Effect of Transmembrane Electrolyte Diffusion on the Detection Limit of

Anal. Chem. 1998, 70, 303-309

Effect of Transmembrane Electrolyte Diffusion on the Detection Limit of Carrier-Based Potentiometric Ion Sensors Sally Mathison and Eric Bakker*

Department of Chemistry, Auburn University, Auburn, Alabama 36849

The detection limit of carrier-based ion-selective electrodes is explained by the presence of a locally elevated concentration of measuring ions at the sample-membrane phase boundary. Since ion-selective electrodes are responsive to phase boundary activities, such elevated concentrations render the potentiometric sensor insensitive to dilute bulk concentration changes. Different mechanisms for the continuous release of measuring ions from the membrane are conceivable. The extraction of inner electrolyte into the backside of the ion-selective membrane is predicted to lead to a concentration gradient of electrolyte across the membrane and therefore to a net flux of measuring ions from the inner filling solution to the sample. This effect is described by an extended model that respects the relevant extraction and diffusion processes. The extent of coextraction at the backside is predicted on the basis of potentiometric measurements on the range of anion interference. These predictions are found to relate well to experimental results with valinomycin electrodes. The presence of lipophilic anions in the inner electrolyte is found to increase detection limits owing to the increased extraction into the membrane. An upper limit apparently exists beyond which the detection limit is no longer increased upon increasing the inner filling solution concentration. Stirring the sample decreases the detection limit owing to increased mass transport from the membrane surface to the bulk sample. Ionophore-based ion-selective electrodes (ISEs) are widely used to detect a variety of nonelectroactive ions such as alkali and alkaline earth metal ions and anionic analytes. The design of a large range of highly selective ionophores has made these sensors particularly well suited for blood electrolyte analysis.1 The concentrations of these target ions are typically quite high, that is, often in the millimolar range. The detection limit of ionselective electrodes has therefore traditionally been of little concern. In recent years, this class of sensors has been expanded to the analysis of heavy metal ions, since interest in trace level analysis has increased in view of environmental monitoring purposes or clinical applications, such as blood lead assays.2-8 (1) Meyerhoff, M. E. Trends Anal. Chem. 1993, 12, 257. (2) Malinowska, E.; Brzo´zka, Z.; Kasiura, K.; Egberink, R. J. M.; Reinhoudt, D. N. Anal. Chim. Acta 1994, 298, 245. S0003-2700(97)00690-2 CCC: $15.00 Published on Web 01/15/1998

© 1998 American Chemical Society

Unfortunately, most ion-selective electrodes show detection limits around the micromolar concentration range. This is a fairly high limit that often prohibits the practical use of these sensors for the detection of low levels of analytes. The use of ion buffers such as EDTA is a well-known procedure to yield lower detection limits in some cases.9 However, it can only be used to detect lower free, and not total, ion concentrations, since the added ion ligand complexes all measuring ions, not only the ones that cause deterioration of the potentiometric response. It is somewhat surprising that very few dedicated studies on the chemical reasons for the detection limit of ISEs have been published.10,11 Interestingly, the respective optical sensors based on thin films that contain the same type of selective chemical components show much lower detection limits, and the measurement of subnanomolar concentrations has been demonstrated for silver and lead as analytes.12,13 To date, this feature seems to be the most striking advantage of optical versus analogous potentiometric sensors. Clearly, the selectivity of some heavy metal ion-selective electrodes is often not the limiting factor, as extremely high selectivities over alkali and alkaline earth metal ions have been found.11,14 Consequently, lower detection limits may intrinsically be possible based on available ionophore chemistry. The most striking difference between ion-selective optode and electrode setups is the lack of an inner filling solution with the former. Traditionally, this inner solution contains a moderately high concentration of a salt of the measuring ion. This salt can, in principle, be coextracted into the ion-selective membrane where it may diffuse along a linear steady-state concentration gradient into the dilute sample, thereby effectively perturbing the interfacial sample composition. Such a (3) Bricker, J.; Daunert, S.; Bachas, L. G.; Valiente, M. Anal. Chem. 1991, 63, 1585. (4) Casabo, J.; Flor, T.; Romero, M. I.; Teixidor, F.; Perez-Jimenez, C. Anal. Chim. Acta 1994, 294, 207. (5) O’Connor, K. M.; Svehla, G.; Harris, S. J.; McKervey, M. A. Talanta 1992, 39, 1549. (6) Kamata, S.; Onoyama, K. Anal. Chem. 1991, 63, 1295. (7) Hassan, S. S. M.; Moustafa, G. A. E. Talanta 1996, 43, 797. (8) Bates, M.-R. M.; Cardwell, T. J.; Cattrall, R. W.; Deady, L. W.; Gregorio, C. G. Talanta 1995, 42, 999. (9) Sokalski, T.; Maj-Zurawska, M.; Hulanicki, A. Mikrochim. Acta 1991, 1, 285. (10) Bakker, E.; Willer, M.; Pretsch, E. Anal. Chim. Acta 1993, 282, 265. (11) Bakker, E. Sens. Actuators, B 1996, 35, 20. (12) Lerchi, M.; Bakker, E.; Rusterholz, B.; Simon, W. Anal. Chem. 1992, 64, 1534. (13) Lerchi, M.; Orsini, F.; Cimerman, Z.; Pretsch, E.; Chowdhury, D. A.; Kamata, S. Anal. Chem. 1996, 68, 3210. (14) Bakker, E. Anal. Chem. 1997, 69, 1061.

