Anal. Chem. 2006, 78, 2744-2751
Calcium Pulstrodes with 10-Fold Enhanced Sensitivity for Measurements in the Physiological Concentration Range Sergey Makarychev-Mikhailov,† Alexey Shvarev,‡ and Eric Bakker*,†
Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, and Department of Chemistry, Oregon State University, Corvallis, Oregon 97331
Ion-selective electrodes ideally operate on the basis of the Nernst equation, which predicts less than 60- and 30mV potential change for a 10-fold activity change of monovalent and divalent ions measured at room temperature, respectively. Typical concentration ranges in extracellular fluids are quite narrow for the electrolytes of key importance. A range of 2.2-2.6 mM for calcium ions, for instance, translates into just a 2.2-mV potential change. The direct potentiometric measurement of physiological electrolytes is certainly possible with direct potentiometry and is done routinely in clinical analyzers and handheld measuring devices. It places, however, strong demands on the precision of the reference electrode and requires careful temperature control and frequent calibration runs. In this paper, a robust 10-20-fold sensitivity enhancement for calcium measurements is attained by departing from the classical response mechanism and operating in a non-Nernstian response mode. Stable and reproducible super-Nernstian responses of these so-called pulstrodes in a narrow calcium activity range can be controlled by instrumental means in good agreement with theory. The potentials may be measured during a galvanostatic excitation pulse (mode I) or immediately after it (mode II), under open-circuit conditions. Subtraction of the potentials, sampled at different times during a single pulse, allows one to obtain a sensitive differential peakshaped signal at a critical and fully adjustable analyte activity range. Calcium pulstrodes based on the diamide ionophore AU-1 were characterized and applied to the measurement in model physiological liquids. SuperNernstian responses exceeding 700 mV/decade were observed in a physiological range of calcium concentration. Such remarkable sensitivity of the pulstrodes, complemented with the well-documented high selectivity of these potentiometric sensors, may provide a significant increase in the accuracy and precision of electrolyte measurements in clinical analysis. Direct potentiometry with ion-selective electrodes (ISEs) is the method of choice for the reliable detection of electrolytes in clinical analysis. Since ion concentrations in such samples only vary by a * To whom correspondence
[email protected]. † Purdue University. ‡ Oregon State University.
should
be
addressed.
2744 Analytical Chemistry, Vol. 78, No. 8, April 15, 2006
E-mail:
few percent, these measurements are very demanding in terms of the required potential stabilities and reproducibilities. For instance, the 95% normal extracellular sodium concentration range varies from 135 to 150 mM and requires a 0.12-mV potential stability. For ionized calcium, the range is 1.0-1.2 mM with the same required 0.12-mV stability to achieve a 5-fold subdivision of the concentration range with a 95% confidence limit.1 Note that the total concentration of calcium is twice higher and comprise 2.2-2.6 mM.2 These numbers illustrate convincingly that such electrolyte measurements are among the most demanding in terms of required potential stability. The reason for this challenge lies in the Nernst equation, which states that each 10-fold activity change results in approximately 60- or 30-mV potential change for monovalent and divalent ions, respectively, when measured at room temperature. A 20% concentration change for a divalent ion, which is the 95% measuring range for ionized calcium, therefore translates into a mere 2.2-mV total potential change. While this range imposes strict requirements on stability of the reference electrode, simplifications of that electrode are difficult to implement since any measurement error at it directly impacts on the overall potential measurement. This also hampers miniaturization of the reference electrode and thus impedes microsensor and sensor array development. This fundamental dilemma is here overcome by using ionselective membranes that are measured under conditions that give non-Nernstian response slopes in a reproducible fashion. This is achieved by applying current pulses across an ion-selective membrane that lacks ion-exchanger properties and forcing concentration polarizations to occur at the sample-membrane interface. This class of sensors has its roots in the principles of voltammetry at the interface between two immiscible electrolyte solutions.3-8 Later, a normal pulse voltammetric mode for such ion-selective