Pulsed Galvanostatic Control of Ionophore-Based Polymeric Ion

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Anal. Chem. 2003, 75, 4541-4550

Pulsed Galvanostatic Control of Ionophore-Based Polymeric Ion Sensors Alexey Shvarev and Eric Bakker*

Department of Chemistry, Auburn University, Auburn, Alabama 36849

This paper describes a pulsed galvanostatic technique to interrogate ion-selective electrodes (ISEs) with no intrinsic ion-exchange properties. Each applied current pulse is followed by a longer baseline potential pulse to regenerate the phase boundary region of the ion-selective membrane. The applied current fully controls the magnitude and sign of the ion flux into the membrane, thus offering instrumental control over an effect that has become very important in ion-selective electrode research in recent years. The resulting chronopotentiometric response curves essentially mimic traditional ISE behavior, with apparently Nernstian response slopes and selectivities that can be described with the Nicolsky equation. Additionally, the magnitude and sign of the current pulse may be used to tune sensor selectivity. Perhaps most important, however, appears to be the finding that the extent of concentration polarization near the membrane surface can be accurately controlled by this technique. A growing number of potentiometric techniques are starting to make use of nonequilibrium principles, and the method introduced here may prove to be very useful to advance these areas of research. The basic characteristics of this pulsed galvanostatic technique are here evaluated with plasticized poly(vinyl chloride) membranes containing the sodium-selective ionophore tert-butyl calix[4]arene tetramethyl ester and a lipophilic inert salt.

Recent years have seen significant advancements in the field of polymeric ionophore-based potentiometric ion sensors. Today, they may reach extremely low detection limits, sometimes to the low parts per trillion concentration range in unbuffered sample solutions.1 Nonequilibrium diffusion processes have been exploited to develop potentiometric sensors for polyions,2,3 to distinguish free from total ion concentrations using potentiometry,4 to fabricate so-called switchtrodes that give very sensitive readouts at critical concentrations,5 and to yield end points in titrations that * Corresponding author. E-mail: [email protected]. (1) Bakker, E.; Pretsch, E. Anal. Chem. 2002, 74, 420A. (2) Fu, B.; Bakker, E.; Yun, J. H.; Yang, V. C.; Meyerhoff, M. E. Anal. Chem. 1994, 66, 2250. (3) Meyerhoff, M. E.; Fu, B.; Bakker, E.; Yun, J.-H.; Yang, V. C. Anal. Chem. 1996, 68, 168A. (4) Ceresa, A.; Pretsch, E.; Bakker, E. Anal. Chem. 2000, 72, 2050. (5) Vigassy, T.; Ceresa, A.; Badertscher, M.; Morf, W. E.; de Rooij, N. F.; Pretsch, E. Sens. Actuators, B 2001, 76, 476. 10.1021/ac034409t CCC: $25.00 Published on Web 07/16/2003

© 2003 American Chemical Society

are larger than theoretically expected.6 Also, a careful understanding of the underlying chemical processes of potentiometric sensors makes it possible to fine-tune their response behavior and selectivity in a predicted manner.7 The goal of the present work is to establish a galvanostatic measuring protocol for ion-selective membranes that yields sensor response curves that have the look and feel of calibration curves of potentiometric sensors. It is anticipated that such a galvanostatic mode will give complete control over (1) the concentration of extracted ions (so that selectivity can be tuned), (2) the charge sign of the ion that is extracted (thereby giving the freedom to measure anions and cations with the same membrane), and (3) the magnitude and sign of ion fluxes across the ion-selective membrane (giving tunable non-Nernstian response regions with reproducible potentials). With potentiometric sensors, the total concentration of membrane ions is adjusted by the concentration of lipophilic ion exchanger, so that variations in selectivity can only be achieved serially, by fabricating a number of sensors containing different concentrations of ion exchanger.8 The charge sign of the measured ions can be varied in potentiometry only serially as well, by fabricating membranes with an ion exchanger of opposite charge. The third point, the adjustment of ion fluxes, can be adjusted in potentiometry mainly by changing the chemical composition of the membrane and inner solution.9 This principle has become very important in recent years and used for the development of numerous new sensor design concepts (see above). Despite the plethora of new applications that are emerging by utilizing so-called “nonequilibrium” potentiometry (referring to situations where the aqueous boundary concentrations near the membrane are different from the sample bulk), this transduction principle is not yet fully satisfactory. Measurements under such nonequilibrium conditions are hard to reproduce, suffer from potential drifts,10 and are therefore only of limited analytical applicability. It is anticipated that a galvanostatic control of such membranes will offer a vast improvement over these limitations and lead to further acceleration of this interesting research direction. This research builds on significant expertise in the fields of potentiometric sensors and of ion-transfer voltammetry. There are (6) Peper, S.; Ceresa, A.; Bakker, E.; Pretsch, E. Anal. Chem. 2001, 73, 3768. (7) Bakker, E.; Bu ¨ hlmann, P.; Pretsch, E. Chem. Rev. 1997, 97, 3083. (8) Eugster, R.; Gehrig, P. M.; Morf, W. E.; Spichiger, U. E.; Simon, W. Anal. Chem. 1991, 63, 2285. (9) Ceresa, A.; Sokalski, T.; Pretsch, E. J. Electroanal. Chem. 2001, 501, 70. (10) Sokalski, T.; Ceresa, A.; Fibbioli, M.; Zwickl, T.; Bakker, E.; Pretsch, E. Anal. Chem. 1999, 71, 1210.

