Anal. Chem. 2005, 77, 7801-7809
Ion-Selective Supported Liquid Membranes Placed under Steady-State Diffusion Control Ka´roly Tompa,† Karin Birbaum,† Adam Malon,† Tama´s Vigassy,† Eric Bakker,*,‡ and Erno 1 Pretsch*,†
Laboratorium fu¨r Organische Chemie, ETH Ho¨nggerberg, CH-8093 Zu¨rich, Switzerland, and Department of Chemistry, 560 Oval Drive, Purdue University, West Lafayette, Indiana 47907
Supported liquid membranes are used here to establish steady-state concentration profiles across ion-selective membranes rapidly and reproducibly. This opens up new avenues in the area of nonequilibrium potentiometry, where reproducible accumulation and depletion processes at ion-selective membranes may be used to gain valuable analytical information about the sample. Until today, drifting signals originating from a slowly developing concentration profile across the ion-selective membrane made such approaches impractical in zero current potentiometry. Here, calcium- and silver-selective membranes were placed between two identical aqueous electrolyte solutions, and the open circuit potential was monitored upon changing the composition of one solution. Steady state was reached in ∼1 min with 25-µm porous polypropylene membranes filled with bis(2-ethylhexyl) sebacate doped with ionophore and lipophilic ion exchanger. Ion transport across the membrane resulted on the basis of nonsymmetric ion-exchange processes at both membrane sides. The steady-state potential was calculated as the sum of the two membrane phase boundary potentials, and good correspondence to experiment was observed. Concentration polarizations in the contacting aqueous phases were confirmed with stirring experiments. It was found that interferences (barium in the case of calcium electrodes and potassium with silver electrodes) induce a larger potential change than expected with the Nicolsky equation because they influence the level of polarization of the primary ion (calcium or silver) that remains potential determining. Conventional ion-selective electrodes (ISEs) ideally obey the Nernst equation, where the observed electromotive force is a function of the potential at the sample-membrane phase boundary.1-4 Other potential contributions, including the one at the membrane-inner solution side, are typically kept constant * To whom correspondence should be addressed. E-mail: pretsch@ org.chem.ethz.ch. † ETH Zurich. ‡ Purdue University. (1) Koryta, J.; Stulik, K. Ion-Selective Electrodes, 2nd ed.; Cambridge University Press: Cambridge, U.K., 1983. (2) Morf, W. E. The Principles of Ion-Selective Electrodes and of Membrane Transport; Elsevier: New York, 1981. (3) Bakker, E.; Bu ¨ hlmann, P.; Pretsch, E. Chem. Rev. 1997, 97, 3083-3132. (4) Bakker, E.; Bu ¨ hlmann, P.; Pretsch, E. Talanta 2004, 63, 3-20. 10.1021/ac051362y CCC: $30.25 Published on Web 10/25/2005
© 2005 American Chemical Society
or their changes are minimized as much as possible. This experimental arrangement still forms the basis for the functioning of most potentiometric sensors used worldwide.5 Textbook knowledge also expects such measurements to obey thermodynamic principles.4 Zero current potentiometry, therefore, is traditionally regarded as one of the few analytical methods that yield information on ion activities, rather than concentrations. In recent years, it has been realized that transmembrane diffusion phenomena, which had been explored earlier by other groups for mechanistic purposes,6-9 may perturb the ion concentrations at the sample-membrane phase boundary.10,11 If an aqueous inner solution is not identical to the sample at the front side of the membrane, the concentration imbalance may lead to significant diffusion of ions in either direction.12 Most recent work has focused on the understanding of such processes and the minimization of the associated effects.13 For highly selective membranes, the optimization of the inner solution and the conditioning/measurement protocols gave rise to the development of potentiometric sensors with detection limits in the nanomolar range or lower.14-16 This has opened new avenues for this class of electrochemical sensors, especially in environmental and clinical analysis.17,18 On the other hand, concentration polarizations at the samplemembrane interface may also be analytically useful.19 Early examples certainly include the potentiometric sensors for the polyions heparin and protamine, pioneered by the laboratories of (5) Bu ¨ hlmann, P.; Pretsch, E.; Bakker, E. Chem. Rev. 1998, 98, 1593-1687. (6) Behr, J. P.; Kirch, M.; Lehn, J.-M. J. J. Am. Chem. Soc. 1985, 107, 241246. (7) Huser, M.; Morf, W. E.; Fluri, K.; Seiler, K.; Schulthess, P.; Simon, W. Helv. Chim. Acta 1990, 73, 1481-1496. (8) Nahir, T. M.; Buck, R. P. Talanta 1994, 41, 335-341. (9) Buck, R. P.; Nahir, T. M.; Cosofret, V. V.; Lindner, E.; Erdosy, M. Anal. Proc. 1994, 31, 301-312. (10) Mathison, S.; Bakker, E. Anal. Chem. 1998, 70, 303-309. (11) Sokalski, T.; Ceresa, A.; Zwickl, T.; Pretsch, E. J. Am. Chem. Soc. 1997, 119, 11347-11348. (12) Sokalski, T.; Zwickl, T.; Bakker, E.; Pretsch, E. Anal. Chem. 1999, 71, 12041209. (13) Bakker, E.; Pretsch, E. Anal. Chem. 2002, 74, 420A-426A. (14) Bakker, E.; Pretsch, E. Trends Anal. Chem. 2005, 24, 199-207. (15) Lindner, E.; Gyurcsa´nyi, R. E.; Buck, R. P. Electroanalysis 1999, 11, 695702. (16) Pergel, E.; Gyurcsa´nyi, R. E.; To´th, K.; Lindner, E. Anal. Chem. 2001, 73, 4249-4253. (17) Ceresa, A.; Bakker, E.; Hattendorf, B.; Gu ¨ nther, D.; Pretsch, E. Anal. Chem. 2001, 73, 343-351. (18) Slaveykova, V. I.; Wilkinson, K. J.; Ceresa, A.; Pretsch, E. Environ. Sci. Technol. 2003, 37, 1114-1121. (19) Bakker, E.; Meyerhoff, M. E. Anal. Chim. Acta 2000, 416, 121-137.
