Anal. Chem. 2003, 75, 6922-6931
Rotating Disk Potentiometry for Inner Solution Optimization of Low-Detection-Limit Ion-Selective Electrodes Aleksandar Radu, Martin Telting-Diaz,† and Eric Bakker*
Department of Chemistry, Auburn University, Auburn, Alabama 36849
The extent of optimization of the lower detection limit of ion-selective electrodes (ISEs) can be assessed with an elegant new method. At the detection limit (i.e., in the absence of primary ions in the sample), one can observe a reproducible change in the membrane potential upon alteration of the aqueous diffusion layer thickness. This stir effect is predicted to depend on the composition of the inner solution, which is known to influence the lower detection limit of the potentiometric sensor dramatically. For an optimized electrode, the stir effect is calculated to be exactly one-half the value of the case when substantial coextraction occurs at the inner membrane side. In contrast, there is no stir effect when substantial ion exchange occurs at the inner membrane side. Consequently, this experimental method can be used to determine how well the inner filling solution has been optimized. A rotating disk electrode was used in this study because it provides adequate control of the aqueous diffusion layer thickness. Various ion-selective membranes with a variety of inner solutions that gave different calculated concentrations of the complex at the inner membrane side were studied to evaluate this principle. They contained the wellexamined silver ionophore O,O′′-bis[2-(methylthio)ethyl]tert-butylcalix[4]arene, the potassium ionophore valinomycin, or the iodide carrier [9]mercuracarborand-3. Stir effects were determined in different background solutions and compared to theoretical expectations. Correlations were good, and the results encourage the use of such stireffect measurements to optimize ISE compositions for real-world applications. The technique was also found to be useful in estimating the level of primary ion impurities in the sample. For an iodide-selective electrode measured in phosphoric acid, for example, apparent iodide impurity levels were calculated as 5 × 10-10 M. For many years, the lower detection limit of polymeric membrane-based ion-selective electrodes (ISEs) was found to be in the micromolar concentration range or even higher.1,2 Lower nominal detection limits were found only with sample solutions where the primary ion activity was kept small with an ion buffer at an otherwise high total ion concentration.3,4 Recently, it was † Present address: Department of Chemistry, Brooklyn CollegesCUNY, Brooklyn, NY 11210. (1) Umezawa, Y. Handbook of Ion-Selective Electrodes: Selectivity Coefficients; CRC Press: Boca Raton, FL, 1990. (2) Buhlmann, P.; Pretsch, E.; Bakker, E. Chem. Rev. 1998, 98, 1593.
6922 Analytical Chemistry, Vol. 75, No. 24, December 15, 2003
established that the lower detection limit is determined by a small flux of primary ions leaching from the membrane into its aqueous surface layer.5-7 A significant lowering of ion fluxes was achieved by utilizing an ion buffer in the inner solution, thus keeping a low activity of primary ions and a relatively high activity of interfering ions.7 Ion-selective electrodes with low detection limits in the submicromolar to picomolar range have been reported so far for Pb2+,8 Ca2+,9 Cd2+,10 Ag+,11 K+,12 Na+,12 I-,13 and ClO4-.13 The practical applicability of ISEs for determining trace levels has been demonstrated by measuring Pb2+ in drinking water and comparing the results to measurements made with ICPMS.8 Clearly, choosing an optimal inner solution composition is currently the most important and perhaps most difficult aspect of developing ISEs with low detection limits. Elevated electrolyte concentrations at the inner side lead to undesired electrolyte transport into the sample. On the other hand, if significant ion exchange occurs at the inner side of the membrane, inward fluxes are induced, siphoning off the primary ions from the sample and thereby inducing their depletion at the sample side of the membrane. Such ISEs exhibit a so-called super-Nernstian response slope with poor practical detection limits as well. For most practical applications, fluxes in either direction should be avoided through close matching of the sample and inner solution in the sense of having similar extents of ion exchange at both sides of the membrane. Several models were developed to calculate the optimal composition of the inner solution,8,11,14,15 and recently, a simplified theory introduced explicit equations in terms of experimentally accessible parameters.11 The latter approach allows one, with good accuracy, to predict the achievable detection limit (3) Morf, W. E.; Kahr, G.; Simon, W. Anal. Chem. 1974, 46, 1538. (4) Morf, W. E. The Principles of Ion-Selective Electrodes and of Membrane Transport; Elsevier: New York, 1981. (5) Gyurcsa´nyi, R. E.; Pergel, E.; Nagy, R.; Kapui, I.; Lan, B. T. T.; To´th, K.; Bitter, I.; Lindner, E. Anal. Chem. 2001, 73, 2104. (6) Mathison, S.; Bakker, E. Anal. Chem. 1998, 70, 303. (7) Sokalski, T.; Ceresa, A.; Zwickl, T.; Pretsch, E. J. Am. Chem. Soc. 1997, 119, 11347. (8) Ceresa, A.; Bakker, E.; Hattendorf, B.; Gunther, D.; Pretsch, E. Anal. Chem. 2001, 73, 343. (9) Sokalski, T.; Ceresa, A.; Fibbioli, M.; Zwickl, T.; Bakker, E.; Pretsch, E. Anal. Chem. 1999, 71, 1210. (10) Ion, A. C.; Bakker, E.; Pretsch, E. Anal. Chim. Acta 2001, 440, 71. (11) Ceresa, A.; Radu, A.; Peper, S.; Bakker, E.; Pretsch, E. Anal. Chem. 2002, 74, 4027. (12) Qin, W.; Zwickl, T.; Pretsch, E. Anal. Chem. 2000, 72, 3236. (13) Malon, A.; Radu, A.; Qin, W.; Qin, Y.; Ceresa, A.; Maj-Zurawska, M.; Bakker, E.; Pretsch, E. Anal. Chem. 2003, 75, 3865. (14) Morf, W. E.; Badertscher, M.; Zwickl, T.; de Rooij, N. F.; Pretsch, E. J. Phys. Chem. B 1999, 103, 11346. (15) Sokalski, T.; Zwickl, T.; Bakker, E.; Pretsch, E. Anal. Chem. 1999, 71, 1204. 10.1021/ac0346961 CCC: $25.00
© 2003 American Chemical Society Published on Web 10/31/2003