Analytical Chemistry, Vol. 75, No. 17, September 1, 2003 4541

a number of works dedicated to the application of nonequilibrium electrochemical methods to plasticized polymeric ion-selective membranes, including voltammetry,11 cyclic and normal pulse voltammetry,12,13 impedance spectroscopy,14-16 and conductivity measurements.17 It was recently shown that the selectivity of ionselective electrodes (ISEs) working in an amperometric mode could be tuned18 or even reversed19 by the magnitude of the applied potential. Chronopotentiometric experiments have shown the possibility for improving the low detection limit of ISEs20,21 and were also used diagnostically to determine the residual concentrations of active components in ion-selective membranes.22 From the many possible nonequilibrium electrochemical methods, normal pulse voltammetry was suggested as a preferred technique for ionophore-based plasticized polymeric membranes.23,24 A sequence of potential pulses was applied to the membrane, and the resulting current was investigated as a function of the sample solution composition.19,25 It was shown that sample ions that were extracted within one measurement period had to be removed from the membrane phase before the next measurements step. Such a recovery of the membrane by applying a baseline or so-called stripping potential is an essential condition to avoid an analytical signal drift.26 Unfortunately, it is currently still difficult and uncommon to directly compare amperometric and voltammetric sensors to each other and to their potentiometric analogues. Recently, an approach was proposed27 to obtain a pseudo-Nernstian response slope for a pH-responsive membrane interrogated by normal pulse voltammetry. It was demonstrated that potentials obtained at different sample pH at an equal current should correspond to equal concentrations of extracted hydrogen ions in the membrane phase. Consequently, these points should ideally represent an apparently Nernstian relationship between applied potential and sample pH. These expectations were confirmed experimentally, and the voltammetric pH sensor showed essentially the same Nernstian response as its potentiometric counterpart based on the same ionophore in a wide pH range. In that work, the appropriate potentials at a given current were found by linear extrapolation from a number of data points in a normal pulse voltammetry scan.27 (11) Koryta, J.; Kozkov, Y. N.; Skalicky, M. J. Electroanal. Chem. 1987, 234, 335. (12) Senda, M.; Katano, H.; Yamada, M. J. Electroanal. Chem. 1999, 475, 90. (13) Amemiya, S.; Bard, A. J. Anal. Chem. 2000, 72, 4940. (14) Mikhelson, K. N.; Bobacka, J.; Ivaska, A.; Lewenstam, A.; Bochenska, M. Anal. Chem. 2002, 74, 518. (15) Xie, S. L.; Cammann, K. J. Electroanal. Chem. 1987, 229, 249. (16) Nahir, T. M.; Buck, R. P. Electrochim. Acta 1993, 38, 2691. (17) Cammann, K.; Ahlers, B.; Henn, D.; Dumschat, C.; Shul’ga, A. A. Sens. Actuators, B 1996, 35, 26. (18) Sawada, S.; Torii, H.; Osakai, T.; Kimoto, T. Anal. Chem. 1998, 70, 4286. (19) Jadhav, S.; Bakker, E. Anal. Chem. 2001, 73, 80. (20) Morf, W. E.; Badertscher, M.; Zwickl, T.; Rooij, N. F. d.; Pretsch, E. J. Electroanal. Chem. 2002, 526, (21) Pergel, E.; Gyurcsanyi, R. E.; Toth, K.; Lindner, E. Anal. Chem. 2001, 73, 4249. (22) Pendley, B. D.; Lindner, E. Anal. Chem. 1999, 71, 3673. (23) Osakai, T.; Nuno, T.; Yamamoto, Y.; Saito, A.; Senda, M. Bunseki Kagaku 1986, 38, 479. (24) Jadhav, S.; Bakker, E. Anal. Chem. 1999, 71, 3657. (25) Jadhav, S.; Meir, A. J.; Bakker, E. Electroanalysis 2000, 12, 1251. (26) Bakker, E., Meir, A. J. SIAM Rev. 2003, 45, 327. (27) Long, R.; Bakker, E. Electroanalysis, in press.