electrodes was proposed, which has advantages over classical cyclic voltammetry as the ions being drawn into the membrane by the applied potential pulse may be released back to the solution at the time between pulses, thus providing a (1) Oesch, U.; Ammann, D.; Simon, W. Clin. Chem. 1986, 32, 1448. (2) Burtis, C. A., Ashwood, E. R., Eds. Tietz Fundamentals of Clinical Chemistry; W. B. Saunders: Philadelphia, 2001. (3) Horvath, V.; Horvai, G. Anal. Chim. Acta 1993, 273, 145. (4) Jadhav, S.; Bakker, E. Anal. Chem. 1999, 71, 3657. (5) Sutter, J.; Morf, W. E.; de Rooij, N. F.; Pretsch, E. J. Electroanal. Chem. 2004, 571, 27. (6) Lindner, E.; Gyurcsanyi, R. E.; Buck, R. P. Electroanalysis 1999, 11, 695. (7) Shvarev, A.; Bakker, E. Anal. Chem. 2003, 75, 4541. (8) Reymond, F.; Fermin, D.; Lee, H. J.; Girault, H. H. Electrochim. Acta 2000, 45, 2647. 10.1021/ac052211y CCC: $33.50
© 2006 American Chemical Society Published on Web 03/10/2006
reproducible sensor response.9 The additional capabilities of multianalyte detection with a single sensor interrogated at different potentials were established for such voltammetric ISEs.10 This formed the basis for a pulsed galvanostatic control of the potentiometric sensors, allowing further instrumental control of ion-selective polymeric membranes and sensor readings that have the look and feel of traditional ion-selective electrodes.7 Here, the applied constant current pulses fully define the ion fluxes across the sample-membrane interface and determine the concentration of the extracted ions in the phase boundary region for membranes, which contain no intrinsic ion-exchange properties. The variation of the pulse parameters influences the response function slope to some extent. The observed apparent Nernstian sensor behavior makes it possible to apply established ISE theory and to directly compare the properties of galvanostatically controlled sensors and their traditional counterparts. Reversible electrochemical detection of small ions in free and complexed forms7,11 and polyions12,13 was demonstrated with this technique. These advances would be very difficult to achieve in a robust fashion with traditional ISEs measured under zero current conditions. The strong super-Nernstian response of the galvanostatically controlled sensors in a critical range of ion activity is the focus of the present work. As was shown,7 the origin of this behavior lies in a concentration polarization at phase boundary under an applied constant current pulse, which is caused by the depletion of the aqueous diffusion layer adjacent to the membrane. There is a complete analogy with similar responses of traditional ISEs, where the super-Nernstian behavior is due to the uptake of primary ions into membrane phase.14 However, in traditional ISEs, there is a variety of parameters that may influence this response, including activities of interfering ions of a sample and inner solution, concentrations of ionophore and lipophilic ion exchanger in the membrane, thickness of the Nernstian diffusion layers, and diffusion coefficients in both phases.15 As a full control over all of these parameters is generally cumbersome, a poor reproducibility and significant drift of the sensor potentials are usually observed in such super-Nernstian region. However, a measurement protocol utilizing super-Nernstian responses of the conventional ISEs was proposed by Pretsch et al.16 and this concept was called “switchtrodes”. In contrast, a pulsed galvanostatic control of potentiometric sensors allows one to obtain robust and fully reproducible potential readings in the super-Nernstian region, as full control on the system is performed by purely instrumental means. Furthermore, as shown recently,17 for the model system the differential responses can be obtained from a single sensor at different pulse parameters and the matching of the sensor response to the desired critical activity of the analyte is much simpler. Importantly, the pulstrode differential response lifts strict requirements on the (9) Jadhav, S.; Meir, A. J.; Bakker, E. Electroanalysis 2000, 12, 1251. (10) Jadhav, S.; Bakker, E. Anal. Chem. 2001, 73, 80. (11) Shvarev, A.; Bakker, E. Talanta 2004, 63, 195. (12) Shvarev, A.; Bakker, E. J. Am. Chem. Soc. 2003, 125, 11192. (13) Shvarev, A.; Bakker, E. Anal. Chem. 2005, 77, 5221. (14) Sokalski, T.; Zwickl, T.; Bakker, E.; Pretsch, E. Anal. Chem. 1999, 71, 1204. (15) Sokalski, T.; Ceresa, A.; Fibbioli, M.; Zwickl, T.; Bakker, E.; Pretsch, E. Anal. Chem. 1999, 71, 1210. (16) Vigassy, T.; Morf, W. E.; Badertscher, M.; Ceresa, A.; de Rooij, N. F.; Pretsch, E. Sens. Actuators, B 2001, 76, 477. (17) Makarychev-Mikhailov, S.; Shvarev, A.; Bakker, E. J. Am. Chem. Soc. 2004, 126, 10548.