for a given membrane composition with known selectivity and a given background electrolyte in the sample. Despite these achievements, calculating the optimal composition of the inner solution is often not practical, likely because unwanted partitioning of other inner solution components can complicate the overall partitioning and diffusion process.10 A dramatic example is the recent development of a cadmium-selective electrode, where the required cadmium activity in the inner solution was found to be about a million fold smaller than the theoretically predicted value.10 Ion-exchange resins have been the only complexing agents found so far that can be used to adequately calculate the optimal inner solution compositions, probably because such resins are unlikely to partition into the membrane phase from the inner solution. Until now, it has also been difficult to judge experimentally whether a given electrode has been properly optimized. A small region of super-Nernstian response slope has often been desirable because it confirmed that the ISE was close to being optimized. For a traditional ISE calibration curve with a Nernstian slope that flattens out at low concentrations, it has so far been impossible to evaluate whether the ISE was properly optimized. So far, the characterization of a series of electrodes with varying inner solutions has therefore been the only reliable means for optimizing the lower detection limit. It has been established that, by stirring a sample with a stirring bar6 or, more effectively, by using a wall jet16 or a rotating electrode configuration,17 detection limits can be improved. The origin of this effect lies in the increased mass transfer of ions from the sensing membrane, which lowers the activity of the primary ion at the phase boundary. Similarly, the ability of a rotating disk electrode to accurately adjust the diffusion layer thickness at the sample side, and hence the mass transfer rate of the analyte, as a function of the rotating speed was used to improve the detection limit of a nonequilibrium polyion-sensitive electrode.18 In this work, the recently established steady-state flux model is applied to show that the inner solution composition has a pronounced effect on the stir effect at the detection limit. With a rotating disk electrode, the potential can be changed predictably as a function of different inner solution compositions through variations in the rotation speed. For the first time, a direct experimental tool is available that can be used to evaluate whether a given ISE is fully optimized in terms of its lower detection limit. THEORY It is well-established that an ion-selective electrode responds ideally to the Nernst equation if no interferences are observed and if the sample activity, aI, is substantially above the detection limit
EM ) E0I +
RT ln aI zIF
(1)
Here, EM represents the observed membrane potential; E0I includes all constant potential contributions; and R, T, zI, and F are the gas constant, the absolute temperature, the charge of primary ion I, and the Faraday constant, respectively. Recent work (16) Pergel, E.; Gyurcsanyi, R. E.; Toth, K.; Lindner, E. Anal. Chem. 2001, 73, 4249. (17) Vigassy, T.; Gyurcsanyi, R.; Pretsch, E. Electroanalysis 2003, 15, 1270. (18) Ye, Q. S.; Meyerhoff, M. E. Anal. Chem. 2001, 73, 332.
has established that the detection limit is normally dictated by two possible processes: (1) thermodynamic ion exchange of the primary ions by interfering ions at the sample side, thereby reducing the primary ion concentration in the membrane, and 2) zero-current concentration polarization at the membrane surface by ion fluxes, thereby biasing the observed potential. In the latter case, eq 1 would normally still be valid but aI, the ion activity at the phase boundary, would be different from the ion activity in the sample bulk. For this second case, a simplified model was developed for ion-selective membranes containing a lipophilic ion exchanger and an electrically neutral ionophore that forms stable complexes of fixed stoichiometry with the primary ion. It assumes that only ion-exchange processes with interfering ions of the same charge sign occur at the membrane-sample side. The interfering ions in the sample are assumed to be much more concentrated than the primary ions and are therefore not subject to concentration polarizations at the membrane side. The inner membrane side contains a fixed concentration of the primary ion-ionophore complex, which is adjusted by the composition of the inner solution of the membrane. For a one-dimensional diffusion problem at steady state, the primary ion concentration gradient can be described as follows
cI - cI,bulk zI+ [ILn ]′ - [ILznI+]
)q)
Dorgδaq Daqδorg
(2)
where cI and cI,bulk are the sample concentrations of the primary ion at the membrane phase boundary and in the sample bulk, respectively; [ILznI+]′ and [ILznI+] are the membrane concentrations of the ion-ionophore complex at the inner and outer membrane sides, respectively; Dorg and Daq are the diffusion coefficients of these species and δorg and δaq the diffusion layer thicknesses of the denoted phases (“org” stands for the membrane phase). These four parameters are combined to give q, as shown in eq 2. At the detection limit, the bulk concentration of the primary ion is zero, and eq 2 reduces to
cI ) q([ILznI+]′ - [ILznI+])
(3)
Equation 3 makes it obvious that a stir effect (a change in δaq) will cause a change in the phase boundary concentration cI if there is a nonzero concentration gradient across the membrane, that is, if [ILznI+]′ - [ILznI+] * 0. This gradient is partly dependent on the concentration of primary ion-ionophore complex at the inner membrane side. As established earlier,8,11 the membrane concentration of the ionophore complex at the sample side is a function of the membrane selectivity, as ion-exchange processes with interfering ions are thermodynamically controlled. It is assumed that coextraction of electrolyte at the sample side is insignificant, which is a reasonable assumption at the low concentrations of primary ions used here. Hence, for interferences of the same charge as the primary ion, one can obtain from the Nikolsky equation and the phase boundary potential11
cI pot cI + KI,J cJ
)
zI[ILznI+] RT
Analytical Chemistry, Vol. 75, No. 24, December 15, 2003
(4) 6923
where RT is the total concentration of lipophilic ion exchanger in the membrane. Equation 4 can be inserted into eq 3 to eliminate the concentration of complex at the sample side of the membrane
(
cI ) q [ILznI+]′ -
RT cI zI c + Kpotc I I,J J
)
(5)
One can define the parameter x to describe the ratio of the complex concentration at the inner membrane side to the ionexchange capacity as follows
