural features that would be capable of forming strong association adducts with extracted ions, and which possess large ionic radii, making the resulting ion pairs less dependent on the size of the counterion. The ion pair formation constant is written for the uncomplexed ion as

(14)

The membrane potential can now be formulated by combining eqs 14 and 4 and the concentration of the ionophore, cL ) LT ncILnR, with eq 2 to give

EM )

RT ln F

x

KILnR KIR

βILn(LT - nRT)n

(15)

which can be solved for the complex formation constant as follows: (32) Armstrong, R. D.; Horvai, G. Electrochim. Acta 1990, 35, 1.

βILn ) (LT - nRT)-n

x

KILnR KIR

exp

( ) EMF RT

(16)

This relationship indicates that the square root of the ratio of the ion pair formation constants is relevant for determining complex formation constants in solvent polymeric membranes. If these two ion pair formation constants differ by a factor of 10, for example, the resulting complex formation constant differs from the one obtained by neglecting ion pairs altogether only by a factor of about 3. This is a small deviation, given that many complex formation constants are on the order of 107-109 kg mol-1.9 The square root relationship is predicted since the free ionic site concentration on both sides of the membrane will be different from each other if the two ion pairs differ in their association constants. Alternatively, one may argue that, from a practical standpoint, the dissociation and formation of the two relevant ion pairs should be regarded as part of the overall complex formation process, so that a formal complex formation constant may be introduced as follows:

βILn (formal) )

cILnR

KILnR

cIRcL

KIR

) n

βILn

(17)

This formal constant is not dependent on the square root of the ratio of the two ion pair formation constants, as discussed above, and therefore cannot be directly obtained from two-layer sandwich membrane measurements without prior knowledge of the ion pair formation constants. Obviously, if all ion pairs have equal association constants, all three ion-ionophore complex formation constants discussed here will, within the assumptions used, be equal in magnitude. EXPERIMENTAL SECTION Reagents. The salts and the membrane components BME44, tert-butylcalix[4]arene tetraethyl ester, N,N,N′,N′-tetracyclohexyl-1,2-phenylenedioxydiacetamide (ETH 2120), S,S′-methylenebis(diisobutyldithiocarbamate) (MBDiBDTC), sodium tetrakis[3,4-bis(trifluoromethyl)phenyl]borate (NaTFPB), sodium tetraphenylborate (NaTPB), potassium tetrakis(4-chlorophenyl)borate (KTpClPB), tetradodecylammonium tetrakis-(4-chlorophenyl)borate (ETH 500), bis(2-ethylhexyl)sebacate (DOS), high-molecularweight poly(vinyl chloride) (PVC), and tetrahydrofuran (THF) were purchased in Selectophore or puriss quality from Fluka Chemika-Biochemika (Ronkonkoma, NY). Valinomycin was obtained from Aldrich. Aqueous solutions were prepared by dissolving the appropriate salts in Nanopure purified distilled water. Membrane Preparation and EMF Measurements. Ionselective electrode membranes were cast by dissolving the ionophores and/or ETH 500 (if needed) and the tetraphenylborate derivative salt (NaTFPB, NaTPB, or KTpClPB), together with PVC and plasticizer DOS (1:2 by weight), to give a total cocktail mass of 140 mg in 1.5 mL of THF and pouring it into a glass ring (2.2cm i.d.) affixed onto a microscope glass slide. The specific membrane compositions are given in Table 1. The solvent THF was allowed to evaporate overnight. A series of 6-mm-diameter