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mechanism would allow addition of some level of control to the detection limits of such ion sensors. There are cases where a high detection limit is even desirable, especially for the measurement of sample anions and/or ligands that bind to these released measuring ions and lead to a reversible potentiometric response.3,11 The success of these types of sensors is strongly dependent on the extent of control and understanding one can exert on the detection limit of solvent polymeric ion-selective electrodes. In this paper, therefore, the principle of transmembrane electrolyte diffusion is evaluated as a tunable and plausible effect on the detection limit of potentiometric ion sensors. THEORY In this section, the potentiometric response of ion-selective electrode membranes is related to the phase boundary ion activity on the sample side of the sample-membrane interface. This local ion activity, in turn, is described by a steady-state electrolyte flux from the inner electrolyte of the electrode across the ion-selective membrane and into the sample. To understand this ion flux, therefore, the extent of coextraction of electrolyte at the membrane-inner electrolyte side has to be characterized. These separate steps are evaluated here. In principle, the treatment presented here is similar to classical membrane transport problems with the difference being that local phase boundary activities are of interest rather than total sample concentrations. As is well known, the idealized response of an ion-selective electrode membrane, that is, without interference from other sample ions, can be described by the Nernst equation:

E ) E0 +

RT ln aM(interface) zF

(1)

aqueous phase in contact with an ion-selective membrane that contains an ionophore L may be extracted into the membrane phase, denoted with (org), to some extent according to the following simple equilibrium:

M+(aq) + L(org) + A-(aq) h ML+(org) + A-(org)

where species denoted with (aq) are in the aqueous phase, that is, either in the inner filling solution or in the sample. For simplicity, it is here assumed that all ions are monovalent, and the neutral ionophore forms 1:1 complexes with the measuring cation. The respective coextraction equilibrium constant is given as:

Kcoex )

304

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[ML+]′[A-]′ aM′aA′[L]′

(3)

where symbols in brackets denote concentrations in the membrane phase and sample activities are shown for species in the aqueous phase. The prime (′) for all symbols denotes that this process occurs at the membrane-inner filling solution phase boundary. If the species shown are the only extracted components, and concentrations of uncomplexed cations are assumed to be small relative to that of the complex owing to strong complexation in the membrane, a simplified charge balance (RT + [A-]′ ) [ML+]′) and mass balance (LT ) [L]′ + [ML+]′) may be written. The symbol LT is the total concentration of ionophore and RT that of the lipophilic anionic site. Inserting these relationships into eq 3 gives