zI x ) [ILznI+]′ RT
(6)
which is inserted into eq 5 to give
(
RT cI xpot zI cI + KI,J cJ
cI ) q
)
(7)
Values of x greater than 1 describe an inner membrane side where electrolyte coextraction occurs, whereas x values smaller than 1 indicate an inner membrane side where ion-exchange processes occur. Even small deviations in x of just a fraction of a percent can induce significant deviations in the detection limit. Optimal, robust detection limits are normally observed with values of x very close to 1. Equation 7 can be explicitly solved for cI to give
cI )
{
1 RT pot q (x - 1) - KI,J cJ + 2 zI
x
[
RT RT pot x + KI,J cJ + q (x - 1) zI zI
pot 4KI,J c Jq
]} 2
(8)
In Figure 1 (top), the logarithm of cI according to eq 8 is plotted as a function of x for a set of typical experimental parameters (zI pot ) 1, q ) 0.001, RT ) 0.005 mol L-1, and log KI,J cJ ) -12). The second, lower line shown is for a 10-fold smaller value of δaq (and therefore q) and predicts the effect of sample stirring as a function of the inner membrane composition on the detection limit. Figure 1 (bottom) shows the membrane concentration of the ionophore complex at the sample side for the same situation as in Figure 1 (top), obtained by inserting eq 8 into eq 4. Obviously, Figure 1 (top) shows that there must be a distinct stir effect. The phase boundary concentration changes as a function of δaq and leads to an improvement of the detection limit. Figure 1 (top) also shows that cI becomes smaller with decreasing x, which is indicative of an improved detection limit. It has been established that a reduction of x to values below 1 is normally not desired because it leads to fluxes of primary ions in the direction of the inner solution and, consequently, to super-Nernstian response slopes. Figure 2 shows three selected response curves for x ) 0.99, 1.00, and 1.01 to illustrate this effect with eq 11 given in ref 11. For practical purposes, x must be close to 1. The response curves shown for x ) 1.00 and 1.01 have the same general shape and distinguish themselves only in a dramatically different detection limit. Experimentally, therefore, it was not possible to judge from 6924
Analytical Chemistry, Vol. 75, No. 24, December 15, 2003
Figure 1. Top: Calculated aqueous phase boundary concentration of the primary ion at the detection limit vs x ) [IL+]′/RT (see eq 6). pot Parameters used: RT ) 5 mmol/kg, log(KAg,Na cJ) ) -12. Bottom: Calculated concentration of the complex at the outer membrane side (facing the sample), [IL+], vs x. Note that phase boundary concentrations remain constant in the top plot as [IL+] shown in the bottom plot drops below RT.
the calibration curve whether an ISE is optimized if an inner solution was chosen so that x > 1. Fortunately, however, the stir effect is distinctly different for each of the cases shown in Figure 2. For a membrane where electrolyte coextraction at the inner membrane side is substantial (x > 1), the stir effect is maximal. For a perfectly optimized membrane (x ) 1), it appears to be onehalf the maximum value, and for a membrane where ion exchange occurs at the inner side (x < 0), the stir effect is negligible. These mathematical results can be understood as described in the subsequent sections for each of the three different cases. A general discussion of such processes on the basis of ion fluxes across the membrane was given elsewhere.15 Strong Electrolyte Coextraction at the Inner Membrane Side (x > 1). This case can be best understood by analyzing eq 7. The second term within parentheses is normally very close to 1 because the level of interference from ions at the sample side is extremely small. The concentration gradient is therefore mainly dictated by the elevated concentration of primary ions at the inner membrane side, due to electrolyte coextraction from the inner solution, and much less by ion exchange at the sample side. Therefore, the concentration gradient in the membrane does not depend on sample stirring, and cI must be proportional to δaq. The actual stir effect, the change in cI as a function of δaq, is in this case described by
cI(2) cI(1)
)
δaq(2) δaq(1)
(9)
If the activity coefficients are constant, eq 9 can be inserted into eq 1 to predict the membrane potential change.
Figure 2. Calculated EMF responses of ion-selective electrodes (eq 11 from ref 11 with different inner solution compositions, x, shown for two values of q (which includes the aqueous diffusion layer thickness). Other parameters as in Figure 1.
No Electrolyte Coextraction or Ion Exchange at the Inner Membrane Side (x ) 1). For a perfectly matched inner membrane side, where no ion-exchange or coextraction process takes place and the concentration of primary ion-ionophore complex at the inner membrane side is given exclusively by the ion-exchange capacity of the membrane, ion fluxes can still occur because ion exchange takes place at the sample side of the membrane. This reduces the concentration at the sample side, hence generating a nonzero concentration gradient across the membrane. When δaq is reduced by stirring, the concentration cI at the membrane phase boundary is further reduced because of enhanced mass transport, and as a result, more interfering ions can exchange with I at this membrane side. This leads to a larger concentration gradient and, therefore, to an enhanced flux of I in direction of the sample. This counteracts the ion-exchange process to some extent, and the stir effect is smaller than for x > 1. Mathematically, this is analyzed by simplifying eq 8 for x ) 1 to give
cI )
[
1 pot -KI,J cJ + 2
x
RT pot + (KI,J cJ)2 zI
pot 4KI,J c Jq
]
(10)
It is assumed that ion-exchange processes at the sample side are small and the concentration decrease of ILznI+on the sample side pot is less than 0.1% of RT. Therefore, KI,J cJ is much smaller than qRT, and eq 10 is simplified to
cI )
x
1 2
RT zI
pot 4KI,J c Jq
(11)
For this case, therefore, the change in cI as a function of a change in δaq is described by
cI(2) cI(1)
)
x
δaq(2) δaq(1)
(12)
