Effect of Lipophilic Ion-Exchanger Leaching on the Detection Limit of

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Anal. Chem. 2001, 73, 5582-5589

Effect of Lipophilic Ion-Exchanger Leaching on the Detection Limit of Carrier-Based Ion-Selective Electrodes Martin Telting-Diaz and Eric Bakker*

Department of Chemistry, Auburn University, Auburn, Alabama 36849

The equilibrium partitioning of lipophilic ion-exchanger salts from ion-selective polymeric membrane electrodes (ISEs) and its possible effect on the lower detection limit of these sensors is described. Predictions are made on the basis of various parameters, including the knowledge of tetraphenylborate potassium salt partitioning constants, the selectivity of ionophore-free ion-exchanger membranes, and ionophore stability constants in the membrane. Ion-exchanger lipophilicities are significantly increased if the membrane contains an ionophore that strongly binds the primary ion. Predicted detection limits are on the order of 10-5-10-8 M for ionophore-free membranes, and may reach levels as low as 10-18 M with adequate ionophores in the membrane. Experiments are performed for well-described lead-selective membranes containing different tetraphenylborate derivatives, and detection limits appear to be independent of the ionexchanger used. However, they are much higher if a more hydrophilic carborane cation-exchanger is incorporated in the membrane. The first finding confirms recent theory, which states that transmembrane ion fluxes, given by a small level of ion-exchange at the sample side by interfering ions, normally dictate the detection limit of these sensing systems. Predicted detection limits on the basis of ion-exchanger leaching alone are here listed for a number of analytically relevant cases. For potassiumselective electrodes containing BME-44 and tetraphenylborate as ion-exchanger, the experimental detection limits are in agreement with predicted values. These results suggest that the detection limit of many current ISEs for ultratrace level analysis are, in optimal cases, dictated by transmembrane ion fluxes; however, because improved chemical solutions are being developed to reduce such effects, simple ion-exchanger partitioning may indeed become an important mechanism that can give higher detection limits than practically desired, and should not be ruled out. Recent insights into the basic processes that govern the lower detection limit of ion-selective electrodes (ISEs) has allowed one to control the ion release at the surface of sensing membranes more strictly.1-6 These studies showed that elevated concentra(1) Ceresa, A.; Bakker, E.; Hattendorf, B.; Gu ¨ nther, D.; Pretsch, E. Anal. Chem. 2001, 72, 343.

5582 Analytical Chemistry, Vol. 73, No. 22, November 15, 2001

tions of ions at the sample-membrane phase boundary preclude electrodes from registering minute concentration changes in the bulk of highly diluted samples. Through careful planning of the sensing membrane and inner filling solution, various parameters minimizing transmembrane ion fluxes have been optimized.1 These zero-current ion fluxes are normally caused by a nonsymmetrical exchange of primary ions at both interfaces by interfering ions, which leads to counterdiffusion fluxes across the membrane that may concentration polarize the contacting aqueous solution. This optimization has led to a dramatic improvement in the detection limit of ISEs and to an improved understanding of these important processes. Recently, low-detection-limit measurements have been reported with potentiometric sensors for lead,7 cadmium,8 calcium,5 and alkali metals.9 Lipophilic mobile ion-exchanger sites of the tetraphenylborate type (see Figure 1) play a key role as added components of cationselective membranes.10 Their main function is to render the ionselective membrane permselective (in order to observe Nernstian response slopes), to optimize sensing selectivity (by defining the ratio of complexed to uncomplexed ionophore concentration in the membrane), and to reduce the bulk membrane impedance. Still, there is a valid concern that such ion-exchanger sites may leach out of the membrane. This process may in principle limit the lifetime of such sensors,11 but it also constitutes a limiting factor in dictating the lower detection limit of ISEs. Indeed, at the detection limit and in the absence of transmembrane counterdiffusion fluxes, the concentration of primary ions at the membrane phase boundary is ultimately given by the leaching of ion-exchanger additives, since the leaching process is described by a coextraction process of the ion-exchanger and its counterion. These same arguments apply also to the anionic impurity sites present in today’s membrane materials, especially poly(vinyl chloride). Although some information about their chemical (2) Mathison, S.; Bakker, E. Anal. Chem. 1998, 70, 303. (3) Sokalski, T.; Ceresa, A.; Zwickl, T.; Pretsch, E. J. Am. Chem. Soc. 1997, 119, 11347. (4) Sokalski, T.; Zwickl, T.; Bakker, E.; Pretsch, E. Anal. Chem. 1999, 71, 1204. (5) Sokalski, T.; Ceresa, A.; Fibbioli, M.; Zwickl, T.; Bakker, E.; Pretsch, E. Anal. Chem. 1999, 71, 1210. (6) Lindner, E.; Gyurcsa´nyi, R. E.; Buck, R. P. Electroanalysis 1999, 11, 695. (7) Ceresa, A.; Pretsch, E. Anal. Chim. Acta 1999, 395, 41. (8) Ion, A. C.; Bakker, E.; Pretsch, E. Anal. Chim. Acta 2001, 440, 71. (9) Qin, W.; Zwickl, T.; Pretsch, E. Anal. Chem. 2000, 72, 3236. (10) Bakker, E.; Bu ¨ hlmann, P.; Pretsch, E. Chem. Rev. 1997, 97, 3083. (11) Bakker, E.; Pretsch, E. Anal. Chim. Acta 1995, 309, 7. 10.1021/ac010526h CCC: $20.00