Kcoex ) where E is the electromotive force, R, T, and F are the universal gas constant, the absolute temperature, and the Faraday equivalent, respectively, z is the charge and aM(interface) the phase boundary activity of the measuring ion Mz+, and all sampleindependent potential contributions are included in E0. When the sample electrolyte activity is high, it is approximately equal to the phase boundary activity. However, at or around the detection limit of the electrode, it may be significantly different. In pure water solutions, or in solutions containing only ions the electrode is not responsive for, it may be assumed that the electrode is responsive to measuring ions that are continuously released from the electrode membrane itself. The origin of this ion flux is the topic of this paper. According to the IUPAC, the detection limit is defined as the cross section of the two extrapolated linear segments of the calibration curve.15 The cross section is given here where the extrapolated Nernst electrode function reaches the potential at the detection limit, aM(DL). If interference from other ions can be excluded, this detection limit aM(DL) corresponds to the sample activity locally present at the samplemembrane phase boundary, i.e., aM(DL) ) aM(interface). This relationship is the basis for the present theoretical treatment. In the following, cation-selective membranes containing a neutral carrier and lipophilic anionic sites are considered. Other systems can be treated in complete analogy. Electrolyte Coextraction at Membrane-Inner Electrolyte Interface. A salt M+A- of the measuring ion contained in an

(2)

(RT + [A-]′)[A-]′ aM′aA′(LT - RT - [A-]′)

(4)

In practice, this coextraction equilibrium will also be influenced by ion-pairing processes within the organic phase. The coextraction constants obtained here are therefore termed apparent constants and should be dealt with carefully. In this study, however, membrane phases of high polarity were used where ionpairing effects are usually less significant.16 It was established previously for the description of the response characteristics that the upper detection limit of neutral ionophorebased cation-selective electrodes is a direct function of this apparent coextraction constant:17

aM(UDL) ) (Kcoex)-1(RT/aA)

(5)

The upper detection limit is defined in analogy to the IUPAC recommendation for the description of the lower detection limit;15 that is, it is given by the cross section of the two upper extrapolated linear segments of the calibration curve. One segment is given by a cationic Nernst response toward log aM, the other by an anionic Nernst response toward log aA. This (15) Buck, R. P.; Lindner, E. Pure Appl. Chem. 1995, 66, 2527. (16) Kuratli, M.; Badertscher, M.; Rusterholz, B.; Simon, W. Anal. Chem. 1993, 65, 3473. (17) Bakker, E.; Xu, A.; Pretsch, E. Anal. Chim. Acta 1994, 295, 253.

relationship allows the estimation of apparent coextraction constants with potentiometric experiments. The concentration of extracted anions at the second organic phase boundary can be approximately described by solving eq 4 for [A-]′. After rearranging eq 4 to

[A-]′2 + (RT + KcoexaM′aA′)[A-]′ KcoexaM′aA′(LT - RT) ) 0 (6) [A-]′ can be explicitly solved using a quadratic equation to give

1 [A-]′ ) {-RT - KcoexaM′aA′ + 2

x(RT + KcoexaM′aA′)2 + 4KcoexaM′aA′(LT - RT)}

(7)

At the detection limit, the concentration of extracted sample anions will be higher at the inner phase boundary of the membrane than at the sample-membrane phase boundary. The next section, therefore, describes the effect of net flux of anions (counterbalanced by complexed ionophore) across the ion-selective membrane on the detection limit of the respective potentiometric sensor. Steady-State Flux of Electrolyte across the Ion-Selective Membrane. As a solvent polymeric membrane ion-selective electrode is brought in contact with an extremely dilute sample such as pure water, the coextraction of electrolyte from the sample into the membrane is negligible. Considering rapid equilibration between sample and membrane, therefore, a concentration gradient of extracted anions counterbalanced by complexed ionophore must exist that leads to a net flux of electrolyte across the membrane into the sample. Upon reaching the samplemembrane interface, the electrolyte is continuously released into the sample where it diffuses away into the sample bulk along a second concentration gradient. For every anion released, a measuring cation is released into the sample as well. This cation effectively perturbs the aqueous-phase boundary for low sample concentration and determines the detection limit of the potentiometric sensor. At steady state, the two ion fluxes must be equal in magnitude, and linear concentration gradients can be assumed in both cases since the system may be described with a onedimensional diffusion profile. The treatment presented here is analogous to previous works dealing with similar diffusion phenomena.18 Accordingly, the ion fluxes within the membrane and aqueous diffusion layer can be expressed as

Jm ) Dm

[A-]′ - [A-] δm

(8)

