A Chronoamperometric Method To Estimate Changes in the

Bradford D. Pendley, Robert E. Gyurcsányi, Richard P. Buck, and Ernö Lindner*. Department of Chemistry, Rhodes College, 2000 North Parkway, Memphis,...
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Anal. Chem. 2001, 73, 4599-4606

A Chronoamperometric Method To Estimate Changes in the Membrane Composition of Ion-Selective Membranes Bradford D. Pendley,† Robert E. Gyurcsa´nyi,‡,§ Richard P. Buck,| and Erno 1 Lindner*,‡

Department of Chemistry, Rhodes College, 2000 North Parkway, Memphis, Tennessee 38112, Joint Graduate Program in Biomedical Engineering, University of Memphis and University of Tennessee Health Science Center, Herff College of Engineering, Memphis, Tennessee 38152, Research Group of Technical Analytical Chemistry of the Hungarian Academy of Sciences, Szent. Gelle´ rt te´ r 4, 1111 Budapest, Hungary, and Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599

A new chronoamperometric method is used to estimate changes in the membrane composition of mobile-site, ionophore-based membranes. The characteristic features of the chronoamperometric curves (initial current, slope, break time) of valinomycin-based, potassium-selective membranes loaded with potassium tetrakis(4-chlorophenyl)borate are correlated with the mobile-site and free ionophore concentration in the membrane. Limiting cases for strong and negligible ion pair formation are distinguished. Replicate measurements indicate a relative standard deviation in the calculated values less than 10%. The practical applicability of the method was tested with membranes incorporated into conventional ion-selective electrode bodies or cast onto microfabricated planar sensor structures. Ion-selective liquid membrane electrodes are widely used as integrated devices in continuous monitoring manifolds and clinical chemical analyzers for the selective determination of ions. During extended period of exposure to the sample, a gradual loss of the membrane components (ion carrier, plasticizer, additives) is inevitable. Such loss affects the membrane characteristics, such as selectivity and electrode calibration slope, and finally leads to a breakdown of the ion measuring capability of the system, i.e., determines the lifetime of these devices.1 The lipophilic character of the sample (blood, plasma, serum, urine, etc.) favors a substantial and fast extraction of membrane components.2 Different approaches are known to address the limited lifetime and the problems related to leaching. The covalent immobilization of active membrane components to the polymeric backbone of the membrane3-6 and the use of self-plasticizing6 or plasticizer†

Rhodes College. Herff College of Engineering. § Research Group of Technical Analytical Chemistry of the Hungarian Academy of Sciences. | University of North Carolina. (1) Oesch, U.; Simon, W. Anal. Chem. 1980, 52, 692. (2) Oesch, U.; Ammann, D.; Simon, W. Clin. Chem. 1980, 32, 1448. (3) Daunert, S.; Bachas, L. G. Anal. Chem. 1990, 62, 1428. (4) Rosatzin, T.; Holy, P.; Seiler, K.; Rusterholz, B.; Simon, W. Anal. Chem. 1992, 64, 2029. ‡

