Potentiometric Sensor for Heparin Polyion: Transient Behavior and

Chronopotentiometry and electrochemical impedance spectroscopy were used to study the transient behavior and the potentiometric response mechanism of ...
0 downloads 0 Views 172KB Size
Download PDF
Anal. Chem. 2007, 79, 2892-2900

Potentiometric Sensor for Heparin Polyion: Transient Behavior and Response Mechanism Jan Langmaier,† Eva Samcova´,‡ and Zdeneˇk Samec*,†

J. Heyrovsky´ Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, Dolejsˇ kova 3, 182 23 Prague 8, Czech Republic, and 3rd Faculty of Medicine, Charles University, Ruska´ 87, 100 00 Prague 10, Czech Republic

Chronopotentiometry and electrochemical impedance spectroscopy were used to study the transient behavior and the potentiometric response mechanism of the polymer membrane-based sensor for heparin. Membrane with a composition of 66 wt % poly(vinyl chloride), 33 wt % o-nitrophenyl octyl ether (plasticizer), and 0.05 M tridodecylmethylammonium chloride (ion exchanger) was deposited on the surface of a silver or a glassy carbon (GC) electrode. In the latter case, the membrane contained also 0.1 M 1,1′-dimethylferrocene/1,1′-dimethylferricenium+ couple ensuring the electronic contact between the membrane and GC. The sensor was dipped in an aqueous solution of 0.1 M LiCl, which was stirred with a magnetic stirrer (2-18.2 Hz), and eventually spiked with heparin (0.05-5 U mL-1). Chronopotentiometric measurements were carried out using either the Ag supported membrane with a thickness >100 µm or the GC supported membrane with a defined thickness of 2-30 µm, which was also used in impedance measurements. Remarkable features of the potentiometric response include the linear dependence of the initial slope of the potential transient on the heparin concentration in the aqueous phase and on the square root of the stirring frequency, and the absence of the effect of the membrane thickness. Impedance measurements (0.1 Hz-10 kHz) made it possible to identify and to evaluate the geometric capacitance and the capacitance of the electric double layer at the membrane/solution interface, the bulk membrane and chargetransfer resistances, and the Warburg impedance of the chloride transport. Changes in the membrane bulk and charge-transfer resistances and the Warburg impedance upon spiking the aqueous solution with heparin were found to be consistent with the steady-state response of ∼ -25 mV, indicating that the bulk chloride concentration in the membrane decreased to about half of its initial value. A novel theoretical model of the transient behavior was developed based on the balance of the charging and the faradic currents of chloride and heparin, in accordance with the ion-exchange mechanism that has been proposed previously. It was concluded that the initial slope of the potential transient is linked to the charging of the double layer coupled to the chloride ion transfer * Corresponding author. Tel.: +420-266052017. Fax: +420-286582307. Email: [email protected]. † J. Heyrovsky´ Institute of Physical Chemistry. ‡ Charles University.