Figure 1. Schematic representation of predicted concentration profiles of measuring ions across the ion-selective membrane that may cause a locally elevated ion concentration at the samplemembrane phase boundary. The distances δaq and δm are the respective Nernst diffusion thicknesses. Under ideal permselective conditions, no concentration gradient and, therefore, no net flux of ions is expected across the ion-selective membrane (shown in A). With traditionally elevated electrolyte concentrations in the inner filling solutions, substantial coextraction into the membrane is expected that leads to a net flux of electrolyte across the membrane and into the sample (B). If the sample contains no measuring ions, the activity at the sample-membrane phase boundary is equal to the detection limit aM(DL). (C) shows that as all carrier molecules at the membraneinner electrolyte side are saturated, no further extraction takes place and a maximum concentration gradient with the membrane is attained that leads to a maximum lower detection limit.

diffusion layer; [A-] and [A-]′ are the phase boundary concentrations of extracted anion at the sample and inner filling solution side, respectively; cM(interface) and cM(bulk) are the sample phase boundary and sample bulk measuring ion concentrations; the symbols δm and δaq are the respective diffusion layer thicknesses (see Figure 1), that is, the thickness of the ion-selective membrane and of the sample Nernst diffusion layer; Dm and Daq are the diffusion coefficients of the electrolyte within the respective phase. At the detection limit, cM(bulk) ) 0 and [A-] ≈ 0, and eqs 8 and 9 can be further simplified. At steady state, both fluxes are equal, and the combination of eqs 8 and 9 gives

Jm ) Jaq )

and

Jaq ) Daq

cM(interface) - cM(bulk) δaq

(9)

where Jm and Jaq denote the flux within the membrane and aqueous (18) Fu, B.; Bakker, E.; Yun, J. H.; Yang, V. C.; Meyerhoff, M. E. Anal. Chem. 1994, 66, 2250.

Dm[A-]′ DaqcM(DL) ) δm δaq

(10)

Dmδaq [A ]′ Daqδm

(11)

and after rearranging

cM(DL) )

Apparently, a linear correlation is expected between the detection Analytical Chemistry, Vol. 70, No. 2, January 15, 1998

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limit and the concentration of extracted anions at the membraneinner electrolyte interface which was described above by a coextraction equilibrium process. Hence, the detection limit of a carrier-based ion-selective electrode can be predicted by combining eqs 7 and 11 to give

cM(DL) )

Dmδaq {-RT - KcoexaM′aA′ + 2Daqδm

x(RT + KcoexaM′aA′)2 + 4KcoexaM′aA′(LT - RT)}

(12)

Interestingly, theory predicts an upper limit for the lower detection limit, which is given by complete saturation of ionophore at the membrane-inner electrolyte interface. In this limiting case, the extracted anion concentration is equal to the originally available free ionophore concentration ([A-]′ ) LT - RT), which leads to a maximum concentration gradient across the ion-selective membrane (see Figure 1C). This upper limit of the lower detection limit is therefore given as

cM(DL) )

Dmδaq (L - RT) Daqδm T

(13)

The upper limit can be estimated with δaq ≈ 100 µm (in unstirred solutions), δm ≈ 200 µm, Daq/Dm ≈ 100, LT ) 0.010 mol L-1, and RT ) 0.005 mol L-1 as log cM(DL) ) -4.6, which appears to be a reasonable value. In pure water solutions, it can be assumed that cM(DL) ≈ aM(DL), since activity coefficients approach unity in this case. In other situations, effects of the sample background electrolyte on activity coefficients will have to be considered. Since the Nernst diffusion layer δaq depends on the stirring rate of the sample, it is expected that sample stirring decreases the detection limit. Generally, sample perturbation is predicted for all cases where the concentrations of extracted electrolyte differ at both phase boundaries of the membrane. Electrolyte flux across the membrane is negligible only for the case where no membraneinternal concentration gradient is observed, i.e., [A-]′ ) [A-]. EXPERIMENTAL SECTION Reagents. The salts, the acids, and the membrane components valinomycin, potassium tetrakis(p-chlorophenyl)borate (KTpClPB), o-nitrophenyl octyl ether (o-NPOE), high-molecularweight poly(vinyl chloride) (PVC), and tetrahydrofuran (THF) were purchased in the highest quality available from Fluka Chemika-Biochemika (Ronkonkoma, NY). Aqueous solutions were prepared by dissolving the appropriate salts in Nanopure purified distilled water. Membrane Preparation and EMF Measurement. Ionselective electrode membranes were cast by dissolving 1.6 mg (10 mmol kg-1) of valinomycin and 0.4 mg (5 mmol kg-1) of K-TpClPB, together with PVC and o-NPOE (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 (2.2-cm i.d.) affixed onto a microscopic glass slide. The solvent THF was allowed to evaporate overnight to form a membrane with a thickness of ∼200 µm. For each electrode, a 6-mm-diameter disk was cut from the parent membrane with a cork borer and incorporated into a Phillips electrode body (IS561, Glasbla¨serei Mo¨ller, Zu¨rich, Switzerland). Solutions of 10-4306