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Meyerhoff and Yang.20 They must function in a nonthermodynamic manner because the high polyion charge is predicted, by the Nernst equation, to give very small electrode slopes. Large, analytically useful sensitivities are observed if the polyions are depleted at the membrane surface as a result of a strong ion flux in direction of the inner solution. This was realized by working with membranes that are void of polyion, contrary to common practice in the field, which always conditions the membrane with solutions that contain large concentrations of the ion to be determined.21 Polyions in the sample now spontaneously exchange with a hydrophilic ion in the membrane, which generates the desired inward polyion flux.22 Membranes initially void of primary ions are also highly beneficial for the characterization of the membrane selectivity of most other ion-selective electrodes, where experimental biases from outward ion fluxes on the potential measurements can be successfully eliminated.23,24 Other examples that make use of such fluxes include the development of so-called steptrodes, where two ion-selective electrodes are measured against each other, each optimized to give a different magnitude of inward ion flux.25 The sample concentration at which the analyte ion depletes at the membrane surface to give a large, so-called super-Nernstian response step is different for the two electrodes. In this case, the differential measurement gives a large bell-shaped response curve at a critical sample concentration that could be useful for chemical alarm systems.25 Similar ion flux effects were also found to be beneficial to make ion-selective electrodes sensitive to total concentration changes in the sample.26 Indeed, concentration polarizations at the sample-membrane interface are diminished if labile complexes of the analyte ion are present in the sample. In other work, it was found that inward ion fluxes may be useful in complexometric titrations: the observed potential change may be significantly larger than thermodynamically predicted.27 Unfortunately, it remains very difficult to experimentally control the magnitude of such transmembrane ion fluxes. Typical thicknesses of solvent polymeric membranes are ∼200 µm, and the diffusion coefficient in established materials, such as poly(vinyl chloride) overplasticized with bis(2-ethylhexyl) sebacate in a 1:2 ratio, is only on the order of 10-8 cm2 s-1. The establishment of a steady state across the membrane takes, therefore, many hours to accomplish. This translates into drifting potential signals and systems that are prone to memory effects and irreproducible behavior. A numerical approximation of the diffusion behavior on such membranes was recently used to evaluate the relevant diffusion kinetics, and these concerns were confirmed.28,29 (20) Meyerhoff, M. E.; Fu, B.; Bakker, E.; Yun, J. H.; Yang, V. C. Anal. Chem. 1996, 68, 168A-175A. (21) Ye, Q.; Meyerhoff, M. E. Anal. Chem. 2001, 73, 332-336. (22) Fu, B.; Bakker, E.; Yun, J. H.; Yang, V. C.; Meyerhoff, M. E. Anal. Chem. 1994, 66, 2250-2259. (23) Sokalski, T.; Ceresa, A.; Fibbioli, M.; Zwickl, T.; Bakker, E.; Pretsch, E. Anal. Chem. 1999, 71, 1210-1214. (24) Bakker, E.; Pretsch, E.; Bu ¨ hlmann, P. Anal. Chem. 2000, 72, 1127-1133. (25) Vigassy, T.; Morf, W. E.; Badertscher, M.; Ceresa, A.; de Rooij, N. F.; Pretsch, E. Sens. Actuators B 2001, 76, 477-482. (26) Ceresa, A.; Pretsch, E.; Bakker, E. Anal. Chem. 2000, 72, 2050-2054. (27) Peper, S.; Ceresa, A.; Bakker, E.; Pretsch, E. Anal. Chem. 2001, 73, 37683775. (28) Sokalski, T.; Lingenfelter, P.; Lewenstam, A. J. Phys. Chem. B 2003, 107, 2443-2452. (29) Radu, A.; Meir, A. J.; Bakker, E. Anal. Chem. 2004, 76, 6402-6409.