reference electrode stability. Moreover, the utilization of the zerocurrent potential measurements, following the current pulse (mode II), allows one to avoid complexities connected to an iR potential drop across the membrane. At full instrumental control, unusually high sensitivity and relative simplicity may significantly improve the precision of potentiometric analysis and may be very attractive for point-ofcare analysis such as blood electrolyte assays. In the present paper, highly sensitive calcium pulstrodes were developed and applied to the analysis in diluted artificial blood serum and plasma. The theoretical description of the galvanostatically controlled potentiometric sensors is extended, and it is shown that a highly sensitive signal may be obtained from a single measurement pulse, recorded during the current pulse (mode I) or immediately following it under open-circuit conditions (mode II). Note that potential measurements performed at open circuit are fully analogous to classical zero-current potentiometry and differ from measurements utilized earlier, when zero current was preset galvanostatically. Single-pulse measurements shorten analysis time down to a few seconds, retaining full functionality of the pulstrode technique. The practical applicability of the pulstrodes for analysis of ionized calcium is demonstrated in good agreement with theory. EXPERIMENTAL SECTION Reagents. Calcium ionophore, dicyclohexyl-N′-phenyl-N′-3-(2propenoyl)oxyphenyl-3-oxapentanediamide (AU-1), was synthesized as described elsewhere.18 Tetradodecylammonium tetrakis(4chlorophenyl)borate (ETH 500), 2-nitrophenyl octyl ether (NPOE), high molecular weight poly(vinyl chloride) (PVC), and tetrahydrofuran (THF) were purchased in a Selectophore grade from Fluka Chemical Corp. (Milwaukee, WI). All other chemicals were purchased from Fluka or Fisher Scientific (Pittsburgh, PA) in analytical reagent grade, Nanopure deionized water (18.2 MΩ cm) was used throughout all experiments. Solutions of 10-times-diluted artificial blood serum (ABS) were prepared from inorganic salts in the following concentrations: NaCl 10 mM, NHCO3 4 mM, NaH2PO4 0.1 mM, KCl 0.4 mM, KH2PO4 0.1 mM, and MgCl2 0.15 mM. The pH was adjusted by HCl to 7.4. Concentration of calcium was varied by the stepwise addition of CaCl2 and covered the range of 0.1-0.6 mM. The resulting total concentrations of the inorganic species, except calcium, were as follows: [Na+] 14.1 mM, [K+] 0.5 mM, [Mg2+] 0.15 mM, [Cl-] 10.6, [CO2]tot 4 mM, and [phosphates] 0.2 mM. Solution of 10-times-diluted artificial blood plasma was prepared from the 10-times-diluted ABS, described above, by dissolving 0.7 wt % albumin and 0.1 ‰ ethanol. Membrane and Electrode Preparation. Solvent polymeric membranes, containing 20 mmol kg-1 (1.04 wt %) calcium ionophore AU-1, 10 wt % lipophilic inert electrolyte ETH 500, polymer (PVC), and plasticizer (NPOE) in ratio 1:2 by weight, were obtained dissolving all components in THF, followed by its evaporation. Disks of 5 mm in diameter were punched out from the parent membrane with a cork borer and glued on a top of the Nalgene PVC tubes (Nalge Nunc Int. Corp., Rochester, NY) with 3.2-mm inner and 6.4-mm outer diameters. The inner filling solution contained 10 mM sodium chloride or phosphate buffer (18) Qin, Y.; Peper, S.; Radu, A.; Ceresa, A.; Bakker, E. Anal. Chem. 2003, 75, 3038.