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1 M KCl, KNO3, or KClO4 were used as the inner filling solution for the assembled electrodes. To enhance EMF stability, 10-4 M KCl was added to the inner filling solutions containing KNO3. The electrodes were conditioned in 10-4 M KCl overnight before measurement. The concentration of this solution was chosen lower than traditionally to minimize the effect of coextraction from the sample side during conditioning (note that potassium ions were already present in the membrane as the countercations of the tetraphenylborate). All membrane electrode potential measurements were performed at laboratory ambient temperature (22 ( 1 °C) in unstirred solutions versus a Teflon sleeve Ag/AgCl reference electrode (Ingold, Wilmington, MA) with 1 M LiOAc as the bridge electrolyte.19 Before measurement, the electrodes were repeatedly (typically 10 times) flushed and inserted into fresh pure water samples until the potentiometric signal was no longer lowered upon further sample change. The unstirred aqueous solution consisting of pure water was subsequently titrated with a solution of potassium chloride, and the potential was recorded as previously described.20 To determine the activity range of anion interference for the valinomycin electrodes, the membranes were measured as described above, but in KCl, KNO3, and KClO4 solutions, respectively. The effect of sample stirring was evaluated with a motorized Barnet mixer Series 10 (Barnet Co., Barlington, IL) and a Nalgene polypropylene stirring rod as the mixer shaft and paddle (Nalge Co., Rochester, NY) which was held on the lowest stirring position. Activity coefficients were calculated according to Meier.21 Detection limits were determined according to IUPAC recommendations.15 RESULTS AND DISCUSSION Ion-selective electrodes are generally responsive to phase boundary activities. It was recognized quite early that the activity at the phase boundary may in some instances be different from the sample bulk. For example, the detection limit of AgCl precipitate-based membranes can be described by a local dissolution equilibrium of the membrane material that leads, compared to the sample, to an elevated silver concentration at the membrane phase boundary.22,23 Similarly, the fact that Ag2S membranes show higher detection limits than dictated by the solubility product was explained by chemical membrane defects, that is, the presence of silver salts of a solubility higher than Ag2S.23 A locally different phase boundary activity than in the bulk sample was also used as an argument to explain the response mechanism of polyion sensors18 and the so-called Hulanicki effect14,24 where superNernstian response slopes are observed if the membrane is brought in contact with a preferred ion of low concentration that is not initially contained in the membrane. In these cases, the measuring ions in the Nernst diffusion layer adjacent to the membrane are depleted since the membrane acts as an effective sink that extracts these ions. The main hypothesis for this work is that carrier-based ionselective membranes constantly release low amounts of measuring ions into the sample that dictate the detection limit of the (19) Dohner, R. E.; Morf, W. E.; Simon, W.; Wegmann, D. Anal. Chem. 1986, 58, 2585. (20) Bakker, E. J. Electrochem. Soc. 1996, 143, L83. (21) Meier, P. C. Anal. Chim. Acta 1982, 136, 363. (22) Pungor, E.; Toth, K. Analyst 1970, 95, 625. (23) Morf, W. E.; Kahr, G.; Simon, W. Anal. Chem. 1974, 46, 1538. (24) Maj-Zurawska, M.; Sokalski, T.; Hulanicki, A. Talanta 1988, 35, 281.