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One solution to this dilemma has been the recent introduction of pulsed galvanostatically controlled ion sensors, so-called pulstrodes.30,31 Rather than relying on a chemically controlled steady state across the membrane, these systems are designed to lack an ion exchanger in the membrane phase. Ion fluxes are imposed during a galvanostatic pulse, and membrane renewal is accomplished with a potentiostatic resting pulse.30 This indeed yields electrochemical sensors with reproducible super-Nernstian response behavior. Recent work has now introduced reproducible polyion sensors, sensors that can distinguish free and total ion concentrations, and differential sensors for the reliable detection of ion concentrations with 10-20-fold sensitivities relative to the Nernstian electrode slope.32 Efficient ion transport across hydrophobic membranes is also important in other fields of research. The group of Buffle, for instance, has reported on the use of supported liquid membranes for environmental sampling purposes. Here, the metal ion of interest is selectively transported from the sample into the interior of a hollow fiber where it is detected by electrochemical33 or optical means.34 Subsequently, supported liquid membranes were also successfully used to study the current response of ISE membranes35 and with the pulsed galvanostatically controlled sensors mentioned above.31 Interestingly, such arrangements bear a strong resemblance to the earliest liquid membrane ion-selective electrodes,36,37 which used simple filter papers soaked with an ionselective liquid. Here, however, the lipophilicity of all active membrane ingredients is much higher than in earlier work. In all these electrochemical sensing systems, the solution at the inner membrane side was sufficiently concentrated in order to ensure robust sensing behavior. This paper introduces and evaluates an experimental setup where transmembrane ion fluxes are sufficiently rapid to reach steady state in analytically acceptable times. This is accomplished with supported liquid membranes based on 25-µm porous hydrophobic films. In view of expanded practical applications, the system is evaluated here with an inner solution that may be concentration polarized at the inner membrane side as well. This is in contrast to earlier work that has attempted to keep this inner side as robust as possible in view of a minimization of the relevant fluxes.13 This modified setup is described and validated with an expanded steady-state diffusion model. THEORY We describe here the steady-state concentration profiles and corresponding boundary potentials of a three-phase system, as shown in Figure 1. Concentration polarizations may occur at the front and back side of the membrane, in contrast to earlier work.38 Electrolyte coextraction from an aqueous side into the membrane is here excluded, and only ion-exchange processes are considered. (30) Shvarev, A.; Bakker, E. Anal. Chem. 2003, 75, 4541-4550. (31) Makarychev-Mikhailov, S.; Shvarev, A.; Bakker, E. J. Am. Chem. Soc. 2004, 126, 10548-10549. (32) Shvarev, A.; Bakker, E. J. Am. Chem. Soc. 2003, 125, 11192-11193. (33) Guyon, F.; Parthasarathy, N.; Buffle, J. Anal. Chem. 2000, 72, 1328-1333. (34) Ueberfeld, J.; Parthasarathy, N.; Zbinden, H.; Gisin, N.; Buffle, J. Anal. Chem. 2002, 74, 664-670. (35) Sutter, J.; Morf, W. E.; de Rooij, N. F.; Pretsch, E. J. Electroanal. Chem. 2004, 571, 27-35. (36) Pioda, L. A. R.; Simon, W. Chimia 1969, 23, 72-73. (37) Frant, M. S.; Ross, J. W. Science 1970, 167, 987-988. (38) Ceresa, A.; Radu, A.; Peper, S.; Bakker, E.; Pretsch, E. Anal. Chem. 2002, 74, 4027-4036.
[ILz+ n ]b )
cib RT z c + Kpot ib ij cjbb
(4)
∑
At steady state, the concentration differences in each Nernst diffusion layer, where cifb and cibb are the solution bulk concentrations of Iz+ at the front and back of the membrane, may be expressed as
Figure 1. Schematic representation of the system under study. The concentration of the primary ions ci is polarized at both sides of the membrane (cifb * cif and cibb * cib), but the concentrations of the interfering ions (cjfb and cjbb) are so high that their gradients in the aqueous phases are negligible. The concentration of the complexes of both ions with the ionophore (L) are polarized in the membrane phase.
The membrane potential may be described as the sum of both phase boundary potentials:2,4
EM )
cif RT ln zF [ILz+] n
[ILz+ n ]b
f
cib
(1)
qf )
cif - cifb z+ [ILn ]b - [ILz+ n ]f
(5)
qb )
cib - cibb z+ [ILn ]f - [ILz+ n ]b
(6)
where the parameter q is defined as
q)
δaqDmem δmemDaq
(7)
with δ the thickness of and D the diffusion coefficient in the respective phase. Note that δaq may be different for the front and back of the membrane, hence the two symbols qf and qb. Combining eqs 5 and 6, and solving for cif gives
cif ) (cibbqf - cibqf + cifbqb)/qb where cif and cib are the aqueous-phase boundary concentrations (strictly, activities) of the primary ion Iz+ at the front and back sides of the membrane, respectively. The two membrane-phase boundary concentrations of the primary ion complex are denoted with brackets, with subscripts f and b for the front and back sides. Equation 1 assumes that concentrations of these primary ion complexes are proportional to the concentrations of the uncomplexed ions,38 which is normally valid when the complex formation constants are sufficiently high39 and an excess ionophore is present in the membrane. In analogy to earlier work, the relationship between the ion concentrations at the aqueous and membrane side of each phase boundary can be understood on the basis of an ion-exchange process with interfering ions Jz+. The selectivity coefficient, Kpot ij , and the concentration of lipophilic ion exchanger in the membrane, RT, may used to describe the concentration ratio at each interface. For primary and interfering ions of equal charge, z:38
ci
z (c + RT i
∑K
(8)
Equations 3-6 comprise four equations for the four unknowns, cif, cib, [ILz+]f, and [ILz+]b. The aqueous boundary concentration on the back, cib, is explicitly written as a function of the concentration on the front, by replacing [ILz+]f and [ILz+]b in eq 5 with the RHS of eqs 3 and 4
cib ) -
zcif2 - zκfcifb + cif(qRT + z(κf - cifb)) zcif(cif - cifb) - κf(qRT + z(cifb - cif))
κb
where
κf )
∑K
pot ij cjfb;
κb )
∑K
pot ij cjbb
(9)
This may be inserted into eq 8 to give an implicit solution for cif:
κb{cif2z - cifbκfz + cif(qRT - zcifb + κfz)} cibb{cif(cifb - cif)z + κf(qRT - zcif + zcifb)}
(2)
qb (10) ) qf (cif - cifb){cif(cif - cifb)z - κf(qRT + (cifb - cif)z)}
Equation 2 is rewritten for the front of the membrane and, after neglecting depletion of the interfering ion because of its higher concentration, transformed to
This cubic equation can be explicitly solved for cif with computer software such as Mathematica, but the solution is impractically long to be displayed here. Still, eq 10 may be conveniently solved for cibb and is written for q ) qf ) qb as
[ILz+ n ]
)
[ILz+ n ]f )
pot ij cj)
cif RT z c + Kpot if ij cjfb
∑
And, in analogy, for the back of the membrane
(3)
cibb ) zcif3 + zcif2{κf - κb - 2cifb} + κfcifb{qRT + z(κb + cifb)} cif{κfqRT - zcifb2 + 2zκfcifb + κb(qRT + zκf - zcifb)} zcif(cif - cifb) - κf{qRT + z(cifb - cif)} (11)
(39) Qin, Y.; Bakker, E. Anal. Chim. Acta 2000, 421, 207-220.
