Determination of Unbiased Selectivity Coefficients of Neutral Carrier

Anal. Chem. 1997, 69, 1061-1069

Determination of Unbiased Selectivity Coefficients of Neutral Carrier-Based Cation-Selective Electrodes Eric Bakker*

Department of Chemistry, Auburn University, Auburn, Alabama 36849

A new procedure for the determination of selectivity coefficients of neutral carrier-based cation-selective electrodes is established that avoids exposure to the preferred ion prior to the measurement of discriminated ions. The method is, therefore, unbiased by the presence of preferred ions in the membrane that otherwise could mask the response to discriminated ion solutions. It is generally applicable as long as a series of considerations are met and can only be applied once for a given membrane. Careful studies with a series of sodium-, silver-, and calcium-selective electrodes reveal that Nernstian response slopes can now be obtained for even highly discriminated cations. Specifically, a 1,3-bridged calix[4]arene derivative as introduced by Yamamoto and Shinkai indeed yields an extraordinary sodium selectivity pot of log KNa,K ) -4.9, with potassium showing Nernst response as well. Analogous measurements with two different silver carriers, a bisthioether-functionalized calix[4]arene and methylenebis(diisobutyldithiocarbamate), and the calcium carrier ETH 129 also show extremely high selectivity, which can satisfactorily be correlated to data obtained previously in ion-buffered solutions. The new procedure promises to be a valuable additional tool for future characterizations of highly selective ion carriers. Carrier-based ion-selective electrodes are well-established analytical tools that are used routinely to measure a wide variety of different ions selectively and directly in complex samples such as whole blood. The key compound of the plasticized polymeric membrane is the incorporated carrier that defines the selectivity of the sensor via selective complex formation. In the past years, a large variety of mainly cation-selective carriers have been synthesized by various research groups that induce extremely high selectivity of many orders of magnitude over other potentially interfering sample ions.1,2 Although the selectivity is, indeed, the most important characteristic of potentiometric sensors, and sensors in general, there have been recent controversial discussions about how potentiometric selectivity should be reported. Only recently, an improved model was introduced that replaces the traditional Nicolskii-Eisenman equation by a new formalism for ions of different charge.3 Nonetheless, the reporting of Nicolskii coefficients was still recommended, given that Nernstian * E-mail address: [email protected]. (1) Bu ¨ hlmann, P.; Bakker, E.; Pretsch, E. Chem. Rev., in preparation. (2) Umezawa, Y. Handbook of Ion-Selective Electrodes: Selectivity Coefficients; CRC Press: Boca Raton, FL, 1990. (3) Bakker, E.; Meruva, R. K.; Pretsch, E.; Meyerhoff, M. E. Anal. Chem. 1994, 66, 3021. S0003-2700(96)00891-8 CCC: $14.00

© 1997 American Chemical Society

response slopes are observed for every ion measured. Unfortunately, as a recent study has revealed, potentiometric sensors of high selectivity usually do not show Nernstian response to all measured ions.4 This questions the practice of reporting experimental Nicolskii coefficients with traditional procedures. Therefore, more authors have started to report selectivity values that are not based on any restrictive theoretical assumptions, and the so-called matched potential method seems to be the method of choice for this purpose.4-7 A different possibility, however, is to eliminate the experimental reasons that lead to non-Nernstian behavior of the electrode. This means that the experiment has to be altered to reveal the ion-exchange selectivity of the sensor, unbiased by other experimental parameters such as detection limit of the electrode. A thorough understanding of the underlying selectivity is important for optimization purposes, for the understanding and possible elimination of the experimental reasons that cause the nonideal behavior, and for the comparison to other analytical methods that make use of the same selective compounds, such as optical sensors. Perhaps most importantly, it lays the foundation to quantify the mixed-ion response of real-world potentiometric sensors. One well-established method for calciumselective sensors is to measure the response to discriminated ions such as sodium and potassium in solutions containing an additional calcium buffer.8,9 This makes sure that any calcium ions present in the sample would be significantly bound by the ligand, enabling the determination of unbiased Nicolskii coefficients that reflect the ion-exchange selectivity of the membrane. An important drawback of this method is that it only applies to primary ions that can be buffered by a ligand, while the interfering ion activity remains unaffected. Sensors that are selective for alkali metal ions cannot be characterized with this approach. In a recent short communication, we have reported on a new conditioning method that yields Nernstian electrode slopes for sodium, potassium, magnesium, and calcium ions for a valinomycin-based ion-selective electrode,10 giving the lowest selectivity values that have yet been reported for this carrier. In this paper, we introduce this new method as a general procedure to characterize the selectivity of neutral carrier-based cation-selective electrodes. The principles of the new procedure, including the (4) Umezawa, Y.; Umezawa, K.; Sato, H. Pure Appl. Chem. 1995, 67, 507. (5) Gadzekpo, V. P. Y.; Christian, G. D. Anal. Chim. Acta 1984, 164, 279. (6) Christian, G. D. Analyst 1994, 119, 2309. (7) Bakker, E. Electroanalysis 1997, 9, 1. (8) Sokalski, T.; Maj-Zurawska, M.; Hulanicki, A. Mikrochim. Acta 1991, 1, 285. (9) Schefer, U.; Ammann, D.; Pretsch, E.; Oesch, U.; Simon, W. Anal. Chem. 1986, 58, 2282. (10) Bakker, E. J. Electrochem. Soc. 1996, 143, L83.