disks were cut with a cork borer from the parent membrane, and these disks were conditioned overnight in 0.01 M KCl, NaCl, or LiCl or 0.005 M AgNO3, depending on the ion indicated in Table 1. For each measurement, one disk was then incorporated into a Philips electrode body, carefully selected to give a potential value within 2 mV for membrane disks cut out of the same parent membrane. This electrode body was the only one used during the entire experiment. All membrane electrode potential measurements were performed at laboratory ambient temperature in unstirred salt solutions (identical to the conditioning and inner filling solution) versus a Ag/AgCl reference electrode with a 1 M LiOAc bridge electrolyte. The sandwich membrane was made by pressing two individual membranes (ordinarily one without ionophore and one with the same components and additional ionophore) together immediately after blotting them individually dry with tissue paper. The drying step is necessary to avoid an aqueous phase between the two membrane segments. The combined segmented membrane was then rapidly mounted into the Philips electrode body and immediately measured. The time required from making the membrane sandwich contact until final membrane potential measurement was typically less than 1 min. The segmented sandwich was visibly checked for air bubbles before mounting. Calculations. Membrane potential values ∆EMF were determined by subtracting the cell potential for a membrane without ionophore from that of the sandwich membrane. The cell potentials for individual segments typically deviated less than 2 mV. Otherwise, the measurement was discarded. Standard deviations were obtained based on the measurements of sets of at least three replicate membrane disks that each were made from the same parent membrane. RESULTS AND DISCUSSION As outlined in the theoretical section, the two phase boundaries of an ion-selective membrane may be effectively uncoupled from each other by fabricating a segmented sandwich membrane where both sides have different chemical compositions. For identical contacting aqueous solutions, the resulting membrane potential is then a direct function of the activity ratio of the particular measuring ion at the aqueous solution-membrane interfaces of both segments. These experiments are intrinsically transient and require careful, repetitive experimentation. The work presented here focuses on the evaluation of the practical utility of this interesting technique. Experiments were performed to elucidate the influence of ion pairing, the concentration and type of ionophore and anionic sites, and the presence of lipophilic inert electrolytes. The five ionophores chosen in this study have all been characterized earlier with different optical and/or potentiometric methods8,9 and provide an appropriate test bed for this evaluation. Most theoretical treatments elucidating the potentiometric response of ionophore-based solvent polymeric membranes rely on three main assumptions:15 namely that (1) ion-transfer reactions are sufficiently rapid so that essentially equilibrium conditions exist at the very phase boundary, (2) the membrane-internal diffusion potential is negligibly small relative to the two phase boundary potentials, and (3) ion pairing is neglectable in solvent polymeric membranes. The second point is still being disputed in some cases, for example, where electrically charged ionophores Analytical Chemistry, Vol. 71, No. 23, December 1, 1999

5283

Table 1. Experimental Membrane Potentials and Corresponding Ionophore Complex Formation Constants Determined with Two-Segment DOS-PVC (2:1) Sandwich Membranes, of Which Only One Side Contains the Indicated Ionophorea

c

ion I+

ionophore LT (mmol kg-1)

K+ K+ K+ K+ K+ K+ K+ K+ K+ K+ K+

6.4 7.4 8.6 10.1 10.1 10.1 10.0 9.9 10.2 10.0 10.2

NaTFPB (5.1) NaTFPB (5.1) NaTFPB (5.1) NaTFPB (4.9) NaTFPB (1.2) NaTFPB (2.1) NaTFPB (5.2) NaTFPB (4.8) NaTFPB (5.1) NaTFPB (5.2) NaTFPB (5.0)

K+ Li+ Na+ K+

9.8 9.9 10.1 9.8

NaTFPB (4.9) NaTFPB (5.1) NaTFPB (5.1) KtpClPB (5.0)

Na+

9.8

anionic sites RT (mmol kg-1)

ETH 500 (mmol kg-1)

membrane potential ∆EMF (mV)

formation const log βILn

Valinomycin (nb ) 1) 0 0 0 0 0 0 0 1.1 5.0 10.2 19.8

410 ( 5c 418 ( 5 449 ( 2 443 ( 7 458 ( 4 450 ( 3 450 ( 4 462 ( 4 460 ( 3 456 ( 1 457 ( 4