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(pH 7.0). All electrodes prior to measurements were conditioned overnight in a 10 mM solution of calcium chloride. Experimental Setup. A conventional three-electrode setup was used for measurements. A stranded platinum wire was used as a counter electrode; an external reference Ag/AgCl electrode (Mettler-Toledo, InLab 302) contained saturated KCl and a salt bridge filled with 1 M LiOAc. Chlorinated silver wires were used as inner reference/working electrodes. A bipotentiostat AFCBP1 (Pine Instruments, Grove City, MA), controlled by DAQPad-6015 data acquisition board and LabView 7.1 software (both from National Instruments, Austin, TX) running on a personal computer, was used for measurements. Three-pulse sequences were applied on the electrochemical cells. First, in mode I, a pulse of dc current of fixed magnitude and duration was applied galvanostatically and the potentials were recorded as a function of time during the pulse. Then the system was disconnected from the galvanostat and switched to the open-circuit mode (mode II), and potentials were recorded as in classical potentiometry under zerocurrent conditions. Details on the low noise potentiostatic/ galvanostatic control switching device may be found elsewhere.7 The last, third, pulse was applied potentiostatically with the especially adjusted baseline potential to ensure effective stripping of ions extracted during the current pulse. Duration of this pulse was usually 30-50 times longer than the corresponding current pulse. Potential measurements were performed with the sampling rate of 1 kS s-1 and were followed by averaging over 100-ms time intervals. THEORY This theoretical section is expanded relative to earlier work7 in two ways: First, the treatment is expanded to divalent analyte ions and monovalent interfering ions. Earlier work was developed for ions of the same charge only. Second, the potential response during a galvanostatic pulse is analyzed in the time domain in order to obtain differential signals that are sampled at different times rather than under different current densities as done earlier. This will allow one to perform such differential experiments in a matter of seconds rather than minutes. The response mechanism of the galvanostatically controlled potentiometric sensors was proposed recently.7 While in contrast to classical potentiometric sensors pulstrodes operate under nonequilibrium conditions and the phase boundary concentrations of ions are dictated mainly by the applied current pulses, the phase boundary model19 that normally describes the response of classical ISEs is also applicable to the pulstrodes. Furthermore, it allows one to use well-established ISE parameters, such as electrode slopes and potentiometric selectivity coefficients, for the characterization of the pulstrode. The well-known equation for the phase boundary potential is assumed to hold for galvanostatically controlled sensors based on neutral carriers:
kIcI RT ln EPB ) zIF [ILzI+] n
(1)
in the aqueous part of the phase boundary; [ILznI+] is the concentration of the cation I, complexed with an ionophore L with a stoichiometry n, in the organic part of the phase boundary; kI includes the free energy of ion phase transfer for I and all other symbols have their conventional meanings. Ion concentrations are used here instead of ion activities for simplicity reasons. If the concentration of I in the membrane phase and all other potential contributions are constant, eq 1 may be transformed to the Nernst equation:
EM ) EI0 +
(19) Bakker, E.; Buhlmann, P.; Pretsch, E. Talanta 2004, 63, 3.
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Analytical Chemistry, Vol. 78, No. 8, April 15, 2006
(2)
A constant [ILznI+] in traditional polymeric ion-selective membranes is usually achieved by the incorporation of a fixed concentration of a lipophilic ion exchanger, which provides ionic sites for hydrophilic ions. The simultaneous sensor response to primary and interfering ions is traditionally described by the semiempirical Nikolski-Eisenman equation,
EM ) EI0 +
RT
ln(cI +
zI F
∑K
pot zI/zJ ) I,J cJ
(3)
J
where cJ is the concentration of any interfering ion J in the aqueous part of the phase boundary and Kpot I,J is the potentiometric selectivity coefficient. The eq 3, while still widely used for ISE selectivity evaluation, is not generally valid when ions I and J are of different charge and both contribute to the membrane potential. A self-consistent formalism describing the mixed response of an electrode to ions of different charge has been developed20 and the membrane potential for the special case of mono- and divalent ions can be expressed by eq 421
EM ) EI0 +
RT F
ln
[∑ 1
2
I Kpot1/z ci1 + I,i1
i1
x(
1
∑K 2
pot1/zI ci1 I,i1
i1
)
2
+
∑K
pot2/zI ci2 I,i2
i2
]
(4)