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Fortunately, the response mechanism of a normal pulse voltammetry experiment can be largely rationalized within the framework of modern ion-selective electrode theory.7,28 The visualization of an apparently Nernstian behavior in voltammetric mode offers a familiar way to represent experimental results and to compare sensor responses to each other by using welldeveloped sensor concepts, such as potentiometric selectivity.29 These recent results form the basis for the protocol introduced in this paper. Clearly, the need to determine the potential at a given fixed current demands a controlled current technique, rather than a controlled potential experiment. On the other hand, a baseline potential still must be applied between two measuring pulses to ensure the effective removal of previously extracted ions. Using opposite current pulses for this purpose is not advisable, because it would force the extraction of counterions from the sample into the membrane, rather than completely strip the previously extracted analyte ions from the membrane. This paper introduces a pulsed galvanostatic/potentiostatic technique for the interrogation of ionophore-based polymeric membranes based on a simple model system containing a sodium-selective ionophore. Eventually, it is anticipated that this technique will be most valuable for situations where nonequilibrium potentiometry is currently used (with corresponding potential drifts and poor reproducibilities) and where a selectivity modulation is desired at a fixed spatial orientation, such as in chemical microscopy or with detectors in separation science. EXPERIMENTAL SECTION Reagents. High molecular weight poly(vinyl chloride) (PVC), 2-nitrophenyl octyl ether (o-NPOE), sodium ionophore tert-butyl calix[4]arene tetramethyl ester, tetradodecylammonium tetrakis(4-chlorophenyl)borate (ETH 500), potassium tetrakis[3,5-bis(trifluoromethyl)phenyl]borate (KTFPB), tetrahydrofuran (THF), and all salts were purchased from Fluka Chemical Corp. (Milwaukee, WI). Aqueous solutions were prepared by dissolving the appropriate salts in Nanopure-deionized water (18.2 MΩ cm). Membrane Preparation. Ion-selective membranes (∼200 µm thick) contained PVC and o-NPOE, 1:2 by weight. The membrane was prepared by solvent casting, with THF as a solvent. Membranes containing 10 mmol kg-1 sodium ionophore and 10 wt % inert lipophilic salt ETH 500, with no additional ion exchanger, were prepared for the chronopotentiometric experiments. For the additional zero current potentiometric experiment, membranes were formulated with 10 mmol kg-1 sodium ionophore and 6 mmol kg-1 KTFPB. Electrodes. The ion-selective membranes were cut with a cork borer (6 mm in diameter) from the parent membrane and incorporated into a Philips electrode body (IS-561, Glasbla¨serei Mo¨ller, Zu¨rich, Switzerland). The membrane area was 8 mm2. The inner solution for chronopotentiometric experiments consisted of 0.1 M NaCl, which was in contact with an internal Ag/AgCl electrode. For the potentiometric measurements, 0.1 M KCl was used as the inner filling solution. The electrodes were conditioned before experiments in a solution identical to the inner filling (28) Bakker, E.; Na¨gele, M.; Schaller, U.; Pretsch, E. Electroanalysis 1995, 7, 817. (29) Bakker, E.; Pretsch, E.; Bu ¨ hlmann, P. Anal. Chem. 2000, 72, 1127.

solution overnight. Therefore sodium-selective membranes prepared for the potentiomentric experiment did not contain sodium ions in the membrane phase prior to the experiment. The external reference electrode consisted of a double-junction Ag/AgCl electrode with a 1 M LiOAc bridge electrolyte. Experimental Setup. Voltammetric measurement were conducted in a three-electrode cell system, where the internal Ag/ AgCl electrode acted as a working electrode, and the external reference electrode and counter electrode (large surface Pt grid) were immersed into the sample. The chronopotentiometric experiments were performed with an AFCBP1 bipotentiostat (Pine Inst., Grove City, PA) controlled by a PCI-MIO-16E4 interface board and LabVIEW 5.0 data acquisition software (National Instruments, Austin, TX) on a Macintosh computer. A solid-state opto-isolated module (Crydom MODC5, distributed by Allied Electronics, Fort Worth, TX) was directly connected to the “Mode” button of the potentiostat and to a digital output on the interface board. This circuit creates a relatively rapid software-controlled switching between the potentiostatic and galvanostatic modes of the instrument. Such automated switching of potentiostats is known from the literature.30 Sampled potentials were obtained as the average value during the last 10% of each 1-s uptake pulse. Baseline potentials were held at 0 V for 10 s. Zero current potentials were measured with a 16-channel EMF monitor (EMF16, Lawson Labs, Phoenixville Pike, PA) versus the same reference electrode. Titrations were performed by adding aliquots from a 1 or 0.1 M stock solution to unstirred samples. All experiments were conducted at laboratory ambient temperature (21.5 ( 0.5 °C). Activity coefficients were calculated according to the DebyeHu¨ckel formalism.31 THEORY With potentiometric sensors, it is known that membrane permselectivity for a given ion is observed when its concentration in the membrane is kept independent of the sample composition.28 This can be illustrated with the established equation for the boundary potential at the sample/membrane interface, EPB, written here for any monovalent ion i:

EPB )

RT kiai(aq,pb) ln F ai(org,pb)

(1)

where ki includes the free energy of transfer for an ion i, ai(aq,pb) and ai(org,pb) are the phase boundary activities of i in the aqueous (aq) and organic (org) phases, and R, T, and F have their established meanings. This equation is known to reduce to the well-known Nernst equation if ai(org,pb) is constant. In potentiometry, the membrane normally contains a fixed concentration of lipophilic ion exchanger in order to keep the concentration of the ion constant. In addition, an ionophore is often added to the membrane phase to discriminate against potentially interfering ions that could otherwise ion exchange with the ion of interest. The complex formation constant between an ion i and the ionophore L, with stoichiometry n, is given by (30) Warner, T. B.; S. S. J. Electrochem. Soc. 1967, 114, 359. (31) Meier, P. C. Anal. Chim. Acta 1982, 136, 363.