9.86 ( 0.08c 9.76 ( 0.09 10.10 ( 0.04 9.82 ( 0.12 9.82 ( 0.07 9.74 ( 0.05 9.95 ( 0.07 10.15 ( 0.06 10.11 ( 0.05 10.00 ( 0.01 10.06 ( 0.09

BME-44 (n ) 1) 0 0 0 0

340 ( 5 112 ( 7 218 ( 9 325 ( 4

8.10 ( 0.08 4.22 ( 0.13 6.00 ( 0.15 7.83 ( 0.07

tert-Butylcalix[4]arene Tetraethyl Ester (n ) 1) NaTFPB (5.1) 0

Na+ Na+ Na+

20.5 20.1 19.6

NaTFPB (5.1) KTpClPB (5.3) NaTFPB (4.4)

ETH 2120 (n ) 2) 0 0 0

Ag+ Na+

20.8 20.8

NaTFPB (4.9) NaTFPB (4.9)

MBDiBDTC (n ) 2) 0 0

301 ( 4

7.60 ( 0.08

280 ( 1 262 ( 2 268 ( 1

8.70 ( 0.01 8.47 ( 0.04 8.48 ( 0.02

500 ( 3 5(2

12.42 ( 0.04 2.8 ( 0.2

a The second segment has otherwise the same composition as the ionophore-containing segment. b n is the assumed complex stoichiometry. Standard deviations are shown from at least three replicate measurements.

are involved,27 but it is now generally accepted that this assumption is justified in most cases. The third assumption is known not to be adequate,31 but is still used by most researchers since experimental ion pair formation data are largely still lacking for solvent polymeric membranes. It was argued that while ion pairing will always be predominant in a hydrophobic environment, its effect on the relevant ion extraction equilibria can be neglected if the ion pairs are nonspecific; i.e., all ion pair formation constants have approximately the same value.8,17 While most ion pair formation data were compiled with voltammetric techniques,32 it would seem most adequate to use experimental methods that depart less from equilibrium. In the theoretical section, it was shown that the apparent response slope of segmented sandwich membranes relative to the total ionic site concentration on one side is expected to be half-Nernstian if ion-pairing effects are strong. This is expected since the free cation concentration, which dictates the potentiometric response, is square root dependent on the total ionic site concentration in this case. This notion was tested by determining the initial membrane potential of a series of membranes, where the ionic site concentration of the segment facing the inner electrolyte was varied while the other segment was kept at a constant composition. Figure 3A shows that the membrane indeed shows an apparent half-Nernstian response behavior with respect to the anionic site concentration, which indicates on the basis eq 12 that essentially all membrane ions are ion paired. In a separate experiment, a large concentration of the inert lipophilic salt ETH 500 was added to both membrane segments under otherwise identical conditions. This electrolyte 5284

Analytical Chemistry, Vol. 71, No. 23, December 1, 1999

is expected to dominate the ion pair formation with the anionic sites, to keep activity coefficients constant,33 and to reduce any possible membrane-internal diffusion potentials. The resulting slope relative to the ionic site concentration in the segment with varying composition is now expected to be Nernstian, since the concentration of free cations will now linearly depend on the concentration of ionic sites. Indeed, as Figure 3B shows, the resulting response slope is nearly Nernstian, which indicates that the underlying response model is applicable. The correspondence of these two experiments to theoretical expectations also confirms that the experimental sandwich membrane method gives meaningful results. Unfortunately, the results shown in Figure 3A cannot be used to estimate ion pair formation constants in this system, since it merely indicates that ions are essentially fully ion paired. Such formation constants could only be estimated if ion pairing is relatively weak. The sandwich method was used to determine the membrane potential if only one segment contains the potassium ionophore valinomycin. In this case, the two segments have a significantly different free potassium concentration, and a large potential shift is expected relative to the single-segment measurement. Figure 4 shows the time response behavior for this experiment. The initial potential increase is thought to be due to the significant potassiumbinding characteristics of valinomycin, which is only present in the segment facing the sample. Since all membrane species can freely diffuse across both ∼200-µm-thick segments, the membrane (33) Na¨gele, M.; Mi, Y.; Bakker, E.; Pretsch, E. Anal. Chem. 1998, 70, 1686.