2892 Analytical Chemistry, Vol. 79, No. 7, April 1, 2007

across the membrane/solution interface and to the diffusion-limited transport of heparin in the solution. The potentiometric assay of heparin could be based on measurements of the initial slope of the potential transient or the potential at a fixed time shortly after the heparin injection. Heparin is a mixture of highly sulfated linear polysaccharide with a molar mass 5-40 kDa and an average charge number of -75,1 which has been used in medicine to prevent blood coagulation.2,3 Its concentrations encountered in therapy (0.1-1.0 U mL-1) and surgical procedures (1-10 U mL-1)2,3 correspond to the range of molar concentrations 0.06-6 µmol L-1, assuming the average molar mass (12 kDa) and the typical activity of heparin preparations (150 U mg-1). Heparin assays are currently based on its anticoagulant effect, which is quantified, for example, by the measurements of plasma or whole blood clotting time.4 Alternative methods for monitoring of heparin in biological samples have been a matter of intensive biosensor research.5 One of the most promising approaches is based on potentiometry with a polymer membrane-based electrode,6 which was shown to exhibit large and reproducible potentiometric response to heparin in both the aqueous and human blood plasma or whole blood samples.6-8 The optimum membrane composition for heparin detection was found to be 66 wt % polymer matrix (poly(vinyl chloride), PVC ), 32.5 wt % plasticizer (dioctyl sebacate, DOS), and 1.5 wt % ion exchanger (tridodecylmethylammonium chloride, TDMACl).6,7 A rotating electrode configuration was evaluated as a means to lower significantly the detection limit toward heparin down to 0.01U mL-1.9 In a recent study, the composition of the sensing membrane has been modified by introducing a protonselective ionophore resulting in the detectable optical absorbance change of the membrane to varying heparin levels.10 While the interaction between heparin and the membrane cation was (1) Linhardt, R. J. J. Med. Chem. 2003, 46, 2551. (2) O’Reilly, R. A. In Basic and Clinical Pharmacology, 5th ed.; Katzung, B. G., Ed.; Prentice Hall: Englewood Cliffs, NJ, 1992; pp 466-470. (3) Jaques, L. B. Pharmacol. Rev. 1980, 31, 99. (4) Abildgaard, U. In Heparin: Chemical and Biological Properties, Clinical Applications; Lane, D. A., Lindahl, U., Eds.; CRC Press: Boca Raton, FL, 1989; pp 495-515. (5) Jelinek, R.; Kolusheva, S. Chem. Rev. 2004, 104, 5987. (6) Ma, S. C.; Yang, V. C.; Meyerhoff, M. E. Anal. Chem. 1992, 64, 694. (7) Ma, S. C.; Yang, V. C.; Meyerhoff, M. E. Anal. Chem. 1993, 65, 2078. (8) Fu, B.; Bakker, E.; Yun, J. H.; Yang, V. C.; Meyerhoff, M. E. Anal. Chem. 1994, 66, 2250. (9) Ye, Q.; Meyerhoff, M. E. Anal. Chem. 2001, 73, 332. (10) Kim, S. B.; Kang, T. Y., Cha, G. S., Nam, H. Anal. Chim. Acta 2005. 10.1021/ac062060e CCC: $37.00

© 2007 American Chemical Society Published on Web 02/23/2007

originally assumed to play the key role,6,7 the response mechanism was later formulated as a simple anion-exchange process at the interface between the membrane (m) and the aqueous solution (w) leading to extraction of heparin into the membrane phase,8

zCl-(m) + Hepz-(w) / zCl-(w) + Hepz-(m)

(1)

It has been shown that the true equilibrium potentiometric response to heparin can be obtained only after a very long equilibration time, yielding the expected Nernstian slope of 200 µm). The aim of this work was to use this methodology for a (11) Samec, Z.; Troja´nek, A.; Langmaier, J.; Samcova´, E. Electrochem. Commun. 2003, 5, 867. (12) Guo, J.; Yuan, Y.; Amemiya, S. Anal. Chem. 2005, 77, 5711. (13) Langmaier, J.; Olsˇa´k, J.; Samcova´, E.; Samec, Z.; Troja´nek, A. Electroanalysis 2006, 18, 115. (14) Langmaier, J.; Olsˇa´k, J.; Samcova´, E.; Samec, Z.; Troja´nek, A. Electroanalysis 2006, 18, 1329. (15) Guo, J.; Amemiya, S. Anal. Chem. 2006, 78, 6893. (16) Manning, G. S. J. Chem. Phys. 1969, 51, 924. (17) Brand, M. J. D.; Rechnitz, G. A. Anal. Chem. 1969, 41, 1185. (18) Buck, R. P. Ion Selective Electrode Rev. 1982, 4, 3. (19) Horvai, G.; Gra´f, E.; To´th, K.; Pungor, E.; Buck, R. P. Anal. Chem. 1986, 58, 2735. (20) To´th, K.; Gra´f, E.; Horvai, G.; Pungor, E.; Buck, R. P. Anal. Chem. 1986, 58, 2741. (21) Buck, R. P. J. Electroanal. Chem. 1986, 210, 1.

