Anal. Chem. 2004, 76, 5570-5578
Chronoamperometry at Micropipet Electrodes for Determination of Diffusion Coefficients and Transferred Charges at Liquid/Liquid Interfaces Yi Yuan, Lei Wang, and Shigeru Amemiya*
Department of Chemistry, University of Pittsburgh, 219 Parkman Avenue, Pittsburgh, Pennsylvania 15260
Chronoamperometry was carried out at liquid/liquid interfaces supported at the tip of micropipet electrodes for direct determination of the diffusion coefficient of a species in the outer solution. The diffusion coefficient was used for subsequent determination of the transferred charges per species from the diffusion-limited steady-state current. A large tip resistance of the micropipets causes prolonged charging current so that the faradic current can be measured accurately only at a long-time regime (typically t > 5 ms). At the same time, the long-time current response at the interfaces surrounded by a thin glass wall of the pipets is enhanced by diffusion of the species from behind the pipet tip. Therefore, numerical simulations of the long-time chronoamperometric response were carried out using the finite element method for accurate determination of diffusion coefficients. Validity of the simulation results was confirmed by studying simple transfer of tetraethylammonium ion. The technique was applied for transfer/adsorption reactions of the natural polypeptide protamine and also for Ca2+ and Mg2+ transfers facilitated by ionophore ETH 129. With the diffusion coefficient of protamine determined to be (1.2 ( 0.1) × 10-6 cm2/s, the ionic charge transferred by each protamine molecule was obtained as +20 ( 1, which is close to the excess positive charge of protamine. Also, the diffusion coefficient of ETH 129 was determined to demonstrate that each ionophore molecule transfers +0.67 and +1 charge per Ca2+ and Mg2+ transfer, respectively, which corresponds to formation of 1:3 and 1:2 complexes with the respective ions. Electrochemical techniques have been successfully used to study charge-transfer reactions at interfaces between two immiscible electrolyte solutions (ITIES), which serve as a simple model of biomembranes and as a basis of many important industrial and analytical systems.1-3 Recently, steady-state voltammetry at micrometer-sized interfaces was established to overcome serious limitations in electrochemical studies at ITIES,4 * To whom correspondence should be addressed. E-mail: amemiya@ pitt.edu. Fax: 412-624-5259. (1) Reymond, F.; Fermin, D.; Lee, H. J.; Girault, H. H. Electrochim. Acta 2000, 45, 2647-2662. (2) Liu, B.; Mirkin, M. V. Anal. Chem. 2001, 73, 670A-677A. (3) Samec, Z.; Samcova´, E.; Girault, H. H. Talanta 2004, 63, 21-32. (4) Liu, B.; Mirkin, M. V. Electroanalysis 2000, 12, 1433-1446.
5570 Analytical Chemistry, Vol. 76, No. 18, September 15, 2004
where capacitive current and iR drop can be suppressed significantly as can be achieved with ultramicroelectrodes in solid/liquid electrochemistry.5 Micrometer-sized liquid/liquid interfaces can be formed at the cylindrical microhole of a thin polymer membrane6 or at the tip of a glass micropipet.7 Steady-state current, id, limited by spherical diffusion of a species to the interfaces is given in general by4
id ) nFDc0ax
(1)
where c0 and D are the bulk concentration and diffusion coefficient of the species, respectively, F is the Faraday constant, n is the charge transferred by each species, a is the radius of the microhole or the pipet tip, and x is a constant dependent on the interfacial geometry. Steady-state current measurements at the microinterfaces were widely used in such applications as electrochemical sensors8-10 and scanning electrochemical microscopy.11-15 Also, steady-state voltammetry simplifies theoretical analysis so that quantitative studies of reaction kinetics were done at ITIES with micrometer16 or nanometer17,18 size. At the same time, however, the diffusion coefficient and the transferred charge cannot be determined separately from steady-state voltammograms unless the reactions are Nernstian. Lack of information about these parameters hinders analysis of kinetically controlled voltammograms, which limits application of steady-state voltammetry at micro-ITIES to simple reactions. Such a limitation of steady-state voltammetry was overcome by chronoamperometry in studies of redox reactions at solid (5) Wightman, R. M.; Wipf, D. O. In Electroanalytical Chemistry; Bard, A. J., Ed.; Marcel Dekker: New York, 1989; Vol. 15, pp 267-351. (6) Campbell, J. A.; Girault, H. H. J. Electroanal. Chem. 1989, 266, 