© 2001 American Chemical Society Published on Web 10/19/2001

Figure 1. Structures of the tetraphenylborate derivatives TPB(tetraphenylborate), TpClPB- (tetrakis(p-chlorophenyl)borate), and TFPB- (tetrakis-[3,5-bis(trifluoromethyl)phenylborate]). Lipophilicities increase in this sequence (see Table 1).

nature12 and approximate concentration13,14 is known, it is more difficult to quantify the leaching behavior from such impurities, especially since their concentration is much smaller and may vary greatly. For these reasons, this paper focuses on the behavior of purposely added lipophilic ion exchangers. Experimental evidence shows that a considerable amount of the less lipophilic derivative, that is, tetraphenylborate (TPB-) is quite rapidly lost when ion carrier-free PVC membranes are first contacted with water.11 Moreover, it has been observed that the detection limit of ionophore-free ion-exchanger membranes is directly dependent on the structure of the tetraphenylborate salt used, with more lipophilic analogues yielding lower detection limits.15 However, it has been shown that the presence of a selective ionophore renders the ion-exchanger much more lipophilic, because most of the counterions of the tetraphenylborates are in the complexed form.11 Partitioning of the salt into the aqueous phase is, thus, greatly reduced. A theoretical description that directly quantifies the lipophilicity behavior of tetraphenylborates in the sensing membrane has been published with the aim of describing the lifetime of such ion sensors.11 This description takes into consideration not only the structure of the anion, as is commonly the case with lipophilicity determined via thinlayer chromatography, for example, for neutral carriers and plasticizers,16 but it encompasses also the coextraction equilibrium of the tetraphenylborate salt and the stability constant of the cation-ligand complex in the membrane. In that work, these parameters were accounted for by performing extraction studies on thin polymeric films.11 Today, stability constants of ionophore complexes in the membrane phase are available from a number of experimental (12) Ye, Q.; Horvai, G.; To´th, A.; Berto´ti, I.; Botreau, M.; Duc, T. M. Anal. Chem. 1998, 70, 4241. (13) Na¨gele, M.; Pretsch, E. Mikrochim. Acta 1995, 121, 269. (14) Qin, Y.; Bakker, E. Anal. Chem. 2001, 73, 4262. (15) Zhang, G. H.; Imato, T.; Asano, Y.; Sonoda, T.; Kobayashi, H.; Ishibashi, N. Anal. Chem. 1990, 62, 1644. (16) Dinten, O.; Spichiger, U. E.; Chaniotakis, N.; Gehrig, P.; Rusterholz, B.; Morf, W. E.; Simon, W. Anal. Chem. 1991, 63, 596.

Figure 2. Mechanism of lipophilic ion-exchanger R- leaching from the membrane into the sample phase, giving rise to an elevated concentration at the membrane phase boundary (cR) (see also eq 15). Partitioning of R- is accompanied by the coextraction of its countercation, which may define the detection limit of the sensor. Other symbols shown are d (membrane thickness) and δ (Nernst diffusion layer thickness).

methods that have recently emerged.7,17-20 Here, this information is directly used to estimate the extent of partitioning of tetraphenylborates salts and the associated predicted detection limits for practical sensing systems. The results define the ultimate low detection limit of ion-selective electrodes containing such mobile ion-exchanger sites. THEORY The partitioning model described here is similar to the one used earlier to describe the lifetime of ionophore-based ion sensors as limited by ion-exchanger leaching effects.11 In contrast to earlier work, it relates ion-exchanger leaching directly to the expected detection limit if other processes are absent and makes use of directly determined complex formation constants and ionexchanger selectivities. Essentially, it is assumed here that (1) concentrations can be used instead of activities, (2) ion pairing in the membrane phase is inconsequential, (3) ionophores form complexes of one fixed stoichiometry, (4) leaching of ion-exchanger is relatively slow, and its organic phase boundary concentrations are equal to their initial bulk values (see Figure 2). The salt partitioning of lipophilic cation-exchanger R- is described with the following coextraction equilibrium constant

KIRz )

( )

[Iz+] [R-] cI cR

z

(1)

where cR and cI are sample concentrations of R- and the primary ion Iz+ (with charge z) and brackets denote membrane concentrations. At the detection limit, the only source of primary ions at the membrane phase boundary is given by leaching of ionexchanger salt from the membrane (see Figure 2). In the absence (17) Qin, Y.; Mi, Y.; Bakker, E. Anal. Chim. Acta 2000, 421, 207. (18) Mi, Y.; Bakker, E. Anal. Chem. 1999, 71, 5279. (19) Bakker, E.; Willer, M.; Lerchi, M.; Seiler, K.; Pretsch, E. Anal. Chem. 1994, 66, 516. (20) Bakker, E.; Pretsch, E. Anal. Chem. 1998, 70, 295.