10.1021/ac010007e CCC: $20.00 Published on Web 08/31/2001

© 2001 American Chemical Society

free7 membranes are ways to ensure extended lifetime. For mobile membrane ingredients, theoretical models and calculations can be used to quantify the loss into the sample on the basis of such variables as lipophilicity, membrane geometry, and hemodynamic conditions.1,8 However, values obtained by such calculations represent a worst-case situation in estimating the lifetime, and the direct or indirect experimental verification of such calculations is extremely difficult or not realistic during practical applications. Accordingly, when the leaching of the membrane components may query the reliability of the measured data, the electrodes have to be checked regularly by repeated calibrations. When ion-selective electrodes are intended for chronic in vivo measurements, small sensor size has various advantages.9 However, ion-selective membrane sensors of extremely small size contain only a few nanograms of active ingredients (ionophore and mobile sites); i.e., the dissolution of membrane components into the sample has decisive importance with respect to the applicability of these sensors for in vivo monitoring. Since the regular and precise calibration of ion sensors implanted in tissue or placed into the blood stream is not feasible, any simple method providing information about changes in the membrane composition may have practical relevance. By monitoring time-dependent changes in the membrane composition, predictions about residual lifetime of the sensor become conceivable. It may also be important for clinical analyzers, as it may signal special service prior to electrode failure or scheduled maintenance. Recently we reported on the use of chronoamperometric transients to estimate the ionophore loss from fixed-site, solvent polymeric membranes.10 In the conclusion section of our paper, we hypothesized that the technique could be extended to membranes containing mobile sites. This extension is essential because most of the ionophore-based membranes are intentionally (5) Reinhoudt, D. N.; Engbersen, J. F. J.; Brozka, Z.; van den Vlekkert, H. H.; Honig, G. W. N.; Holterman, H. A. J.; Verkerk, U. H. Anal. Chem. 1994, 66, 3618. (6) Heng, L. Y.; Hall, E. A. H. Anal. Chem. 2000, 72, 42. (7) Lindner, E.; Cosofret, V. V.; Ufer, S.; Buck, R. P.; Kao, W. J.; Neuman, M. R.; Anderson, J. M. J. Biomed. Mater. Res. 1994, 28, 591. (8) Dinten, O.; Spichiger, U. E.; Chaniotakis, N.; Gehrig, P.; Rusterholz, B.; M., W. E.; Simon, W. Anal. Chem. 1991, 63, 596. (9) Lindner, E.; Buck, R. P. Anal. Chem. 2000, 72, 336A. (10) Pendley, B. D.; Lindner, E. Anal. Chem. 1999, 71, 3673.

Analytical Chemistry, Vol. 73, No. 19, October 1, 2001 4599

membrane area, F is the Faraday constant, Cionophore is the ionophore concentration in the membrane, Rohm is the ohmic resistance of the membrane, Dionophore is the diffusion coefficient of the ionophore in the membrane, and Vappl is the applied voltage. Similar to fixed-site membranes, after application of a potential step to mobile-site membranes (Figure 1B), the initial current is related to the applied voltage and the ohmic resistance of the membrane. However, in this case, the initial, ohmic current linearly decreases with a characteristic slope until the break time, as shown in the Figure 1 inset. The break time is related to the complete depletion of free ionophore at one interface of the membrane in the same way as with the fixed-site membranes. However, the free ionophore concentration is a function of the total ionophore and negative-site concentration due to the overall electroneutrality in the membrane. Accordingly, the break time appears to be a function of both the ionophore and the mobilesite concentration. If the complexation equilibrium between the ionophore (L) and the primary cation (Mn+) is

Mn+ + kL ) MLn+ k

Figure 1. Current-time transients of fixed- (A) and mobile-site (B and inset) membranes after a potential step: (A) 1 wt % valinomycin, Vappl ) -15 V. (B) 1 wt % valinomycin with 51 mol % KTpClPB, Vappl ) -4 V. The inset shows the initial portion of a current-time transient for a mobile-site membrane and illustrates how the various parameters were determined.

loaded with mobile sites to reach optimal sensor performance (e.g., resistance, response time, selectivity) and because lipophilic additives can also leach from the membranes. THEORETICAL SECTION Chronoamperometric transient responses to an externally applied potential step were used to study the transport mechanism and for determining diffusion coefficients in ion-selective membranes.11-15 The shape and characteristic features of the chronoamperometric transients are different for fixed- and mobile-site membranes (Figure 1).14,15 For fixed-site membranes, the measured current is relatively stable until a characteristic break time (shown in Figure 1A), when the current starts to decay in Cottrell fashion13 and eventually approaches a limiting value. This break is indicative of the total depletion of ionophore at one interface of the membrane and can be related to the ionophore concentration in the membrane:12

τ1/2 )

FARohmCionophorexDionophoreπ 2Vappl

(1)

where τ is the break time in the current transient, A is the (11) Iglehart, M. L.; Buck, R. P. Talanta 1989, 36, 89. (12) Iglehart, M. L.; Buck, R. P.; Horvai, G.; Pungor, E. Anal. Chem. 1988, 60, 1018. (13) Nahir, T. M.; Buck, R. P. J. Electroanal. Chem. 1992, 341, 1.