βi,n ) aiLn(org)/ai(org)aL(org)n

(2)

In this paper, a pulsed chronopotentiometric method is introduced to yield response functions that mimic the behavior of potentiometric sensors measured at zero current. The goal of the experiment is to keep ai(org,pb) in eq 1 constant by instrumental, rather than chemical means. The membrane will have no appreciable ion-exchange properties. Rather, an applied current pulse will be responsible to keep ai(org,pb) constant. At the start of the experiment, therefore, this means that there are no intrinsically present transferable ions inside the membrane phase. When a so-called cathodic (negative) current i is applied across the ion-selective membrane, an ion flux of fixed magnitude will occur. Since no transferable anions are present in the membrane that could partition into the sample phase, a cathodic current forces the extraction of cations from the sample into the membrane. In the general case, this flux J is given by the sum of the individual fluxes of available (monovalent) ions i, Ji, so that the following relationship should hold:

J)

∑J ) i/FA i

(3)

i

where i is the applied current and A is the membrane area. If the interfacial ion-transfer reaction is fast, the concentrations at the membrane phase boundary will be determined by mass transport in at least one of the two diffusion layers. Electrical migration is here neglected because the sample and membrane each contain an excess of background electrolyte (the polymeric membrane contains a lipophilic inert salt R+R-, which is present in large excess to the neutral ionophore). In a one-dimensional system, therefore, the flux of any transferable ion i may be described by Fick’s law:

Ji ) (Daq/δaq){ci(aq,pb) - ci(aq,bulk)}

(4)

Ji ) (Dorg/δorg){ci,tot(org,bulk) - ci,tot(org,pb)}

(5)

where D and δ are the diffusion coefficient and diffusion layer thickness in the respective phase, ci(aq,pb) and ci(aq,bulk) are the concentrations of i at the sample phase boundary and in the bulk sample, and ci,tot(org,pb) and ci,tot(org,bulk) are the total concentrations of i at the organic phase boundary and in the bulk membrane. The last value is assumed to be always zero because of the pulsed experiment employed here. Assuming that the membrane ions can be in either their uncomplexed or complexed form of fixed stoichiometry, eq 5 is rewritten as

Ji ) - (Dorg/δorg){ci(org,pb) + ciLn(org,pb)}

(6)

The total ionophore concentration in the membrane, LT, is assumed to be constant throughout the membrane and is given by the mass balance:

LT ) cL(org) +

∑n c i

i iLn(org)

Analytical Chemistry, Vol. 75, No. 17, September 1, 2003

(7) 4543

For simplicity, any ions i in the membrane and aqueous phase are here assumed to have equal diffusion coefficients D. The thickness of the diffusion layer in each phase can be approximated as

Nernstian response slope, and the occurrence of an apparent super-Nernstian response slope, are observed when cI(aq,pb) in eq 4 approaches zero. This critical bulk concentration may be predicted by inserting eq 8 into 4 as

δ ) 2xDt

cI(aq,critical) ) - (2i/FA)xt/Daq

(8)

Here, two competing monovalent cations, I+ and J+, are considered to be present in the sample at the same time, and a local ionexchange equilibrium is assumed to hold, described by

Kex )

aI(aq,pb) aJ(org,pb)

(9)

aI(org,pb) aJ(aq,pb)

In the following, it is assumed that all activity coefficients are constant and that concentrations may be used instead of activities. The seven unknowns, cL(org), cILnJ(org,pb) cJLnJ(org,pb), cI(org,pb), cJ(org,pb), cI(aq,pb), and cJ(aq,pb), can be explicitly solved with two eqs 2 (one for each ion), eq 3, two eqs 4 and 6 (one for each ion), and eqs 7 and 9. The resulting general equations were obtained explicitly, but are somewhat cumbersome to show here. Therefore, some simplified cases are discussed for illustration purposes. Case 1: No Interference from J+. Here, it is assumed that complex formation constants (eq 2) are much larger for I+ than for J+. At relatively small currents, the extraction and diffusion of primary ions I+ are always assisted by the ionophore L, and I+ in the membrane is predominantly in the complexed form (cILnI(org,pb)). Under these conditions, JI . JJ and J ) JI (eq 3). In this case, eqs 3 and 6 are equal:

i/FA ) -(Dorg/δorg)ciLn(org,pb)

(10)

Inserting eq 8 into 10 eliminates δorg and shows that the complexed ion concentration at the phase boundary can be dictated by the applied current and the duration t of the applied current pulse:

ciLn(org,pb) ) - (2i/FA)xt/Dorg

(11)

The observed phase boundary potential for this situation can be obtained by inserting eqs 11, 2, and 7 into eq 1:

EPB )

(

x {

-kIβI,nFA RT ln F 2i

Dorg 2i LT + n t FA

x }) t Dorg

n

+

RT ln aI(aq,pb) (12) F For a constant current pulse of fixed duration t, the first part of the left-hand side of eq 12 is a constant. The pseudo-Nernstian equation is the basis for the present work. A near-Nernstian response slope is expected as long as concentration polarizations at the sample side are negligible (aI(aq,pb) ) aI(aq,bulk)). Equation 4 shows that such a polarization is, again, dependent on the magnitude of the applied current. Complete breakdown of 4544

Analytical Chemistry, Vol. 75, No. 17, September 1, 2003

(13)

If cI(aq,bulk) is significantly higher than cI(aq,critical), a Nernstian response slope of the electrode can be expected. If both values are comparable, the membrane will operate under conditions where sample depletion is relevant to the sensor response. Case 2: Mixed Ion Response at Currents Below the Limiting Current. At small applied currents, the ion extraction process is fully assisted by the ionophore and extraction of uncomplexed ions can be neglected. Consequently, eqs 3 and 6 can be simplified and combined to yield

cILnI(org,pb) + cJLnJ(org,pb) ) (-2i/FA)xt/Dorg (14) The first two terms on the left-hand side of eq 14 can be combined with the complex formation constant (eq 2) and the ion-exchange constant (eq 9), assuming an equal complex stoichiometry n for both ionophore complexes, to give