Analytical Chemistry, Vol. 69, No. 6, March 15, 1997 1061

effect of low levels of preferred impurities and possible long-term potential drifts, are discussed. The general utility of the method is established experimentally with a variety of highly selective carriers for sodium, silver, and calcium. PRINCIPLES One important goal of this work is to find the required experimental conditions that give Nernstian electrode slopes for even highly discriminated ions. The selectivity data obtained can then be used to characterize the ion-exchange selectivity of the electrode membrane. This paper also quantifies the limiting concentration of extremely preferred impurities in discriminated ion salts with equations that describe the steady-state response of the electrode (so-called Hulanicki effect) and predicts the magnitude of the overall long-term potential drift after prolonged exposure to highly preferred ions. The two latter effects are both quite important for the determination of selectivity according to the new method introduced here. Ideal Characteristics of the Nicolskii Coefficient. It is wellestablished that the Nicolskii coefficient is, ideally, an activityindependent parameter for a given ion-selective electrode. Although the Nicolskii-Eisenman equation itself has been shown to be appropriate only for ions of the same charge, a new, different formalism has been recently introduced that utilizes the Nicolskii coefficient as well.3 It is, therefore, fortunate that most established procedures to determine Nicolskii coefficients do not make use of the mixed-ion response of the electrode but either require separate ion solutions (so-called separate solution method) or make use of separate sections of the calibration curve, each referring to the response of one ion only (so-called fixed interference method).2,11 A general equation to calculate Nicolskii 2 coefficients Kpot IJ from experimental data is given as

log Kpot IJ )

( )

zIF(EJ - EI) aI + log z /z 2.303RT aJ I J

(1)

log Kpot IJ )

zIF (E0 - E0I ) 2.303RT J

(4)

Apparently, the Nicolskii coefficient is mainly dependent on the respective E0 values that incorporate all constant potential contributions. The present treatment elucidates the experimental conditions to obtain selectivity coefficients that most closely reflect eq 4. How Can Nernstian Electrode Slopes Be Obtained? To find the conditions to obtain Nernstian response slopes toward even highly discriminated ions, we have to describe the membrane potential as a function of the ion distribution between the aqueous sample and the organic membrane phase. This may be done by describing the membrane potential as a function of the well-established boundary potential between sample and membrane:12

E ) E0 +

kIaI RT ln + zIF [IzI ]

(5)

where [IzI+] stands for the concentration of uncomplexed primary ions in the organic phase boundary contacting the sample solution, and kI is a function of the relative free energies of solvation in both the sample and the membrane phase (k1 ) exp(-{µ0I (org) - (µ0I (aq)}/RT, where µ0I (org) and µ0I (aq) are the chemical standard potentials of the ion IzI+ in the respective solvent). All other constant potential contribution of the membrane are included in E0. At this stage, it can be seen that [IzI+] (or [JzI+] for the measurement of the interfering ion) must be independent of aI (or aJ) to reduce eq 5 to the Nernst equation 2 (or 3). For the most common case where a neutral carrier L is incorporated into the membrane together with anionic sites R-, + the complex stability constant βILnI for the formation of ILznII within the membrane phase, nI being the stoichiometric factor, can be formulated as

[ILznII ] +

where EI and EJ are the measured membrane potentials for a solution containing the salt of the primary ion IzI+ and interfering ion JzJ+, with charges zI and zJ, respectively. The symbols F, R, and T have their usual meanings. The Nicolskii coefficient is only a constant parameter for a given electrode if Nernstian response slopes are observed. This is illustrated by inserting the Nernst equation for the primary ion,

EI ) E0I +

2.303RT log aI zI F

(2)

and for the interfering ion,

EJ ) E0J +

2.303RT log aJ zJ F

(3)

into eq 1 to obtain an activity-independent form of the Nicolskii coefficient: (11) Guilbault, G. G.; Durst, R. A.; Frant, M. S.; Freiser, H.; Hansen, E. H.; Light, T. S.; Pungor, E.; Rechnitz, G.; Rice, N. M.; Rohm, T. J.; Simon, W.; Thomas, J. D. R. Pure Appl. Chem. 1976, 48, 127.

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Analytical Chemistry, Vol. 69, No. 6, March 15, 1997

βILnI )

[IzI ][L]nI

(6)

+

where [ILznII and [L] are the concentrations of complex and free carrier in the organic phase boundary contacting the sample. Equation 6 is now inserted into eq 5 to give +

E ) E0 +

nI RT kIβILnI[L] aI ln + zIF [ILzI ]

(7)

nI

A Nernstian slope is expected if the concentrations of complex and free carrier remain sample-independent.13,14 Under the exclusion of interfering ion-exchange or coextraction processes with other sample ions, these concentrations are defined by the total concentration of anionic sites RT and ion carrier LT in the membrane. Hence, for stable complexes, the simplified charge zI+ balance (RT ) zI[ILnI ]) and mass balance equations (LT ) + [ILznII ] + [L]) are inserted into eq 7 to give a membrane potential (12) Karpfen, F. M.; Randles, J. E. B. Trans. Faraday Soc. 1953, 49, 823. (13) Bakker, E.; Xu, A.; Pretsch, E. Anal. Chim. Acta 1994, 295, 253. (14) Bakker, E.; Na¨gele, M.; Schaller, U.; Pretsch, E. Electroanalysis 1995, 7, 817.

that may be reduced to the Nernst equation 2 by incorporating all constant parameters into the E0 term: nI

RT kIβILnIzI(LT - nIRT /zI) ln aI E)E + zIF R-

0

(8)

T

It is evident that a Nernstian slope for interfering ions is only observed if an equation analogous to eq 8 is valid for the interfering ion as well. Hence, the ion of interest must completely exchange with the primary ion to observe Nernstian slope. If this is fulfilled, the Nicolskii coefficient can be correlated to stability constants and total membrane concentrations by inserting eq 8, and the one for the interfering ion in complete analogy, into eq 1 to obtain

Kpot IJ

nJ zI/zJ (kJβJLnJ(zJ/RT )(LT - nJRT /zJ) )

)

nI kIβILnI(zI/RT )(LT - nIRT /zI)

(9)