where indexes i1 and i2 correspond to monovalent and divalent pot pot ions; KI,i1 and KI,i2 are potentiometric selectivity coefficients. The summations in eq 4 involve all ions, including the analyte ion I, in which case Kpot I,J ) 1. If ions of the same charge only are present in solution, eq 4 reduces to the Nikolski-Eisenman equation (eq 3). Using this formalism, the phase boundary concentrations of ions can be related to the total concentration of ionic sites in the membrane phase,22 usually denoted as RT:
cI [ILznI+]
)
[∑
zI 1 RT 2
I Kpot1/z ci1 + I,i1
i1
x( ∑ 1
2
Here cI is the concentration of the cation I, with the charge of zI,
RT ln cI zI F
i1
I Kpot1/z ci1 I,i1
)
2
+
∑ i2
I Kpot2/z ci2 I,i2
]
zI
(5)
If the primary ions are divalent (i.e., calcium) and only one type
of (monovalent) ion such as sodium may influence the potential response, eq 5 is reduced to
cI [ILznI+]
)
2 pot 2 (cJxKpot I,J + x4cI + cJ KI,J ) 2RT
may be approximated by the simple relationship, holding for each phase:
δ ) 2xDt
(12)
(6) Inserting eqs 10 and 12 into eq 8 gives the following relationship
In the case of galvanostatically controlled electrodes, the phase boundary concentrations of ions extracted into the membrane are determined by the current pulse, which imposes fluxes of ions in the direction of membrane:
i ) FA(z I JI + z J JJ)
(7)
JI ) -
[ILznI+]xDorg 2t
and a similar one may be obtained for the ion J. Inserting these two into eq 7 with some simple rearrangements yields
zI[ILznI+] + zJ[JLznJ+] ) where A is the membrane area and JI and JJ are the ionic fluxes, expressed here by the first Fick’s law for both aqueous and organic phases and assuming linear concentration profiles:
JI )
Daq Dorg (c - cI,bulk)) ) ([ILznI+] - [ILznI+]bulk) δaq I δorg
JJ )
Daq Dorg zJ+ (cJ - cJ,bulk) ) ([JLn ] - [JLznJ+]bulk) (9) δaq δorg
[ILznI+]bulk ) [JLznJ+]bulk ) 0
(10)
The aqueous-phase boundary concentration of the interfering background ions J is assumed to be equal to its aqueous bulk concentration, as at high background concentrations no depletion of the interfering ions in the aqueous part of the phase boundary is expected:
cJ ) cJ,bulk
(11)
The diffusion layer thickness, being dependent on pulse time t, (20) Bakker, E.; Meruva, R. K.; Pretsch, E.; Meyerhoff, M. E. Anal. Chem. 1994, 66, 3021. (21) Nagele, M.; Bakker, E.; Pretsch, E. Anal. Chem. 1999, 71, 1041. (22) Ceresa, A.; Radu, A.; Peper, S.; Bakker, E.; Pretsch, E. Anal. Chem. 2002, 74, 4027.
2i FA
x
t Dorg
(14)
Taking into account eqs 10 and 12, eq 8 may be also rewritten as
[ILznI+] ) -
(8)
here Daq and Dorg are ionic diffusion coefficients and δaq and δorg are diffusion layer thicknesses for aqueous and organic phases, correspondingly. These values are assumed to be equal for the two ions I and J in the corresponding phases. Concentrations of ions in the bulk of the two phases are denoted with a subscript. The ion-ionophore complex stoichiometry of n is assumed to be equal for both ions. Furthermore, the bulk concentrations of ions in organic phase, [ILznI+]bulk and [JLznJ+]bulk, are supposedly zero as the sensor membrane contains no intrinsic ionic sites and ionic diffusion coefficients in solvent polymeric membranes are relatively small (usually in order of 10-8 cm2 s-1), so the ions do not penetrate deeply into membrane phase during the current pulse:
(13)
xDaq (c - c ) I I,bulk xDorg
(15)
Substitution of RT in eq 5 with the sum of the ions in the organic part of the phase boundary from eq 14 gives a generalized equation, too cumbersome to present here. However, by reducing the case to divalent primary ions I and one type of monovalent interfering ions J, eq 6 gives after some rearrangement
cI (cI - cI,bulk)
)-
x
FA 4i
Daq 2 (c Kpot + x4cI + cJ Kpot I,J ) t Jx I,J (16)
After substitution of known or estimated parameters, eqs 15 and 16 represent a set of two equations with two unknowns (cI and [ILznI+]) and can be solved explicitly (see Supporting Information). Inserting these obtained expressions into the equation for the phase boundary potential (eq 1) describes the pulstrode response and shows the dependence of the measured potential on the current pulse parameters. RESULTS AND DISCUSSION The calcium ionophore AU-1 is a derivative of the widely used ionophore ETH 12923,24 and was recently proposed for covalent grafting into the polymer matrix.18 The selectivity of calcium ionselective electrodes based on AU-1 is somewhat inferior to those pot based on ETH 129 (for example, log KCa,Na ) -6.0 for AU-1based and -8.3 for ETH 129-based PVC-NPOE membranes),24 yet is sufficient for calcium determination in clinical analysis. The selectivity decrease was explained by the smaller complex stability constant of AU-1 ionophore with calcium, which was determined by the segmented sandwich membrane method25 as log β3 ) 23.3, almost 6 orders of magnitude lower than that for the complex (23) Schefer, U.; Ammann, D.; Pretsch, E.; Oesch, U.; Simon, W. Anal. Chem. 1986, 58, 2282. (24) Bakker, E. Anal. Chem. 1997, 69, 1061. (25) Mi, Y. M.; Bakker, E. Anal. Chem. 1999, 71, 5279.