potentiometric sensor at low sample concentrations. The continuous release of measuring ions has indeed been observed in the literature.25 This effect can be used to quantitatively explain the anion response characteristics of silver carrier-based electrodes.3,11 Halide ions decrease the activity of the released silver ion via solubility equilibria, and an anion response curve toward these halide ions is observed. The upper detection limit of the anion response range is given by the selectivity of the silver responsive membrane; that is, the anion response deteriorates if other cations start to ion exchange with silver ions.11 There are numerous possible reasons for the continuous release of measuring ions from the membrane. Because ionselective electrodes are measured under zero-current conditions, the release of measuring cations must be accompanied by a simultaneous release of an anion or an uptake of a sample cation. However, ion-exchange processes with sample ions can be excluded in this present discussion since ion-exchange equilibria describe the selectivity of such sensors and are the scope of other papers.14 If coextraction of a cation with an anion is the most likely explanation for the release of measuring ions from ionselective membranes, there are a variety of anions that are possible candidates for this effect: (1) sample anions that were coextracted in a previous experiment where the membrane made contact with a concentrated solution and that are now released again into the dilute sample; (2) lipophilic site additives that are purposely added to the membrane; (3) anionic impurities that are intrinsically present in the membrane; and (4) anions that are, together with measuring ions, coextracted at the backside of the membrane and that continuously diffuse to the dilute sample. Possibility 1 will almost always arise if the membrane is exposed to solutions that contain widely different ion concentrations. This is sometimes observed as peak tailing in flow injection analysis, although part of this effect may be associated with the logarithmic response behavior of ion-selective electrodes.26 Apparently, extremely low detection limits may only be achieved for ion-selective electrode membranes that are in contact with dilute samples only. Effect 2 is in principle possible, although it has recently been shown that the leaching of anionic additives is negligible if the cation-carrier complex is stable.27 Moreover, such a limitation would render the corresponding optical sensors short-lived, which is not observed in practice. Nonetheless, this effect might be a major factor for ion-exchanger-based membranes without added ion carrier and for membranes that contain ion additives of poor lipophilicity and/or chemical stability.24,28 Possibility 3 remains largely unexplored since the lipophilicity of anionic impurities in the membrane matrix remains poorly characterized. Effect 4 is the topic of this paper. In the theoretical section, therefore, a mathematical model was developed that relates the expected detection limit of a cationselective electrode to the electrolyte activity in the inner filling solution of the membrane. This principle is schematically presented in Figure 1. Under ideal permselective conditions, the measured cation is the only extractable ion and no effective (25) Bu ¨ hlmann, P.; Yajima, S.; Tohda, K.; Umezawa, K.; Nishizawa, S.; Umezawa, Y. Electroanalysis 1995, 7, 811. (26) Nann, A.; Pretsch, E. J. Chromatogr. 1994, A 676, 437. (27) Bakker, E.; Pretsch, E. Anal. Chim. Acta 1995, 309, 7. (28) Rosatzin, T.; Bakker, E.; Suzuki, K.; Simon, W. Anal. Chim. Acta 1993, 280, 197.

Figure 2. Anion interference range of valinomycin-based potassiumselective electrodes. Solid line with Nernstian slope of 58.5 mV decade-1; dotted lines with Nernstian anion slope of -58.5 mV decade-1. The upper detection limit is given by the cross section of these two lines and is used to predict the extent of electrolyte coextraction at the backside of the membrane.

electrolyte transport is expected (see Figure 1A). This idealized demand reflects the necessity of ion-selective membranes to have ion-exchanger properties; that is, the extraction of counterions must be negligible relative to the concentration of lipophilic anionic sites. However, it is well-known that some level of anion coextraction will always be present, although it only deteriorates the potentiometric response on the sample side as the concentration of extracted anions is significantly high. Ultimately, at very high anion concentrations, this carrier-mediated process leads to saturation of all available carrier molecules so that the membrane effectively contains complexed ionophore and anionic sites as well as extracted anions as counterions.17 In this activity range, the electrode will be anion-responsive. This effect is most severe for high sample electrolyte concentrations, stable cation complexes, high lipophilicities of extracted cations and anions, and low concentration of anionic sites. These processes are quite well understood and described since they are relevant to the understanding of the upper detection limit of ion-selective electrodes.29,30 Figure 2 illustrates this effect with potentiometric responses of a valinomycin membrane electrode to various potassium anion salts; the extent of anion interference follows the Hofmeister selectivity sequence. These data are used to calculate effective electrolyte coextraction constants (see below). In the present discussion, where the detection limit of ionselective electrodes is evaluated, the sample will contain low analyte levels so that anion coextraction on the sample side is negligible. On the other hand, the traditionally employed high electrolyte concentration in the inner filling solution may cause substantial coextraction of electrolyte into the membrane at the second, inner-phase boundary. Within the membrane, therefore, (29) Morf, W. E.; Kahr, G.; Simon, W. Anal. Lett. 1974, 7, 9. (30) Buck, R. P.; Toth, K.; Gra`f, E.; Horvai, G.; Pungor, E. J. Electroanal. Chem. 1987, 223, 51.