{

}

aJ(aq,pb) aI(org,pb)aL(org,pb)n βI,n + βJ,nKex ) aI(aq,pb)

x

-2i FA

t (15) Dorg

This relationship is inserted into eq 1, together with the mass balance eq 7 to describe the phase boundary potential as a function of the applied current:

EPB )

x (

RT -kIFAβI,n ln F 2i

{

Dorg 2i LT + t FA

x ) t Dorg

n

+

βJ,n RT ln aI(aq,pb) + K a (aq,pb) F βI,n ex J

}

(16)

The pulsed chronopotentiometric mixed-solution membrane response is expected to obey the Nicolsky equation, where the selectivity coefficient is given by Kex βJ,n/βI,n. This is in complete analogy to known ionophore-mediated ion-selective electrode behavior.32 Case 3: Mixed Ion Response at Currents Above the Limiting Current. As the applied current is increased, the ion extraction processes is eventually no longer assisted by the ionophore. This is illustrated by eq 10, which shows that the case discussed above is only applicable if sufficient ionophore is available to complex all ions transferred from the sample phase. At higher current, the fraction of ions extracted above clim, the maximum concentration extracted in their complexed form, must be uncomplexed (see eq 6). Consequently, eqs 3 and 6 (32) Morf, W. E. The Principles of Ion-Selective Electrodes and of Membrane Transport; Elsevier: New York, 1981.

can be simplified and combined to give

cI(org,pb) + cJ(org,pb) + clim ) (-2i/FA)xtDorg

(17)

This equation can be combined with the ion-exchange constant (eq 9) to give

{

} x

cJ(aq,pb) -2i cI(org,pb) 1 + Kex ) FA cI(aq,pb)

t - clim Dorg

(18)

and this result is inserted into eq 1 to describe the phase boundary potential as

EPB )

x ( x

RT ln kI F

Dorg -2i t FA

t - clim Dorg

)

-1

+

RT ln{aI(aq,pb) + KexaJ(aq,pb)} (19) F

This relationship is again analogous to the Nicolsky equation for ion-selective electrodes, now with Kex as the selectivity coefficient. The selectivity is expected to be identical to an ionophore-free ion-exchanger electrode.32 RESULTS AND DISCUSSION The theory describes the expected response behavior of a pulsed galvanostatic ion-selective membrane without intrinsic ionexchange properties. In brief, a constant applied current of fixed duration forces the extraction of a defined concentration of ions into the sensing membrane. If no interference from other ions is observed, the amount of extracted ions is largely independent of the sample concentration. In analogy to ion-selective electrode theory,28 the observed constant current potential may show an apparently Nernstian behavior. Theory predicts that the observed potential is dependent on the length of the applied current pulse. Consequently, reproducible potential readings are possible only if each current pulse is followed by a regeneration step, where the membrane is held at baseline potential. The chronopotentiometric measuring mode is potentially much more attractive than published normal pulse voltammetry measurements,19,25 since it yields sensor responses that look and feel very much like established ion-selective electrodes. The sensor selectivity is a function of the applied current and can be directly, rather than indirectly,19 tuned. The iR drop across the membrane is assumed to be constant for a constant applied current because the membrane contains a large excess of lipophilic salt. This further simplifies the theoretical treatment of these devices. Figure 1 shows a calculated response function for a hypothetical membrane selective for monovalent ions. For these plots, the fully calculated response function was utilized (see text after eq 9). The following parameters were used: t ) 1 s, i ) -1 µA, A ) 0.1 cm2, Daq ) 10-5 cm2 s-1, Dorg ) 10-8 cm2 s-1, Kex ) 10-6, and aJ(aq,bulk) ) 0.1 M. In Figure 1A, the chronopotentiometric response shows a Nernstian slope at high sample concentrations. Figure 1B confirms that, in this concentration range, the phase boundary concentration of complexed primary ion is constant. This is an important prerequisite for obtaining pseudo-Nernstian

Figure 1. (A) Theoretical response behavior of an ion-selective membrane by pulsed chronopotentiometry to a monovalent ion in a discriminated electrolyte background (see text). (B) Calculated phase boundary concentration of the analyte ion complex in the organic phase as a function of the sample composition. The region of constant concentration predicts an apparently Nernstian response slope (see (A) and eq 1). (C) Theoretical sample concentration polarization as a function of the bulk sample composition. At the superNernstian step observed in (A), concentration polarization becomes significant.

response behavior (see eq 1). Figure 1C shows the expected extent of polarization in the aqueous diffusion layer near the membrane. At high sample concentrations, polarization is negligible. At the critical bulk concentration (dotted vertical line; see eq 13), maximum sample polarization occurs, which indicates the onset of a strong apparently super-Nernstian response slope. Analogous behavior has been found repeatedly with ion-selective electrodes measured under zero current conditions,9 but here the super-Nernstian response region is fully controlled by instrumental means. At lower sample concentrations, the observed potential is dictated by the extraction of background ions. This is analogous to ion-selective electrode behavior.33 If interference from the (33) Ceresa, A.; Radu, A.; Peper, S.; Bakker, E.; Pretsch, E. Anal. Chem. 2002, 74, 4027.