465-469. (7) Taylor, G.; Girault, H. H. J. Electroanal. Chem. 1986, 208, 179-183. (8) Lee, H. J.; Girault, H. H. Anal. Chem. 1998, 70, 4280-4285. (9) Lee, H. J.; Pereira, C. M.; Silva, A. F.; Girault, H. H. Anal. Chem. 2000, 72, 5562-5566. (10) Qian, Q.; Wilson, G. S.; Bowman-James, K.; Girault, H. H. Anal. Chem. 2001, 73, 497-503. (11) Solomon, T.; Bard, A. J. Anal. Chem. 1995, 67, 2787-2790. (12) Shao, Y.; Mirkin, M. V. J. Phys. Chem. B 1998, 102, 9915-9921. (13) Amemiya, S.; Bard, A. J. Anal. Chem. 2000, 72, 4940-4948. (14) Sun, P.; Zhang, Z. Q.; Gao, Z.; Shao, Y. H. Angew. Chem., Int. Ed. 2002, 41, 3445-3448. (15) Yatziv, Y.; Turyan, I.; Mandler, D. J. Am. Chem. Soc. 2002, 124, 56185619. (16) Shao, Y.; Osborne, M. D.; Girault, H. H. J. Electroanal. Chem. 1991, 318, 101-109. (17) Shao, Y.; Mirkin, M. V. J. Am. Chem. Soc. 1997, 119, 8103-8104. (18) Yuan, Y.; Shao, Y. H. J. Phys. Chem. B 2002, 106, 7809-7814. 10.1021/ac0493774 CCC: $27.50
© 2004 American Chemical Society Published on Web 08/17/2004
ultramicroelectrodes.19 At inlaid disk microelectrodes, the transient current, id,inlaid(t), limited by diffusion of an electroactive species can be expressed as a function of time, t, in the normalized form with respect to the steady-state current, id,inlaid, as20
id,inlaid(t) a + ) f(t) ) 0.7854 + 0.4431 id,inlaid xDt xDt)
0.2146e-0.3912(a/
(2)
where id,inlaid is given by eq 1 with x ) 4. Therefore, with knowledge of the disk radius, a comparison of eq 2 with experimental chronoamperometric responses in their normalized form gives the diffusion coefficient of the electroactive species directly.19,21-24 The number of electrons participating in the electrode reaction, which corresponds to n in eq 1, can be determined subsequently from the steady-state current if the bulk concentration is known.19 Despite the potential usefulness, however, there are few studies of chronoamperometric or transient responses at liquid/liquid microinterfaces.25-28 This is because the time scale for carrying out potential step experiments at microITIES is seriously limited by the large resistance at the narrow microhole of polymer membranes29 or at the small tip of micropipets.29,30 At 10-µm-diameter water/1,2-dichloroethane interfaces, for example, a capacitance, Cd, of 8 pF31 and an uncompensated cell resistance, Ru, of 10 MΩ29,30 result in the cell time constant, CdRu,32 of 80 µs. A potential step is fully established after ∼5CdRu of 400 µs, which is nearly 3 orders of magnitude larger than the time required at a water/metal microelectrode interface with the same size.33 At 1 ms after the potential step, however, the faradic current has not reached the steady state. Indeed, id,inlaid(1 ms)/ id,inlaid ) 3 in eq 2 with D ) 10-5 cm2/s and a ) 5 µm. Therefore, long-time chronoamperometric experiments at micro-ITIES will allow accurate measurement of the faradic current without serious interference by charging current and fulfill the assumption of an instantaneous change in surface concentration of the diffusionlimiting species at t ) 0.34 Here we demonstrate for the first time that chronoamperometry at liquid/liquid microinterfaces can be used to determine (19) Denuault, G.; Mirkin, M. V.; Bard, A. J. J. Electroanal. Chem. 1991, 308, 27-38. (20) Shoup, D.; Szabo, A. J. Electroanal. Chem. 1982, 140, 237-245. (21) Kakihana, M.; Ikeuchi, H.; Sato, G. P.; Tokuda, K. J. Electroanal. Chem. 1980, 108, 381-383. (22) Kakihana, M.; Ikeuchi, H.; Sato, G. P.; Tokuda, K. J. Electroanal. Chem. 1981, 117, 201-211. (23) Winlove, C. P.; Parker, K. H.; Oxenham, R. K. C. J. Electroanal. Chem. 1984, 170, 293-304. (24) Baur, J. E.; Wightman, R. M. J. Electroanal. Chem. 1991, 305, 73-81. (25) Beattie, P. D.; Delay, A.; Girault, H. H. J. Electroanal. Chem. 1995, 380, 167-175. (26) Liao, Y.; Okuwaki, M.; Kitamura, F.; Ohsaka, T.; Tokuda, K. Electrochim. Acta 1998, 44, 117-124. (27) Peulon, S.; Guillou, V.; L’Her, M. J. Electroanal. Chem. 2001, 514, 94-102. (28) Slevin, C. J.; Liljeroth, P.; Kontturi, K. Langmuir 2003, 19, 2851-2858. (29) Beattie, P. D.; Delay, A.; Girault, H. H. Electrochim. Acta 1995, 18, 29612969. (30) Shao, Y.; Mirkin, M. V. Anal. Chem. 1998, 70, 3155-3161. (31) Trojanek, A.; Lhotsky, A.; Marecek, V.; Samec, Z. J. Electroanal. Chem. 2004, 565, 243-250. (32) Oldham, K. B. Electrochem. Commun. 2004, 6, 210-214. (33) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications, 2nd ed.; John Wiley & Sons: New York, 2001; p 216. (34) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications, 2nd ed.; John Wiley & Sons: New York, 2001; p 163.