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Figure 3. Potentiometric KCl responses of valinomycin electrodes containing varying KCl concentrations in the inner filling solution. Higher KCl concentrations lead to higher detection limits.

a concentration gradient is expected that leads to a net flux of electrolyte from the inner electrolyte to the sample (see Figure 1B). This gradient reaches its maximum when all available carrier molecules are complexed at the inner-phase boundary. Upon further increase of the inner electrolyte concentration, the concentration of extracted electrolyte is no more increased due to the lack of availability of uncomplexed ionophore. This maximum gradient is illustrated in Figure 1C and should lead to a maximum flux of electrolyte from the inner electrolyte into the sample. It is well-established that ion-selective electrodes are responsive to phase boundary ion activities in the aqueous phase. A locally elevated ion concentration due to transport of electrolyte from the membrane will render the ion-selective electrode effectively insensitive to low levels of analyte in the sample bulk. According to the accepted IUPAC definition,15 this locally elevated ion concentration is equal to the detection limit of the potentiometric sensor (see above). In the theoretical section, this phase boundary activity was described with a steady-state model. Accordingly, a stable electrode response is expected if the electrolyte flux across the membrane is equal to the flux across the Nernstian diffusion layer in the aqueous phase adjacent to the membrane. At the detection limit, the sample bulk concentration is nearly zero, and this assumption allows for simplified equations. These theoretical expectations were tested with a wellestablished electrode system where the counteranion of the measured cation could be widely varied. Specifically, valinomycin electrodes were chosen and the concentration of KCl, KNO3, and KClO4 as inner electrolyte was varied from 10-4 to 1 M in different experiments. In Figure 3, the KCl response characteristics of potassium-selective electrodes are shown with varying KCl concentrations in the inner filling solution. It is evident that the inner electrolyte concentration may have a decisive effect on the lower detection limit of these electrodes, with lower concentrations giving lower detection limits. Figure 4 summarizes the measured detection limits for the experiment shown in Figure 3 as well as 308 Analytical Chemistry, Vol. 70, No. 2, January 15, 1998

Figure 4. Dependence of the detection limit of the KCl response of valinomycin-based potassium-selective electrodes on the kind and concentration of inner filling electrolyte at the backside of the ionselective membrane. Inner electrolytes contained KCl, KNO3, or KClO4 in the indicated activity. Dotted lines: predicted on the basis of eq 5 and coextraction constants determined potentiometrically (see Figure 2).

for analogous experiments containing KNO3 and KClO4 in the inner filling solution. As predicted by theory, there is an upper limit beyond which the lower detection limit is no longer increased upon increasing the concentration of electrolyte in the inner filling solution. Interestingly, this upper limit is effectively the same for all three electrolytes tested and is very close to the one predicted theoretically (see above). This suggests that the ratios of the diffusion coefficients in the membrane and aqueous solution are very similar for all electrolytes tested, since these are the only variables in eq 13. Upon decreasing the electrolyte concentration, the detection limit decreases most readily for Cl-, followed by NO3- and ClO4-. This behavior is expected, since the three tested anions have significantly different lipophilicities which will alter the effective coextraction constant (see eq 3). These relative horizontal distances can be predicted on the basis of the coextraction experiments shown in Figure 2, where the potentiometric responses toward these same salts, now contained in the sample, are shown. These data were related to eq 5, and effective coextraction constants logKcoex of -1.2 (for KCl), 1.4 (for KNO3), and 3.5 (for KClO4) were obtained. Subsequently, the theoretical curves shown in Figure 4 were calculated on the basis of these constants and eq 12. Apparently, the experimental data are fairly well predicted for high concentrations of inner filling solution electrolyte with the exception of KClO4. In that case, the uptake of electrolyte into the membrane may lead to a local depletion of inner electrolyte at the inner-phase boundary which might explain the lower than expected detection limits. These deviations also indicate that the use of extremely dilute inner electrolytes is not generally advisable as they are more easily perturbed by electrolyte diffusion into the membrane and sample and/or contamination with ions originating from concentrated samples. Equation 12 suggests that the use of thicker membranes (increase of δm) and increase of the membrane viscosity (Dm)18 are alternative ways to reduce the electrolyte flux from the inner filling solution.