Analytical Chemistry, Vol. 75, No. 17, September 1, 2003

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Figure 2. Observed typical amplitude-time behavior of the current (A) and potential (B) during the potentiostatic/galvanostatic switching experiment in 0.01 M NaCl. Labels G denote the time at which the galvanostatic mode was applied (at -5 µA), while labels P correspond to the time when the potentiostatic baseline potential was started. The potential values below each pulse shown in (B) are the averaged potential values from the last 100 ms of the pulse, which are used to represent the sensor response in the following figures.

background is stronger, the super-Nernstian response region will start to disappear (calculations not shown). Figure 2 shows the acquired raw data for a typical experiment (sodium-selective membrane in 0.01 M NaCl solution) if constant current pulses (-5 µA, 1 s) were applied. The top plot describes the observed current readings, and the bottom plot the corresponding potential values. Note that each applied current pulse (of 1-s duration) is followed by a controlled potential pulse (of 10-s duration). During the galvanostatic pulse, the potential is monitored as a function of time. As expected from theory (eq 12), the potential changes as a function of pulse time. Girault has shown that the capacity of the electrical double layer at the membrane/water interface is much smaller than at metal electrodes.34 The non-Faradaic current is therefore negliglibly small, and the potentials are controlled by the diffusion of components in the membrane phase.35 After ∼100 ms of the pulse, the potential readings appear to be very reproducible from pulse to pulse (see Figure 2). Each current pulse is followed by a 10-s baseline potential pulse in order to regenerate the membrane. The observed current during this pulse continuously decreases to zero and is indicative of ions diffusing back from the membrane into (34) Girault, H. H.; Schiffrin, D. J. J. Electroanal. Chem. 1985, 195, 213. (35) Beattie, P. D.; Delay, A.; Girault, H. H. Electrochim. Acta 1995, 40, 2961.

4546 Analytical Chemistry, Vol. 75, No. 17, September 1, 2003

Figure 3. Pulsed chronopotentiograms for a PVC-o-NPOE membrane containing 10 wt % of the inert lipophilic salt ETH 500 and the sodium ionophore tert-butyl calix[4]arene tetramethyl ester. (A) Response in separate solutions of 0.01 M NaCl or KCl. (B) Solid line: response in a mixed solution of 0.01 M NaCl and KCl.

the sample. In all experiments shown further below, the average potential reading from the last 100 ms of each current pulse was used. The corresponding values are given in Figure 2B under each potential pulse and are quite reproducible. For the experiment shown in Figure 2, potential values were recorded for a sequence of 25 pulses, each averaged by the method above, and the standard deviation for these pulses was found to be 0.5 mV. It was recently demonstrated with normal pulse voltammetric experiments19 that the selectivity of plasticized poly(vinyl chloride) membranes based on the sodium-selective ionophore tert-butyl calix[4]arene tetramethyl ester can be altered by the magnitude of applied potential. To properly evaluate the pulsed galvanostatic method introduced here, the same membrane composition was chosen as a model system. A sequence of increasing cathodic current pulses (from 0 to -50 µA) was imposed on the membrane to obtain current-dependent potential readings, each separated by a prolonged period at baseline potential. The observed potentials in separate 0.1 M NaCl and KCl solutions are plotted as a function of the applied current in Figure 3A. In the current region from -1 to -15 µA, the membrane

shows a distinct preference for sodium. It is well known that this ionophore induces a high preference for sodium over potassium in potentiometric membranes.19,36 At ∼-20 µA, the limiting current for the ionophore-assisted ion uptake process is observed. At currents more negative than -25 µA, the membrane clearly prefers potassium over sodium. Such high currents lead to ion fluxes that can no longer be assisted by the ionophore, and uncomplexed ions start to extract into the membrane. Because potassium ions are more lipophilic than sodium, sensor selectivity is reversed. This behavior was observed earlier with normal pulse voltammetry19 and is confirmed here. Note that the pulsed chronopotentiograms are here smooth and lack the undesired potential dips that have been observed with normal pulse voltammetry.19 The response in mixed solution (Figure 3B, solid line) demonstrates that the membrane truly works as a selective sensor for both ions. The mixed ion response overlaps perfectly with the separate solution sodium response curve at low applied currents, confirming that the sensor is only responsive to sodium under these conditions. Conversely, the mixed ion response perfectly follows the separate solution potassium response at high currents. The theory developed above predicts that the sensor response at currents above or below the limiting current can both be described with the Nicolsky equation:

EM ) K + RT/F ln{aI(aq) + Kpot IJ aJ(aq)}

(20)

where K is a constant value (at a given constant current), Kpot IJ is the selectivity coefficient, and the sample activities shown are phase boundary activities. According to theory, the selectivity coefficient is drastically different for each current region discussed above. If eq 20 is valid, it should be possible to calculate the selectivity coefficient as a function of the applied current by using the established separate solutions method, which is obtained for monovalent ions as37

log Kpot IJ )

aI(aq) F(EJ - EI) + log 2.303RT aJ(aq)