diffusion coefficients directly. The transferred charges can be determined subsequently from the diffusion-limited steady-state current. Silanized micropipet electrodes were used for this study, which allows reproducible formation of well-defined disk-shaped interfaces at the tip as confirmed by video microscopy30 and scanning electrochemical microscopy.12,13 At the same time, the micropipets are fabricated by heating and pulling glass capillaries so that the interfaces are surrounded by a thin glass wall (RG ) rg/a ) ∼1.5, where rg is the outer radius of the pipet tip) unless a special fabrication procedure is used.35 Therefore, when the diffusion field grows beyond the outer edge of the pipets, diffusion from behind the electrodes enhances the flux. This current enhancement due to back diffusion was first demonstrated by Shoup and Szabo in numerical simulations based on the hopscotch algorithm for chronoamperometric responses at disk ultramicroelectrodes surrounded by a thin insulating layer.36 They predicted that the current responses at a long-time regime become larger than those predicted by eq 2. Others also carried out numerical simulations based on the explicit finite difference method,37 the Galerkin finite element method,12 and the finite difference alternating-direction implicit method38 to confirm the enhancement of the steady-state current by back diffusion. At the same time, Shoup and Szabo pointed out the possibility of a limitation in accuracy of their simulations as a result of the complicated electrode geometry.36 No theoretical treatment of the long-time chronoamperometric responses, however, has been reported since then. Also, the current enhancement was demonstrated experimentally only at the steady state.12,30,39-41 We calculated long-time chronoamperometric responses at micropipet electrodes using FEMLAB, a commercial program based on the finite element method. Numerical simulations were carried out for different relative thicknesses of the pipet wall with RG values of 1.1-100. Validity of the theoretical responses was confirmed by studying a well-established system, i.e., transfer of tetraethylammonium ion (TEA+), demonstrating enhancement of the long-time chronoamperometric currents. Then, chronoamperometry was used to study ion-transfer reactions based on more complicated mechanisms. One is transfer and adsorption of polypeptide protamine,42 which has ∼20 excess positive charges.43,44 The other is facilitated transfer of Ca2+ and Mg2+ by neutral ionophore ETH 129, which forms 1:3 and 1:2 complexes with the respective ions in crystals and in plasticized polymer membranes.45 THEORY Although the following treatment is applicable also to electrontransfer reactions, we consider two representative types of ion(35) Evans, N. J.; Gonsalves, M.; Gray, N. J.; Barker, A. L.; Macpherson, J. V.; Unwin, P. R. Electrochem. Commun. 2000, 2, 201-206. (36) Shoup, D.; Szabo, A. J. Electroanal. Chem. 1984, 160, 27-31. (37) Fang, Y.; Leddy, J. Anal. Chem. 1995, 67, 1259-1270. (38) Amphlett, J. L.; Denuault, G. J. Phys. Chem. B 1998, 102, 9946-9951. (39) Dayton, M. A.; Brown, J. C.; Stutts, K. J.; Wightman, R. M. Anal. Chem. 1980, 52, 946-950. (40) Zhao, G.; Giolando, D. M.; Kirchhoff, J. R. Anal. Chem. 1995, 67, 25922598. (41) Schulte, A.; Chow, R. H. Anal. Chem. 1996, 68, 3054-3058. (42) Amemiya, S.; Yang, X.; Wazenegger, T. L. J. Am. Chem. Soc. 2003, 125, 11832-11833. (43) Ando, T.; Yamasaki, M.; Suzuki, K. Protamines: Isolation, Characterization, Structure and Function; Springer-Verlag: New York, 1973. (44) Sorgi, F. L.; Bhattacharya, S.; Huang, L. Gene Ther. 1997, 4, 961-968. (45) Schefer, U.; Ammann, D.; Pretsch, E.; Oesch, U.; Simon, W. Anal. Chem. 1986, 58, 2282-2285.