This square-root relationship translates into one-half the potential change upon changing δaq as compared to the case where x > 1 (eq 9). The stir effect is therefore smaller. Ion Exchange at the Inner Membrane Side (x < 1). If a substantial portion of primary ions is exchanged at the inner membrane side, a super-Nernstian response slope is ordinarily observed (see Figure 2), and it is obvious to the experimentalist that the electrode is not optimized. Without any primary ions in the sample, the stir effect appears to be absent and can be used as an additional experimental tool to evaluate the level of optimization of the ISE. At the detection limit, there are no primary ions in the sample, and an inward flux of these ions can no longer be sustained. Therefore, an elevated concentration of primary ions at the membrane surface relative to the bulk sample can be observed only if an outward flux, albeit of a very small magnitude, is established here as well (see Figure 3, ISE 8, in ref 15). This demands that the concentration of the complex at the outer membrane side is nearly equal to that at the inner membrane side, and approaches xRT/zI. The only chemical process that can lead to this concentration reduction at the sample side is again ion exchange with interfering ions. Because the extent of ion exchange at the sample side is quite large (the membrane concentrations of primary ions on the two sides of the membrane are comparable), the membrane concentration of interfering ions must approach (1 - x)RT/zI. This means that the outer membrane concentrations of primary and interfering ion complex are constant, as also is the concentration of the interfering ion in the sample (see assumption above). Because a local equilibrium is assumed at the phase boundary, cI is now fully dictated by these three constant concentrations, and there cannot be an influence of sample stirring on cI. An alternate explanation for the lack of stir effect can be made on the basis of the phase boundary potential, which can be formulated for the interfering ion as well. Because the concentrations of interfering ions are constant at the aqueous and membrane sides of the phase boundary, the potential must be constant and independent of δaq. Analytical Chemistry, Vol. 75, No. 24, December 15, 2003
6925
EXPERIMENTAL SECTION Reagents. Silver ionophore IV (O,O′′-bis[2-(methylthio)ethyl]tert-butylcalix[4]arene, Ag IV), potassium ionophore I (Valinomycin), potassium tetrakis(p-chlorophenyl)borate (KTpClPB), tetradodecylammonium chloride (TDAC), 2-nitrophenyloctyl ether (oNPOE), bis(2-ethylhexyl)sebacate (DOS), high-molecular-weight poly(vinyl chloride) (PVC), tetrahydrofuran (THF), and Silver Ion Standard solution (for ion-selective electrodes) were purchased from Fluka (Fluka Chemical Corp., Milwaukee, WI). Sodium tetrakis[3,5-bis(trifluoromethyl)phenyl]borate (NaTFPB) was purchased from Dojindo Laboratories (Japan). The ion-exchanger resins (cation-exchanger Dowex Monosphere C-350 H+ form, 3080 mesh, and anion-exchanger Amberlite IRA-400 Cl- form, 2050 mesh) were from Fluka. The ionophore [9]mercuracarborand3 (MC3) was prepared as described elsewhere.19 Sodium nitrate of ReagentPlus grade was from Aldrich. Sodium chloride and sodium iodide were from Fluka in puriss grade, and orthophosphoric acid was from Fisher in certified ACS grade. Aqueous solutions were prepared by dissolving the appropriate salts in Nanopure purified water. Membranes. The silver-selective membranes contained 22.37 mmol kg-1 (1.78 wt %) Ag IV, 5.54 mmol kg-1 (0.51 wt %) NaTFPB, 29.73 wt % PVC, and 67.98 wt % DOS. The iodide-selective membranes contained 1.33 mmol kg-1 (0.14 wt %) MC-3, 0.741 mmol kg-1 TDACl, 33.09 wt % PVC, and 66.71 wt % DOS. The potassium-selective membranes contained 9.27 mmol kg-1 (1.03 wt %) valinomycin, 4.38 mmol kg-1 (0.22 wt %) KTpClPB, 33.82 wt % PVC, and 64.93 wt % o-NPOE. The components (totaling 417 mg for the silver-selective system and 240 mg for iodide- and potassium-selective systems) were dissolved in THF (5.0 mL) and poured into a glass ring (70-mm i.d. for Ag+ or 28-mm i.d. for Iand K+) fixed onto a glass plate. Overnight evaporation yielded transparent membranes of about 200-µm thickness. Ion Exchange Resins. For preparing the inner filling solutions using the cation-exchange resin, 10 g of the resin in H+ form was equilibrated with 100 mL of 1 M NaOH for 12 h under constant stirring. The resulting Na+ form was then washed with deionized water and dried overnight at 90 °C. Its cation-exchange capacity was determined as 5.14 mequiv/g by titration of the dry H+ form (0.5 g) with 0.1 M NaOH.20 The selectivity KAg,Na ) 1.86 (given as KAg,Na ) mAg,resinmNa,aq/mNa,resinmAg,aq) was obtained by stirring the Na+ form (0.1 g) for 12 h with 50 mL of 5 × 10-3 M AgNO3 and then determining the Ag+ concentration with an ISE as 1.19 × 10-3 M. Its selectivity toward potassium has been determined previously as KK,Na ) 1.9.12 For preparing the inner filling solution for the iodide electrodes, the Cl- form of the anion-exchange resin was dried overnight at 90 °C. Its selectivity KCl/I ) 7.26 and capacity C ) 3.1 mequiv/g were obtained from ref 21. Electrodes. A disk of 6-mm diameter was punched from the above membrane and glued to a plasticized PVC tubing with a THF/PVC slurry. Two electrode constructions were used: In construction A, small tubing of 3.2-mm o.d. and 1.6-mm i.d. was inserted into tubing of 3.2-mm i.d. before the latter was attached (19) Zinn, A. A.; Zheng, Z.; Knobler, C. B.; Hawthorne, M. F. J. Am. Chem. Soc. 1996, 118, 70. (20) Harland, C. E. Ion Exchange: Theory and Practice, 2nd ed.; Royal Society of Chemistry: Herts, U.K., 1993. (21) Sengupta, M.; Chakravarti, A. K.; Pal, G. C.; Mukherjee, P. Ion Exch. Membr. 1973, 1, 149.
6926 Analytical Chemistry, Vol. 75, No. 24, December 15, 2003
Table 1. Inner Solution Compositions and Calculated Activities of Ag+ and Resulting Parameter xa
IFS 1 IFS 2 IFS 3 IFS 4 IFS 5 IFS 6 IFS 7 IFS 8 IFS 9 IFS 10 IFS 11
[AgNO3] (M)
[NaNO3] (M)
1.00 × 10-1 2.66 × 10-2 1.72 × 10-2 1.17 × 10-2 5.00 × 10-3 1.00 × 10-3 4.00 × 10-5 2.50 × 10-5 2.00 × 10-5 7.50 × 10-6 3.80 × 10-6
0 0 0 0 0 0 1.00 × 10-4 1.00 × 10-4 1.00 × 10-4 1.00 × 10-4 1.00 × 10-4
resin activity (g) of Ag+ (M) 0 0 0 0 0 0 1 1 1 1 1
7.32 × 10-2 2.24 × 10-2 1.49 × 10-2 1.04 × 10-2 4.62 × 10-3 9.64 × 10-4 5.75 × 10-9 3.21 × 10-9 2.47 × 10-9 8.31 × 10-10 4.07 × 10-10
x
error in x
1.38 1.052 1.024 1.0118 1.0024 1.000 100 0.9991 0.9985 0.9981 0.995 0.990
0.02 0.002 0.001 0.0005 0.0001 0.000 005 0.0003 0.0004 0.0005 0.001 0.003
a Equation 6, ratio of complex concentration at inner membrane side to ion-exchanger capacity.