(21)

where EI and EJ are the observed membrane potentials in solutions containing the ion activities aI(aq) and aJ(aq) alone. Figure 4 represents the selectivity coefficient obtained with eq 21 as a function of the applied current for the data shown in Figure 3A. The sign of the logarithmic selectivity coefficient changes drastically around the limiting current of ∼20 µA. At -3 µA, the logarithmic selectivity coefficient assumes an optimal value for the measurement of sodium (-2.7), which is comparable to the selectivity of sodium-selective electrodes based on this ionophore. At -25 µA, the logarithmic selectivity coefficient changes to +2.2, which is consistent with the behavior of an ionophore-free ionexchanger membrane (see eq 19). The same behavior with an ion-selective membrane containing a sodium ionophore is also observed when a significant excess of lipophilic ion exchanger is present over the ionophore, which forces the extraction of a (36) Cadogan, A.; Gao, Z. Q.; Lewenstam, A.; Ivaska, A.; Diamond, D. Anal. Chem. 1992, 64, 2496. (37) Guilbault, G. G.; Durst, R. A.; Frant, M. S.; Freiser, H.; Hansen, E. H.; Light, T. S.; E. Pungor; Rechnitz, G.; Rice, N. M.; Rohm, T. J.; Simon, W.; Thomas, J. D. R. Pure Appl. Chem. 1976, 48, 127.

Figure 4. Selectivity coefficient, logKpot Na,K, obtained by the separate solutions method (eq 21) as a function of the applied current from data shown in Figure 3A. Orthogonal selectivity is observed for the same device.

substantial concentration of uncomplexed ions into the membrane.19 Here, the applied current assumes the function of the added lipophilic ion exchanger with ion-selective electrode membranes. Figure 5A shows a calibration curve of varying NaCl concentrations in a 0.01 M KCl background, measured at an applied current of -3 µA. The membrane showed a rapid, linear, and nearNernstian response slope (56.4 mV decade-1) in the concentration range of 10-4-10-1 M sodium chloride. The theoretical detection limit according to eq 20 is at ∼10-4.3 M, which is consistent with the experimental results shown in Figure 5A. Figure 6 represents the sensor response times during the Na+ titration shown in Figure 5A. Each calibration point corresponds to one potential step (comprising ∼15 current pulses) in Figure 5A. For each concentration of NaCl, the standard deviation of the potential readings did not exceed 1.5 mV. This indicates that the magnitude of the potential remained stable during each titration step, with no apparent drift. Response times were not yet optimized in this work but were found to be less than 20 s. The long-term stability was found to be very good. Sensing membranes that were repeatedly used for one week and subsequently stored in 10 mM NaCl for one month showed potential readings in 1 mM NaCl that deviated less than 3 mV from their last measured values. This excellent long-term stability indicates that the membrane resistance remains practically unchanged over a long period of time. Moreover, the standard deviation from the potential deviation between four different electrodes prepared at the same time from the outer region of the same parent membrane was found to be (5 mV, indicating good interelectrode reproducibility. At more negative applied currents of -30 µA, a calibration curve for potassium chloride was obtained in a background of 0.01 M NaCl. As shown in Figure 5B, a linear response slope was observed at KCl concentrations between 10-4 and 2 × 10-2 M. This demonstrates that the same membrane can be used to measure two different ions reversibly and selectively, simply by adjusting the magnitude of the applied current. The response slope found in Figure 5B was somewhat larger than Nernstian (64.3 Analytical Chemistry, Vol. 75, No. 17, September 1, 2003

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Figure 7. (A) Pulsed chronopotentiometry: response to Na+ at -6 µA in a background of 0.01 M MgCl2, consisting of an apparently super-Nernstian response region. (B) Zero current potentiometry: response function to Na+ for a sodium-selective membrane (10 mmol kg-1 sodium ionophore and 6 mmol kg-1 KTFPB), giving a superNernstian response region. The arrows are labeled with the corresponding log aNa values. Figure 5. (A) Response to Na+ in a background of 0.01 M KCl at -3 µA. Solid line with slope of 56.4 mV. (B) Response to K+ in a background of 0.01 M NaCl at -30 µA. Solid line with slope 64.3 mV. (C) Response to Cl- in a background 0.01 M K2SO4 at +3 µA. Solid line with slope of 56.2 mV.

Figure 6. Time-dependent response for the sodium calibration curve shown in Figure 5A. The numbers above the trace are the corresponding log aNa values.

mV decade-1), and in other experiments, the slopes tended to also generally increase with increasing applied current (data not shown). This observation indicates a practical limitation of the theory described above, and a more rigorous treatment will have to more fully consider the influence of applied current on the phase boundary potential. 4548 Analytical Chemistry, Vol. 75, No. 17, September 1, 2003

At cathodic applied currents, cations are forced to extract into the membrane phase because the membrane contains no transferable ions that could be expelled under these conditions.24 Conversely, if an anodic current is applied, one expects that sample anions are extracted into the membrane, and the sensor should be rendered anion-responsive. It was observed earlier that ionselective membranes showed an anionic response at positive potentials in normal pulse voltammetry and exhibited a preference for more lipophilic over less lipophilic anions according to the Hofmeister selectivity sequence.25 It is expected that in the pulsed galvanostatic mode introduced here, the sodium-selective membrane should behave as an anion-selective electrode with Hofmeister selectivity. Figure 5C presents the experimentally observed response curve for Cl- at +3 µA within a background of 0.01 M K2SO4. The slope of the linear regression fit is 56.2 mV and quite close to the Nernstian value. The nature of cations (either sodium or potassium) did not have an influence on the anionic response, as expected (data not shown). Since no ionophore is present in this system to selectively complex the extracted sample anion, no reversal of selectivity at higher currents is expected. The methodology introduced in this paper allows one to use just one ion-selective membrane for the parallel and selective measurement of up to three different ions present in the same sample. In Figure 7A, a calibration curve for NaCl in a background of 0.01 M MgCl2 is presented, measured at applied current pulses of -6 µA. Since the membrane is more selective over magnesium than over potassium, a super-Nernstian response region