Figure 4. Observed time response behavior of a two-layer sandwich membrane containing valinomycin in the segment facing the sample over the first 5 h after initial contact. The initial large potential increase relative to the measurement of one single-membrane segment reflects the potassium activity ratio at both interfaces of the concentration polarized membrane and is used to determine the complex formation constant of valinomycin (see text). Sample and inner electrolyte are 0.01 M KCl. Eventually, the membrane components diffuse across both segments to again yield a uniform membrane composition.

Figure 3. Observed membrane potentials for ionophore-free segments with varying concentrations of NaTFPB in the segment facing the inner electrolyte, without (A) and with (B) a 20 mmol kg-1 excess of the inert lipophilic electrolyte ETH 500 in both segments. The observed apparent half-Nernstian slope in (A) indicates that strong ion pairing occurs in PVC-DOS membranes, as expected by theory (see text). The observed apparent near-Nernstian slope in (B) suggests that the underlying assumptions of the method are justified (see text). Error bars are standard deviations from at least three replicate measurements.

will eventually reach equilibrium where the cell potential again approaches that for a single-segment measurement. Indeed, after ∼2 h the potential approaches the value for one single segment, indicating that valinomycin is now nearly uniformly distributed across the membrane. Figure 4 also shows that the initial membrane potential after freshly preparing the membrane is stable for nearly 30 min, which leaves sufficient time for a reliable measurement. In practice, the membrane potentials for the individual segments and for the combined sandwich membrane were each recorded for 5 min. Earlier experiments with membranes containing a second, H+selective ionophore had shown a complex formation constant of valinomycin in PVC-DOS of log βKL ) 9.3.8,9 For the same concentration of valinomycin (10 mmol kg-1) and anionic sites (5 mmol kg-1), this work found a somewhat higher value of log βKL ) 9.8 (see Table 1). This discrepancy might originate from the possibility that the reference ionophore used in the earlier works was binding to potassium to some small extent, since that would introduce a negative bias in the obtained stability constants. The existence of a membrane internal diffusion potential might also explain this discrepancy, although the earlier potentiometric method corresponded perfectly to data obtained with an optical extraction method,8 where diffusion potentials are irrelevant. To

further probe this possibility, experiments were performed with membranes that contained varying amounts of the inert lipophilic electrolyte ETH 500. As Table 1 shows, the resulting logarithmic stability constants for the potassium-valinomycin complex were all approximately equal around 10.0. This result is highly interesting, for two reasons. First, it indicates that diffusion potentials are indeed small since otherwise significant membrane potential deviations would be expected with changing ETH 500 concentrations. Second, it shows that ion-pairing effects are largely irrelevant to the obtained complex formation constant. If the ion pair formation constants would be significantly different for the free and complexed potassium, an incremental concentration increase of ETH 500 would asymmetrically affect the free ion concentration in both segments, and the resulting membrane potential would vary. The experimental finding is in agreement with theory, which predicts that only the square root of the ratio of the two ion pair formation constants affects the obtained complex formation constant (see eq 16). As long as ion-pairing effects are relatively nonspecific, the complex formation constants obtained by neglecting ion pairing would be very close to the true complex formation constants. If this notion is correct, the obtained complex formation constants should be nearly invariant of the chosen anionic site additive as long as specific ion-pairing effects can be ruled out. Sandwich experiments were performed with membranes containing the sodium ionophore ETH 212034 and the different anionic additives NaTFPB, KTpClPB, and NaTPB. As Table 1 shows, the apparent complex formation constant for ETH 2120 is somewhat larger if NaTFPB is incorporated in the membrane. Since TFPBis the largest anionic additive, it will likely form the weakest ion pairs among the three tetraphenylborates tested. This effect can (34) Maruizumi, T.; Wegmann, D.; Suter, G.; Ammann, D.; Simon, W. Mikrochim. Acta 1986, I, 331.