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Figure 2. Selectivity characterization of the pulstrode: responses to calcium and interfering ions in unbuffered solutions in mode II sampled at 2 s, after a 3-s cathodic current pulse of -3 µA.
Figure 1. Calibration curves for calcium in a 1 mM NaCl background: (A) mode I, under applied current pulses of 1 s; (B) mode II, at open-circuit conditions after 1 s, succeeding the cathodic current pulse. A 30-s baseline potential of 50 mV was applied after the twopulse sequence in order to ensure sensor membrane renewal.
stability constant for ETH 129.18 The diminished ion-ionophore complex stability in the membrane, however, significantly improves the higher detection limit of the sensors as it prevents anion interference at high concentrations of the analyte due to the coextraction of counterions into membrane phase. The latter was shown to affect the sensors based on ETH 129 and ETH 1001 calcium ionophores.26 In this work, early experiments with pulsed galvanostatically controlled membrane electrodes based on ETH 129 revealed a high ion selectivity, but it was difficult to find proper baseline potential conditions where the current would reliably decrease to zero (data not shown). This was likely caused by the high complex formation constant mentioned above. Consequently, the ionophore AU-1 was explored and found to be adequate. Figure 1 presents calibration curves of a typically AU-1 based galvanostatically controlled sensor recorded at different pulse currents. The data are in agreement with previous findings11 and the theory.7 A super-Nernstian response slope is observed in both modes (measurement of the potential during the current pulse, mode I, and immediately after the pulse under open circuit, mode II) in a calcium activity range that depends on the current pulse magnitude.17 At a -10 µA current in mode I, the super-Nernstian region of the pulstrode calibration curve covers the physiological range of calcium concentration in 10-times-diluted blood. Selectivity evaluation of the calcium pulstrode was performed in nonbuffered solutions of the primary and interfering ions at elevated (26) Lee, M. H.; Yoo, C. L.; Lee, J. S.; Cho, I. S.; Kim, B. H.; Cha, G. S.; Nam, H. Anal. Chem. 2002, 74, 2603.
2748 Analytical Chemistry, Vol. 78, No. 8, April 15, 2006
concentrations (Figure 2). As the response slopes of the AU-1 sensors toward calcium and interfering ions at relatively high activities remain close to Nernstian with no anion interference observed, the pulstrode selectivity coefficients were calculated pot using the methodology of classical ISEs27 as log KCa,Na ) -5.7 ( pot pot 0.1, log KCa,K ) -7.6 ( 0.1, log KCa,Li ) -4.9 ( 0.1, and log pot KCa,Mg ) -7.8 ( 0.1, which are in good agreement with previous findings18 and sufficient for calcium measurements in 10-folddiluted blood28 Figure 3 A shows a theoretical chronopotentiometric response function of the pulstrode in mode I with the following parameters used: i ) -3 µA, A ) 8 mm2, cJ ) 1 mM, log Kpot I,J ) -5.7, Daq ) 4 × 10-5 cm2 s-1, and Dorg ) 10-8 cm2 s-1. Experimental chronopotentiograms of the calcium pulstrode at different activities of calcium in a 1 mM NaCl background are shown in Figure 3B. The larger value of calcium ion diffusion coefficient in aqueous phase than the tabulated one29 (0.792 × 10-5 cm2 s-1) is used for better fit, which may be explained by contributions of convection and migration to the overall calcium ion transport, which were not accounted for in the model. While the migration might be diminished to some extent by a higher concentration of a background electrolyte, any convection originating from vibrations and solution density fluctuations caused by the passing electrical current is more difficult to take into account. As predicted by the theory, two potential waves can be distinguished in mode I, attributed to the processes of extraction of calcium and background ions, correspondingly. This can be illustrated by the calculated ion concentration profiles depicted in Figure 4, where linear diffusion profiles and a Cottrellian behavior of the diffusion layer thickness are assumed as a first approximation. At high concentrations of calcium (Figure 4A) no depletion in the aqueous part of the phase boundary takes place during the current pulses and the current-induced ion flux is solely maintained by the primary ions, as the calcium phase transfer is facilitated by the ionophore present in membrane. However, if the calcium sample concentration is relatively low, polarization in the aqueous diffusion layer near the membrane exists and background ions must be (27) Bakker, E.; Pretsch, E.; Buhlmann, P. Anal. Chem. 2000, 72, 1127. (28) Bakker, E.; Meyerhoff, M. E. In Encyclopedia of Electrochemistry; Bard, A. J., Stratmann, M., Wilson, J. S., Eds.; Wiley: New York, 2002; Vol. 9. (29) Lide, D. R., Ed. CRC Handbook of Chemistry and Physics, Internet Version 2005, ; CRC Press: Boca Raton, 2005.