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Equation 11 can either be solved numerically for a set of bulk concentrations in a given experiment or be solved explicitly for a broad range of phase boundary concentrations with routine spreadsheet software to plot trend lines and general predictions. Once a given set of variables, cibb, cifb, and cif, are identified with eq 11, the corresponding value of cib is calculated with eq 9. The membrane potential (eq 1) is then obtained from these values after inserting them into eqs 3 and 4. EXPERIMENTAL SECTION Reagents. Celgard 2500 microporous flat sheet polypropylene membranes of 0.057 × 0.22 µm2 pore size, 25-µm thickness, and 55% porosity were purchased from Celgard Inc. (Charlotte, NC). High-molecular-weight poly(vinyl chloride) (PVC), the Ca2+ ionophore, N,N-dicyclohexyl-N′,N′-dioctadecyl-3-oxapentanediamide (ETH 5234), and the Ag+ ionophore, O,O′′-bis[2-(methylthio)ethyl]-tert-butylcalix[4]arene, bis(2-ethylhexyl) sebacate (DOS), potassium and sodium tetrakis[3,5-bis-(trifluoromethyl)phenyl]borate (K- or Na-TFPB), and tetrahydrofuran (THF) were Selectophore from Fluka AG (Buchs, Switzerland). Aqueous solutions were prepared with deionized water (>18 MΩ cm specific resistance) obtained with a NANOpure reagent-grade water system (Barnstead, 4009 Buchs, Switzerland). The salts BaCl2, Cd(NO3)2, Cu(NO3)2, KCl, MgCl2, AgNO3, and Sr(NO3)2 were puriss. p.a. from Fluka, CaCl2 was Suprapure from Merck (Darmstadt, Germany), and KNO3 was puriss. p.a. from Merck. Pb(NO3)2 solutions were diluted from the 0.1 M Pb2+ standard solution Fluka (for ion-selective electrodes), and HNO3 solutions were diluted from concentrated nitric acid Suprapure from Merck. Membranes. The Ca2+-selective Celgard-based membranes contained ETH 5234 (1.2 wt %, 15.0 mmol kg-1), K-TFPB (0.5 wt %, 5.0 mmol kg-1), and DOS (98.3 wt %). A total of 101.7 mg of these components was dissolved in 2 mL of THF. After stirring for 1 h, the solvent was let to evaporate and a Celgard membrane disk of 1.8-cm diameter was impregnated with 10 µL of this membrane cocktail. The resulting membrane was immediately mounted in a plexiglass membrane holder and placed in a symmetrical Teflon cell allowing an exposed area of 0.79 cm2 and with compartments of 20 mL on either side. Before starting the measurements, the membrane was symmetrically conditioned in the appropriate solution. The membrane solution of the Ag+selective Celgard membrane consisted of Ag+ ionophore (1.2 wt %, 14.4 mmol kg-1), Na-TFPB (0.4 wt %, 5.0 mmol kg-1), and DOS (98.4 wt %). A total of 307.9 mg of these components was dissolved in 5 mL of THF, and the membrane was prepared according to the procedure above. The membranes with 20 wt % PVC contained ETH 5234 (1.2 wt %, 15.0 mmol kg-1), K-TFPB (0.5 wt %, 5.0 mmol kg-1), DOS (78.7 wt %), and PVC (19.7 wt %). Membranes of ∼250µm thickness were obtained by casting a solution of 200.1 mg of these components dissolved in freshly distilled THF (∼5 mL) into a glass ring (2.8-cm i.d.) fixed on a glass plate. After overnight evaporation of the solvent, a disk of 1.8-cm diameter was punched from this master membrane, mounted in the plexiglass membrane holder, placed in a symmetrical Teflon cell, and conditioned as described above. Emf Measurements. Measurements were performed with a 16-channel electrode monitor (Lawson Labs Inc., Malvern, PA) at ambient temperature (21-23 °C). During measurements in a symmetrical Teflon cell, the solutions in both compartments of 7804 Analytical Chemistry, Vol. 77, No. 23, December 1, 2005
pot Table 1. Selectivity Coefficients, log KCa J, Standard Deviations (N ) 4), and Slopes of the Calibration Curves (in Parentheses) Obtained with Ca2+-Selective Membranes Based on Celgard and Two Different PVC Membranesa
J
Celgard
20% PVC
33% PVC23
H+ Mg2+ Sr2+ Ba2+ Cd2+ Cu2+
-3.4 ( 0.1 (61.5) -8.0 ( 0.4 (27.6) -0.9 ( 0.1 (31.8) -2.6 ( 0.1 (31.7) -3.1 ( 0.1 (34.9) -6.3 ( 0.1 (32.3)
-2.6 ( 0.3 (61.3)
-3.8 ( 0.4 (43.0) -8.6 ( 0.3 (25.0) -1.1 ( 0.1 (22.3) -3.1 ( 0.1 (22.8)
aSlope
-3.1 ( 0.1 (32.8) -2.9 ( 0.1 (35.3) -6.5 ( 0.3 (31.1)
for the primary ion, 31.0 ( 0.7 mV.