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be expected to be strongest if the countercation is not complexed, since the ion radius of that ion will be smaller than the complexed form. This would lead to a higher free cation concentration for the ionophore-free segment and, therefore, indeed to a higher apparent binding constant. Again, these effects seem to be relatively minor as the obtained logarithmic constants vary by ∼0.2 unit. The same trend was observed for membranes containing the potassium ionophore BME-44,35 as the logarithmic complex formation constant is 0.3 unit higher with NaTFPB than with KTpClPB as anionic additives (see Table 1). It is somewhat surprising that the membrane containing ETH 2120 and NaTPB showed a nearly identical behavior to the one containing KTpClPB. Ordinarily, one would expect that NaTPB leaches out rapidly from the ionophore-free segment into the sample,36 which would lead to much smaller ∆EMF values. The present findings suggest that this leaching process is slow on the time scale of the experiment. The above experiments indicate that membranes with and without inert electrolyte show nearly identical membrane potentials. Since real world potentiometric sensors are ordinarily prepared without additional membrane electrolyte, it was omitted in further experiments. The results also show that complex formation constants should preferably be performed with the lipophilic anionic site NaTFPB, since ion-pairing effects seem to be least relevant with this additive. The segmented sandwich membrane technique was tested with the five ionophores valinomycin (K+ selective), BME-44 (K+ selective),35 MBDiBDTC (Ag+ selective),37 tert-butylcalix[4]arene tetraethyl ester (Na+ selective),38 and ETH 2120 (Na+ selective)34 (see Figure 2 for structures). The four alkali metal-selective ionophores had been characterized earlier with a potentiometric two-ionophore method,9,14 and the obtained logarithmic complex formation constants were 9.3 (for valinomycin-K+), 7.9 (for BME44-K+), 7.6 (for calix[4]arene-Na+ complex), and 8.3 (for ETH 2120-Na+). These four ionophores were now studied with the sandwich method by using otherwise identical compositions: 5 mmol kg-1 anionic sites NaTFPB and 10 (for n ) 1) or 20 mmol kg-1 (for n ) 2) ionophore, depending on the assumed complex stoichiometry n. Table 1 indicates that the sandwich method gives comparable results, since the obtained logarithmic complex formation constants are only higher by 0.5 (for valinomycin), 0.2 (for BME-44), 0.0 (for the calixarene), and 0.4 units (for ETH 2120). As briefly discussed above, the observed stability constants are usually somewhat larger with the sandwich method. The most likely explanation for this finding is that the H+-selective ionophore used with the reference method has some residual affinity for alkali metal ions in the membrane. Since repeatabilities of both methods are on the order of 0.1 logarithmic unit, a systematic deviation is present but relatively small. The two potassium ionophores had been previously characterized with a two-ionophore optical method, and the obtained complex formation constant was essentially identical to the one calculated from the corresponding potentiometric experiment. That optical method was also used with the silver ionophore (35) To´th, K.; Lindner, E.; Horva´th, M.; Jeney, J.; Bitter, I.; Agai, B.; Meisel, T.; To´ke, L. Anal. Lett. 1989, 22, 1185. (36) Bakker, E.; Pretsch, E. Anal. Chim. Acta 1995, 309, 7. (37) Kamata, S.; Onoyama, K. Anal. Chem. 1991, 63, 1295. (38) Cadogan, A. M.; Diamond, D.; Smyth, M. R.; Deasy, M.; McKervey, M. A.; Harris, S. J. Analyst 1989, 114, 1551.