Figure 3. Pulstrode chronopotentiometric responses in mode I in solutions with variable activity of calcium (logarithmic units): (A) theoretical predictions (for parameters see text); (B) experimental data in a 1 mM NaCl background with -3 µA current pulses.
extracted into membrane (Figure 4B), which is the origin of the pulstrode super-Nernstian response. The pulstrode response under open-circuit conditions after the current pulse also exhibits a super-Nernstian jump, shifted to the lower analyte concentrations (Figure 1). The chronopotentiograms recorded in the mode II are shown in Figure 5. The important distinction of this mode from mode I is that the measured potentials are not influenced by the iR drop, which is always present in measurements performed under passing current. As no net ion flux occurs, the potential is determined by the three concurring processes as flattening of the primary ion concentration in the aqueous phase, diffusion of ions in membrane, and zerocurrent ion exchange at the interface.17 A more detailed theoretical description of the pulstrode response in mode II is yet to be developed. In analogy to the current-dependent potentiometric response (Figure 1), a family of traditional calibration curves in coordinates potential-logarithmic activity can also be evaluated from the chronopotentiograms, sampling potentials at different time intervals. This allows one to tune the position of the super-Nernstian jump within a single pulse. Moreover, the highly sensitive peakshaped differential response, obtained by subtraction of the potentials, sampled at different times, can also be evaluated from one pulse only. This is illustrated by the measurements in artificial 10-times-diluted physiological liquids (see Figure 6). The artificial solutions contained all inorganic electrolytes (serum) and albumin (plasma) in concentrations common for real physiological samples.28 For this experiment, the pulse current was adjusted so that the family of response curves covered the physiological range (Figure 6A and B). The required calcium concentration range can be easily
Figure 4. Calculated calcium concentration profiles induced by the cathodic current applied across the calcium-selective membrane: (A) in 10 mM calcium solution, no polarization; (B) in 0.1 mM calcium solution with concentration polarization in the aqueous diffusion layer near the membrane.
Figure 5. Experimental pulstrode chronopotentiometric responses in mode II in solutions with variable activity of calcium (denoted in logarithmic units) in a 1 mM NaCl background, after 3-s current pulses of -3 µA.
accessed by choosing the appropriate curve. A sensitivity as high as 400 mV decade-1 for measurements in mode I and more than 700 mV decade-1 for mode II were achieved in the range of 0.1 logarithmic unit of calcium concentration change. Similar results were obtained in plasma; however, the corresponding superNernstian regions were shifted to higher concentrations, perhaps because of the lower free calcium activity in plasma due to calcium binding with albumin, which was not accounted for (data not shown). The differential responses of the pulstrode may be evaluated from the calibration curves (Figure 6C and D). The subtraction of the potential values measured at two different pulse times leads to a peak-shaped signal, with maximum at the ion activity that Analytical Chemistry, Vol. 78, No. 8, April 15, 2006
2749
Figure 7. Reproducibility of the pulstrode response in calcium solutions with 1 mM NaCl background. Each pulse sequence at -10 µA current and at zero current was followed by a 60-s potential baseline pulse, which is not shown on the plot for clarity.