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and the ion pair formation equilibrium between the positively charged complex and the negatively charged mobile sites in the membrane can be formulated as MLn+ k + nS ) MLkSn

the mass balances for the ionophore and the negatively charged sites (monovalent tetraphenylborate derivative) are given in eqs 2 and 3, where CL and Csite are the total concentration of the

CL ) Cfree + kCMLn+ + kCMLkSn L k Csite ) Cfree + nCMSn + nCMLkSn ≈ Cfree L site + nCMLkSn

(2) (3)

ionophore and negatively charged sites (S-) in the membrane, respectively. CMLn+ is the concentration of the positively charged k complex of the ionophore with Mn+ cation, and MLkSn and MSn are the uncharged ion pairs. In eq 3, we assumed that the free cation (Mn+) concentration is negligible compared to the concentration of complex (MLn+ k ) in the membrane, and consequently, the concentration of the uncharged ion pair (MSn) is negligible compared to MLkSn (CMSn , nCMLkSn).16,17 Furthermore, the influence of intrinsic negative sites in the PVC matrix (covalently anchored to the polymeric backbone) is neglected in our analysis, because the membranes used in our studies have at least 10 times more mobile negative sites than originally present in the PVC membrane due to the addition of tetraphenylborate derivative.16,18 (14) Nahir, T. M.; Buck, R. P. J. Phys. Chem. 1993, 97, 12363. (15) Nahir, T. M.; Buck, R. P. Talanta 1994, 41, 335. (16) Buck, R. P.; Toth, K.; Graf, E.; Horvai, G.; Pungor, E. J. Electroanal. Chem. 1987, 223, 51. (17) Armstrong, R. D. Electrochim. Acta 1987, 32, 1549. (18) van den Berg, A.; van der Wal, P. D.; Skowronska-Ptasinska, M.; Sudho ¨lter, E. J. R.; Reinhoudt, D. N.; Bergveld, P. Anal. Chem. 1987, 59, 2827.

The requirement for electroneutrality in the membrane can be formulated as

CMLn+ ) k

1 free C n site

(4)

the optimized membrane composition can have a detrimental effect on the membrane’s performance,19,20 and accordingly, for an analytically relevant method, the loss of sites must also be determined. Nahir and Buck14 have shown that the initial, ohmic resistance, Rohm, of a mobile-site polymeric membrane is given by

Combining eqs 2, 3, and 4 gives the free ionophore concentration as a function of the total ionophore and site concentrations:

k ) CL - Csite Cfree L n

(5)

When the ionophore concentration in eq 1 is substituted with the free ionophore concentration (eq 5), it becomes clear how the increased mobile-site concentration influences the break time:

τ1/2 )

Rohm )

FA(CL - (k/n)Csite) xDLπ 2Iinit

(6)

Vappl Iinit

RTd

) AF

∑

2

z2i

(10) D iC i

i

where R is 8.314 J/K mol, T is the absolute temperature, d is the membrane thickness, and Di and Ci are the diffusion coefficient and concentration of the ionic species in the membrane, respectively. For a valinomycin-based membrane loaded with mobile sites the expression of the resistance can be given by

Rohm )

RTd ) AF2(Cfree D site site + CKval+DKval+)

where

RTd AF2Cfree site (Dsite

Iinit ) Vappl/Rohm For the valinomycin-based potassium-selective membrane k ) n ) 1 and eq 6 can be simplified. In our further treatment, only this simplified case (monovalent cation-selective membrane with 1:1 stoichiometry) is discussed and the terms CL, MLn+, MLkSn, and DL are replaced by Cval, Kval+, KvalS, and Dval, respectively:

τ1/2 )

FA(Cval - Csite) xDvalπ 2Iinit

slope )

Ifinal - Iinit τ- 0

(8)

βKvalS ) CKvalS/Cfree site CKval+

4(Ifinal - Iinit)

I2init

F2A2Dvalπ (Cval - Csite)2

(9)

Accordingly, the initial slope should be a linear function of 2 Iinit (Ifinal - Iinit)/(Cval - Csite)2. Equations 7 and 9 are not independent. They both provide alternative means of assessing the free ionophore concentration in the membrane but do not allow for the determination of the absolute amount of either ionophore or mobile site. To evaluate the ionophore and site concentrations independently, an additional relationship is needed. It is especially important in mobile-site membranes since the free ionophore concentration may change through leaching of the ionophore, the sites, or both. Changes in