Figure 1. Scheme of the potentiometric sensor with the o-NPOE plasticized PVC membrane attached to the surface of the glassy carbon.

clarification of both the transient and the steady-state potentiometric response of the polymer membrane-based sensor for heparin. Originally, we intended to investigate the heparin sensor with the membrane of the exact same composition as described above. However, the preliminary impedance measurements indicated that the DOS plasticized PVC membranes have a rather high resistance, and those plasticized with the more polar o-nitrophenyl octyl ether (o-NPOE) must be thinner than ∼10 µm to allow a reliable analysis of impedance data. We shall show that the measured impedance can be interpreted in terms of the geometric capacitance and the capacitance of the electric double layer at the membrane/solution interface; the bulk membrane and charge-transfer resistances and the Warburg impedance of the chloride transport. We shall further show that, upon the injection of heparin into the aqueous solution, these components undergo a remarkable change, which is likely to be associated with the ion exchange described by eq 1. By anticipating this mechanism, we shall develop a theoretical model of the transient behavior, which includes the effects of charging and ion transfer at the membrane/solution interface, as well as ion transport in the membrane and aqueous phase. EXPERIMENTAL SECTION Reagents. LiCl (Microselect, Fluka), heparin lithium salt from porcine intestinal mucosa (Fluka, u ) 190 U mg-1), TDMACl (purum, Fluka), PVC (high molecular weight, Fluka), 1,1′dimethylferrocene (DMFc, 97%, Aldrich), o-NPOE (Selectophore, Fluka), and tetrahydrofuran (THF, Riedel-de-Hae¨n, Germany) were used as received. Aqueous electrolyte solutions were prepared from highly purified water (Millipore). Preparation of the Sensor. Scheme of the sensing electrode is shown in Figure 1. The electrode was made from glassy carbon rod (V25 type, 3-mm diameter, Le Carbone, Lorraine, France) insulated on sidewall by PVC heat-shrinkable tubing (VW-1 SUMIPAC CSA, 4.8-mm diameter, Sumitomo Electric Interconnect Products, Inc.). The polished surface (Winter Diaplast-SS-D3, Ernst Winter & Sohn, Diamantwerkzeuge GmbH&Co.) of the glassy carbon disk oriented upward was spin-coated at 1000 rpm by the drop (10-50 µL) of the solution containing 50 mg PVC in 1 mL of THF, which was mixed with the appropriate amount of (22) Samec, Z., Langmaier, J.; Troja´nek, A. J. Electroanal. Chem. 1999, 463, 232. (23) Langmaier, J.; Stejskalova´, K.; Samec, Z. J. Electroanal. Chem. 2002, 521, 81.

Analytical Chemistry, Vol. 79, No. 7, April 1, 2007

2893

0.05 M TDMACl and 0.1 M DMFc in o-NPOE to form the film containing 66 wt % PVC over whole base of the electrode. Approximately 1% of the purchased DMFc was present in the oxidized form, as estimated from the voltammetric measurements of the DMFc+ ion transfer across a water/1,2-dichloroethane interface.24 The deposition procedure was eventually repeated several times to prepare the membrane with a thickness within the range 2-30 µm. The geometric area of the GC disk and the membrane exposed to the aqueous solution was 0.07 cm2 and 0.16 cm2, respectively. Alternatively, we employed a polished Ag wire (1-mm diameter) covered with a membrane of the thickness >100 µm, which was formed by multiple dipping in membrane solution without DMFc. The membrane was prepared fresh prior to each potentiometric or impedance measurement. The electrode was dipped into the aqueous solution of 0.1 M LiCl, eventually spiked with heparin (0.05-5 U mL-1). Solutions were stirred using a magnetic stirrer equipped with the rotation frequency control (218.2 Hz). A silver/silver chloride electrode in 0.1 M LiCl was used as a reference electrode. The cell can be described by the scheme