to the ion-selective membrane. In construction B, the membrane was glued onto tubing of 6.4-mm o.d. and 3.2-mm i.d. without the insertion of smaller tubing. When an ion-exchanger resin was used in the inner filling solution (IFS), a specified amount of resin was equilibrated overnight in 10 mL of solution containing specified concentrations of the primary ion (either Ag+, I-, or K+) and an interfering ion (either Na+, Cl-, or Na+). All types of electrodes were first conditioned for ca. 12 h in 10-3 M AgNO3, NaI, or KCl as the sample and IFS. In the cases where resin was used in the IFS, the initial inner solution was changed for the appropriate composition, and the electrodes were again conditioned for 12 h in samples containing 10-5 M NaNO3 and 10-9 M AgNO3 in the case of the silver-selective system or 10-3 M H3PO4 and 10-9 M NaI for the iodide-selective system. Potassium-selective electrodes were conditioned in the same solution after the IFS replacement. The final inner solution compositions for the silver electrodes are given in Table 1. The inner solution compositions for the potassium-selective systems were as follows: IFS K1 contained 1 M KCl with 6.04 × 10-1 M free K+; IFS K2 contained 1 × 10-4 M KCl, 1 × 10-3 M NaCl, and 0.5 g of resin, giving 3.1 × 10-7 M free K+; IFS K3 was made with 1 × 10-6 M KCl, 1 × 10-3 M NaCl, and 0.5 g of resin giving 3.1 × 10-9 M free K+; and IFS K4 contained just 1 × 10-3 M NaCl. For the iodide-selective systems, two inner solutions were used: IFS I1 contained 2.0 × 10-2 M NaI, 1 × 10-4 M NaCl, and 1 g of resin, giving 3.7 × 10-5 M free I-, and IFS I2 contained 2.5 × 10-3 M NaI, 1 × 10-4 M NaCl, and 1 g of resin, giving 2.6 × 10-6 M free I-. EMF Measurements. Potentials were monitored through a PCI MIO16XE data acquisition board (National Instruments, Austin, TX) utilizing a four-channel high Z interface (WPI, Sarasota, FL) at room temperature (22 °C) in stirred solutions, in the galvanic cell Ag/AgCl/3M KCl/1M LiOAc/sample solution/ ISE membrane/IFS/10-3M NaCl/AgCl/Ag with a double-junction reference electrode (type 6.0729.100, Methrom AG, Herisau, Switzerland). The experiments were performed in a 100-mL polyethylene beaker pretreated overnight in 0.1 M HNO3. All EMF values were corrected for liquid-junction potentials according to the Henderson equation. Activity coefficients were calculated by the Debye-Huckel approximation. Selectivity coefficients for membranes containing the iodide-selective ionophore (MC3) for iodide versus H2PO4- were determined by the modified separate solution method by recording separate calibration curves for the
interfering ion and primary ion as established earlier.22 For this experiment, ortho-phosphoric acid was used instead of the commonly used salt in order to overcome the possible interference by OH- ions.13,23 Rotator System. A Pine Instrument Co. (Grove City, PA) analytical rotator (model ASR) and an ASR motor control box (1000 rpm/V, 100-10 000 rpm range) were used for all experiments. Most necessary adjustments have been described elsewhere.18 However, because of the delicate nature of the inner solutions in the cases in which a resin was used, the electrode construction was altered as follows: small tubing (3.2-mm o.d and 1.6-mm i.d.) was inserted into the larger tubing about 5 mm from the larger tubing’s distal end where the membrane was glued. After membrane attachment, the electrode was filled with 10-3 M AgNO3 solution as the inner and outer conditioning solution. Later, the inner solution was changed for the IFS of the indicated composition, and the electrode was further conditioned in a solution of 10-5 M NaNO3 and 10-9 M AgNO3. Before measurement, the electrode was assembled by inserting a plastic pipet tip filled with a cotton plug into the small tubing, and the top compartment was filled with 10-3 M NaCl as a bridge electrolyte. No bridge electrolyte was used for potassium- and iodide-selective systems. Coextraction Constant Calculations. The silver nitrate coextraction constant was estimated from measurements at the upper detection limit. In contrast to earlier work,6,24 the entire experimental response curve was used for calculations, rather than just the value for the upper detection limit. The silver electrode described above was measured in samples containing increasing silver nitrate concentrations in the range of 10-4-10-1 M. The following equation was used to describe the response curve in this region
EM ) E 0 + s log
{
}
aAg(LT - RT - [NO3-]) RT + [NO3-]
(13)
where LT is the total membrane concentration of ionophore (0.019 93 mol kg-1); RT here was 0.004 69 mol kg-1; s is the experimental response slope of 59.5 mV decade-1; and [NO3-] is the concentration of nitrate ions in the organic phase boundary, which was obtained by combining the coextraction equilibrium constant, Kcoex ) [AgL+][NO3-]/(aAgaNO3[L]), with the charge balance (RT + [NO3-] ) [AgL+]) and mass balance (LT ) [L] + [AgL+]) equations as
1 [NO3-] ) [-aNO3aAgKcoex - RT + 2
x(a
NO3aAgKcoex
+ RT)2 - 4aNO3aAgKcoex(RT - LT)] (14)
This equation assumes that no ion pairing takes place in the membrane phase and is written for monovalent ions and the formation of 1:1 complexes in the membrane. Error Calculations. The prediction error for the parameter x was estimated by a standard error-propagation calculation by considering the following errors: The selectivity of the ionexchange resin KR ) 1.86 ( 0.02 (n ) 3), the capacity of resin ) (22) Bakker, E.; Pretsch, E.; Buhlmann, P. Anal. Chem. 2000, 72, 1127. (23) Ceresa, A.; Qin, Y.; Peper, S.; Bakker, E. Anal. Chem. 2003, 75, 133. (24) Qin, Y.; Bakker, E. Anal. Chem. 2002, 74, 3134.