(12)

By combining eqs 3, 4, and 12 (n ) 1), βKvalS can be expressed as free a function of Csite and Csite : free 2 βKvalS ) (Csite - Cfree site )/(Csite )

(13)

free By transforming eq 13 to the usual quadratic function, Csite can be expressed as

where the slope, Ifinal, and Iinit are determined as shown in the Figure 1 inset. By inserting τ (eq 7) into eq 8 one gets

slope )

(11)

free because, according to eq 4, CKval+ ) Csite . free To determine Csite from eq 11, the relationship between Csite and Csite has to be known. It has been suggested that ion pairing is very strong in PVC membranes cast with nonpolar membrane plasticizer, such as DOS.21,22 An ion pair formation constant βKvalS can be defined as

(7)

According to eq 7, τ1/2 is a linear function of (Cval - Csite)/Iinit. The initial slope of the chronoamperometric transients is also a function of the free ionophore concentration in the membrane. The slope can be expressed as

+ DKval+)

Cfree site )

x1 + 4βCsite

-1

2β

(14)

and the free site concentration can be substituted into eq 11:

Rohm )

2βRTd AF (x1 + 4βCsite ) - 1)(Dsite + DKVal+) 2

(15)

Equation 15 can be simplified when assumptions for strong or weak ion pairing are made. In the case of strong ion pairing, (19) Ammann, D.; Pretsch, E.; Simon, W.; Lindner, E.; Bezegh, A.; Pungor, E. Anal. Chim. Acta 1985, 171, 119. (20) Ceresa, A.; Bakker, E.; Hattendorf, B.; Gunther, D.; Pretsch, E. Anal. Chem. 2001, 73, 343. (21) Armstrong, R. D.; Horvai, G. Electrochim. Acta 1990, 35, 1. (22) Mi, Y.; Bakker, E. Anal. Chem. 1999, 71, 5279.

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free Csite , Csite and Rohm becomes inversely proportional to Csite1/2:

Rohm )

RTdxβ

xCsite(Dsite + DKVal

2

AF

)

(16)

+

However, when the ion pairing between K+-valinomycin and the free free anionic sites is negligible weak (Csite . CKvalS and Csite ≈ free Csite ), a linear relationship can be predicted between Rohm and 1/Csite:

Rohm )

RTd AF Csite(DKVal+ + Dsite) 2

(17)

After the initial ohmic resistance (i.e., Vappl/Iinit) of the membrane is measured, a calibration plot based on eq 16 or 17 can be used for the determination of the site concentration (Csite). This determination allows for the concentration of ionophore to be calculated based on the results from eqs 7 or 9. EXPERIMENTAL SECTION Reagents. Valinomycin, potassium tetrakis(4-chlorophenyl)borate (KTpClPB), high molecular weight poly(vinyl chloride) (PVC), and bis(2-ethylhexyl) sebacate (dioctyl sebacate, DOS) were purchased from Fluka (Fluka Chem. Corp., Milwaukee, WI). Poly(2-hydroxyethyl methacrylate) was a product of Scientific Polymer Products Inc (Ontario, NY). Tetrahydrofuran (ACS reagent grade) was purchased from Aldrich (Milwaukee, WI). Cyclohexanone (Certified) and potassium chloride (ACS Certified) were purchased from Fisher Scientific (Pittsburgh, PA). All other chemicals were of at least reagent grade and were used as received. Water was purified using a Milli-Q Gradient A10 system (Millipore Corp.). Apparatus. An EG&G Princeton Applied Research model 283 potentiostat/galvanostat (Oak Ridge, TN) interfaced to a Dell Optiplex GX-1 computer was used to perform the chronoamperometric studies. EG&G model 250 research electrochemistry software was used to control the potentiostat. The PAR 283 potentiostat was used to control the potential across the cell. When the applied voltage exceeded -4 V, a locally built voltage divider reduced the voltage sensed by the reference electrode circuit of the potentiostat. Electrodes and Cells. A locally built cell was used to house the membrane for all chronoamperometric experiments. The cell consisted of two electrolyte compartments separated by the membrane. A detailed description is given in our earlier paper.10 Conventional ion-selective electrodes were assembled by incorporating a 7-mm polymeric membrane disk inside a Philips body (Moller Glassbla¨serei, Zu¨rich, Switzerland). Microfabricated planar sensors were constructed as described previously.23 Membranes. Membranes comprising approximately 33 wt % poly(vinyl chloride), 66-67 wt % dioctyl sebacate, 0.5-1.2 wt % valinomycin, and up to 70 mol % KTpClPB were prepared as described in the literature24 using a THF/cyclohexanone mixture as solvent. A 1.75-cm-diameter ring of polymer membrane was (23) Nagy, G.; Gyurcsanyi, R. E.; Cristalli, A.; Neuman, M. R.; Lindner, E. Biosens. Bioelectron. 2000, 15, 265. (24) Moody, G. J.; Oke, R. B.; Thomas, J. D. R. Analyst 1970, 95, 910.