In this case, the selectivity coefficient can be directly related to the ion-exchange characteristics of the membrane by rewriting eq 9 as

( )

[ILznII ] aJ[L]nJ +

aI[L]

nI

zI/zJ

kIβILnI )

+ [JLznJJ ]

(kJβJLnJ)zI/zJ nJ zI/zJ ((zJ/RT )(LT - nJRT /zJ) )

)

-1 (Kpot IJ )

nI (zI/RT )(LT - nIRT /zI)

(10)

Of course, the selectivity coefficient is only an equilibrium constant in special cases, i.e., for ions of equal charge forming complexes of equal stoichiometry.15 In other cases, the Nicolskii coefficient is a conditional equilibrium constant, i.e., it is constant for a given electrode but is defined not only by the nature of carrier and membrane solvent but also by absolute concentrations of the membrane components. This concentration dependency has been successfully exploited to optimize the ion selectivity for particular applications.16,17 If the interfering ion is only partially complexed by the carrier, eq 9 must be extended to account for a substantial concentration of uncomplexed ions in the membrane. Generally, the potentiometric selectivity is related to the ion-exchange selectivity of the membrane, not only of the carrier itself. The above considerations establish the necessary conditions in the membrane to observe Nernstian slopes and ideal Nicolskii coefficients. The usual practice of conditioning the ion-selective electrode membrane in a primary ion salt guarantees a stable and reproducible response of the electrode toward the primary ion. If the membrane is exposed to a solution of an interfering ion that is not too heavily discriminated, these ions will completely displace the primary ions from the phase boundary region of the electrode membrane so that Nernstian electrode slope is obtained for that ion. However, if the interfering ion cannot completely displace these primary ions from the phase boundary region of the (15) Morf, W. E. The Principles of Ion-Selective Electrodes and of Membrane Transport; Elsevier: New York, 1981. (16) Meier, P. C.; Morf, W. E.; La¨ubli, M.; Simon, W. Anal. Chim. Acta 1984, 156, 1. (17) Eugster, R.; Spichiger, U. E.; Simon, W. Anal. Chem. 1993, 65, 689.

electrode membrane, sub-Nernstian response is expected. The response of the electrode will then be masked by the detection limit, i.e., by small levels of primary ions that are continuously released from the membrane into the sample, thereby prohibiting substantial uptake of interfering ions. The potentiometric response is, in this case, effectively a mixed-ion response. In the past, such effects have been accounted for by adding a ligand to the sample that selectively binds the primary ion. It thereby lowers the activity of released primary ions at the phase boundary so that interfering ions can now be extracted into the membrane.8 However, this method of lowering the detection limit is only effective if the primary ion is buffered while the interfering ion is not. It is, therefore, not generally applicable, as no suitable watersoluble ligands are available for alkali metal ions. Therefore, a new conditioning procedure is introduced where the membrane, before any contact with the preferred primary ion, is first exposed to the discriminated ion. This allows the discriminated ions to completely saturate the membrane, and the respective electrode should give Nernstian responses in accordance with the equations established above. Only after all discriminated ion salts of interest have been measured is the membrane exposed to relatively high levels of primary ion solutions. Since this ion is highly preferred by the membrane, the initially contained discriminated ion is readily displaced, and a Nernstian electrode slope that follows eq 8 is again expected. For the phase boundary region, this new procedure alters only the experimental sequence, not the actual ion-exchange equilibrium of interest. It should, therefore, allow for the characterization of the ion-exchange selectivity of the membrane without deteriorating influence on the detection limit of the sensor. Naturally, some prior knowledge of the relative selectivity sequence of the membrane is needed to succesfully plan experiments with this method. Preliminary selectivity data, therefore, have to be at hand before the method discussed here can be applied. Sub-Nernstian slopes and potentials around the detection limit could indicate that the experiment has to be repeated with an ion that is more discriminated. Response to Low Levels of Extremely Preferred Ions: The Hulanicki Effect. Commercial salt solutions are never absolutely pure and often contain significant concentrations of ions the ionselective electrode is responsive for. It is known from Hulanicki and co-workers that ion-selective electrodes based on nonspecific ion-exchangers are relatively insensitive to low levels of extremely preferred ions if these are not initially contained in the membrane.18 As the sample concentration is raised, the electrode exhibits super-Nernstian behavior toward that ion until, at high sample concentrations, the expected Nernstian response is observed. The intermediate super-Nernstian response can be explained as due to a discrepancy between ion activities in the bulk and at the phase boundary; i.e., the uptake of ions by the membrane results in a depletion zone of analyte ions within the Nernst diffusion layer. This nonequilibrium pseudo-steady-state response is treated here for neutral carrier-based membranes in analogy to a recent description for polyion sensors,19 since it is the same basic mechanism that is responsible for the analytically useful response range of these electrodes. The treatment is especially important here to evaluate the maximum allowed level of preferred impurity ions in the measurement of discriminated ion salts. (18) Maj-Zurawska, M.; Sokalski, T.; Hulanicki, A. Talanta 1988, 35, 281. (19) Fu, B.; Bakker, E.; Yun, J. H.; Yang, V. C.; Meyerhoff, M. E. Anal. Chem. 1994, 66, 2250.