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Figure 1. Scheme of ion-transfer reactions considered in this work. The arrows in the outer solution represent diffusion of (A) the ion, In, and (B) the ionophore, L, which limits mass-transfer process.
transfer reactions (Figure 1). In one case, an ion, In, is initially in the outer solution and then is transferred into the inner solution across the interface (Figure 1A). The transient current is limited by diffusion of the ion in the outer solution when the transfer process is not coupled with any other reaction (simple transfer)
In (outer solution) h In (inner solution)
Figure 2. Defined space domain for the numerical analysis of a micropipet electrode.
species. The assumptions are such that diffusion process in the inner solution was neglected. The boundary conditions are
c(r,0,t) ) 0
[
or when the transfer process is facilitated by complexation with an ionophore, L, (facilitated transfer) that is in excess in the inner solution
[
c(r,z,t) ) c0
r)rg
)0
)0
(interface)
(7)
a < r < rg (insulator)
(8)
-20a < z < 0 (insulator)
(9)
rg < r < 100a,
z ) -20a, r ) 100a,
-20a < z < 100a, and 0 < r < 100a, z ) 100a (simulation space limit) (10)
I (outer solution) + sL (inner solution) h
Another case is also a facilitated transfer, where the ion is initially in the inner solution and is transferred into the outer solution that contains the ionophore (Figure 1B)
z)0
]
∂c(r,z,t) ∂r
n
ILs (inner solution) (4)
]
∂c(r,z,t) ∂z
(3)
0 < r < a, 0 < t
[
]
∂c(r,z,t) ∂r
r)0
)0
0 < z < 100a (axis of symmetry) (11)
The initial condition is given as
In (inner solution) + sL (outer solution) h ILs (outer solution) (5)
This facilitated transfer results in transient current controlled by ionophore diffusion when the ionophore concentration is much smaller than that of the ion. Model Assumptions. We assume that a large-amplitude potential step was established instantaneously at the interface so that the surface concentration of a species changes to zero after t ) 0. Also, it is assumed that the resulting current is controlled by diffusion of the species in the outer solution of the pipet. The diffusion problem based on the assumptions was formulated as follows. Figure 2 shows the geometry of micropipet electrodes defined in cylindrical coordinates, where r and z are the coordinates in directions parallel and normal to the interface, respectively. Diffusion of a species in the outer solution can be expressed as
[
]
∂c(r,z,t) ∂2c(r,z,t) 1 ∂c(r,z,t) ∂2c(r,z,t) )D + + ∂t r ∂r ∂r2 ∂z2
(6)
where c(r,z,t) is the local concentration of the diffusion-limiting 5572
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c(r,z,0) ) c0
(12)
The transient current, id,RG(t), at a pipet electrode with a RG value can be obtained by integrating the flux over the liquid/liquid interface
id,RG(t) ) 2πnFD
∫
a
0
r
[
]
∂c(r,0,t) dr ∂z
(13)
This time-dependent diffusion problem was solved by FEMLAB version 2.3 (COMSOL, Inc., Burlington, MA), which applies the finite element method. Simulation Results. Figure 3 shows the theoretical chronoamperometric responses at micropipet electrodes with different wall thicknesses. The transient currents, id,RG(t), were normalized with respect to the steady-state current at inlaid disk electrodes with the same radius, id,inlaid, in order to emphasize the current enhancement at a long-time regime. The accuracy of our simulations was tested as follows. The diffusion-controlled steady-state currents were compared with previously reported ones. It was found that our results agree very well with those reported by Shao and Mirkin12 and by Amphlett and Denuault38 within 1.0%. Indeed,
Table 1. Parameters in Eqs 1, 15, and 16 for Different RG Values
Figure 3. Chronoamperometric responses based on numerical simulations for micropipet electrodes with different wall thicknesses. The transient currents, id,RG(t), were normalized with respect to the steady-state current at inlaid disk electrodes with the same disk radius, id,inlaid. The curves are for RG ) 1.1, 1.5, 2.0, and 100 from the top. The bottom curve is overlapping with eq 2.
our simulation results agree with an approximate analytical equation for the current versus RG for microdisk electrodes46
id,RG id,inlaid
) 1.000 +
0.1380 (RG - 0.6723)0.8686
(14)
where id,RG is the diffusion-limited steady-state current at a disk electrode with a RG value. At the same time, the values as obtained by extrapolating the long-time transient currents in the simulations by Shoup and Szabo36,40 are slightly smaller than our results while those reported by Fang and Leddy37 are significantly larger. Also, the transient response at RG ) 100 was compared with eq 2. In the time window of 0.01 < Dt/a2 < 250, they agree within 1.5%. Equation 2 predicts values of id,inlaid(t)/id,inlaid that are consistently larger than the simulation result by Heinze47 within 0.6%. At the same time, our simulation result at RG ) 100 is consistently smaller than that by Heinze47 and larger than that by Kakihana,22 where difference between ours and others is within 1.0%. Moreover, our simulation results at RG ) 1.1, 1.5, and 2.0 agree with those numerically calculated by Shoup and Szabo36 within 1.0%. Indeed, the current enhancement at a long-time regime also was clearly observed in our simulations. When the insulating sheath is thin, the chronoamperometric responses level off at a longtime regime, approaching to a high steady-state current. This deviation is due to diffusion from behind the plane of the electrode, which enhances flux to the electrode. Such a deviation occurs at a shorter time for an electrode with a thinner insulating sheath, where the diffusion field needs to grow less to reach the outer edge of the insulating sheath. The chronoamperometric responses at micropipet electrodes with small RG values can be expressed using approximate equations depending on the time window. In these equations, the transient current at a micropipet electrode was normalized with respect to the steady-state current id,RG at the same electrode using eqs 1 and 14, which is more convenient for use in analysis of (46) Zoski, C. G.; Mirkin, M. V. Anal. Chem. 2002, 74, 1986-1992. (47) Heinze, J. J. Electroanal. Chem. 1981, 124, 73-86.