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cut and weighed. The thickness of the membrane was estimated from the dimensions, weight, and density of the cut PVC membrane. The membrane density (1.07 g/cm3) was calculated from the individual densities of the poly(vinyl chloride)/dioctyl sebacate mixture.1 Membrane thicknesses were ∼100 µm. Procedures. For most experiments, a membrane was placed inside the transport cell, and ∼9 mL of 1 mM KCl solution was placed in each compartment. The membrane was soaked in the potassium chloride solution for at least 1 h prior to commencing the experiment. A stir bar was placed into each compartment, and the solutions in both compartments were stirred throughout the experiment. The counter/reference electrode lead was connected to one Ag/AgCl electrode while the other Ag/AgCl electrode was connected to the working/sense lead. Voltage steps between -1 and -10 V were applied, and the resulting current was measured. For replicate measurements, membranes were allowed to stand at open circuit for a minimum of 1.5 h. The 1.5-h relaxation time was selected by a series of measurement where the relaxation time between the individual experiments was systematically varied from 15 to 160 min. Between the experiments, the cell voltage was continuously recorded and the deviation (∆E) from its equilibrium value at the start of a new experiment was correlated with the parameters of the chronoamperometric transients. As it can be seen in Figure 2, for relaxation times larger than 1 h the residual standard deviation (RSD) of the experimentally determined τ1/2 values was within 0.5%. These results suggest that 1.5 h after the perturbation the depleted side of the membrane has essentially recovered. However, insufficient relaxation times resulted in significant decreases of the break time and its square root values. When the chronoamperometric experiments were repeated with 30-min or only 15-min relaxation times, the τ1/2 values decreased by 7 and 22%, respectively. By assuming that the membrane internal diffusion potential is negligible, the EMF of the cell gives a fair estimate of how far the membrane activities are from their equilibrium value since the potassium activity of the contacting solutions was kept constant. Five-millivolt deviation from the equilibrium membrane potential can be interpreted as 20% difference between the interfacial concentrations at the two sides of the membrane (∆E ) 59.2 log a′/a′′). By assuming symmetrical concentration distribution in the membrane, it translates to an expected 10% negative error in τ or 3% in τ1/2. The data summarized in Figure 2B demonstrate that the variations in the experimentally determined τ1/2 and IInit values are insignificant when the measured EMF is less than 5 mV from its equilibrium value at the start of the experiment. For experiments involving conventional Philips ISE bodies, potassium-selective membranes containing 66% DOS, 33% PVC, 1% valinomycin, and 48 mol % KTpClPB, relative to valinomycin, were used. A 7-mm disk of the polymeric membrane was placed inside a Philips body and the inner solution compartment was filled with 1 mM KCl. The fully assembled electrode was conditioned overnight in 1 mM KCl. The ISE was placed in a beaker containing a stirred 1 mM KCl solution in combination with an Orion single-junction reference electrode. One millimolar KCl was used as filling solution in the reference electrode. A voltage of -3 or -4 V was applied and the resulting current transient measured.