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To simplify the mathematical description, it is here assumed that the concentration of free carrier within the membrane remains unaltered during the steady-state ion-exchange process. In this case, the phase boundary potential equation for neutral carrierbased membranes’ response to discriminated ions JzJ+ can be simplified as follows:

E ) E0 +

nJ aJ RT kJβJLnJ[L] RT aJ ≈ E0′ + ln ln + z zJ F zJF [JLzJ+] [JL J ] nJ

(11)

nJ

In analogy to ref 19, the concentration of the complexed preferred + (or primary) ion [ILznII ] within the organic phase boundary can be related to the sample bulk concentration cI,bulk by assuming linear concentration profiles across the Nernst diffusion layers within the two phases:

[ILznII ] ) +

Daδm c Dmδa I,bulk

(12)

where Da and Dm are the diffusion coefficients of IzI+ in the aqueous + phase and ILznII in the organic phase, and δm and δa are the thicknesses of the two diffusion layers. For the organic phase, the charge balance equation can be written as zI zJ RT ) zI[ILnI ] + zJ[JLnJ ] +

zJaJ RT ln zJF R - z [ILzI+] T

I

E)

(13)

+

The combination of eqs 12 and 13 with eq 11 describes the steadystate potential after exposure to small levels of preferred ions IzI+ as

E ) E0′ +

tial extraction of impurity ions (see below). On the other hand, the purposeful measurement of Nernstian response toward ions that are not initially contained in the membrane, as the method introduced herein demands, requires relatively high ion concentrations above 10-4 M to overcome this same depletion effect at the electrode surface. Long-Term Drifts upon Contact with Extremely Preferred Ions. The new conditioning procedure described in this work requires the initial presence and measurement of discriminated ions before recording the potential jump after the first exposure to the most preferred ion. While this potential difference is being used to calculate the ion-exchange selectivity of the membrane, there are long-term drift effects that have to be considered. Specifically, the extracted primary ions will, after prolonged exposure, diffuse across the membrane, where they can compete with the discriminated ions at the membrane-inner electrolyte interface if no primary ions are present in the inner electrolyte. This can lead to substantial potential drifts after a certain amount of time. Upon first initial contact with extremely preferred ions, the membrane and inner filling solution still largely contain the discriminated ion JzJ+. For neutral carrier-based membranes, the overall membrane potential is given by the difference of the two individual phase boundary potentials as

nI

z JaJ RT ln ≈ E0′ + zJ F Daδm Rc T - zI Dmδa I,bulk

(14)

RT nJ ln(kJβJLnJ(zJ/RT )(LT - nJRT /zJ) aJ′) (16) zJ F

where the second term designates the phase boundary potential at the second interface, and aJ′ is the discriminated ion activity in the inner electrolyte. As time proceeds, the extremely preferred ion IzI+ will diffuse across the membrane and successfully displace the discriminated ion JzJ+ contained at the second interface until the membrane is completely equilibrated with IzI+. In this limiting case, the membrane potential is given by

E) The initial deviation from Nernstian response toward the initially present ion JzJ+ is then described as

∆E ) -

(

)

zI Daδm RT ln 1 - cI,bulk zJF R Dmδa T


RT nI ln(kIβILnI(zI/RT )(LT - nIRT /zI) aI) zI F RT nI ln(kIβILnI(zI/RT )(LT - nIRT /zI) aI(DL)′) (17) zIF

(15)

Apparently, the potential increases very rapidly as the expression in the logarithmic term approaches zero. Indeed, the final stage, where saturation occurs as the initially present ion is completely displaced by IzI+, is not accounted for in the model. With eq 15, the maximum tolerated bulk concentration of preferred ions IzI+, if they are not allowed to interfere in the measurement of JzJ+ alone, can be evaluated. With estimated values of zI ) zJ ) 1, RT ) 3 mmol L-1, Da/Dm ) 100, and δm/δa ) 1, a deviation of ∆E ) 5 mV is expected with cI,bulk ) 5.3 × 10-6 M, and 1 mV with cI,bulk ) 1.1 × 10-6 M. Apparently, care must be taken not to exceed these approximate concentrations. As some commercial salts of high purity still contain ionic impurity levels of 0.01%, measurements with salts solutions around 0.01 M will sometimes start to show steady-state mixed-ion response effects that reflect substan1064

RT nI ln(kIβILnI(zI/RT )(LT - nIRT /zI) aI) zI F

Since no primary ions were deliberately added to the inner electrolyte, the potential at this interface is now given by the detection limit aI(DL)′, i.e., by the concentration of primary ions locally present at the phase boundary due to leaching/release from the membrane. The overall membrane potential change between initial and prolonged exposure to an extremely preferred primary ion solution is now given by subtracting eq 16 from eq 17, and can be significantly simplified by introducing the Nicolskii coefficient as established in eq 9: nJ zI/zJ RT (kJβJLnJ(zJ/RT )(LT - nJRT /zJ) aJ′) ln ∆E ) zIF k β (z /R-)(L - n R-/z )nIa (DL)′ I ILnI

)

I

T

zI/zJ pot RT KIJ (aJ′) ln zIF aI(DL)′

T

I T

I

I

(18)