RG
x
A
B
C
10 2.0 1.5 1.1
4.062 4.427 4.644 5.140
0.8892 0.7536 0.6646 0.6533
0.4168 0.3930 0.3818 0.3384
1.6841 1.0902 0.7057 0.4384
experimental data. When t is smaller than a value, tmin, the transient current is indistinguishable from that at inlaid disk electrodes. Compared with eq 2, the smaller RG value causes a change in the normalized current only by increasing the steadystate current. Therefore, the normalized current for a specific RG value in this time regime can be obtained by normalizing id,inlaid(t) in eq 2 with respect to id,RG as obtained using eqs 1 and 14, which results in
id,RG(t) 4 ) f (t) id,RG x
(15)
where id,RG(t) ) id,inlaid(t). When the chronoamperometric response extends into a longer time regime beyond t ) tmin, transient current becomes larger at an electrode with a smaller RG value. In this case, the chronoamperometric response can be represented accurately only by simulation results. The current responses in Figure 3 were plotted in the normalized form so that analytical expressions were obtained by fitting the resulting curves with an approximate equation analogous to eq 2,20,22 i.e.,
id,RG(t) Ba x + (1 - A)e-(Ca/ Dt) )A+ id,RG xDt
(16)
Table 1 shows the parameters, A, B, and C, thus obtained for different RG values. Equation 16 agrees with the simulation results within 1.0% in the time window of 0.01 < Dt/a2 < 250. In summary, the chronoamperometric responses in their normalized form can be expressed by eqs 2, 15, or 16. When RG > 10, all equations are equivalent at any time. When RG < 10 and t < tmin, eqs 15 and 16 are equivalent and accurate. When RG < 10 and t > tmin, only eq 16 is accurate. EXPERIMENTAL SECTION Chemicals. LiCl and MgCl2‚6H2O from Fisher Chemicals (Fair Lawn, NJ) and CaCl2‚2H2O from EM Science (Gibbstown, NJ) were used as aqueous electrolytes. 1,2-Dichloroethane (DCE, 99.8% HPLC grade) and chlorotrimethylsilane (98%) were obtained from Aldrich (Milwaukee, WI). Tetraethylammonium chloride (TEACl), N,N,N′,N′-tetracyclohexyl-3-oxapentanediamide (ETH 129), and tetradocecylammonium tetrakis(4-chlorophenyl)borate (TDDATPBCl, ETH 500) were obtained from Fluka (Milwaukee, WI). Protamine sulfate (grade III, from herring) was from Sigma (St. Louis, MO). All reagents were used as received. All aqueous solutions were prepared with 18.3 MΩ cm-1 deionized water (Nanopure, Barnstead, Dubuque, IA). Fabrication of Micropipet Electrodes. Micropipets were made from borosilicate glass capillaries (o.d./i.d.)1.0 mm/0.58 mm, 10 cm in length) from Sutter Instrument Co. (Novato, CA) Analytical Chemistry, Vol. 76, No. 18, September 15, 2004
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using laser-based pipet puller (model P-2000, Sutter Instrument). Appropriate pulling programs were selected to fabricate patchtype micropipets to minimize the iR drop inside the narrow shaft. All micropipets were inspected using an optical microscope model BX 41 (×100-×500, Olympus America, Melville, NY) before experiments. The inner or outer wall of each pipet was silanized30 to fill the inside with an organic or aqueous electrolyte solution, respectively. Electrochemical Measurements. A computer-controlled CHI 660B electrochemical workstation equipped with CHI 200 picoamp booster and faraday cage (CH Instruments, Austin, TX) was used for all electrochemical measurements. A two-electrode arrangement was used with Ag/AgCl and Ag/AgTPBCl electrodes as aqueous and organic reference/counter electrodes, respectively. All electrochemical experiments were performed at 22 ( 3 °C. The potential, E, was defined with respect to the half-wave potential of TEA+ transfer determined from the reversible voltammograms. The current carried by a positive charge from the aqueous phase to the DCE phase was defined to be positive. The electrochemical cells employed are as follows
Ag | AgCl | 0.206 mM TEACl or 0.024 mM protamine sulfate in 0.01 M LiCl (aq) || 0.01 M TDDATPBCl (DCE) | AgTPBCl | Ag (cell 1) Ag | AgCl | 0.01 M CaCl2 or 0.1 M MgCl2 (aq) || 0.5 mM ETH 129 in 0.01 M TDDATPBCl (DCE) | AgTPBCl | Ag (cell 2) Pipets were filled with the organic solution in cell 1 and with the aqueous solution in cell 2 from the back using a 10-µL syringe. Evaluation of Micropipet Tip Resistance. The micropipet tip resistance, which determines the time window and iR drop in chronoamperometry, was evaluated by ac impedance using CHI 660B.25 When 5-20-µm-radius pipets filled with 0.01 M LiCl were immersed in the same aqueous solution, the total impedance of the cell was 0.2-0.5 MΩ. Similar experiments using 0.01 M ETH 500 in DCE as inner and outer solutions gave the values of 1020 MΩ. These impedance values are close to those reported for micropipet