5.14 × 10-3 ( 3 × 10-5 equiv/g (n ) 3), the selectivity coefficient pot of the silver-selective membrane electrode KAg,Na ) 4 × 10-8 ( 1 -8 × 10 (n ) 3), and the silver nitrate coextraction constant Kcoex ) 0.18 ( 0.03 (n ) 3). An absolute error of 5 µg for all weight measurements was used, originating from the analytical balance (Mettler Toledo AG245). A 0.1-mL error was assumed for the volumetric errors that involved the use of a 10-mL adjustable volume pipet (Finnpipete, Fisher). The concentration and corresponding errors of free Ag+ in inner solution,12 of the nitrate concentration at the inner membrane side (eq 14), and of the parameter x were subsequently estimated. RESULTS AND DISCUSSION The sample activities of primary ions at the phase boundary dictate the observed membrane potential of the ISE if the membrane selectivity is sufficiently high. The theoretical section explains that a change in the aqueous diffusion layer thickness can have a dramatic effect on this phase boundary concentration, and through it, on the observed potential. It assumes that no primary ions are present in the sample bulk, that is, the electrode is characterized at the detection limit. The magnitude of this stir effect is strongly dependent on the composition of the inner solution of the ISE, which dictates, through electrolyte coextraction and ion-exchange equilibria, the concentration of primary ion-ionophore complex at the inner membrane side. ISEs with inner solutions that induce substantial electrolyte coextraction will suffer from a high detection limit, and such electrodes are predicted to show the strongest stir effect. This stir effect is expected to disappear completely if substantial ion exchange occurs at the inner membrane side. Such ISEs are normally also not desired because their response functions exhibit an activity region with a super-Nernstian response slope. ISEs with a perfectly optimized inner solution that induce neither coextraction nor ionexchange effects are expected to show intermediate behavior, with a stir effect that is one-half its maximum value. It has long been realized that changes in the Nernst diffusion layer thickness of the sample can lower the detection limit.6,16-18 The goal of studies investigating this issue was mainly to improve the detection limit of ISEs. Here, the stir effect is introduced as a diagnostic tool to evaluate the level of optimization of the inner solution. The diffusion layer thickness in the aqueous phase was adjusted by using a rotating disk electrode configuration, which was adapted from the work of Ye and Meyerhoff.18 According to established theory, the diffusion layer thickness δaq is a direct function of the rotational speed of the electrode, and can be calculated as follows25
δaq )
1.61Daq1/3ν1/6 ω1/2
(15)
where ν represents the kinematic viscosity of the sample and ω is the angular rotational frequency. This system was initially evaluated with a silver-selective electrode containing an inner solution where strong electrolyte coextraction must occur (IFS 1). For this situation, the stir effect should be maximal and obey eq 9. Figure 3 shows the time traces for this electrode in a pure water sample without added silver ions. The top trace describes (25) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications, 2nd ed.; John Wiley & Sons: New York, 2002.
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Figure 3. Effect on sample stirring for a silver-selective electrode with 0.1 M AgNO3 as the inner solution in a pure water sample. Top time trace: Effect of stirring the sample with a magnetic stirring bar. Bottom time trace: Effect of stirring the sample by using the ISE as a rotating disk electrode at either 2000 and 100 rpm.
the behavior of a classical stir experiment, when a magnetic stirring bar was stopped or stirred at fixed time intervals. As expected, the potential decreases when the sample is stirred. This effect is thought to originate from an enhanced mass transport of primary ions from the membrane into the sample bulk, thereby decreasing the phase boundary concentration of primary ions and therefore the observed potential. The diffusion layer thickness in the absence of sample stirring is ill-defined, and a strong upward potential drift is observed. These results strongly resemble the earlier data obtained by Mathison6 with a potassium-selective electrode. The bottom traces of Figure 3 describe the behavior of the same electrode in a rotating disk electrode configuration. The rotational speed of the ISE was altered between 100 and 2000 rpm. According to eq 15, this should cause a decrease of the Nernst diffusion layer thickness of 0.66 logarithmic units. According to the Nernst equation (eq 1), the ISE should therefore read potential values that are 38.6 mV lower at the higher rotational speed. Again, this assumes that coextraction at the inner side is relevant and that eq 9 is valid. In Figure 3, bottom trace, the experimentally observed potential change was found to be 36 mV, which is acceptably close to the calculated value. As shown in Figure 3, the potentials were found to be stable for at least 3 min and showed good reproducibility. Figure 4 presents the calibration curve for a silver-selective electrode with the same IFS 1 as shown in Figure 3, but measured in a 10-3 M NaNO3 as a background solution, rotated either at 2000 or at 100 rpm. Here, the detection limit for the more rapidly rotating ISE in Figure 4 was improved by 0.65 logarithmic units. This improvement corresponds to an observed stir effect of 38.1 mV (theory predicts 38.6 mV), and is in excellent agreement with the time traces shown in Figure 3 and with eq 9. The results shown in Figures 3 and 4 were obtained after some modification of the experimental setup and protocol. It was necessary to wash freshly conditioned electrodes in pure water under constant sample stirring before the start of the experiment. If this step was omitted, the stir effects were poorly reproducible, although the detection limits were not found to be dramatically different. This washing step was likely important to ensure that the concentration gradients in the membrane were close to linear, 6928 Analytical Chemistry, Vol. 75, No. 24, December 15, 2003
Figure 4. Silver calibration curves for a silver-selective electrode with a 0.1 M AgNO3 inner solution, rotated at either 100 or 2000 rpm. At the detection limit, the observed potential difference between the two curves is 38 mV, as expected by theory (eq 9).