the cell were magnetically stirred or unstirred, as indicated. Activity coefficients were obtained from the Debye-Hu¨ckel approximation, and emf values were corrected for liquid-junction potentials with the Henderson equation. The reference electrodes were Metrohm double-junction Ag/AgCl reference electrode (No. 6.0729.100 with 3 M KCl or 1 M KCl as reference electrolyte and 1 M NH4NO3 as bridge electrolyte) or from Oesch Sensor Technology (Sargans, Switzerland) (type 3311S DJR reference electrode S7, the other one is a modified version filled with 4 M KCl or 2 M KCl). RESULTS AND DISCUSSION Conventional polymeric membranes are constructed in a way to avoid concentration/emf changes at the inner phase boundary. While such changes have been observed,40-42 the time required to achieve a steady-state response at the back side of the membrane is on the order of 5-10 h.40 Therefore, supported liquid membranes are used here that are based on a microporous polypropylene matrix (Celgard 2500) of 25-µm thickness. The elliptical pores (0.057-0.22-µm2 pore size) formed by extrusion, annealing, and stretching were shown by scanning electron microscopy to be oriented with their major axes parallel to the film surface.43 With an inner solution of 10-3 M CaCl2, the response behavior of Celgard membranes is similar to that of PVC membranes, but because of the stronger transmembrane ion fluxes, the lower detection limit is higher by ∼1.5 orders of magnitude.35 The potentiometric responses of a DOS-based Ca2+selective Celgard membrane have been determined for a series of cations by first investigating the discriminated ions and then the preferred ones.40 Within the concentration range of 10-110-4 M, near-Nernstian responses have been obtained for all investigated ions (Table 1). As shown in Table 1, the selectivity coefficients calculated from these responses by the separate solution method24 are, within 0.1-0.2 logarithmic unit, the same as for conventional PVC membranes based on the same ionophore.23 The moderately interfering ion Ba2+ with a potentiometric pot selectivity coefficient of log KCaBa ) -2.6 was selected to (40) Bakker, E. Anal. Chem. 1997, 69, 1061-1069. (41) Pu ¨ ntener, M.; Fibbioli, M.; Bakker, E.; Pretsch, E. Electroanalysis 2002, 14, 1329-1338. (42) 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, 2104-2111. (43) Sarada, T.; Sawyer, L. C.; Ostler, M. I. J. Membr. Sci. 1983, 15, 97-113. (44) Long, R.; Bakker, E. Anal. Chim. Acta 2004, 91-95.
demonstrate the influence of fast transmembrane ion fluxes on the response behavior of the membranes. The time responses of two membranes were compared. One was based on a DOS solution of the Ca2+ ionophore and the ion exchanger K-TFPB immobilized in a Celgard membrane, and the other had the same composition but was immobilized in a polymeric membrane containing 20 wt % PVC. The lower than conventional (33 wt %) content of PVC brings about a four times higher diffusion coefficient.44 First, the membranes were symmetrically conditioned in a solution of 10-6 M CaCl2 with 10-3 M BaCl2. Then, at t ) 0, the solution at the front side was changed to 10-5 M CaCl2 with the same background. As shown in Figure 2, the initial response of the PVC membrane of 21.2 mV, which is somewhat smaller than expected according to the Nicolsky equation (22.8 mV), is followed by a backward drift of 1.5 mV. This drift mainly origins from concentration changes at the back side of the membrane. At steady state, which is reached after ∼3 h, ion fluxes lead to concentration polarization in all three contacting phases (cf. Figure 1). The same experiment with the Celgard membrane shows that the steady state is reached within
a few minutes. The faster response is due to the absence of PVC and the smaller thickness of the Celgard membrane.35 The potential step with this membrane is smaller not only because of pot the somewhat inferior selectivity (log KCaBa ) -2.6 as compared to -3.1 for the PVC membrane; expected response according to the Nicolsky equation, 16.9 mV) but mainly because of the much stronger flux effects. The back side response becomes noticeable from the very beginning of the concentration step. As shown in Figure 2, the theoretical steady-state responses calculated with q ) 0.0016 for PVC and q ) 0.0007 for Celgard are close to the observed data (see also below). These results indicate that steady state is reached so fast that more involved models describing timedependent responses28,29 are not required. To study the response behavior of the supported liquid membrane, it was initially conditioned symmetrically in a solution of 10-6 M CaCl2 with 10-4 M BaCl2. Figure 3 shows the observed emf response of a Celgard membrane exposed to concentration changes of Ca2+ (left panels) and Ba2+ (right panels) at the front side, followed by stopping of the stirrer in both aqueous solutions after ∼5 min. The stir effect makes it clear that ion fluxes are
Figure 2. Time response of a solvent polymeric membrane (left) and a Celgard-based supported liquid membrane (right) conditioned in a solution of 10-6 M CaCl2 with 10-3 M BaCl2. At t ) 0, the solution at the front side was changed to 10-5 M CaCl2 with the same background. Dotted lines: theoretical steady-state responses calculated with q ) 0.0016 for PVC and q ) 0.0007 for Celgard.