GC/0.05 M TDMACl, 0.1 M DMFc, (m) PVC, o-NPOE/0.1 M LiCl/AgCl/Ag (w) or

Ag/0.05 M TDMACl, PVC, o-NPOE/0.1 M LiCl/AgCl/Ag (m) (w) Apparatus. Chronopotentiometric measurements were carried out in a two-electrode cell using either the programmable potentiostat Autolab (PGSTAT 30, Eco-Chemie, The Netherlands), controlled by the GPES software version 4.9, or the potentiostat/ galvanostat EG&G PAR (model 273A), equipped with the operating corrosion software (M352, EG&G PAR, Princeton, NJ). The measured potential E of the cell includes the potential differences at the GC or Ag/membrane interface, ∆M m φ, the membrane/ aqueous solution interface, ∆wmφ, and the potential of the reference electrode, Eref. The former interface represents an electronic contact to the membrane,17 with the potential difference being controlled by the DMFc+/DMFC or the Ag/AgCl redox reaction. We assumed that this potential difference remains constant during the measurements, and that the measured potential reflects only the changes in ∆wmφ, w w E ) ∆M m φ - ∆mφ - Eref = - ∆mφ - E′ref

(3)

where M ) GC or Ag. Impedance measurements were carried out in the same cell with the help of a frequency response analyzer (1255 FRA Solartron, Solartron Instruments) and a potentiostat (1287 Electrochemical Interface Solartron, Solartron Instruments). The system was equipped with software (ZPlot/ZView, Scribner Associates, Inc.) for computer control of impedance measurements and for the nonlinear least-squares fitting of impedance data. (24) Troja´nek, A.; Langmaier, J.; Samec, Z. J. Electroanal. Chem. 2007, 599, 160.

2894 Analytical Chemistry, Vol. 79, No. 7, April 1, 2007

Figure 2. Chronopotentiometric responses of the Ag/PVC (d > 100 µm) (O) and the GC/PVC (d ) 5.4 µm) (b) sensors to heparin (0.5 U mL-1) in the stirred aqueous solution of 0.1 M LiCl (15.9 Hz). For the sake of comparison, the potentials measured with the Ag/PVC sensor were shifted positive by 60 mV, corresponding to the difference between the initial potentials of the two sensors.

Impedance spectra of the GC/PVC sensor with a thin membrane ( 100 µm), cf. also the inset for the expanded view of the initial part of the potential responses. Upon spiking the aqueous phase with heparin, the potential E decays exponentially from the initial to the final steady-state value, which is reached after a relatively long time (>103 s). The effect of the stirring frequency on the potential transient is demonstrated in Figure 4, panel A. Several features of the transient behavior are worth mentioning. First, the initial slope of the potential transient, which was evaluated by a numeric fit of the initial part of the transient ( 100 µm) to heparin in the stirred aqueous solution of 0.1 M LiCl (15.9 Hz) at various heparin concentrations c0,w (U mL-1), 5 (O), 1 (b), 0.5 (0), h 0.2 (9), 0.1 (4), and 0.05 (2) (A); the initial slope of the response vs c0,w (circles) and the linear fit Y ) -0.0775 - 0.568X (dotted line) h (B). Solid point represents the average value -0.240 ( 0.039 V ks-1 obtained from a series of measurements with the GC/PVC sensor for nine different values of the membrane thickness d ) 2-30 µm, -1 and c0,w h ) 0.5 U mL . Inset in panel B shows the response potential difference at the fixed time of 40 s (crosses) and the linear fit Y ) -1.4 - 15.6X (dotted line).

the heparin concentration c0,w h (Figure 3, panel B). Such a linear plot can be also obtained by measuring the response potential at a fixed time shortly after spiking the stirred test solution with heparin (Figure 3, inset in panel B). Second, the initial slope varies linearly with the square root of the stirring frequency f (Figure 4, panel B). Third, the potential response does not depend on the thickness of the membrane (Figure 3, panel B). In particular, a series of measurements using the GC/PVC sensor for nine different values of the membrane thickness d ) 2-30 µm and -1 provides the average value of the initial slope c0,w h ) 0.5 U mL -0.240 ( 0.039 V ks-1, which falls on the line obtained from a series measurements with the Ag/PVC sensor with a thick membrane (d > 100 µm) at different heparin concentrations, cf. the solid point in Figure 3, panel B. Fourth, the final steady-state value of the potential does not depend on the stirring frequency (Figure 4, panel A) and only weakly depends on the heparin concentration yielding a slope of 10 Hz) is characterized by the depressed semicircle, which represents an overlap of the ideal semicircles associated with the parallel combination of the geometric capacitance Cg and the bulk membrane resistance Rm, and the parallel combination of the double layer capacitance Cdl and the charge-transfer resistance Rct (Figure 5, panel A). The identification of Cg and Rmis supported by the observed effect of the membrane thickness d indicating that Cg is proportional to d -1 (Figure 8, panel B) and Rm is proportional to d (Figure 8, panel A), in agreement with the wellknown relationships,