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MBDiBDTC,13 and it was concluded that this ionophore essentially forms no complexes with sodium ions in the membrane. Table 1 shows that this finding is also confirmed with the sandwich method, as the membrane potential increases by a mere 5 mV after the segments are conditioned in sodium chloride solutions (without silver). With silver ions in solution, the membrane potential drastically increases to 500 mV (see Table 1). Since binding of this ionophore with sodium can essentially be ruled out, this value should correspond approximately to the one found with selectivity measurements on ordinary MBDiBDTC-containing membranes. Indeed, recent selectivity studies involving this ionophore showed that the potential increases by 5.5 mV from a solution containing sodium chloride to one containing silver nitrate.39 Table 1 indicates that the corresponding logarithmic complex formation constant is quite large at 12.4 with n ) 2. The excellent selectivity of this silver ionophore originates in the strong stabilization of silver, but also in the extremely weak binding behavior to alkali metal ions. The sandwich method can be used to determine complex formation constants toward other, discriminated ions. Table 1 shows the observed complex formation constants of BME-44 toward Li+ and Na+. The corresponding complexes are clearly weaker than for K+, which reflect the high binding selectivity of this ionophore. Interestingly, the previously reported potentiometric two-ionophore method obtained logarithmic stability constants that were each smaller by 0.8 unit for Li+ and for Na+, while the potassium complex was found to be nearly equally stable.9 This discrepancy suggests that careful experimentation must be performed to obtain formation constants for discriminated ion complexes. As explained in detail elsewhere,39,40 inadequate conditioning, the presence of zero-current ion fluxes of preferred ions from the membrane interior, or sample impurities may all contribute to such experimental deviations. Since the presented method is intrinsically transient, it may prove difficult to always reliably eliminate such interferences. It seems currently most prudent to calculate complex formation constants for discriminated ions from the constant involving the primary ion and the appropriate selectivity coefficients. In principle, the segmented sandwich membrane method may be used to determine complex stoichiometries and the influence of different ionic site concentrations on the binding behavior. Such concentration variations will however also influence the extent of ion pair formation, the activity coefficients, and, if applicable, the magnitude of the diffusion potential in the membrane. These influences were assessed by performing experiments with the ionophore valinomycin, which is known to form 1:1 complexes with potassium. Changes in the complex formation constants should ideally be invariant as long as sufficient ionophore is available to complex all extracted potassium ions. Table 1 shows the results for experiments where the anionic site concentration as well as the ionophore concentration was systematically varied. The total ionophore concentration was always kept above that of the anionic site concentration. Indeed, as the ionophore concentration is decreased, the observed membrane potential decreases as well. The resulting logarithmic complex formation constant remains approximately constant between 9.8 and 10.1, and no (39) Bakker, E. Anal. Chem. 1997, 69, 1061. (40) Bakker, E. Trends Anal. Chem. 1997, 16, 252.

decreasing or increasing trend is evident as a function of concentration. Similarly, decreasing the concentration of anionic sites relative to the ionophore from 50 to 10% shows no significant effect on the complex formation constants, as they appear identical within experimental error. These results may suggest that concentration variations within solvent polymeric membranes may, within the indicated variation, indeed be used to determine complex stoichiometries and other important binding properties of ion-selective ionophores directly in solvent polymeric membranes. CONCLUSIONS This paper has shown that reliable complex formation data can be extracted from transient membrane potential measurements involving the fusion of two membrane segments to form a polarized membrane. Five ionophores were characterized, and the resulting complex formation constants were somewhat larger than the ones obtained earlier with a reference method, but otherwise

highly comparable. The effects of ion pairing, inert lipophilic electrolyte, and varying concentrations were all elucidated. Unlike the previously reported methods, this sandwich technique will likely allow the convenient characterization of heavy metalselective ionophores, anion-selective ionophores, and electrically charged ion carriers in a variety of polymeric environments. This will be the focus of further studies. ACKNOWLEDGMENT The authors thank the National Institutes of Health (Grant R01GM58589) for financial support and K. N. Mikhelson for stimulating discussions.

Received for review June 3, 1999. Accepted September 8, 1999. AC9905930

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