Analytical Chemistry, Vol. 73, No. 22, November 15, 2001

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of chelators in the sample, the following relationship may hold at the detection limit.

cR ) zcI(DL)

(2)

Therefore, the detection limit cI is given by eliminating cR from combining eqs 1 and 2, and solving the result for cI to give

log cI(DL) )

[Iz+][R-]z 1 log z+1 z zK

(4)

[Iz+][L]n

In addition, the ionophore mass balance is given as

LT ) n[ILz+ n ] + [L]

(5)

where LT is the total ionophore concentration in the membrane, and [ILz+ n ] and [L] are the membrane concentrations of complexed and free ionophore, respectively. It is here assumed that if an excess of ionophore is present, eq 5 can be approximated by LT ) [L]. The charge balance for the membrane phase is written as -

[R ] )

z[ILz+ n ]

z+

+ z[I ]

(6)

Elimination of [ILz+ n ] in eqs 5 and 6, and solving the result for [Iz+] gives

[Iz+] ) [R-]/{z + zβILLTn}

(7)

Inserting this result into eq 3 explicitly describes the detection limit as a function of the membrane concentrations, ion-exchanger salt partitioning constant, and ionophore complex formation constant.

log cI(DL) )

[R-]z+1 1 log z+1 z+1 z KIRz(1 + βILLTn)

(8)

Each of the listed parameters (KIRz and βIL) is experimentally accessible. In practice, ion-exchanger salt lipophilicities (eq 1) are conveniently reported for one specific counterion, in this case, potassium.

KKR )

[K+] [R-] cK cR

(9)

The lipophilicity for a salt containing any other counterion can be estimated from the potentiometric selectivity coefficient of a membrane containing the ion exchanger R-. This selectivity 5584

Analytical Chemistry, Vol. 73, No. 22, November 15, 2001

[R-]1-z z

(10)

which has been derived on the basis of earlier work by Meier et 23 al.22 In eq 10, Kpot I,K is the unbiased selectivity coefficient, and KI,K is the ion-exchange constant.

KI,K )

In the membrane phase, the primary ion [Iz+] may be complexed by an ionophore L, with the stability constant.

[ILz+ n ]

Kpot I,K ) KI,K

(3)

IRz

βIL )

coefficient, Kpot I,K , is described by (see eq 42 of ref 21)

( )

[K+] [Iz+] cK cI

z

(11)

Therefore, the partitioning constant for any salt IRz can be determined on the basis of a known KKR value (with potassium as counterion) and the selectivity coefficient Kpot I,K for the ionophore-free ion-exchanger membrane. Therefore, combination of eqs 1, 9, and 10 gives

KI,Kz )

KKRz KKRz [R-]1-z ) pot KI,K z K

(12)

I,K

This equation makes it possible to calculate ion-exchanger salt lipophilicities for a number of counterions. These values, together with known complex formation constants and membrane compositions, may be inserted into eq 8 to obtain predicted detection limits on the basis of the ion-exchanger leaching mechanism.

log cI(DL) )

- 2 Kpot 1 I,K [R ] log z z+1 z KKRz(1 + βILLTn)

(13)

This relationship directly compares to the optimum lower detection limit on the basis of zero current transmembrane counterion fluxes, which is written for primary and interfering ions of the same charge as1

log cI(DL) )

1 1 log Kpot c (aq)q[R-] 2 z I,J J

(

)

(14)

where q incorporates the ratio of the diffusion coefficients and Nernst diffusion layer thicknesses in both phases, and Kpot I,J is the selectivity coefficient of primary ion I over interfering ion J. Both predicted lower detection limits are based on different mechanisms. Whichever formalism predicts a higher detection limit is expected to be the limiting factor. EXPERIMENTAL SECTION Reagents. All solutions were prepared with freshly deionized water (18 MΩ cm specific resistance) obtained using a Nanopure Millipore water purification system. Salts and acids of the highest purity available were used. Chloride salts of Na+, K+, Ca2+, and Mg2+ and the nitrate salts of Ag+, Pb2+, Cd2+, and Cu2+ were all (21) Bakker, E.; Meruva, R. K.; Pretsch, E.; Meyerhoff, M. E. Anal. Chem. 1994, 66, 3021. (22) Meier, P. C.; Morf, W. E.; La¨ubli, M.; Simon, W. Anal. Chim. Acta 1984, 156, 1. (23) Bakker, E.; Pretsch, E.; Bu ¨ hlmann, P. Anal. Chem. 2000, 72, 1127.