Cg ) 0A/d RTd

Rm ) F2A

∑

(6) (7)

m cm i Di

i

where  and 0 represent the permittivity of the membrane phase

and vacuum, respectively, A is the area of the membrane exposed to the solution (0.16 cm2), Dm i ’s are the diffusion coefficients, and cm ’s are the concentrations of the free ions in the membrane i phase. The slope of 1.43 × 10-15 F‚m as read from Figure 8, panel B, yields  ) 10.1, which fits in the sequence of  ) 14 for the 33 wt % PVC membrane plasticized with o-NPOE and  ) 21 for pure liquid o-NPOE,26 indicating that the permittivity correlates with the PVC content.26 The increase of Rm by a factor of ∼2 upon spiking the aqueous phase with heparin (Figure 7, panel C) can be ascribed to replacement of about half of the chloride anions present in the membrane phase by much less mobile heparin, in an agreement with the potential change of ∼ -25 mV corresponding to a decrease of the bulk chloride concentration in the membrane to about half of its initial value. It is noteworthy that practically the same values of Cg and Rm are obtained by fitting the initial part of the impedance plot (Z′,Z′′ f 0) without introducing the assumption of the negligible impedance of the GC/membrane interface. At lower frequencies, the impedance associated with the charging and the DMFc+/ DMFc electron-transfer reaction at the GC/membrane interface could play a role, in particular at lowest frequencies where the Warburg impedance prevails. However, the effect of the heparin injection on the impedance parameters supports the assumption made. As can be seen from Figure 7, both the Warburg impedance coefficient σ0 ) Y-1 0 (panel A) and the charge-transfer resistance Rct (panel C) increase by a factor of ∼2, which like the change of membrane resistance reflects the decrease of the membrane chloride concentration by the same factor. The charge-transfer resistance was used to estimate the apparent rate constant k of chloride transfer from the aqueous to the membrane phase, k ) 0,w -8 cm s-1 indicating a strong inhibition, RT/F2AcCl -Rct ) 8 × 10 because the ion-transfer rates measured using the 25 wt % PVC membrane plasticized with o-NPOE are higher by ∼5 orders of magnitude.27 The values that these two parameters attained prior to the heparin injection could then be used to estimate the diffusion coefficient of chloride in the membrane. By taking into account the migration contribution to the ion transport,21,28 σ0 is expressed by the equation

σ0 ) Y0-1 )

(

)

1 1 RT 1 RT + m1/2 0,m ≈ 2 w1/2 0,w m1/2 0,m 2F2A DCl c D c 2F A D CCl- ClCl- cCl(8)

where the simplification made follows from the assumption that m w -6 Ω-1 DCl - , DCl-. However, the substitution of Y0 ) 3.5 × 10 0,m 1/2 -3 s (Figure 7, panel A), cCl- ) 50 mol m , and A ) 0.16 × 10-4 m -14 cm2 s-1. m2 yields an unexpectedly low value DCl -) 3.4 × 10 So far we have ignored the ion association inside the membrane phase, which could be due to a relatively low permittivity, and which could affect both the membrane resistance and Warburg impedance. The dissociation of TDMACl in the membrane is a chemical reaction that precedes the chloride ion transfer, which represents a CE mechanism. The theory of impedance for the CE case29 implies that eq 8 could be applicable only when the (26) Armstrong, R. D.; Horvai, G. Electrochim. Acta 1990, 35, 1. (27) Langmaier, J.; Stejskalova´, K.; Samec, Z. J. Electroanal. Chem. 2001, 496, 143. (28) Samec, Z.; Troja´nek, A.; Samcova´, E. J. Electroanal. Chem. 1995, 389, 1. (29) Sluyters-Rehbach, M.; Sluyters, J. H. J. Electroanal. Chem. 1970, 4, 1.