Figure 3. Time curves for the emf of a symmetrically conditioned membrane (10-6 M CaCl2 with 10-4 M BaCl2) upon changing the primary ion (left) or the interfering ion concentration (right) by (0.5 logarithmic unit on the front side of the membrane. The logarithmic concentrations of the respective ions are shown as labels.
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Figure 4. Top panels: time curves for the emf for changing the concentration of the primary (left) or interfering ions (right). The logarithmic concentration changes are shown as labels. Between the measurements, the membrane is symmetrically conditioned in the background solution (B) of 10-6 M CaCl2 with 10-4 M BaCl2. After ∼5 min, the stirrer is stopped (S) after each sample change. Calculated responses are shown below the measured ones. Bottom panels: calculated responses at the front and back sides on the same time scale as for the top panels.
important and the aqueous diffusion layers are concentration polarized. The lack of observed significant signal drift confirms that the steady state is accomplished across the membrane in a matter of minutes. The observed potential changes shown in Figure 3 do not follow the Nernstian or the Nicolsky equation. According to the latter, Ba2+ is moderately interfering at a 10-4 M concentration, giving ∼20% interference. Therefore, a decrease in the Ca2+ activity to 10-6.5 should only result in an emf change of -10.1 mV instead 7806 Analytical Chemistry, Vol. 77, No. 23, December 1, 2005
of the Nernstian step of -14.8 mV. On the other hand, a corresponding increase in the Ca2+ activity to 10-5.5 should change the emf by +12.9 mV. The emf change upon dilution is smaller because the level of interference increases. As shown in Figure 3 (left panels), the responses are smaller with the thin supported liquid membrane than expected from the Nicolsky equation and show a strong dependence on the level of stirring of the sample. For instance, the initial emf change upon decreasing the Ca2+ activity from 10-6.0 to 10-6.5 is only -5.9 mV, which reduces to
Table 2. Measured and Calculated Data for Different Concentrations of CaCl2 on the Front Side of the Membrane at a Constant Background of 10-4 M BaCl2a log cCa -6.0 -6.5 -6.3 -6.1 -5.9 -5.7 -5.5
a
stirring on off on off on off on off on off on off on off
∆E(meas) /mV
∆E(calc) /mV
Efront(calc) /mV
Eback(calc) /mV
log cCa,front
log cCa,back
log [ILz+]f
log [ILz+]b
0.0 0.0 -4.9 -0.3 -3.5 -0.5 -1.5 -0.3 1.4 0.2 5.5 1.6 9.5 3.3
0.0 0.0 -3.8 -0.6 -2.8 -0.5 -1.2 -0.2 1.5 0.3 5.1 1.4 9.8 3.5
0.0 0.0 -6.1 -4.4 -4.3 -3.1 -1.7 -1.2 2.0 1.4 6.6 5.0 12.0 9.6
0.0 0.0 2.3 3.8 1.5 2.6 0.5 1.0 -0.5 -1.1 -1.5 -3.6 -2.2 -6.1
-6.000 -6.000 -6.280 -6.196 -6.193 -6.135 -6.073 -6.052 -5.918 -5.941 -5.734 -5.798 -5.533 -5.620
-6.000 -6.000 -6.102 -6.168 -6.066 -6.114 -6.023 -6.042 -5.978 -5.954 -5.939 -5.853 -5.910 -5.754
-2.701 -2.701 -2.775 -2.749 -2.748 -2.733 -2.717 -2.713 -2.686 -2.690 -2.659 -2.667 -2.639 -2.646
-2.701 -2.701 -2.724 -2.741 -2.716 -2.727 -2.706 -2.710 -2.697 -2.692 -2.690 -2.675 -2.684 -2.661
Composition of the back side solution, 10-6 M CaCl2 and 10-4 M BaCl2. The potentials are normalized relative to the symmetric case.