Apparently, the overall negative long-term drift increases with increasing preference for IzI+ (i.e., decreasing Kpot IJ ) and decreasing electrolyte activity in the inner electrolyte. An increased detection limit at this second interface, as defined by aI(DL)′, also increases the overall EMF shift. It is important to note that this effect cannot be caused by a diffusion potential within the membrane phase, since any initial concentration gradients would eventually disappear as the preferred ion saturates the entire membrane. Also, eq 18 indicates that such drifts should occur only for extremely preferred ions. Depending on the detection limit and activity of the inner electrolyte, less discriminated ions -3 or larger should not lead to with Kpot IJ values of about 10 potential drifts, thus enabling such secondary ions to be measured without difficulties. To make meaningful measurements of the extremely preferred ion according to the new method established here, calibration curves must be measured before primary ions start to reach the second interface and induce significant potential shifts. The time required for this to happen depends on the sample concentration, thickness of the membrane, and diffusion coefficient of the complexed primary ion in the organic phase. Typically, such drifts are not observed for about 30 min after the first contact with high levels of primary ions for classical ∼200 µm thick membranes (see below), which is usually sufficient time to record a calibration curve. Very similar effects have been observed for polyion sensors19 and for the response of tetraphenylborate-based membranes to neutral surfactants,20 where the extracted species also diffuses to the second interface and alters the membrane potential. EXPERIMENTAL SECTION Reagents. All salts and the membrane components N,N,N′,N′tetracyclohexyl-3-oxapentanediamide (ETH 129), S,S′-methylenebis(diisobutyldithiocarbamate) (MBDiBDTC), sodium tetrakis[3,5bis(trifluoromethyl)phenyl]borate (NaTFPB), potassium tetrakis(p-chlorophenyl)borate (KTpClPB), dioctyl sebacate (DOS), onitrophenyl octyl ether (NPOE), high molecular weight poly(vinyl chloride) (PVC), and tetrahydrofuran (THF) were purchased in puriss p.a. or Selectophore quality from Fluka Chemika-Biochemika (Ronkonkoma, NY). The 1,3-bridged calix[4]arene was a gift from R. Kopelman (University of Michigan, Ann Arbor), and dithioether-functionalized calix[4]arene was obtained from M. Meyerhoff (University of Michigan). Aqueous solutions were prepared by dissolving the appropriate salts in Nanopure (Millipore)-purified distilled water. Membrane Preparation and EMF Measurement. Ionselective electrode membranes were cast by dissolving the carrier and tetraphenylborate salt (either NaTFPB or KTpClPB), together with PVC and plasticizer (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 specific membrane compositions were as follows: 14 mmol kg-1 carrier and 4 mmol kg-1 NaTFPB (for silver-selective electrodes), 10 mmol kg-1 carrier and 5 mmol kg-1 NaTFPB (for calcium-selective electrodes), and 10 mmol kg-1 carrier and 5 mmol kg-1 KTpClPB (for sodium-selective electrodes). The concentrations given here are relative to total membrane mass. The solution was allowed to evaporate overnight. For each electrode, a 6 mm diameter disk was cut with a cork borer from the parent membrane and (20) Espadas-Torre, C.; Bakker, E.; Barker, S.; Meyerhoff, M. E. Anal. Chem. 1996, 68, 1623.

incorporated into a Phillips electrode body (IS-561, Glasbla¨serei Mo¨ller, Zu¨rich, Switzerland). As specified in the tables, 0.01 M NaCl, 0.01 M KCl, 0.01 M CaCl2, or 0.005 M AgNO3 served as the internal filling solution for the assembled electrodes. For the new conditioning procedure, this solution was of a discriminated ion salt. The electrodes were conditioned in a solution identical to the inner filling solution overnight before measurement. All membrane electrode potential measurements were performed at laboratory ambient temperature (21.5 ( 0.5 °C) versus a doublejunction Teflon sleeve Ag/AgCl reference electrode (Ingold, Wilmington, MA) in a galvanic cell of the type

Ag | AgCl | KCl l 1 M LiOAc ll sample || membrane || inner filling solution | AgCl | Ag

Potentials were measured in unstirred solutions via a Macintosh computer equipped with a LAB-MIO-16XL-42 A/D input board (National Instruments, Austin, TX) and up to four batterypowered four-channel High Z interface modules with built-in lowpass filters (World Precision Instruments, Sarasota, FL) controlled by LabView software (National Instruments) at a software adjustable gain of 10. To minimize the noise, 30 consecutive EMF data values were rapidly acquired every 5 s and averaged. The final EMF value was calculated as the mean of these individual data over the last minute of measurement. Selectivity Coefficients. All EMF data were corrected for the liquid junction potential according to the Henderson equation. Activity coefficients were calculated according to the ref 21. Selectivity coefficients were calculated according to eq 1 by using the EMF values for the highest measured ion activities unless otherwise indicated (see tables). RESULTS AND DISCUSSION In the theoretical section above, the experimental conditions are outlined that are required in order to observe Nernstian response slopes of even highly discriminated ions. Very recently, we reported in a short communication on a novel conditioning method that gave Nernstian response slopes for Na+, K+ Mg2+, and Ca2+ for a valinomycin-based ion-selective electrode, yielding potassium selectivity values that are smaller than those previously reported for this carrier.10 Here, we are establishing the method to be generally useful by critically evaluating it with a number of highly successful neutral carriers. Specifically, selectivity values were obtained with a new and extremely selective sodium ionophore, 1,3-bridged calix[4]arene derivative that was first introduced by Yamamoto and Shinkai22 and resynthesized and characterized for use in miniaturized optical sensors by the group of Kopelman.23 Moreover, the well-established calcium carrier ETH 129 and two different silver carriers, dithioether-functionalized calix[4]arene24 and MBDiBDTC,25,26 were also evaluated in this study as carriers of high selectivity. As outlined in the theoretical part, Nernstian response slopes for discriminated ions are observed only if that ion can fully (21) Meier, P. C. Anal. Chim. Acta 1982, 136, 363. (22) Yamamoto, H.; Shinkai, S. Chem. Lett. 1994, 1115. (23) Shortreed, M.; Bakker, E.; Kopelman, R. Anal. Chem. 1996, 68, 2656. (24) Malinowska, E.; Brzozka, Z.; Kasiura, K.; Egberink, R. J. M.; Reinhoudt, D. N. Anal. Chim. Acta 1994, 298, 245. (25) Lerchi, M.; Reitter, E.; Simon, W.; Pretsch, E.; Chowdhury, D. A.; Kamata, S. Anal. Chem. 1994, 66, 1713. (26) Kamata, S.; Onoyama, K. Anal. Chem. 1991, 63, 1295.