Analytical Chemistry, Vol. 79, No. 7, April 1, 2007

2897

dissociation reaction is very fast. On the other hand, in the case of the slow dissociation, the Warburg impedance should be inversely proportional to the concentration of free ions, and hence, 0,m 0,m cCl - is to be replaced by RcCl- , where R is the degree of dissociation. Provided that the diffusion coefficients of TDMA+ and Cl- ions in the membrane are equal, eq 7 and eq 8 give the diffusion coefficient in the membrane, Dm ) (σ0d/Rm)2 ) 1.6 × 10-7 cm2 s-1, which upon the substitution in either eq 7 or eq 8 yields R ) 10-4. Owing to a number of assumptions made, this is only a rough estimate, which nevertheless points to a significant ion association in the membrane phase. It is also quite likely that an easy hydration of a thin membrane26 causes a decrease of its resistance, which in turn would lead to an overestimation of Dm and to an underestimation of R. The value of the double layer capacitance Cdl ≈ 10 nF cm-2 of the membrane/solution interface (Figure 7, panel B) appears to be surprisingly low. In fact, the previous impedance measurements of the o-NPOE plasticized PVC membrane with PVC content of 33 30 or 25 wt %27 have shown that Cdl increases sharply with the increasing potential difference ∆wmφ from ∼10 µF cm-2 at the zero-charge potential difference ∆wmφ ≈ 0 V to ∼100 µF cm-2 at ∆wmφ ≈ -0.3 V;27 and even sharper increase has been reported for the 33 wt % PVC membrane.30 It is noteworthy that the double layer capacitance of the interface between the 25 wt % PVC membrane and the aqueous solution was found to be comparable with that obtained for the liquid/liquid interface.27 An extrapolation to potential differences as negative as the standard potential 0 31 suggests that difference for chloride ion, ∆wmφCl -) -0.514 V, -2 the capacitance of ∼300 µF cm can be expected. According to the classical theory,32 the behavior of the electric double layer at large interfacial potential differences is associated with the dielectric properties of the inner layer rather than with the potential and charge distribution in the space charge (diffuse) region. A possible origin of this discrepancy could be then the effect of frequency on the inner layer capacitance. This type of effect has been discussed extensively in literature in relation to the behavior of dipoles in viscous media,33 see, for example, ref 34 for a review. A simplest description of the frequency-dependent capacitance in the present case would be34

Cdl )

C0dl 1 + (iωτ)ν

+ C∞dl

(9)

where C0dl ≈ 300 µF cm-2 and C∞dl ≈ 10 nF cm-2 represent the zero and infinite frequency limit of the capacitance, respectively, τ is the dipole relaxation time, ω ) 2πf is the angular frequency of the applied ac voltage, and the exponent ν e 1. For example, when ν ) 1 and τ ) 100 s, the capacitance of the 66 wt % PVC membrane/solution interface should approach the high-frequency limit at frequencies f > 100 Hz (ωτ > 6.28 × 104), while the lowfrequency limit is attained at frequencies f < 0.001 Hz (ωτ < 0.628) corresponding to a time scale of 103 s. Owing to much lower viscosity of the 25 wt % PVC membrane phase, the dipole (30) Armstrong, R. D.; Proud, W. R.; Todd, M. Electrochim. Acta 1989, 34, 977. (31) Wilke, S.; Zerihun, T. J. Electroanal. Chem. 2001, 515, 52. (32) Grahame, D. C. Chem. Rev. 1947, 41, 441. (33) Debye, P. Polar molecules, Chemical Catalog Co., New York, 1929. (34) Awayda, M. S.; Van Driessche, W.; Helman, S. I. Biophys. J.1999, 76, 219.