electrodes by others.25,29,30 RESULTS AND DISCUSSION Simple TEA+ Transfer. To check validity of our theoretical results, chronoamperometric responses based on simple TEA+ transfer were investigated. First, cyclic voltammetry was carried out at a micropipet electrode to determine the potential range, where the current is limited by TEA+ diffusion (Figure 4A). With TEA+ initially only in the outer aqueous phase, a sigmoid wave was observed during the forward scan, where spherical diffusion of TEA+ from the outer aqueous phase to the interface was followed by TEA+ transfer into the inner DCE phase. The backward wave was peak-shaped because of liner diffusion of TEA+ in the inner solution, which was followed by back transfer of TEA+ into the outer solution. Then, the interfacial potential was set to -0.142 V to record a chronoamperometric response controlled by TEA+ diffusion in the outer aqueous phase (Figure 4B). At t-1/2 < 10 s-1/2 (t > 10 ms), the charging current became so small that the faradic current could be identified precisely in 5574
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this time regime. The background-corrected chronoamperometric response for TEA+ transfer was compared with theoretical ones as obtained by numerical simulations. The experimental and theoretical responses were plotted in the form of the normalized current, id,RG(t)/id,RG, versus t-1/2. The parameter a/D1/2 was adjusted for the theoretical curves based on eq 16 at different RG values to obtain the best fit. Since the charge number is known, the diffusion coefficient and the electrode radius could be determined simultaneously by combining the optimum parameter a/D1/2 and eq 1 (Table 2). The experimental response fits very well with the theoretical one at RG ) 1.5, yielding the value of 0.26 s1/2 for a/D1/2 (Figure 4C). Combination of the parameter and eq 1 with the limiting current of 0.65 nA gave the diffusion coefficient and the tip radius as 8.9 × 10-6 cm2/s and 7.9 µm, respectively. The electrode radius is consistent with the value determined by optical microscopy. The average diffusion coefficient obtained using three pipets with different sizes is (9.3 ( 0.7) × 10-6 cm2/s, which agrees well with the value reported in the literature (9.3 × 10-6 cm2/s).48 Similar diffusion coefficient and electrode radius were also obtained by fitting the experimental curve with the theoretical one at RG ) 2.0. These good agreements confirm the electrode geometry used here. Indeed, it was shown previously by scanning electrochemical microscopy12,13 and video microscopy30 that a typical RG value of micropipet electrodes is ∼1.5 (RG of the original glass capillaries is 1.7) and that the interface is formed at the pipet apex, i.e., neither recessed nor protruding. The same experimental curve was also analyzed using eq 2 (Figure 4D). Again, only the parameter of a/D1/2 for the theoretical curve was adjusted to obtain the best fit. Interestingly, the experimental and theoretical curves fit apparently well in a narrower time window (t-1/2 < 7 s-1/2). The analysis, however, gave the diffusion coefficient and pipet radius that are significantly larger and smaller, respectively, than the values at RG ) 1.5 and 2.0 (Table 2). This result can be explained as follows. While the chronoamperometric current is independent of RG at a short-time regime, the theoretical curve at RG ) 1.5 becomes less steep than eq 2 at a long-time regime (a/(Dt)1/2 < 2 in Figure 3) because of the current enhancement by diffusion from behind the electrode. Indeed, such a change in the slope was observed in the experimental curve. Both curves, however, are almost linear with respect to t-1/2 in the long-time regime so that they can be fitted apparently. This apparent fit, of course, gives inaccurate parameters because the long-time current in eq 2 does not involve the enhancement effect by back diffusion. The enhancement of the long-time transient current became clearer when it was compared with eq 15 at RG ) 1.5 (Figure 4E). This equation was obtained by normalizing the transient current in eq 2 with respective to the steady-state current at RG ) 1.5 using eqs 1 and 14. Therefore, this equation should be valid at the time regime at which the chronoamperometric current is indistinguishable from that at inlaid disk electrodes. Indeed, the experimental response fits well with the theoretical one at t-1/2 > 5 s-1/2. Also, the parameter of a/D1/2 was obtained to be 0.26 s1/2 from the fit, yielding reasonable values of the diffusion coefficient and the tip radius as 9.0 × 10-6 cm2/s and 7.8 µm, respectively. (48) Wandlowski, T.; Marecek, V.; Holub, K.; Samec, Z. J. Phys. Chem. 1989, 93, 8204-8212.