Figure 8. (A) Pulsed chronopotentiometry: time-dependent response for the data shown in Figure 7A with good potential stability in the super-Nernstian response region. Magnified inset shows potential stability. (B) Zero current potentiometry: time-dependent response for the data shown in Figure 7B showing strong potential drift in the super-Nernstian region. The arrows are labeled with the corresponding log aNa values.

is observed below 10-4 M NaCl. As explained in the Theory section, this potential drop is indicative of concentration polarization processes at the sample side of the membrane. Equation 13 describes the critical ion concentration at which the potential drop is expected to occur (see dotted line in Figure 1). In this region, the boundary concentration of sodium is significantly lower than its sample bulk value. In potentiometry, such super-Nernstian responses have gained significant interest in recent years. In zero current potentiometry, however, the potentials observed in this region often show strong drifts and are poorly reproducible.10 This is mainly because the associated diffusion profiles are continuously changing with time. For the pulsed galvanostatic method developed here, this situation may be different because the fluxes are fully controlled by instrumental means. Figure 8A shows the potential-time trace for the calibration curve in Figure 7A. The potentials in the super-Nernstian response region, monitored over several minutes, are indeed quite stable. This implies that many of the published experiments relying on or exploring super-Nernstian response slopes could be drastically improved by using the method developed here. An additional zero current potentiometric experiment was performed in order to compare the stability of the potentials in the super-Nernstian region for the chronopotentiometric and the traditional zero current potentiometric sodium-selective sensors. It is well established that super-Nernstian response slopes are found in sensors where a zero current ion flux forces the depletion of analyte ions at the membrane surface. Such a flux is effectively

induced if a concentration gradient of the analyte is present in the direction of the inner filling solution. Such effects are important in view of lowering the detection limit of ion-selective electrodes,33 and to design potentiometric polyion sensors.2 While it is well established that the corresponding potentiometric responses in the super-Nernstian response region are not very stable, a direct comparison was done here with membranes that contained the same sodium ionophore. The ion flux was induced by choosing a membrane with potassium rather than sodium as the counterion of the lipophilic ion exchanger, and the inner solution contained KCl. Figure 7B shows the potentiometric response for this membrane upon first contact with NaCl solutions of incrementing concentrations, and the expected super-Nernstian region is indeed observed. Since the concentration gradients are changing continuously, the super-Nernstian response region is not as steep as observed with the chronopotentiometric method, where the diffusion layer thickness in the organic phase is always renewed from pulse to pulse. Indeed, earlier theoretical treatments have always predicted a larger response slope than experimentally observed.33 Figure 8B shows the potential-time trace for the calibration curve shown in Figure 7B. Obviously, very strong potential drifts are observed in the super-Nernstian response region. This result is typical for passive experiments under zero current conditions, and this limitation can be avoided with the technique introduced here (Figure 8A). This should make it possible to develop sensing principles that operate reproducibly and reversibly under conditions where sample depletion processes are relevant.

CONCLUSIONS Applying galvanostatic detection pulses, each followed by a baseline potential period, to a membrane without intrinsic ionexchange properties forms a potentially important technique for the interrogation of ion-selective polymeric membranes. The use of constant current pulses forces ions to extract into the membrane under defined flux conditions. This yields chronopotentiometric response functions that have the look and feel of established ionselective electrode responses measured at zero current, with demonstrated apparently Nernstian response slopes. This means that established calibration and characterization protocols can be fully applied to such systems. The full control of ion fluxes by instrumental means offer advantages that cannot be met with current ion-selective electrodes. These include the tunability of the selectivity by the magnitude and sign of the applied current pulse. The current may be understood in analogy to the concentration and charge sign of the lipophilic ion exchanger in traditional ion-selective electrode membranes, since a given flux adjusts the concentration of extracted ions in the phase boundary region. In this paper, the individual calibration and detection of sodium, potassium, and chloride was demonstrated in different mixed sample solutions, thereby demonstrating orthogonal selectivity with the same device. The pulsed galvanostatic technique offers other advantages that may be impossible to match with zero current potentiometry. The instrumental control over the magnitude, duration, and sign of transmembrane ion fluxes makes this technique potentially very powerful for use in situations where Analytical Chemistry, Vol. 75, No. 17, September 1, 2003

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sample polarizations are relevant to sensor response. It was shown here that potential readings in the so-called super-Nernstian response region are much more stable and reproducible than with ion-selective electrodes measured at zero current. This will likely be relevant to the development of polyion sensors,3 sensors for improved endpoint detection,6 and “switchtrodes”,5 where differential measurements between two electrodes with different super-Nernstian response regions are performed at a critical ion concentration.

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ACKNOWLEDGMENT The authors are grateful to the Petroleum Research Fund (administered by the American Chemical Society) and the National Institutes of Health (GM59716) for financial support of this research. Received for review April 18, 2003. Accepted June 13, 2003. AC034409T