2898

Analytical Chemistry, Vol. 79, No. 7, April 1, 2007

relaxation time is probably much shorter, and the capacitance can be close to its low-frequency limit over the whole range of frequencies of the applied ac voltage. Response Mechanism. Steady-state response of the potentiometric sensor, as well as the changes of the impedance parameters Rm, σ0, and Rct, are clearly consistent with the ionexchange mechanism described by eq 1. On the other hand, the dynamic behavior of the sensor could be related to several relaxation processes including the charging of the geometric capacitance coupled to the bulk ion transport, the charging of the double layer coupled to the interfacial charge transfer, or the transport of charge carriers within the membrane and the test aqueous solution.18,35 Since the time constant τ ) RmCg ) 0.4 ms of the former relaxation process is very small, the transient response should be controlled by the charging of the membrane/ solution interface and the interfacial ion-transfer reactions. The interfacial transfer of heparin polyion across a polarized liquid/ liquid12 or PVC plasticized11,13-15 interface was studied by cyclic voltammetry. These studies have shown that the transfer follows the mechanism described by eq 2 comprising the accumulation of the ion pair between heparin and the membrane or the organicphase cation at the interface. Besides, evidence has been provided12,14 that the transfer of chloride to the organic phase is energetically more favorable than the transfer of TDMA+ to the aqueous phase, but less favorable than the transfer of all other organic cations studied. Consequently, in the presence of chloride in both the aqueous and the membrane phase and in the absence of heparin, the equilibrium chloride potential can establish only in the presence of TDMA+, while for all other organic cations, the balance of the chloride and cation currents gives rise to a mixed potential. Another relevant feature of the voltammetric behavior is that the heparin current density measured using either the rotating electrode configuration13,14 or a micropipet-supported liquid/liquid interface12 approaches the stationary diffusion limit at the potential close to the formal ion-transfer potential of chloride 0′ ECl -, which in the potentiometric configuration and the presence of TDMA+ can be supposed to control the initial potential Ei according to eq 5. A stepwise increase in the heparin concentration in the aqueous phase should then lead to a stepwise increase in the heparin current density to its limiting value jlim h , which is followed by the potential response η(t) ) E(t) - Ei subject to the balance of the charging current and the faradic currents of chloride and heparin. Since the latter current is controlled exclusively by the stationary diffusion of heparin in the aqueous phase, the transient response is not affected by the accumulation of heparin at the interface, though this process undoubtedly takes place. In an agreement with the theoretical approach, which was originally developed to describe the transient response of ISE to a stepwise change in the target ion concentration,26 the balance of the currents can be described as

Cdl

dη ) jCl- + jlim h dt

(10)

where jCl- is the chloride current density. Here, the current is (35) Morf, W. E. In The Principles of Ion-Selective Electrodes and of Membrane Transport, Akade´miai Kiado´: Budapest, 1981; pp 375-400. (36) Senda, M. J. Electroanal. Chem. 1994, 378, 215.

considered to be positive when a positively charged ion is transferred in the direction from the aqueous phase to the membrane. The limiting current density jlim h can be expressed by w 0,w jlim h ) -zFmh ch

(11)

where mwh is the mass-transfer coefficient. Since the forced convection in the stirred aqueous phase is likely to have a velocity profile similar to that in the rotating disk electrode configuration,9,13,14 the mass-transfer coefficient should be then proportional to the square root of the stirring frequency, mwh ∼ f 1/2. We shall consider two limiting cases of eq 10. In the first one, the chloride current density is supposed to be controlled by the kinetics of chloride ion transfer across the membrane/solution interface, which follows a first-order kinetic law,37

Figure 9. Schematic description of the balance of the current densities of chloride and heparin ion transfer, jCl- ) - jh ) const, neglecting the effect of the double layer charging. The decrease of jCl- with time caused by the depletion of chloride from the membrane side of the interface induces the negative shift of the overpotential η.