Figure 4. (A) Cyclic voltammograms at the water/DCE interface (a) with and (b) without TEACl in the aqueous phase. Scan rate, 20 mV/s. (B) Chronoamperometric data based on TEA+ transfer (curves a and c) and the background data (curves b and d). The data were displayed with respect to t for curves a and b and to t-1/2 for curves c and d. The potential was stepped from 0.158 to -0.142 V. The sampling rate was 1 ms per point. The same pipet with a ) 7.9 µm was used for both cyclic voltammetric and chronoamperometric measurements. The backgroundcorrected current, id,RG(t), was normalized with respect to the diffusion-limited steady-state current, id,RG, and compared with theoretical curves based on (C) eq 16 at RG ) 1.5, (D) eq 2, and (E) eq 15 at RG ) 1.5. All parameters for eqs 15 and 16 at RG ) 1.5 are given in Table 1.
At a longer time regime (t-1/2 < 5 s-1/2), however, the theoretical curve deviates from the experimental one and approaches the intercept smaller than 1, which is an error caused by lack of enhancement effect of the transient current in eq 15. Overall, eq 15 is not only less general but also practically less useful than eq 16. The former equation requires a data point at a shorter time regime, at which precise identification of the faradic current is more difficult because of the larger charging current. Also, to obtain the transient and steady-state currents by single chrono-
amperometric recording, the time window of the i-t curve measurement usually spans the transient and the steady-state regions, where the back-diffusion effect needs to be considered for accurate data analysis. Therefore, eq 16 was used in the following analysis. Protamine Transfer. Chronoamperometry at micropipet electrodes is useful to study complicated reactions based on transfers of multiple charges. Transfer of natural polypeptide protamine, which was recently studied by us using micropipet Analytical Chemistry, Vol. 76, No. 18, September 15, 2004
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Table 2. Diffusion Coefficients of TEA+ and Pipet Radii As Determined by Chronoamperometry
a
RG
D (× 10-6 cm2/s)
a (µm)
∞a 10 2.0 1.5 1.1
13.4 11.5 9.8 8.9 7.8
6.1 7.0 7.5 7.9 8.1
the voltammogram was analyzed by assuming protamine’s charge of +20. While analysis of the diffusion-limited steady-state current using eq 1 gives a reasonable value for the diffusion coefficient of protamine,42 the forward wave is much broader than that for reversible reactions with n ) +20 as given by
E ) E1/2 +
RT 1 - iRG/id,RG ln nF iRG/id,RG
(17)
Equation 2 was used to obtain the parameters.
Figure 5. (A) Cyclic voltammograms at the water/DCE interface (a) with and (b) without protamine sulfate in the aqueous phase. Scan rate, 20 mV/s. The closed and open circles represent theoretical curves for reversible reactions based on eq 17 and irreversible reactions with R ) 0.12,42,49 respectively (n ) +20 for both curves). The positions of the theoretical curves are arbitrary. (B) Backgroundcorrected chronoamperometric data following a step in the potential from -0.121 to -0.321 V. The sampling rate was 5 ms per point. The same pipet with a ) 7.6 µm was used for both cyclic voltammetric and chronoamperometric measurements. The transient current, id,RG(t), was normalized with respect to the diffusion-limited steadystate current, id,RG. The solid line represents eq 16 at RG ) 1.5.