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Table 1. Experimental Selectivity Coefficients for Na+-Selective DOS-PVC (2:1) Membranes Containing 1,3-Bridged Calix[4]arene and KTpClPB membranes conditioned in 0.01 M KCl

membranes conditioned in 0.01 M NaCl

ion Jz+

slopea,b (mV decade-1)

log pot b KNaJ


log pot b KNaJ

Na+ K+ Mg2+ Ca2+

61.3 ( 1.5 56.3 ( 0.6 26 ( 1 31.2 ( 0.7c

0.0 -4.9 ( 0.1 -8.0 ( 0.1 -7.7 ( 0.1c

59.5 ( 0.1 20.8 ( 0.5 19 ( 2 24.2 ( 0.7c

0.0 -3.5 ( 0.1 -4.5 ( 0.1 -4.2 ( 0.1c

a Slope: between log a ) -3 and -1. b Average from three electrodes; standard deviation given. c Calculated from data between log a ) -4 and -2.5 (see text).

Figure 1. Determination of fundamental Nicolskii coefficients of sodium-selective DOS-PVC (2:1) membranes containing 1,3-bridged calix[4]arene and KTpClPB. While the classical procedure involves conditioning the membrane in a 0.01 M NaCl solution (B), only the electrode conditioned in a discriminated ion solution of 0.01 M KCl (A) shows near-Nernstian response slopes toward the ions (b) Na+, (O) K+, (9) Mg2+, and (0) Ca2+, thereby allowing the calculation of unbiased selectivities. Dotted lines with Nernstian response slopes at 21.5 °C (58.4 and 29.2 mV decade-1, respectively).

displace the ion initially contained in the membrane. In this work, this is accomplished by making sure the ion-selective electrode membrane is not brought in contact with the preferred ion before the experiment. As outlined previously, a specific experimental sequence has to be observed for neutral carrier-based cationselective electrodes.10 Most importantly, no primary ions must 1066 Analytical Chemistry, Vol. 69, No. 6, March 15, 1997

initially be present in the membrane and the inner filling and conditioning solutions. Entire calibration curves for discriminated ion salts are recorded; at the end of the experiment, a calibration curve for the extremely preferred ion is obtained, preferably within 30 min (depending on the membrane thickness) to avoid potential drifts. The ion-selective electrode can be used normally after this sequence if the inner filling solution is replaced with one containing a primary ion salt. Otherwise, some potentiometric instability may be encountered. In Figure 1, the responses of a 1,3-bridged calix[4]arene based sodium ion-selective electrode toward various electrolytes are shown according to the new procedure by conditioning in 0.01 M KCl (A) and after classical conditioning in 0.01 M NaCl (B). It is apparent that both methods yield Nernstian response slopes for sodium ions, but that only the new conditioning procedure shows near-Nernstian slopes toward even highly discriminated ions. In Figure 1A, the calcium measurement shows superNernstian response at concentrations around 0.01 M. This effect stems from the relatively high concentration of sodium ions contained in commercially available calcium chloride salts of high purity, indicated as 0.01% by weight by the manufacturer. Indeed, this high level of impurity is expected to show a Hulanicki-type interference that has been calculated in the theoretical part to occur around 0.01 M sample solution concentrations. Therefore, the selectivity coefficients were calculated on the basis of the three lowest measured concentrations as indicated in Figure 1A that showed Nernstian response slope. Analogous impurity problems prohibited the reliable selectivity measurement of corresponding fiber-optic sensors.23 The very large potential shift between potassium and sodium response runs parallel throughout the entire calibration curve, giving much confidence about the reliability of the new method, and translates into a selectivity pot ) -4.9 (see Table 1), an extremely small coefficient log KNa,K number that may indicate that this carrier could be the most selective sodium carrier available to date. Although further studies are needed to confirm this, the carrier characterized here seems to be about 2 orders of magnitude more selective than any previously reported sodium carrier2 and could allow for the first time interference-free potentiometric intracellular sodium determinations to be performed. Interestingly, this electrode is more selective for sodium than valinomycin-based electrodes are for potassium.10 This fact is extremely surprising, since it reflects an even higher selectivity of complex formation of the carrier, given that potassium ions are more lipophilic ions than sodium.15

Table 2. Experimental Selectivity Coefficients for Ag+-Selective DOS-PVC (2:1) Membranes Containing MBDiBDTC and NaTFPB membranes conditioned in 0.01 M NaCl

membranes conditioned in 0.005 M AgNO3

ion Jz+


log pot b KAgJ


log pot b KAgJ

Ag+ Na+ K+ Ca2+ Pb2+ Cu2+

58.8 ( 0.9 58.7 ( 1.2 59.2 ( 1.2 25.3 ( 1.8 35 ( 2 32 ( 2

0.0 -8.7 ( 0.1 -8.2 ( 0.1 -11.0 ( 0.1 -10.3 ( 0.1 -10.5 ( 0.1

58.7 ( 0.3 -5.1 ( 0.8 -5 ( 2 -5 ( 2 -5 ( 1 -6 ( 3

0.0 -3.0 ( 0.1 -3.0 ( 0.2 -4.4 ( 0.2 -4.6 ( 0.1 -4.4 ( 0.2

a Slope: between log a ) -3 and -1. b Average from three electrodes; standard deviation given.

Table 3. Experimental Selectivity Coefficients for Ag+-Selective DOS-PVC (2:1) Membranes Containing Dithioether-Functionalized Calix[4]arene and NaTFPB membranes conditioned in 0.01 M NaCl

membranes conditioned in 0.005 M AgNO3

ion Jz+


log pot b KAgJ


log pot b KAgJ

Ag+ Na+ K+ Ca2+ Pb2+ Cu2+

58.2 ( 0.6 57.3 ( 0.7 58.2 ( 0.6 26.8 ( 0.9 44.8 ( 0.4 33.9 ( 0.4

0.0 -6.2 ( 0.1 -5.7 ( 0.1 -8.0 ( 0.1 -6.0 ( 0.1 -7.7 ( 0.1

56.7 ( 0.1 9(2 11 ( 4 3(3 10.9 ( 0.3 10 ( 3

0.0 -3.4 ( 0.1 -3.3 ( 0.1 -4.0 ( 0.1 -4.3 ( 0.2 -4.1 ( 0.1


Figure 2. Determination of fundamental Nicolskii coefficients of silver-selective DOS-PVC (2:1) membranes containing MBDiBDTC and NaTFPB. While the classical procedure involves conditioning the membrane in a AgNO3 solution (B), only the electrode conditioned in a discriminated ion solution of 0.01 M NaCl (A) shows near-Nernstian response slopes toward the nitrate salts of the ions (b) Na+, (O) K+, ([) Ag+, (0) Ca2+, (4) Cu2+, and (1) Pb2+ (see also caption to Figure 1).