sample. A limited selectivity toward H+ or Li+ (from the bridge electrolyte of the reference electrode) also appears to be a possible explanation for the flatting of the curves, but considering the small concentrations of these interfering ions and the high selectivity of valinomycin electrodes,20 this seems less convincing. Clearly, lower detection limits seem intrinsically possible to achieve by careful experimentation.

Figure 5. Effect of sample stirring on valinomycin-based membrane electrodes containing varying concentrations of KNO3 in the inner electrolyte and pure water as the sample.

The data in Figure 4 start to deviate for the lowest inner filling solution concentrations, giving higher than predicted detection limits. Other effects seem to be important here that were not considered by the model. For this purpose, the effect of sample stirring was evaluated for valinomycin-based membranes with KNO3 as inner electrolyte (see Figure 5). According to eq 12, sample stirring should decrease the Nernst diffusion layer thickness and hence enhance mass transport from the membrane surface into the sample bulk. Consequently, if the detection limit is caused by the presence of ions at the membrane-phase boundary that are originating from the backside of the membrane, sample stirring should decrease the detection limit. If, however, the response is given by ions that are contained in the sample bulk, or by equilibrium partitioning effects only, stirring should not influence the potentiometric response substantially. As Figure 5 shows, the effect of sample stirring is very significant for the electrodes containing a high inner electrolyte concentration, lowering the detection limit reversibly by nearly 1 order of magnitude. For more dilute inner filling solutions, however, the effect of sample stirring is much less pronounced and disappears nearly completely for the lowest concentration. Interestingly, according to Figure 4, these also correspond to the data points that correlate poorly with theoretical expectations; that is, the detection limits seem to be caused by effects unrelated to the present treatment. This is a valuable indication that the lowest detection limits observed in these experiments are caused by measuring ions contained in the sample, and cross-contamination is a likely explanation for this behavior since up to eight ion-selective electrodes were simultaneously measured in the same

CONCLUSIONS The experiments described herein suggest that transmembrane diffusion processes play an important role in dictating the lower detection limit of carrier-based ion-selective electrodes. The effect may be semiquantitatively described by using extraction equilibria and steady-state diffusion processes. The described effect appears to be a main reason why ion-selective electrodes show higher detection limits than the corresponding optodes, and the use of low inner filling solution concentrations is recommended to reduce this discrepancy. On the other hand, the principle described herein may also be exploited analytically, as it seems especially valuable for potentiometric sensors that rely effectively on a chemical decrease of this detection limit via precipitation equilibria. It was previously shown that analytically valuable anion sensors, such as silver-selective electrodes that are responsive to halide anions, can be constructed by making use of this principle.3,11 It must be mentioned that no special experimental precautions were used to lower the detection limit to trace levels, since the fundamental characterization of the expected transmembrane diffusion process was the main focus of this work. It is anticipated that improved experimental conditions, such as the use of a well-defined flow-through system as with optodes may lead to substantially lower detection limits in some cases. Nonetheless, other effects remain to be studied such as sample carry-over error, release of previously extracted sample ions from the membrane, and leaching of measuring ions together with tetraphenylborates or anionic impurities as counteranions. ACKNOWLEDGMENT Partial financial assistance from the Petroleum Research Fund (administered by the American Chemical Society) and the Auburn University Grant-in-aid Program is appreciated. The authors thank Roderick Goines (Auburn University) for valuable undergraduate laboratory work. Received for review July 1, 1997. Accepted October 29, 1997.X AC970690Y X

Abstract published in Advance ACS Abstracts, December 15, 1997.

Analytical Chemistry, Vol. 70, No. 2, January 15, 1998

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