Figure 6. Super-Nernstian response curves (A) in mode I, (B) in mode II, and differential signals of the pulstrode (C) in mode I, and (D) in mode II, recorded in artificial 10-times-diluted blood serum at pH 7.4. The peak was instrumentally adjusted to the physiological range of calcium concentration (denoted by the dashed lines).
lies between the middle points of the two super-Nernstian jumps. Depending on the time interval chosen, the magnitude of the peak may comprise tens of millivolts, which makes the sensor very sensitive to a small activity change. The calculated calcium pulstrode differential signals approach 70 mV for the physiological range of 0.22-0.26 mM calcium in 10-times-diluted extracellular samples. The pulstrode with a differential signal could be used as a chemical alarm system. Once an analyte level changes and goes out of a predefined range, the drastic change of potential occurs and could be detected and processed for an alarm. Such highly sensitive and robust systems could, for instance, be installed near the patient beds for immediate and precise control over blood electrolyte levels. The position of the super-Nernstian jump on the analyte concentration scale is a function of current pulse parameters and a simple relation for the critical concentration, at which the drastic change in potential takes place, was derived earlier:7
cI(critical) ) -
2i FA
x
t Daq
(17)
The magnitude of the super-Nernstian jump, however, also depends on the selectivity of the pulstrode and background concentration of interfering ions. As the blood electrolyte concentrations usually vary in narrow and well-documented ranges, the theory can predict the magnitudes of super-Nernstian jumps. Thus, for an AU-1-based pulstrode, the logarithmic selectivity coefficient for sodium (the most drastically interfering ion) is pot KCa,Na of -5.7, which gives ∼150 mV at 1-s pulse of -3 µA in 0.01 M NaCl solution, which value appears to be in a full agreement with the experiment. This is not a fundamental limit pot as better selectivity with KCa,Na ) -8.3, reported for ion-selective 2750 Analytical Chemistry, Vol. 78, No. 8, April 15, 2006
electrodes based on ETH 129,24 could potentially give pulstrodes super-Nernstian responses exceeding 200 mV. Full instrumental control over the processes taking place at the membrane-solution interface provides a remarkable stability of the pulstrode signal. The potentiostatic pulse with the baseline potential, applied after the measurement pulse sequence, ensures effective stripping of the extracted ions and renewal of the membrane surface. According to the theory,30 a stripping pulse of at least 20 times longer than the duration of the preceding uptake pulse is sufficient for reproducible pulsed sensor behavior. The time traces of the potentials, recorded in two alternating solutions of different calcium activity, are presented in Figure 7. The response curvatures remain unchanged after switching between solutions, and the averaged potentials in the corresponding samples after 2 s of the current pulse and after 2 s of the following open-circuit pulse remain constant within a couple of millivolts. This is quite remarkable considering that the sensor signals approached -1.5 V in mode I. This accuracy was observed without any special precautions on a laboratory table and was mainly dictated by the imperfections of temperature control, the galvanostat, and data acquisition system. As the physiological electrolyte concentration varies in a narrow range (for calcium 2.2-2.6 mM in whole blood), and the potential range for calcium measurements according to the Nernst equation is 2.2 mV, a 10100-µV precision of the traditional potentiometric measurements is usually required, which is achieved by careful temperature and flow control in flow-through cells. Here, in contrast, the same accuracy was achieved with common laboratory equipment due to the extremely high sensitivity of the pulstrode technique. Further improvement of the measurements accuracy is certainly possible through consistent depression of noise and fine-tuning of the electronic equipment. CONCLUSIONS The pulstrode technique introduces new dimensions to traditional potentiometry, namely, current and time. The complex multidimensional sensor signal carries information about the (30) Bakker, E.; Meir, A. J. SIAM Rev. 2003, 45, 327.
system that is hardly accessible in classical potentiometric analysis. The pulstrode response under nonequilibrium conditions allows one to overcome certain thermodynamic limits. While various kinetic effects can be used to enhance the sensitivity and selectivity of the ion-selective electrodes, only full instrumental control over the sensor may provide practically useful stability and reproducibility of the response. A deeper understanding of the underlying processes and a detailed theoretical description of the pulstrode response will provide further development of this attractive technique.
ACKNOWLEDGMENT The authors thank the National Institutes of Health (Grant GM071623) for financial support of this research. SUPPORTING INFORMATION AVAILABLE Explicit solution for eq 16. This material is available free of charge via the Internet at http://pubs.acs.org. Received for review December 14, 2005. Accepted February 8, 2006. AC052211Y
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