puriss p.a. from Fluka (Milwaukee, WI). Poly(vinyl chloride) (PVC), 2-nitrophenyl octyl ether (2-NPOE), bis(2-ethylhexyl) sebacate(DOS), 4-tert-butylcalix[4]arene-tetrakis(N,N-dimethylthioacetamide) (lead ionophore IV, Pb-1), BME-44 [2-dodecyl-2methyl-1,3-propanediyl bis[N-[5′-nitro(benzo-15-crown-5)-4′-yl]carbamate]] (potassium ionophore III, K-2), sodium tetrakis[3,5bis(trifluoromethyl)phenylborate] (NaTFPB), potassium tetrakis(pchlorophenyl)borate (KTpClPB), sodium tetraphenyl borate (NaTPB), and tetrahydrofuran were of Selectophore quality (Fluka, Buchs, Switzerland). The 11-[(-butylpentyl)oxy]-11-oxoundecyl-4-{[9-(dimethylamino)5H-benzi[a]phenoxazin-5yl-idene] aminobenzoate (ETH 5418, chromoionophore VII), disodium nitrilotriacetic acid (Na2NTA), tris(hydroxymethyl)aminomethane (TRIS), and the Dowex Monosphere C-350 resin were also purchased from Fluka. The cesium carborane salt was from Strem Chemicals (Newburyport, MA). Membrane Preparation and Measurements. Unless otherwise indicated, ISE membranes of ca. 200 µm thickness were prepared by pouring a solution of ca. 240 mg of membrane components, dissolved in 2.5 mL of THF, into a glass ring (28.5 mm i.d.) affixed onto a glass plate. After allowing overnight solvent evaporation, 6-mm-diameter membrane disks were cut from the parent membrane and glued to the end of plasticized PVC tubetype electrodes with a THF/PVC slurry. The stability constants (βPbL) of the lead ionophore IV (Pb-1) in DOS and 2-NPOE plasticized membranes were determined by the sandwich method technique reported earlier.18 Both the Pb-1 membranes and the lipophilic additive NaTFPB blank membranes contained 4.7-5.0 mmol kg-1, 65.5-66.5 wt % plasticizer 2-NPOE or DOS and 32.033.0 wt % PVC. These measurements were carried out using Philips electrode bodies in solutions containing 10-3 M Pb(NO3)2 with a 10-4 M HNO3 background. Selectivity coefficients for ion-exchanger membranes incorporating the lipophilic derivative NaTFPB were all determined from response curves obtained in the 10-4-10-2 M range of the discriminating ions. The solutions were measured separately from the most discriminated to the least discriminated ion.24 Calculations were performed based on readings taken at the 10-2 M concentration level. Detection Limit Measurements. Lead sensing membranes were prepared as indicated above except that ca. 830 mg of membrane components in ∼6 mL THF were poured into 7-cmi.d. glass rings. Batches of four electrodes were prepared from parent membranes, each containing a different lipophilic additive salt. Membrane compositions were as follows: 0.67 mmol kg-1 Pb-1, 0.32 mmol kg-1 lipophilic borate or carborane salt, 0.15 mmol kg-1 Pb(NO3)2 (added as 62 µL of a 1.2 × 10-7 M solution), and 2-NPOE and PVC (2:1 by weight). As recently established,1 the aqueous lead nitrate solution is added to eliminate an additional conditioning process in a more concentrated lead ion solution. Exposure to an extremely dilute (nanomolar) lead nitrate solution would otherwise not be sufficient during conditioning to replace all original sodium counterions of the tetraphenylborate by lead. Electrodes were assembled with internal filling solutions consisting of 10-3 M Na2NTA and 10-4 M Pb(NO3)2 and were adjusted to pH 7.0 with 1 M NaOH. The calculated free Pb2+ activity is 6.9 (24) Bakker, E. Anal. Chem. 1997, 69, 1061.

× 10-9 M.25 All measurements were performed in stirred solutions at ambient temperature (21 ( 0.5 °C) against a Ag/AgCl reference electrode (Metrohm 6.0729.100) in cells of the following type