In Figure 2 an analogous experiment is shown with a highly selective silver carrier, MBDiBDTC. This carrier was first introduced by Kamata and Onoyama for use in lead-selective electrodes26 and was later shown to induce high silver selectivity in corresponding bulk optodes.25 Recently, we have shown that this carrier is also useful in silver-selective electrodes.27 Again,

the classically silver-conditioned membranes showed largely activity-independent potentials for the nitrate salts of discriminated cations, reflecting the lower detection limit of this sensor (see Figure 2B). Only the membrane conditioned with the discriminated ion sodium showed near-Nernstian response slopes for all ions, enabling unbiased selectivity coefficients to be calculated that are extremely small (see Figure 2A and Table 2). A different silver carrier, as introduced by Reinhoudt and co-workers,24 dithioether-functionalized calix[4]arene, showed somewhat inferior selectivity over alkali and alkaline earth metals (see Table 3) but otherwise behaved very similarly to MBDiBDTC. It is well-known that unbiased selectivity coefficients can also be determined by buffering the silver ions released from the membrane to such an extent that the discriminated sample cation can compete in the ion-exchange process.8 With silver-selective electrodes, this can be accomplished with anion salts that form a precipitate with silver. Recently, this was applied to the measurement of sodium iodide and sodium sulfide with MBDiBDTC-based membranes, showing cationic response functions toward sodium pot that translated into a selectivity coefficient of log KAg,Na ) -7.7.27 In the same study, dithioether-functionalized calix[4]arene showed pot again a larger selectivity coefficient of log KAg,Na ) -6.8.27 As shown in Tables 2 and 3, the values from the new conditioning method compare reasonably well with these previously reported values, confirming that the procedure introduced here is a valid approach to determine the ion-exchange selectivity of ion-selective electrode membranes. (27) Bakker, E. Sens. Actuators B 1996, 35, 20.


1067

Table 4. Experimental Selectivity Coefficients for Ca2+-Selective DOS-PVC (2:1) Membranes Containing ETH 129 and NaTFPB membranes conditioned in 0.01 M NaCl

membranes conditioned in 0.01 M CaCl2

ion Jz+


log pot b KCaJ


log pot b KCaJ

Ca2+ Na+ K+ Mg2+

33.2 ( 0.2 58.3 ( 0.5 58.5 ( 0.4 30.5 ( 0.9

0.0 -6.2 ( 0.4 -7.7 ( 0.4 -9.7 ( 0.3

34.9 ( 0.1 1.6 ( 0.4 0.6 ( 0.1 2.5 ( 0.2

0.0 -3.6 ( 0.1 -4.0 ( 0.1 -4.9 ( 0.1


Table 5. Experimental Selectivity Coefficients for Ca2+-Selective NPOE-PVC (2:1) Membranes Containing ETH 129 and NaTFPB membranes conditioned in 0.01 M NaCl Figure 3. Observed EMF behavior of a DOS-PVC (2:1) membrane conditioned in NaCl containing the silver-selective carrier MBDiBDTC and NaTFPB after continuous exposure to 0.005 M AgNO3. While the large initial potential jump after the addition of AgNO3 is used to determine the ion selectivity of the membrane, a long-term drift is observed starting after about 30 min. This drift is assigned to silver ions eventually reaching the membrane-inner filling solution interface. Its magnitude is related to the membrane selectivity as well (see text).

In the theoretical part, long-term drifts have been expected with the new measurement procedure that originate from primary ions diffusing across the membrane to the membrane-inner electrolyte interface, where they successfully displace the initially contained discriminated ion from the membrane. This effect has been observed in practice and is shown in Figure 3 for a MBDiBDTC-based silver-selective membrane. The large potential jump for a sodium-conditioned ion-selective electrode after initial exposure to silver ions is used to calculate the selectivity of the membrane according to eq 1. After about 30 min, the potential starts to drift until after about 7 h a relatively stable potential is reached that reflects the detection limit of the sensor at the inner filling solution (see eq 17). At this stage, the entire membrane is fully saturated with silver ions, and the measurement of unbiased selectivity coefficients according to the new method is no longer possible. Since the inner filling solution contains 0.01 M NaCl (log aNa ) -2.04), the detection limit can be estimated from the solubility product of AgCl (log Ksp ) -9.74) as log aAg(DL)′ ) -7.70.27 This information can be inserted, together with the observed overall potential drift of ∆E ) -190 mV, into eq 18 to pot estimate log KAg,Na as -8.9, which is very close to the value presented in Table 2. Apparently, in the case that the detection limit at the inner electrolyte is known, the selectivity of the sensor can also be calculated from the magnitude of this long-term drift. Again, this result confirms the applicability of the theoretical model to this kind of drift behavior. The well-established calcium ionophore ETH 129 was also tested with the new procedure by determining the ion selectivity with a sodium-conditioned membrane and comparing the data to those from classical experimental procedures (see Tables 4 and 5. Since it is well-known that the calcium selectivity is improved with a more polar plasticizer, the selectivity of ISE membranes based on DOS as well as NPOE as plasticizer was evaluated. As 1068 Analytical Chemistry, Vol. 69, No. 6, March 15, 1997