as demanded by the steady-state model. Moreover, modifications of the electrode setup were necessary to achieve an acceptable agreement with theory. Initial attempts used an additional inner tubing inserted into the electrode body, as reported before (see construction A in the Experimental Section), but the potential changes never exceeded more than 25 mV for the experiment shown in Figure 3, bottom trace. It must be suspected that this electrode construction does not lead to a one-dimensional diffusion profile as demanded by theory, owing to the spatial restriction in the inner solution. When this inner tubing was removed (see construction B in the Experimental Section), stirring effects were as expected. ISEs with inner tubings were found earlier to have lower detection limits than those with other configurations,11 possibly because of this different diffusion profile. For this work, subsequent experiments were continued with ISEs of construction B. It is possible that the hydrodynamic pressure from the sample in the rotator experiment could lead to some distortion of the membrane, which could lead to some bias in the results. On the other hand, the group of Meyerhoff18 used essentially the same general electrode design and found a quantitative correlation between polyion response theory and eq 15, indicating that such a bias must be acceptably small. The time traces shown in Figure 3 encouraged us to apply the rotating disk electrode setup to evaluate the level of optimization of the inner solution of ion-selective electrodes. For this purpose, a well-understood system was chosen where all relevant parameters could be adequately predicted with available theory. According to eq 8, one requires accurate information about the membrane composition, membrane selectivity, and concentration of primary ion-ionophore complex at the inner membrane side. A silver-selective membrane formulation, thoroughly characterized before,11 was chosen for this purpose. The concentration of the complex at the inner membrane side was calculated on the basis of the equation
[IL+]′ )
aI′RT pot KI,J aJ′ +
aI′
+ [NO3-]′
(16)
where the primes indicate membrane concentrations and inner solution activities at the inner side of the membrane; and I+, J+, and NO3- are the primary ion (here, silver ions), the interfering cation (sodium), and the interfering anion (nitrate), respectively. The concentration of NO3- is calculated with eq 14. All ions must be monovalent for eq 16 to hold. The first term on the right-hand side describes the inner complex concentration when ion exchange with interfering ions is the only relevant equilibrium process at the inner membrane side. This is most conveniently described on the basis of the established selectivity formalism pot (Nikolskii equation), and the selectivity coefficient log KAg,Na ) -7.4 was used here. The second term encompasses concentration increases from electrolyte coextraction equilibria, and is also dependent on the total membrane concentration of ionophore, LT (see eq 14). The coextraction constant was calculated as Kcoex ) 0.18 by using an established coextraction model to evaluate the response behavior of a silver-selective electrode at the upper detection limit in silver nitrate solutions (see the Experimental Section). Different inner solution compositions were chosen on the basis of an ion-exchange resin as chelator, to avoid undesired additional extraction processes. This approach was used before to reach excellent agreement between experiment and theory. The resulting complex concentrations at the inner membrane side relative to the ion-exchange capacity (parameter x), calculated according to eqs 6 and 14, are given in Table 1. Estimated errors in x are also given. In addition to the data shown in Table 1, the following parameters important to eq 8 were used: Daq ) 1.65 × 10-5 cm2 s-1;26 Dorg ) 1 × 10-8 cm2 s-1;27 δorg ) 200 µm; δaq ) 0.0147 cm (at 100 rpm) and 0.0033 cm (at 2000 rpm), calculated from eq 15; pot log KAg,Na ) -7.4; and RT ) 0.0055 mol L-1. Two series of experiments were performed, each in a sample background of either 10-5 or 10-3 M NaNO3. Figure 5A shows the observed potential change upon altering the rotation speed from 2000 to 100 rpm in 10-5 M NaNO3. The solid line corresponds to the theoretically expected behavior, obtained by inserting all parameters listed above and in Table 1 into eq 8 for each of the two rotation speeds and predicting the potential difference on the basis of the Nernst equation (eq 1). In this series of experiments, one electrode for each inner solution composition was used, and an excellent agreement between theory and experiment was obtained. Measuring the stir effect is shown to be quite accurate in evaluating the delicate influence of the inner solution on sensor response in dilute solutions. For a highly selective ionophore such as Ag IV, a mere 0.01% of primary ion exchange at the inner side of the membrane can lead to an electrode that is no longer optimized (see values of x in Table 1). In a second set of experiments, the sample background was increased to 10-3 M NaNO3 (see Figure 5B) with various inner solutions, giving a range of calculated x values (see Table 1). Here, standard deviations were determined from measurements with (26) Cussler, E. L. Diffusion, Mass Transfer in Fluid Systems; Cambridge University Press: Cambridge, U.K., 1984. (27) Puntener, M.; Fibbioli, M.; Bakker, E.; Pretsch, E. Electroanalysis 2002, 14, 1329.
Figure 5. Observed stir effects for silver-selective electrodes recorded upon changing the electrode rotation speed from 2000 to 100 rpm in Ag+-free samples consisting of (A) 10-5 M NaNO3 or (B) 10-3 M NaNO3. Solid line: Theoretical prediction of the dependence of the stir effect vs the calculated relative complex concentration at inner membrane side, x (see Table 1 and eq 8). Error bars for part B are standard deviations from measurements on three different electrodes.
at least three electrodes for each inner solution composition. The theoretical curve for the stir effect now assumes a flatter slope compared to Figure 5A since the level of interference from the sample is larger. Agreement between experimental data and theory is again quite good and shows that a simple stir effect can give important information on whether the ISE is fully optimized for a particular application. Note that the points deviate more strongly from the predicted curve for x > 1, where coextraction processes are relevant. According to the predicted errors given in Table 1, the observed deviation is likely not due to random error. Indeed, ion-exchange processes can be predicted quite accurately from experimental selectivity determinations (see the discussion of x < 1), whereas coextraction processes cannot currently be quantified satisfactorily.24 A rigorous treatment would have to take all relevant ion-pairing equilibria into account, for which no direct experiments are available. An interesting feature was observed for the two series of experiments shown in Figure 5. An electrode with inner solution 10 (see Table 1) was earlier shown to give a detection limit that was far from optimal and to give a strong super-Nernstian response slope.11 Indeed, in a 10-5 M NaNO3 background, the stir effect was found to be just 1.4 mV (theory predicts 0.4 mV), indicating that the ISE was not well optimized for that particular sample background. However, in the higher background of 10-3 M NaNO3, the stir effect was observed as 9.4 mV (theory predicts 11.6 mV), which is not far from the optimum value. The resulting Analytical Chemistry, Vol. 75, No. 24, December 15, 2003