Ag | AgCl | 1 M KCl | 1 M NH4NO3 | sample || ISE membrane || inner filling solution | 10-3 M KCl | AgCl | Ag The lead electrodes were conditioned for 48 h in a 10-9 M Pb(NO3)2, 10-3 M CaCl2 solution. Calibration curves were obtained by volumetric additions of Pb2+ standards to a freshly prepared 500-mL-volume solution (in polypropylene beakers pretreated with 0.1 M HNO3 for 24 h). The composition of the measurement solution was identical to the conditioning solution, except for the addition of 10-4 M HNO3 prior to initiating measurements. For low-detection-limit measurements of potassium ions, the electrode membranes consisted of 15 mmol kg-1 potassium ionophore III (K-2) and 7 mmol kg-1 NaTPB in PVC/DOS (1:2).9 The internal filling solution of these electrodes consisted of 1 mL of solution containing 0.2 g of Dowex resin in a 10-3 M NaCl background. This provides a ca. 5.5 × 10-7 M K+ concentration, as recently reported.9 Electrodes were conditioned for 24 h in 10-6 M KCl, after which time they were transferred to 500 mL of pure water for titration with dilute KCl solutions. The instrumentation used to acquire potentiometric data has been described earlier.26 Typical electrode responses were 1020 min for concentrations below 10-7 M and much shorter as concentrations increased. All EMF values were corrected for liquid junction potentials using the Henderson formalism. Single ion activities were calculated according to the Debye-Hu¨ckel approximation.27 Leaching Experiments. Optode membranes of ca. 2 µm thickness containing either NPOE or DOS as a plasticizer and PVC (2:1 by weight), the tetraphenylborate salt (7.5 mmol kg-1), and the chromoionophore ETH 5418 (7.5 mmol kg-1, 0.37 wt %) were spin-cast onto quartz glass plates and mounted into a custombuilt flow-through cell28 placed in a Hewlett-Packard 8452A photodiode array spectrophotometer. After equilibrating the membranes with pure water for at least 10 min, a 5 × 10-3 M KOH solution, when measuring 2-NPOE-based membranes, or 2 mM KCl buffered to pH 8.5 with Tris-HCl for the KTpClPB/ DOS membrane was pumped at a flow rate of 1.5 mL min-1. Absorbance data were acquired continuously for periods of up to 48 h for the most lipophilic NaTFPB additive, but shorter times were needed for the more hydrophilic additives. The extraction constants KKR for each tetraphenylborate (see eq 9) were calculated from the protonation changes incurred by the chromoionophore over time,11 which was related to the residual tetraphenylborate concentration in the membrane by considering the ion-exchange equilibrium constant. The initial rate of decay was related to the lipophilicity pR with the following equation, which is based on the mechanism outlined in Figure 2 (25) Sille´n, L. G.; Martell, A. E. Stability Constants of Metal-Ion Complexes; Special Publication No. 17; The Chemical Society: London, 1964. (26) Bakker, E. J. Electrochem. Soc. 1996, 143, L83. (27) Meier, P. C. Anal. Chim. Acta 1982, 136, 363. (28) Morf, W. E.; Seiler, K.; Rusterholz, B.; Simon, W. Anal. Chem. 1990, 62, 738.

Analytical Chemistry, Vol. 73, No. 22, November 15, 2001

5585

ln

[R-]T(org,0) -

[R ]T(org,t)

)

Daq t pR-dδ

(15)

Table 1. Potassium Tetraphenylborate Coextraction Constants between Water and Plasticized PVC log KKR ion-exchanger salt

PVC/NPOE

PVC/DOSa

KTPB KTpClPB KTFPB

4.9 6.0 9.0

4.6 5.8 8.4

[R-]T(org,0)

and [R-]T(org,t) are the total concentration additive R- in the membrane phase at time t ) 0

where of the anionic and t > 0; d is the membrane thickness; δ the thickness of the Nernstian boundary layer contacting the organic phase; Daq, the diffusion coefficient of R- in the aqueous phase; and pR- is the lipophilicity of R-, that is, the equilibrium partition coefficient between the aqueous and the organic phases ([R-]/cR). The lipophilicity pR was obtained from a given experiment by eliminating the unknown constant Daq/(dδ) from an otherwise identical leaching experiment of KTpClPB from PVC/DOS, for which case the lipophilicity value is known.11 The coextraction constant (eq 9) was then calculated by inserting the initial concentration of potassium in the membrane, which is obtained from the extent of deprotonation of the indicator upon exposure to the sample solution and the known potassium activity in the sample. RESULTS AND DISCUSSION Simple partitioning of lipophilic ion-exchangers from the ionselective membrane phase into the sample solution may in principle dictate the lower detection limit by co-extracting the hydrophilic counterion into the sample. In dilute solutions, such a process would increase the local primary ion activities at the membrane surface relative to the sample bulk. Since ion-selective electrode membranes are sensitive to phase-boundary activity changes, this process could in principle dictate the lower detection limit. Lipophilic ion-exchanger salt partitioning is a simple equilibrium process, and the theory developed above shows that it is relatively straightforward to model this process. Nonetheless, the extent of partitioning depends not only on the lipophilicity and membrane concentration of the ion-exchanger, but also on that of the counterion. For electroneutrality reasons, the loss of an ion-exchanger molecule must be accompanied by the concomitant loss of the counterion. The uncomplexed concentration and type of this counterion also dictates the extent of partitioning. If an ionophore is present in the membrane that complexes the counterion significantly, the uncomplexed ion concentration is dramatically decreased, which decreases the extent of ionexchanger leaching. As shown in eq 8, this process can be adequately modeled with the coextraction constant of the (uncomplexed) ion-exchanger salt in question, the complex formation constant between ionophore and primary ion in the membrane, and the known membrane composition. It would be experimentally cumbersome to directly determine the coextraction constant for any ion-exchanger salt, since data are needed for any of potentially over a dozen different counterions. As suggested in previous work,11 ion-exchanger salt coextraction constants are directly determined only with a standard counterion, in this case, potassium. For hydrophilic tetraphenylborate salts, these KKR values were originally determined by direct two-phase extraction followed by spectrophotometric detection. The more lipophilic derivatives were characterized by monitoring the leaching behavior from thin polymeric films in continuous flow-through experiments. The literature values de5586 Analytical Chemistry, Vol. 73, No. 22, November 15, 2001

a

Data for PVC/DOS are from ref 11.