membranes conditioned in 0.01 M CaCl2

ion Jz+


log pot b KAgJ


log pot b KAgJ

Ca2+ Na+ K+ Mg2+

33.5 ( 0.8 53.1 ( 0.3 43.6 ( 0.3 23.7 ( 1.4

0.0 -8.3 ( 0.2 -10.1 ( 0.2 -9.3 ( 0.1

33.4 ( 0.1 -3.1 ( 0.4 -3.3 ( 0.2 0.2 ( 0.3

0.0 -3.4 ( 0.1 -3.8 ( 0.1 -4.6 ( 0.1


expected, the NPOE-based membranes showed improved calcium selectivity as compared to DOS, although the selectivity values with the latter are still quite small. Interestingly, the NPOE-based membranes showed somewhat less than theoretical slopes for discriminated ions. Still, the observed slopes are much more reassuring than the ones obtained with the classical calciumconditioned membranes, and the respective selectivity coefficients are significantly smaller as well (see Table 5). The selectivity of ETH 129-based calcium electrodes has traditionally also been characterized in calcium-buffered solutions in order to obtain ionexchange selectivities of the membrane. Indeed, for NPOE-based membranes containing 53 mol % anionic sites, a selectivity pot coefficient over sodium and potassium of log KCa,Na ) -7.4 and pot log KCa,K ) -8.0 had been determined in calcium-buffered samples.9 These values are quite comparable to, albeit somewhat larger than, the ones obtained with the new method presented here (see Table 5). It is important to note that the traditional ion buffering method could not be applied to magnesium ions, since they will bind to the added calcium ligand as well. The effects of interfering ions solutions, ion impurities, and the detection limit of the electrode itself all may contribute to the apparent practical selectivity behavior of solvent polymeric membrane electrodes. Even in perfectly pure solutions measured with perfectly selective electrodes, the high detection limits of ionselective electrodes lead to classically determined apparent selectivity coefficients that may not exceed about 5 orders of magnitude. The experiments reported here may, therefore, reveal important insights into the practical response of ion-selective electrodes (conditioned in primary ion solutions) to solutions containing interfering ions or mixed electrolytes. If such ions are discriminated by many orders of magnitude, as shown for the silver-selective systems, the detection limit of the electrode is fully

governing the response. Since the signal is nearly completely independent of the interfering ion activity, the matched potential method or other classical methods would give meaningless results. The response of the electrode would have to be described with a modified Nernst equation by accounting for a minimum background primary ion activity. For the other electrodes described here, interfering ions are normally discriminated to an extent that they may only partially compete with the primary ions released from the membrane. This yields apparent sub-Nernstian responses of the electrode that are governed by the detection limit as well as by the interfering ion activity. This intermediate response is difficult to describe in theory as long as the proper reasons for the detection limit are not fully known. Many classical methods to determine selectivity, including the matched potential method, seem often to operate in this response range of the electrode. While this is certainly an important real-world behavior of the electrode, it is not the response to the interfering ion alone that is measured. Consequently, models that deal with the mixedion response of the electrode will have to be modified in the future to account for this behavior. The method introduced here allows us to distinguish between practical and ideal behavior toward interfering ions solutions, and thus is a valuable step in achieving this goal. Sometimes such non-Nernstian responses originate from high impurity levels of the electrolytes used. Again, these are experimental artifacts that occur in practice and may heavily bias experimental selectivity coefficients. These need to be eliminated to unravel the response of the electrode to the interfering ion of interest. Even if the interfering ion is preferred over the primary ion, care has to be taken to choose appropriate experimental conditions. Too low interfering ion levels may lead to depletion of the Nernst diffusion layer adjacent to the electrode surface and give too low potential readings, and transient responses may occur after a certain time as well (see above). In all these cases, quantifying the underlying ion-exchange selectivity of the membrane is important in order to identify the true reasons for the practical apparent selectivity behavior of ion-selective electrodes. CONCLUSIONS In this paper, the selectivity of a large variety of neutral carrierbased cation-selective electrodes has been characterized according

to a newly established procedure that involves conditioning the electrode membrane in discriminated ion solutions before measurement. The main advantage of this method over employing ion buffers to decrease the detection limit of the sensor is that it is generally applicable, independent of the nature of primary or interfering ions. Accordingly, selectivity coefficients have been found that are generally much smaller than those previously reported with classical methods, revealing the underlying ionexchange selectivity of the membrane. In cases where ion buffers can be used, e.g., with silver- or calcium-selective electrodes, the selectivity data compare well to each other, giving confidence that the same basic information is obtained in both experiments. The results from this study clearly show that it is often not the selectivity of the membrane that defines the detection limit of the sensor, but other effects that still remain to be studied extensively. Moreover, non-Nernstian electrode response toward discriminated ions is apparently a consequence of the high preference for the ion that is initially present in the membrane. As this study has shown, it is not an inherent kinetic limitation for the extraction/ complexation process of the discriminated ion. The major drawbacks of the new procedure are the rigid sequence of exposure to different electrolyte and the high purity of salt solutions (especially for conditioning the membrane) that is required. Once the membrane is exposed to the most preferred ion, the electrode will no longer respond in a Nernstian manner to extremely discriminated ions. Consequently, the method is applicable only for scientists who are able to fabricate their own ion-selective electrode membranes. Nonetheless, the method described herein promises to be an important step toward understanding the apparent selectivity behavior of real-world solvent polymeric membrane electrodes. ACKNOWLEDGMENT The author thanks Auburn University and the Petroleum Research Fund (31553-G3) for financial support and Sally Mathison (Auburn University) for careful reading of the manuscript. Received for review September 5, 1996. January 8, 1997.X

Accepted

AC960891M X

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


1069

Determination of Unbiased Selectivity Coefficients of Neutral Carrier

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