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logarithmic detection limit of -8.35 after the entire calibration curve had been recorded was indeed quite close to the theoretically expected optimum (-8.7), making this ISE useful for practical measurements in an elevated sample background. This shows clearly that ISEs must be optimized for each new sample background, which makes accurate calculations cumbersome for most application-oriented scientists. The use of stir effect evaluations, as introduced here, appears as a welcome experimental approach to the optimization of ISE compositions for real-world applications. To further explore the possibility of using the stir effect in practice, two more systems were studied. Here, a quantitative determination of the primary ion-ionophore complex concentration at the inner side was not attempted. Rather, the degree of optimization of the inner solution was evaluated with the stir effect and correlated to the observed detection limit. A potassiumselective valinomycin-based system was tested first. Electrodes with different inner solutions were prepared, and the stir effect was measured. For IFS K1, a 27.4-mV stir effect was observed, with a corresponding logarithmic detection limit of -6.95. An electrode that shows such a relatively high stir effect is not expected to show an optimal detection limit, and an improvement of about one-half order of magnitude can be expected by altering the inner solution. Indeed, the stir effect with IFS K2 (with a lower concentration of free potassium ions) was found as 16.2 mV, which is very close to the optimal value. The logarithmic detection limit for this system was found to be lower as well, at -7.45. Subsequently, the stir effects for IFS K3 and K4 decreased to 12.0 and 2.0 mV, as qualitatively expected. These last two inner solutions did not induce any super-Nernstian response slope of the electrode, and the lower detection limit was unaffected as well (-7.3 and -7.4, respectively). This suggests that stir effect experiments give more sensitive information about the level of electrode optimization than simple electrode calibrations. Note that recent results by the group of Pretsch found even lower detection limits than those reported here.12 Stir effects were also evaluated with an iodide-selective electrode on the basis of the anticrown ionophore [9]mercuracarborand-3. Recently, such electrodes were found to reach very low detection limits in the nanomolar concentration range.13 The experiments were performed in a pH 3 phosphoric acid solution in order to keep the hydroxide concentration low, which would otherwise give rise to higher detection limits. On the basis of the high selectivity of such membranes, however, the detection limit should have been even lower, and it was argued that sample impurities, such as very low levels of iodide ions, might be responsible for the experimental result. No direct evidence was available at the time to support the notion of sample impurities. The rotational electrode experiments introduced here can provide additional evidence to support whether sample impurities are relevant to the detection limit. Consider first a well-optimized electrode where an outward flux of primary ions is observed at the detection limit (no super-Nernstian response slope, Figure 2). If no primary ions are present in the sample bulk, a stir effect is observed. If primary ion impurities are present in the sample, the electrode is now evaluated above, rather than at the detection limit, and the stir effect must become smaller (see Figure 2). A series of iodide-selective electrode with an optimized inner solution IFS 6930 Analytical Chemistry, Vol. 75, No. 24, December 15, 2003
Figure 6. Bottom: Solid curve, theoretically predicted EMF change upon rotating an iodide electrode from 2000 to 100 rpm as a function of the sample iodide background. Dotted line, experimentally observed EMF change of 5.8 mV, corresponding to a 5 × 10-10 M iodide impurity background in the sample. Top: iodide calibration curve for the same ISE containing IFS I2. Solid line, theoretically predicted response curve with an iodide background of 5 × 10-10 M (see text).
I1 gave a logarithmic detection limit of -9.8 ( 0.1 in a pH 3 background (phosphoric acid), while exhibiting a sub-Nernstian response slope of 50 mV decade-1. At the detection limit, a stir effect was absent. This suggests that sample impurities might be present. An iodide electrode showing an inward flux of primary ions using IFS I2 was also evaluated (see Figure 6). At the true detection limit, with no primary ions present in the sample, a stir effect should be absent. According to Figure 2, however, one expects a stir effect when the ISE is measured above the detection limit. In addition, the stir effect must be of opposite sign compared to the case shown in Figure 2 because the primary ion is here negatively rather than positively charged, giving a negative slope for the electrode response. Here, a stir effect of 5.8 mV was observed with the iodide-selective electrode. A theoretical relationship predicting this behavior quantitatively is shown in Figure 6, bottom, on the basis of eq 10 of ref 11. The parameters used for calculating the theoretical curve were as follows: x ) 0.9711, RT -11 M, and ) 0.000 75 mol kg-1, log Kpot I,OH ) -1.64, cOH ) 1 × 10 -5 -4 q ) 8.64 × 10 (at 2000 rpm) and 3.85 × 10 (at 100 rpm). The logarithmic selectivity coefficient over phosphate was determined as -9.9 ( 0.1, suggesting that hydroxide is still the larger interference under these conditions. The value of x was obtained on the basis of eq 16 (neglecting the second part of the RHS), pot and the selectivity coefficient log KI,Cl ) -4.5 was determined
experimentally. The predicted potential change upon changing the rotation speed shown in Figure 6, bottom, suggests that such experiments are very sensitive, with 10-10 M levels of iodide impurities giving measurable stir effects. The observed stir effect of 5.8 mV is indicated as a horizontal dotted line in the figure and corresponds to an iodide impurity of about 5 × 10-10 M (log aI ) -9.35). This is acceptably close to the detection limit observed with the ISEs containing IFS I1 (-9.8; note that the sub-Nernstian response slope observed with those ISEs makes this value less reliable). The calculated background concentration was used to predict the response curve for the ISE that contained IFS I2 and was rotated at 2000 rpm (see Figure 6, top). The correlation was excellent; no curve fitting was performed. This result is interesting in two respects. On one hand, this technique appears to be useful for evaluating the mechanistic causes for the observed detection limit. On the other hand, one might be able to measure extremely low levels of primary ions with electrodes that show superNernstian response slopes.
tions very easily. An excellent correlation was achieved after some modifications to the electrode configuration, including removing an inner tubing in the inner solution compartment and reconditioning fresh electrodes in pure water before measurement of the stir effect. Once these problems were solved, a well-characterized electrode system was used to predict the stir effect for a range of inner solutions and different sample backgrounds. An excellent quantitative correlation between theory and experiment was observed, which confirmed that this method is very useful for electrode optimization purposes. With electrodes showing a superNernstian response slope, stir effects were found to strongly depend on the concentration of the primary ion in the sample. The results with iodide-selective electrodes suggest that ultratrace levels of primary ions can be assessed in the response range of an electrode that lies below the IUPAC definition of the low detection limit. This might open up new possibilities for developing ISEs for ultratrace-level measurements.
CONCLUSIONS The potentiometric measurement of the stir effect at the detection limit, preferably by use of a rotating electrode setup, appears to be an elegant technique for evaluating whether an ISE is properly optimized for low-detection-limit measurements. The technique was first tested with inner solutions in which substantial coextraction occurs and, therefore, the potential changes upon change of the rotational speed of the ISE should follow expecta-
ACKNOWLEDGMENT The authors thank the National Institutes of Health (EB0002189) for financial support of this research.
Received for review June 26, 2003. Accepted September 25, 2003. AC0346961
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