Table 2. Experimental Selectivity Coefficients log Kpot I,K for Ionophore-Free Membranes Containing NaTFPB as Lipophilic Ion-Exchanger PVC-DOSa

PVC-NPOE ion I

log Kpot I,K

slope [mV]

log Kpot I,K

Na+ K+ H+ Ag+ Mg2+ Ca2+ Pb2+ Cd2+ Cu2+

1.23 ( 0.04 0.0 1.5 ( 0.1 -0.21 ( 0.07 0.8 ( 0.1 0.5 ( 0.2 0.6 ( 0.1 1.15 ( 0.07 1.13 ( 0.07

48 ( 2 55 ( 1 51 ( 2 56 ( 1 25 ( 2 27 ( 3 30 ( 2 30 ( 1 31 ( 1

0.45 0.0 -0.35 0.45 1.33 1.30 1.18 1.33 1.30

a

Data calculated from selectivity coefficients given in ref 7.

termined for PVC/DOS membranes are listed in Table 1. Here, similar leaching experiments were performed to characterize the coextraction constants for more polar PVC/NPOE membranes, which is the other widely used membrane formulation, especially for the detection of divalent ions. Simple partitioning experiments were difficult to perform because of the strong UV absorbance characteristics of NPOE, which also partitions into the aqueous phase to some extent. Leaching experiments were performed using different tetraphenylborate derivatives (NaTFPB, KTpClPB, and NaTPB; see Figure 1) dissolved in the polymeric membrane together with a molar equivalent of the lipophilic H+ indicator ETH 5418. Upon exposure to 0.005 M KOH, ∼20% of the indicator became deprotonated as a result of the extraction of potassium into the film. The potassium tetraphenylborate salt was continuously leached from the membrane in flow-through experiments, which were standardized to the known leaching behavior of KTpClPB from PVC/DOS. The least lipophilic KTPB leached from the membrane in fractions of minutes, KTpClPB in a matter of 1-2 h, and KTFPB showed very little discernible leaching behavior within the 48 h experiment. The data were fitted to established theory by using eq 15, which is based on the mechanism outlined in Figure 2. The results are shown in Table 1. Evidently, all of the obtained coextraction constants are somewhat larger for PVC/NPOE than for PVC/DOS, by 0.2 to 0.4 orders of magnitude. This may appear surprising at first, considering the difference in polarity of the two plasticizers, but could be explained by additional π-π interactions with the aromatic plasticizer NPOE. The lipophilicity data in Table 1 also indicate that the known limited solubility of KTPB in water (1.5 × 10-4 M29) is never problematic in this two-phase partitioning (29) Siska, E. Magy. Kem. Foly. 1976, 82, 275.

Figure 3. Structures of electrically neutral ionophores considered in this work.

experiment. A PVC/DOS membrane containing 5 mmol kg-1 of KTPB, for example, will give an equilibrium KTPB concentration of 2 × 10-5 M in the aqueous sample, which is significantly below the solubility limit of this salt. To obtain useful information on expected detection limits due to lipophilic ion-exchanger leaching from the membrane, extraction constants with other counterions are needed (eq 8). For this purpose, the KKR values shown in Table 1 need to be recalculated for the chosen counterion. This is accomplished by determining the selectivity coefficients for potassium over any other ion for an ionophore-free ion-exchanger membrane. According to theory (eq 10), the selectivity coefficient is directly related to the

lipophilicity of the ions of interest. These relationships are used to conveniently calculate the coextraction constant for any desired ion-exchanger salt (eq 12). Ion-exchanger membrane selectivities were determined for PVC/NPOE membranes containing the ion-exchanger TFPB-. Measurements were performed as recently recommended23 by acquiring separate solution calibration curves for each of the cations of interest. The selectivity data are shown in Table 2, together with literature values for PVC/DOS.7 These data may now be combined with the coextraction constants shown in Table 1 to obtain the desired coextraction constants for any of the listed counterions. Analytical Chemistry, Vol. 73, No. 22, November 15, 2001