jCl- ) j0(Ei){exp[βFη/RT ] - exp[-(1 - β)Fη/RT]} ≈

j0(Ei)Fη η )RT Rct

the balance of the heparin and the chloride current densities

(12)

where j0(Ei) < 0 is the ion-exchange current density for chloride at the initial potential, β is the charge-transfer coefficient, and Rct ) -RT/Fj0(Ei) is the charge-transfer resistance. Exponential functions in eq 12 were linearized by assuming that βF|η|/RT , 1 and β ) 0.5. These assumptions appear to be plausible, because the experimental values of the charge-transfer coefficient for various ion-transfer reactions at liquid/liquid interface were found to be close to 0.5,37 and the present analysis is confined to |η| < 5 mV. Substitution of eq 12 into eq 10 and integration yields the expression describing the potential transient and its initial slope

η ) Rctjlim h [1 - exp(-t/RctCdl)]

(13)

and

dη dt

( )

tf0

)

jlim -zFmwh c0,w h h ) Cdl Cdl

(14)

respectively. This model predicts correctly the observed effects of the heparin concentration and stirring frequency, as well as the absence of the effect of the membrane thickness. The limiting current density jlim h can be estimated from the voltammetric measurements of heparin on a rotating disk electrode, which was coated with the 25 wt % PVC membrane (0.79 cm2) plasticized with o-NPOE.13 The heparin current was found to attain the limiting value of -0.22 µA at the frequency of rotation f ) 16.6 Hz and the heparin concentration of 1 U mL-1,13, i.e., j lim h ) -0.28 µA cm-2. With this value and the experimental slope of -0.75 × 10-3 V s-1 obtained for 1 U mL-1 heparin and f ) 15.9 Hz (Figure 3, panel B), Cdl is calculated from eq 14 as 373 µF cm-2. In the other limiting case, it is assumed that the charging of the double layer coupled to the interfacial charge transfer is a very fast process, so that the transient behavior is controlled by (37) Samec, Z. Pure Appl. Chem. 2004, 76, 2147.

jCl- ) -jlim h ) const

(15)

which follows from eq 10 for dη/dt f 0. In this case, the overpotential η(t)is given by the Nernst equation m cCl -(0,t) w cCl -(0)

0′ ) exp[F(E(t) - ECl -)/RT] )

0.m cCl 0,w cCl -

exp(Fη/RT) (16)

m where cCl -(0,t) is the time-dependent concentration of chloride w on the membrane side of the interface (x ) 0), and cCl -(0) is the concentration of chloride on the aqueous solution side of the interface, which is directed by the stationary convective diffusion and is independent of time. The origin of the potential transient is shown schematically in Figure 9. Essentially, at a constant potential, the current density jCl- would decrease with time due to the depletion of chloride on the membrane side of the interface leading to a decrease of the concentration gradient. To keep the concentration gradient constant as required by eq 1, the concenm tration cCl -(0,t) must decrease and the overpotential η(t) must shift negative. Assuming that the transport of chloride in the aqueous and membrane phase is controlled by the stationary convective diffusion and the finite linear diffusion, respectively, the relationships for the interfacial chloride concentrations have been derived. Their substitution into the eq 16 yields the expressions for the initial slope of the transient,

dη dt

( )

)

tf0

RTjlim h

(17)

0,m F2dcCl -

and

dη dt

( )

) tf0

-1/2 RTjlim h t m1/2 0,m F2π1/2DCl - cCl-

f∞

(18)

for a very thin (d f 0) and a very thick (d f ∞) membrane, Analytical Chemistry, Vol. 79, No. 7, April 1, 2007

2899

respectively (see Supporting Information for details). While both these equations predict correctly the effects of the heparin concentration and the stirring frequency, the expected dependence on the membrane thickness (eq 17) or t1/2-dependence with the initial slope approaching infinity (eq 18) has not been observed. CONCLUSIONS It is shown that the character of the electrode support (Ag, GC) has practically no effect on the potential response to heparin, except for a difference in the initial potential. The initial slope of the potential transient is found to be proportional to heparin concentration in the aqueous phase and to the square root of the stirring frequency, while it is independent of the membrane thickness. The steady-state potential measured after ∼1 h from the heparin injection is shown to be independent of the stirring frequency and only weakly dependent on the heparin concentration (