RESULTS AND DISCUSSION Figure 3A shows the effect of applied voltage on the current time transients of a valinomycin-based potassium electrode loaded with 40 mol % KTpClPB. As observed by Nahir and Buck,15 the initial current depends on the applied voltage and the ohmic resistance of the membrane. This initial, ohmic current decreases until the free carrier has been depleted at one interface, at which time the current decays further in a Cottrell fashion and then eventually approaches a limiting value. Compared to fixed-site membranes, the initial (ohmic) current values are larger because the membrane resistances of the mobile-site membranes are much smaller. The selection of the voltage used in the experiment is a more delicate task compared to fixed-site membranes. As we pointed out in our original paper,10 the break in the current transient is most pronounced when the initial ohmic and final limiting currents are significantly different. According to Iglehart and Buck,16 the limiting current, Il, is

Il )

2FA(Cval - Csite)Dval d

(18)

Combining eqs 11 and 18 and simplifying yields

Iinit Vappl FCfree site (DKval+ + Dsite) ) Il 2RTDval(Cval - Csite) Figure 2. Chronoamperometric transients (A) and the experimentally determined parameters of the chronoamperometric curves (B) as the function of the relaxation time between the individual experiments. The curves were recorded with a single PVC/DOS membrane containing 1% valinomycin and 40 mol % KTpClPB using the same experimental conditions (Vappl ) 2 V; time applied voltage, 200 s; bathing solutions, 10-3 M KCl); only the relaxation times between the individual measurements were varied between 15 and 160 min.

Screen-printed planar sensors on a ceramic substrate with a 2-mm-diameter silver disk electrode in a 100-µm-deep well were cleaned with acetone and methanol and allowed to dry. Experimental conditions of screen-printing are described elsewhere.23 The silver electrode was electroplated with silver chloride in 0.1 M NaCl solution by applying +0.03 mA/electrode anodic current for 5 min. Before chloridization, the electrode surface was also cleaned electrochemically with -0.03 mA/electrode cathodic current for 25 s. A 1.5-µL portion of hydrogel (1:1 mixture of 1 mM KCl and polyHema solution (2 g of polyHema in 5.49 g of methanol)) was placed inside the electrode well and allowed to dry. Next, a portion (5-7 µL) of polymer cocktail (66% DOS, 33% PVC, 1% valinomycin, 48 mol % KTpClPB in 1:1 THF/cyclohexanone) was placed over the dry hydrogel, and the solvent was allowed to evaporate. These planar sensors were soaked for at least 24 h in 1 mM KCl prior to the chronoamperometric experiments. The planar ISE along with a planar Ag/AgCl reference electrode (not coated with hydrogel and polymer) were placed inside a beaker containing a stirred 1 mM KCl solution, and a potential (-1 to -3 V) was applied.

(19)

Equation 19 predicts that the ratio between the initial and limiting currents increases as the applied voltage increases, as shown in Figure 3A. However, if the applied voltage is too large, Donnan exclusion failure can occur, leading to a breakdown of membrane permselectivity. On the basis of eq 6, a larger applied voltage shortens the break time and increases the uncertainty in its determination. These conflicting factors limit the choice of applied voltage. Equation 19 also predicts that the ratio between the initial and limiting currents increases as the free ionophore concentration decreases and as the free-site concentration increases. At constant total ionophore concentration and increasing site concentration, the free ionophore concentration decreases. Figure 3B shows current transients for three membranes, each containing ∼1% valinomycin but variable amounts of KTpClPB. As the concentration of KTpClPB increases, the difference between the initial and limiting currents increases and the break in the transient becomes more pronounced. To test our hypothesis that eqs 7 and 9 could be used to determine the free ionophore concentration in mobile-site polymeric membranes, numerous membranes of known, yet varied concentration of valinomycin (0.5-1.14%) and KTpClPB (0-70 mol %) were prepared and the current transients obtained. From these data, we constructed calibration plots of τ1/2 versus (Cv Cs)/Iinit (Figure 4A) and the slope of the curve before the break time versus (Ifinal - Iinit)[Iinit/(Cv - Cs]2 (Figure 4B). The slope of the curve before the break time was determined by obtaining the best-fit line to the data between t ) 0 and t ) τ as shown in Figure 1 insert. Typically, 100 or more of the data were used to determine the slope. The correlation coefficients were 0.99 or better. Analytical Chemistry, Vol. 73, No. 19, October 1, 2001