5587

Table 3. Experimental Complex Formation Constants for Different Ionophoresa with Indicated Complex Stoichiometries, n, and Predicted Detection Limits if Tetraphenylborate Leaching Is the Predominant Effect PVC-DOS ionophore K+ (no ionophore) K-1 K-2 K-3 Na+ (no ionophore) Na-1 Na-2 Na-3 Na-4 Mg2+ (no ionophore) Mg-1 Mg-2 Ca2+ (no ionophore) Ca-1 Ca-2 Ca-3 Ca-4 Ag+ (no ionophore) Ag-1 Pb2+ (no ionophore) Pb-1

n

log βILn

1 1 1

10.1 7.8 6.9

2 2 1 1

7.7 8.8 6.6 7.7

3 2

9.7 7.3

2 3 3 2

19.7 25.5 22.1 8.7

2

12.4

1

15.8

PVC-NPOE

TFPB-

TpClPB-

TPB-

-6.6 -10.6 -9.5 -9.0 -6.3 -8.2 -8.7 -8.6 -9.2 -8.5 -9.7 -9.6 -8.5 -13.7 -15.0 -13.9 -10.1 -6.3 -10.5 -8.5 -13.1

-5.2 -9.3 -8.1 -7.6 -5.0 -6.8 -7.4 -7.3 -7.8 -6.7 -7.9 -7.8 -6.7 -11.9 -13.2 -12.1 -8.3 -5.0 -9.2 -6.7 -11.3

-4.6 -8.7 -7.5 -7.0 -4.4 -6.2 -6.8 -6.7 -7.2 -5.9 -7.1 -7.0 -5.9 -11.1 -12.4 -11.3 -7.5 -4.4 -8.6 -5.9 -10.5

log βILn 11.6 10.0 10.2 9.4 10.9 9.2 10.3 13.8 12.2 24.5 29.2 27.4 12.9

21.3

TFPB-

TpClPB-

TPB-

-6.8 -11.6 -10.8 -10.9 -6.2 -8.9 -9.7 -9.8 -10.4 -6.4 -10.3 -10.5 -6.6 -16.8 -18.2 -17.3 -11.0 -6.9

-5.3 -10.1 -9.3 -9.4 -4.7 -7.4 -8.2 -8.3 -8.9 -4.9 -8.8 -9.0 -5.1 -15.3 -16.7 -15.8 -9.5 -5.4

-4.8 -9.6 -8.8 -8.9 -4.2 -6.9 -7.6 -7.8 -8.3 -4.4 -8.3 -8.5 -4.5 -14.8 -16.1 -15.2 -9.0 -4.9

-6.5 -16.2

-5.0 -14.7

-4.5 -14.1

a Complex formation constants for potassium, sodium, magnesium, and calcium ionophores14 for Ag-118 are from the indicated references. The values shown for Pb-1 are from this work.

Fortunately, a number of convenient methods to determine the complex formation constants of ion-ionophore complexes in the membrane phase have been described in recent years, including (1) the use of absorbance measurement on thin polymeric films containing extremely selective reference indicator ionophores, (2) potentiometric measurements of similar twoionophore membranes, (3) potentiometric-concentration-polarized two-layer sandwich membranes without the need for any reference ionophore, and (4) potentiometric selectivity measurements relative to a reference ion that is assumed not to complex the ionophore. All of these methods have been shown to yield very similar formation constants, and data for over 20 ionophores are so far available. Here, the sandwich method, 3, was used to determine the stability constant of the successful lead ionophore IV (Pb-1) in ion-selective membranes. For PVC/DOS, the sandwich membrane potential was found to be 559 ( 6 mV, which resulted in a logarithmic complex formation constant of 21.34 ( 0.3. This ionophore was also characterized in PVC/DOS membranes, yielding 390 ( 15 mV, which translated into log βIL ) 15.8 ( 0.3, which is identical to the value reported by Ceresa and Pretsch.7 The results, together with literature data for various relevant ionophores (see Figure 3), are shown in Table 3. The separate experiments discussed above yield all of the necessary parameters to adequately predict the lower detection limit of polymeric membrane cation-selective electrodes if ionexchanger leaching is the predominant effect. This process is here modeled with eq 13. Table 3 shows expected logarithmic detection limits based on this mechanism, calculated using eq 13 and the data presented in Tables 1 and Table 2, as a function of the ionophore complex formation constant in the membrane. The membranes are assumed to contain 10 mmol kg-1 ionophore and 5 mmol kg-1 lipophilic cation exchanger. Clearly, the expected detection limits improve significantly with increasing formation 5588 Analytical Chemistry, Vol. 73, No. 22, November 15, 2001