Table 3. Measured and Calculated Data for Different Concentrations of BaCl2 on the Front Side of the Membrane at a Constant Background of 10-6 M CaCaCl2a log cBa -4.0 -4.5 -4.3 -4.1 -3.9 -3.7 -3.5
a
stirring on off on off on off on off on off on off on off
∆E(meas) /mV
∆E(calc) /mV
Efront(calc) /mV
Eback(calc) /mV
log cCa,front
log cCa,back
log [ILz+]f
log [ILz+]b
0.0 0.0 -6.5 -13.5 -4.0 -7.7 -1.5 -2.4 1.5 3.1 5.1 8.0 8.4 13.2
0.0 0.0 -6.7 -13.1 -4.3 -7.9 -1.6 -2.7 1.8 2.7 5.7 8.3 10.0 14.1
0.0 0.0 -4.7 -9.1 -3.0 -5.2 -1.1 -1.7 1.2 1.6 3.8 4.7 6.6 7.8
0.0 0.0 -2.0 -4.0 -1.3 -2.7 -0.5 -1.0 0.6 1.1 1.9 3.6 3.4 6.3
-6.000 -6.000 -6.101 -6.269 -6.064 -6.151 -6.022 -6.046 -5.977 -5.957 -5.932 -5.884 -5.888 -5.828
-6.000 -6.000 -5.918 -5.835 -5.944 -5.888 -5.979 -5.958 -6.024 -6.047 -6.081 -6.158 -6.152 -6.290
-2.701 -2.701 -2.644 -2.663 -2.662 -2.675 -2.687 -2.691 -2.718 -2.714 -2.760 -2.746 -2.814 -2.791
-2.701 -2.701 -2.686 -2.672 -2.691 -2.681 -2.697 -2.693 -2.706 -2.711 -2.719 -2.739 -2.737 -2.779
Composition of the back side solution, 10-6 M CaCl2 and 10-4 M BaCl2. The potentials are normalized relative to the symmetric case.
-0.3 mV when stirring is stopped. This smaller than expected emf change can be explained on the basis of ion fluxes, which increase the Ca2+ concentration on the front side of the membrane (cif > cifb, see Figure 1) and decrease it on the back side (cib < cibb). Because of the increasing thickness of the aqueous diffusion layers, these effects are stronger if the stirrer is stopped. On the other hand, the responses to changes in the concentration of the interfering ions (Figure 3, right panels) are larger than expected according to the Nicolsky equation, i.e., -1.9 or +4.7 mV upon decreasing or increasing the Ba2+ concentration by 0.5 logarithmic unit, respectively. The observed corresponding responses of -6.5 and +8.4 mV can again be explained by ion flux effects. A decrease in the sample concentration of the interfering ions also decreases its concentration in the membrane surface layer; i.e., it increases the corresponding Ca2+ concentration. The resulting concentration gradient induces an ion flux toward the back side of the membrane, which decreases the Ca2+ concentration cif and increases cib. Consequently, the observed response to changes in the concentration of the interfering ions is, in fact, largely due to the flux-induced changes in the primary ion concentration. When the stirrer is stopped, the concentration
polarization increases and the response is -13.5 or +13.2 mV instead of the -1.9 or +4.7 mV expected in the absence of ion fluxes. A series of measurements are shown in Figure 4, where the concentrations of primary or interfering ions were first reduced and then increased by 0.5, 0.3, and 0.1 logarithmic unit (starting conditions as for Figure 3). After each concentration change, the stirrer was stopped (labels S) as soon as the emf was stable (∼5 min). Then, the membrane was again symmetrically conditioned in fresh background solutions of 10-6 M CaCl2 with 10-4 M BaCl2 (labels B). The observed emf values are given in the third column of Table 2 for the measurements with the primary ions (Figure 4, left) and in Table 3 for those with interfering ions (Figure 4, right). The theoretical responses obtained with eqs 1 and 11 are shown in Figure 4A below the experimental curves and given in column 4 of the tables. Except the flux parameters, q (eq 7), all required data are experimentally accessible. The flux parameters were adjusted to 0.001 and 0.01 for stirred and unstirred solutions, respectively. The same values were also successfully used to describe similar measurements with Cd2+ and Cu2+ as interfering ions (results not shown). Since the theoretical model assumes a Analytical Chemistry, Vol. 77, No. 23, December 1, 2005
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Figure 5. Responses of a symmetrically conditioned Ag+-selective supported liquid membrane to changes in the primary (left) or interfering ion concentration (right) by 0.6 logarithmic unit relative to different symmetrical cases (AgNO3, 10-4.5-10-7.0 M; KNO3, 10-2 M). Open circles, stirred solutions; dots, unstirred solutions. Full lines, responses calculated with the presented model; dashed lines (in the first panel), responses according to the Nicolsky equation.