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Figure 3. Current-time transients of mobile-site membranes after a potential step: (A) effect of applied voltage on the chronoamperometric transients of a PVC/DOS membrane cast with 1 wt % valinomycin and 40 mol % KTpClPB; (B) effect of mobile-site concentration of the chronoamperometric transients of a PVC/DOS membrane cast with 1 wt % valinomycin but varying amounts of KTpClPB (Vappl ) -4 V).

Figure 4. Dependence of the characteristic break time (A) and initial slope (B) of the chronoamperometric transients on the normalized free ionophore concentration. The calibration plots are based on eqs 7 (A) and 9 (B) and were used for the determination of free valinomycin in fixed- and mobile-site membranes.

From the results presented in Figure 4, it appears that both plots provide suitable means of assessing the free ionophore 4604

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concentration (r2 of 0.97 and 0.95 for panels A and B of Figures 4, respectively). Furthermore the diffusion coefficient for valinomycin, (1.5 ( 0.1) × 10-8 cm2/s, calculated from the fitted curve in Figure 4A, is in close agreement with the value of 1.7 × 10-8 cm2/s given by Iglehart.12 Similarly, the diffusion coefficient calculated from the fitted equation in Figure 4B was (1.78 ( 0.04) × 10-8 cm2/s, again in good agreement with Iglehart’s results. To test our hypothesis that the membrane resistance could be used to determine the mobile-site concentrations in the membrane, two calibration plots were constructed based on eqs 16 (-Vappl/Iinit vs 1/xCsite) and 17 (-Vappl/Iinit vs 1/Csite), reflecting our assumptions on strong or weak ion pair formation (Figure 5). The data points were from the same current transients used to construct Figure 4 with the only exception that the data from membranes with 0% additive were not included in this analysis due to uncertainties in free-site concentration in these membranes. Linear regression analysis of the two sets of data points, summarized in Figure 5, showed that the quality of the fittings was essentially the same (r2 0.966 or 0.967, respectively) for the two limiting cases. The r2 values were further improved when d/Csite1/2 or d/Csite was plotted against -Vappl/Iinit. However, the good quality of fitting somewhat contradicts the fact that, in contrast to the suggestions of eqs 16 and 17, the fitted lines have nonzero intercepts, -293 339 and +76 357 Ω, respectively. This discrepancy can have several reasons. In the derivation of eqs 16 and 17, it was assumed that the membrane resistance dominates the overall resistance of the cell (e.g., charge-transfer and solution resistances were not considered). This assumption may not be justified at low membrane resistances (high site concentrations). In addition, the intrinsic site concentrations were neglected in our analysis. The latter may be important because the slopes in the calibration plots, shown in Figure 5, are dominated by the data points measured with membranes containing only small amounts

Figure 6. Current-time transient of a membrane containing 1 wt % valinomycin and 48 mol % KTpClPB on a planar sensor substrate. Vappl ) -3 V.

Figure 5. Dependence of the initial membrane resistance (as determined from the chronoamperometric transients) on the site concentration for the limiting cases of strong (A) and weak (B) ion pair formation. The calibration plots are based on eqs 16 (A) and 17 (B) and were used for the determination of the residual KTpClPB in mobile-site membranes.