constants. In general, lower detection limits range from about 10-5 M for an ionophore-free ion-exchanger system to nearly 10-18 M for a divalent ion-selective electrode with an ionophore giving very stable complexes. These theoretical results show a great variability of the extent of leaching from ion-selective membranes, which is primarily dependent on the ionophore complex formation constant. Ionophore-fee ion-exchanger membranes are much more likely to suffer from a high detection limit, but the limits are still low if the most lipophilic ion-exchanger, TFPB-, is used. Membranes containing an ionophore that exhibit high complex formation constants are predicted to have extremely low detection limits, far beyond the limits that appear to be experimentally achievable. This theoretical result is reassuring and suggests that tetraphenylborate leaching is today, often not a limiting factor if TFPB- is used as the ion-exchanger. A series of lead-selective electrodes based on the ionophore Pb-1 (see Figure 3) containing the different tetraphenylborate derivatives (Figure 1) and the carborane anion were constructed and tested in terms of their low detection limits. Recently, lead electrodes of this general composition were successfully used for the subnanomolar detection of lead in samples of drinking water and represented an adequate test bed to assess whether the detection limit was given by transmembrane counterdiffusion fluxes, as originally assumed, or by tetraphenylborate leaching. The original paper1 used an excess of an inert lipophilic salt, ETH 500, to decrease the activity coefficients for lead in the membrane phase, which is known to increase selectivity.30 To evaluate the possible effects of different tetraphenylborates, it was not possible to use ETH 500, because the common counteranion of this salt is TpClPB- (see Figure 1), which could bias the detection limit by (30) Na¨gele, M.; Mi, Y.; Bakker, E.; Pretsch, E. Anal. Chem. 1998, 70, 1686.

Figure 4. Response functions for four lead-selective electrodes having the same composition, but with the indicated lipophilic ionexchanger salts. The detection limits are essentially identical for membranes containing tetraphenylborates (see Figure 1), but are much higher with the less lipophilic carborane anion.

leaching. Otherwise, the compositions of the membrane and inner electrolyte, as well as conditioning and measuring procedures were adopted essentially unaltered. The calibration curves for the different electrode membranes containing different ion-exchangers are presented in Figure 4. All detection limits for membranes containing the tetraphenylborates are found to be identical, even with TPB- as the ion-exchanger. This result indicates that counterion fluxes, as originally suggested, are here indeed responsible for the lower detection limit of these sensors. The experimental results are also in agreement with the data presented in Table 3, which predicts a 10-14 M detection limit for the sensing membrane containing TPB-. Lead-selective electrode membranes containing the icosahedral carborane anion CB11H11- as a weakly coordinating anion were also evaluated.31 The membrane containing the carborane anion showed a significantly higher detection limit, as shown in Figure 4. An analogous thin-film leaching experiment was performed to evaluate the lipophilicity of this anion, and the carborane quantitatively transferred into the aqueous phase upon first contact with water (data not shown). This confirms that the carborane anion is much more hydrophilic than even TPB-, thus leading to a higher detection limit according to the mechanism outlined here. Table 3 suggests that some alkali metal ion-selective electrodes may exhibit relatively high detection limits with weakly complexing ionophores. Pretsch and co-workers have recently reported (31) Jelinek, T.; Baldwin, P.; Scheidt, W. R.; Reed, C. A. Inorg. Chem. 1993, 32, 1982.

that the use of a solid ion-exchanger in the inner filling solution may decrease the detection limit of potassium-selective electrode membranes containing the ionophore BME-44 (K-2) and TFPBdown to 5 × 10-9 M.9 These experiments were repeated here in complete analogy, but with TPB- as the membrane additive. The detection limits for four different electrodes were found to be log aK(DL) ) -7.8 ( 1.0 (1.5 × 10-8 M), which is in agreement with expectations (-7.5, see Table 3). It is fortunate that the lower detection limit is expected to decrease if the ionophore binds strongly to the primary ion (the model presented here) and for membranes that show high selectivities (the counterion diffusion model). According to both models, ionophore-free membranes are expected to show the highest detection limits, which agrees with general knowledge. So far, it appears that traditional membranes with optimized membrane compositions and inner electrolytes show detection limits that can be mostly described with the counterdiffusion model. As experimental solutions will be found to further decrease these fluxes, tetraphenylborate leaching effects, together with the genuine selectivity limitation of such sensors, will likely dictate the lower detection limit of these sensors. According to the theoretical results presented here, these predicted limits can be sufficiently low for true trace level applications of potentiometric ion sensors. CONCLUSIONS The low detection limit of ISEs, as given by tetraphenylborate salt leaching from the membrane, is strongly dependent on the ion-exchanger structure, the charge type and lipophilicity of the primary ion, and the stability of the ion-ionophore complexes in the membrane. It also depends to some extent on the polarity of the plasticizer and the concentrations of the active membrane components. Detection limits are expected to decrease significantly if an ionophore is present that forms stable complexes. This trend goes parallel to the counterdiffusion flux theory, which predicts significantly lower detection limits for membranes that show higher membrane selectivity. In most practical cases with today’s ion-selective electrode membranes, and if the most lipophilic ion-exchangers available are used, the detection limit is expected to be mostly governed by counterdiffusion fluxes, and not by ion-exchanger leaching. This will likely change soon, because novel approaches are being sought to eliminate undesired transmembrane ion fluxes to reach even lower detection limits. ACKNOWLEDGMENT The authors gratefully acknowledge financial support from the National Institutes of Health (GM59716 and GM58589) for this research. Received for review May 8, 2001. Accepted September 7, 2001. AC010526H

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