steady state, its utility for describing the responses confirms that the processes in supported liquid membranes are sufficiently fast for practical purposes. In fact, the responses on the front side and back side are simultaneous and not resolved with such membranes (see also Figure 2). However, the contributions of both membrane sides to the observed emf can be calculated with the theoretical model (Figure 4B and columns 5 and 6 of Tables 2 and 3). It is apparent that the back side response partly compensates that of the front side if primary ion concentrations are changed (Figure 4, left and Table 2) and enhances it in the case of interfering ions (Figure 4, right and Table 3). The model also provides a detailed picture of the concentration profiles in the three diffusion layers. Columns 7 and 8 of both tables give the primary ion concentrations cif and cib to be compared with the corresponding bulk concentrations adjusted in the experiments. For example, at cifb ) 10-6.5, the concentration near the membrane, cif, is 10-6.28 in stirred samples and 10-6.20 M in unstirred ones. Simultaneously, the ion fluxes decrease the sample concentration at the inner membrane surface, cib, from 10-6.0 to 10-6.10 and 10-6.17 for the stirred and unstirred solutions, respectively. The corresponding data of Table 3 confirm that the response to changes in interfering ion concentrations is mainly due to the flux-induced concentration changes of the primary ions. The concentration profile in the membrane can be found from the values at the phase boundaries [ILz+]f and [ILz+]b (last columns of Tables 2 and 3). Based on the selectivity coefficient of log pot KCaBa ) -2.6, 20.1% of Ca2+ is replaced by Ba2+ in the symmetrically conditioned membrane (eq 3). After a decrease in the primary ion concentration on the front side by 0.5 logarithmic unit, the difference in the concentrations of the primary ions on both sides of the membrane is ∼10% of their total concentration and it is only 1.6% if the stirrer is stopped (see Table 2, last 7808 Analytical Chemistry, Vol. 77, No. 23, December 1, 2005
columns, lines 4 and 5). The corresponding values upon a decrease in the interfering ion concentration by the same amount are -10 and -3%. Note that the different influence of sample stirring in the case of primary (Table 2) and interfering ions (Table 3) has its origin in the opposite signs of the transmembrane concentration gradients. A consequence of these results is that the changes in emf do not depend only on the concentration changes at the front side of the membrane but also on the concentrations at its back side. In the following, the requirements will be evaluated to obtain useful information from ion fluxes on the composition of the solution at the back side of the membrane. First, ion fluxes must lead to significant differences between the concentrations of the primary ions in the solution bulk and at the membrane surface. This is expected in the concentration range where super-Nernstian responses occur, i.e., at cib < 10-6 M for conventional PVC membranes. Because of higher ion fluxes in the Celgard membranes used here, the super-Nernstian step occurs at cib ) ∼10-5 M (not shown). A second condition is that the product of the activity of the interfering ion and the corresponding selectivity coefficient, Kpot ij cj, must be reasonably close to the activity of the primary ion, ci (Nicolsky equation). This is required to replace a significant amount of primary ions by interfering ones in the membrane phase (see eq 3). Since, however, the emf must be predominantly controlled by the primary ions, this product must be smaller than ci (ci > Kpot ij cj) Quantitative studies along these lines are shown in Figure 5. For demonstrating the feasibility of the method for another primary ion, an Ag+-selective membrane was used with K+ as interfering ion (log Kpot AgK ) -6.1). The initial concentration of Ag+ was varied in the range of 10-4.5-10-7.0 M at a constant background of 10-2 M KNO3. After symmetrically conditioning
the membranes, the concentration of either the primary ion (Figure 5, left) or interfering ion (Figure 5, right) was decreased (top panels) or increased (bottom panels) by 0.6 logarithmic unit. The responses in stirred (open circles) and unstirred solutions (dots) are shown as a function of the primary ion concentration after the changes. The lines display calculated responses using the experimental data and q values of 0.050 and 0.0045 for stirred and unstirred solutions, respectively. Again, the same q values were used for all experiments. Their deviation from the values used in Figure 4 may originate from the differences in ionic mobility in both phases as well as from the somewhat different geometry of the cells used in the two experiments. The emf increases upon lowering the concentration of interfering ions and vice versa (Figure 5, right) at high primary ion concentrations. This is a consequence of changes in activity coefficients that are also considered in the calculation. The theoretical response according to the Nicolsky equation is shown as a dashed line in the top left panel. It is apparent that a flux-independent response to the primary ions is only observed at cib > ∼10-5. Obviously, this is the range where stirring no longer influences the responses. Similarly, the response to the interfering ions does not depend on ion fluxes if cib < ∼10-7.0. The variation of the composition of the sample on the front side of the membrane may provide useful information about the composition of the solution on the back side of the membrane when flux effects are relevant, i.e., when the responses in stirred and unstirred solution are significantly different. According to Figure 5, this is possible for over a concentration range of the primary ion that is somewhat larger than 1 order of magnitude. To describe the principles of the new approach, we have used primary ion concentrations around the micromolar level. The method is, however, applicable whenever a weakly interfering ion
is present in the sample. This means that the primary ion concentration may be much lower whenever the interfering ions are more strongly discriminated or have lower concentrations than in the cases shown here. First experiments with a Pb2+-selective membrane indicate that lead determination in environmental samples might become possible with a detection limit of ∼10-8 M (data not shown). CONCLUSIONS We demonstrated that the diffusion processes in thin supported liquid membranes are sufficiently fast to observe the sum of emf responses at both sides of the membrane within minutes. There exists a concentration range of primary ions at which the responses depend on the composition of the sample on the back side of the membrane upon changing the solution on its front side. Transmembrane ion fluxes tend to decrease the response to primary ions and increase it to interfering ions. The amplification of the response to interfering ions may be understood by flux-induced changes of the primary ion concentrations at both sides of the membrane. Due to the different sign of the concentration gradients, stir effects are different for responses to primary or interfering ions. ACKNOWLEDGMENT This research was financially supported by grants from the National Institutes of Health (EB002189), the Swiss National Science Foundation, and an internal research grant of the ETH Zurich. Received for review July 31, 2005. Accepted September 23, 2005. AC051362Y
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