of mobile-site additives (10-25 mol %). The contribution of intrinsic sites to the total membrane conductivity is the largest when the added site concentration is the smallest. Finally, above a critical site concentration, the membrane resistance does not decrease with increasing total salt concentrations because the dissociation in the nonpolar membrane phase is completely suppressed.19 Since the best fits to the data points shown in Figure 5 have nonzero intercepts, the reliability of the calculated values for DKval+ + Dsite, based on eqs 16 and 17, is questionable. Indeed they are very different (8.65 × 10-9 and (4.05 ( 0.13) × 10-9 cm2/s, respectively) from the published values for Kval+ (1-1.9) × 10-8 cm2/s)12,17,25 and tetraphenylborate (TPB-, 0.29 × 10-8 cm2/s).17 In the case of eq 16, the ion pair formation constant published by Armstrong21 (β ) (7.14 ( 1.0) × 106 cm3/mol) has been used to calculate DKval+ + Dsite. On the other hand, the good linear relationship in Figure 5 indicates that such analysis is practically useful to determine the concentration of ionic sites in ion-selective membranes. When eq 15 is fitted to the experimental data (Rohm vs Csite), both ion pair formation constant and the sum of the diffusion coefficients can be determined at the same time. However, the reliability of the values giving the best fit (β ) (1.57 ( 0.41) × (25) Thoma, A. P.; Viviani-Naurer, A.; Arvanitis, S.; Morf, W. E.; Simon, W. Anal. Chem. 1977, 49, 1567.

105 cm3/mol and Dsite + DKval+ ) (4.7 ( 0.2) × 10-9 cm2/s) remains questionable; e.g., the ion pair formation constant determined by this curve fitting is ∼50 times smaller compared to the value of Armstrong (β ) 7.14 × 106 cm3/mol).21 According to our data, we find that the calculated diffusion coefficient values are in fair agreement with the literature value for the diffusion coefficient of the TPB-, suggesting that the flux of Kval+ and TPB- is determined by the slower moving TPB-. Note that the potential profile across the membrane is not linear when the concentration profiles of the sites are tilted. It is logarithmic and depends on the coupled diffusion coefficient where 1/D ) 1/Dsites + 1/Dval. We tested the applicability of this chronoamperometric method to microfabricated sensors using screen-printed, planar sensors coated with a conventionally formulated PVC membrane (66% DOS, 33% PVC, 1% valinomycin, 48 mol % KTpClPB). As seen in Figure 6, the characteristic features of the current transients for mobile-site membranes remained the same even though the geometrical arrangement of the experiment was completely different. This was also true for membranes placed inside conventional ISE bodies. From the initial current and break time of these curves, we determined the concentrations of KTpClPB and valinomycin using the calibration plots of Figure 4A and 5). The results were in reasonable ((10%) agreement with the concentrations known from the membrane formulation. The uncertainty is partly related to the uncertainty in the estimation of the “active” surface area of the sensing membrane span into the Philips electrode body or cast over the screen-printed sensor. For evaluating the ionophore and KTpClPB concentrations in the membrane of the screen-printed sensor, the area in contact with the inner Ag/AgCl electrode was used. The membrane area spread over the insulating blue glaze material outside the sensor well was not considered. We were also concerned about how this measurement to assess membrane component loss might affect the calibration of the sensor. Calibration of the sensor before current polarization gave a Nernstian response. After current polarization and allowing the membrane to relax (i.e., leaving the sensor at open circuit) Analytical Chemistry, Vol. 73, No. 19, October 1, 2001

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for 1.5 h, the calibration curve was also Nernstian but the intercept was slightly different (less than 10 mV) from the prepolarization calibration curve. CONCLUSIONS A chronoamperometric method and theoretically derived equations were used to estimate the ionophore and mobile-site concentrations in plasticized PVC-based ion-selective membranes. The model was confirmed by the close to perfect correlation between and the characteristic break time (τ) in the chronoamperometric transients and the free ionophore concentration. Strong and weak (negligible) ion pair formation were considered by correlating the initial membrane resistance (Rohm) and the reciprocal value of either the site concentration or the square root of site concentration. Ion pair formation constant and the membrane diffusion coefficients were determined for PVC/DOS membranes. The power of the method was demonstrated by

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determining the free ionophore and site concentrations in microfabricated, planar, and commercially available macroelectrodes of very different geometries using the calibration curves determined under optimized laboratory conditions. It was proved that the method could be utilized with appropriate accuracy when the surface area and the membrane thickness of the studied sensor were known. With respect to practical applications, it is very encouraging that the electrodes have Nernstian calibration shortly after the chronoamperometric test. The determination of residual lifetime of implanted ion sensors or those used in continuous clinical analyzers becomes conceivable by tracking the gradual loss of membrane ingredients in time.

Received for review January 5, 2001. Accepted July 20, 2001. AC010007E