voltammetry,42 is such a case. When DCE was used as the inner organic phase and the outer aqueous phase contains protamine, a voltammogram as shown in Figure 5A was observed. The sigmoid wave indicates that protamine diffusion in the outer aqueous phase limits mass transfer during the forward scan, which was followed by the very sharp desorption peak during the backward scan. Since two-thirds of the ∼30 total amino acids in protamine are arginine, the excess positive charges of protamine in a solution at physiological pH or lower is ∼20.43,44 Therefore, 5576
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where iRG is the steady-state current at the potential E. Therefore, the charge transferred by each protamine cannot be confirmed directly from the voltammogram. Indeed, our previous analysis based on the assumption of n ) +20 indicated that the voltammogram is irreversible.42 Chronoamperometric current limited by protamine diffusion was measured to determine the diffusion coefficient of protamine directly, which allows subsequent determination of the transferred charge per protamine. A chronoamperometric response is shown in Figure 5B. In this analysis, the pipet radius was determined by optical microscopy and confirmed by analyzing the limiting current of TEA+ transfer. Therefore, the diffusion coefficient of protamine in the aqueous phase was the only adjustable parameter. The experimental curve agrees very well with the theoretical one based on eq 16 at RG ) 1.5. Also, while the experimental time scale is much longer than that for TEA+, the normalized currents are comparable because of slower diffusion of protamine. Indeed, analysis of several chronoamperometric data gave the diffusion coefficient of protamine as (1.2 ( 0.1) × 10-6 cm2/s, which agrees well with previously reported values.42,43 The diffusion coefficient was used to determine the transferred charge per protamine using eq 1 at RG ) 1.5 (x ) 4.64). The charge thus determined was +20 ( 1, which is close to the expected charge of protamine. Although the voltammogram is complicated because of the slow transfer kinetics and the following adsorption process, the diffusion coefficient and the transferred charge were determined separately under a diffusion-limited condition. Therefore, these values can be reliably used to analyze the kinetically limited voltammograms. Indeed, the forward wave fits closely with an equation for irreversible reactions,49 as demonstrated in our previous paper (for discussion about the small transfer coefficient of 0.12 as obtained from the fit, see ref 42). Facilitated Transfers of Ca2+ and Mg2+ by ETH 129. As another application, chronoamperometry was carried out to determine the stoichiometry of complexes involved in Ca2+ and Mg2+ transfers facilitated by ETH 129, which forms 1:3 and 1:2 complexes with the respective ions in crystals and in plasticized polymer membranes.45 When ionophore concentration in the outer organic solution is much lower than that of the ions in the inner aqueous solution, the mass-transfer process during the forward and backward scans is limited by ionophore diffusion (Figure 6A and B). The shape of voltammograms controlled by ionophore diffusion depends on the complexation stoichiometry.50-52 Indeed, (49) Oldham, K. B.; Zoski, C. G. J. Electroanal. Chem. 1988, 256, 11-19. (50) Samec, Z.; Homolka, D.; Marecek, V. J. Electroanal. Chem. 1982, 135, 265283. (51) Homolka, D.; Holub, K.; Marecek, V. J. Electroanal. Chem. 1982, 138, 2936. (52) Kakiuchi, T.; Senda, M. J. Electroanal. Chem. 1991, 300, 431-445.
steady-state voltammograms for reversible reactions at microholesupported ITIES was obtained as53
RT 2 ln E ) E1/2 + nF
s-1
(1 - iRG/id,RG)s iRG/id,RG
(18)
where s is the complexation stoichiometry defined in eq 5. Therefore, the stoichiometry of the ionophore-ion complexes can be determined using eq 18 when the voltammograms are reversible and the charge of the transferred ion is known. The voltammograms of Ca2+ and Mg2+ transfers, however, are much broader than eq 18 with s ) 3 and 2, respectively. Also, it was found that the wave shape does not change using micropipets with different radii in the range of 2-15 µm. These results suggest that the facilitated transfers are reversible reactions with higher stoichiometries or irreversible reactions. Chronoamperometry was carried out to determine the diffusion coefficient of the ionophore. The stoichiometry can be determined subsequently by analyzing the diffusion-limited steady-state current using53
id,RG ) (n/s)FDc0ax
(19)
Chronoamperometric responses for Ca2+ (Figures 6C) and Mg2+ (data not shown) transfers were measured with pipet electrodes, the diameter of which was determined by optical microscopy. Charging current was significant within 10 ms after the potential step, indicating a large cell constant. Indeed, the tip resistance of water-filled pipets was reported to be 10-20 MΩ when they were immersed in the organic phase.29 Therefore, the faradic current could be measured accurately only in the long-time regime. The diffusion coefficient of ETH 129 in the DCE phase was determined using eq 16 at RG ) 1.5 to be (4.7 ( 0.6) × 10-6 and (5.7 ( 0.6) × 10-6 cm2/s from the Ca2+ and Mg2+ data, respectively. These values were used to determine the stoichiometry of the ionophore-ion complexes using eq 19. With n ) +2, the stoichiometries of Ca2+ and Mg2+ complexes were determined to be 3.0 ( 0.4 and 2.0 ( 0.1, respectively, which agree with the values in crystals and in plasticized polymer membranes.45 Also, with the stoichiometries as determined by chronoamperometry, the voltammograms agree well with the theoretical ones that were numerically obtained for irreversible transfers of divalent cations (see Supporting Information), yielding the transfer coefficient of 0.50. Importantly, it was found that the dependence of the irreversible waves on the stoichiometry is very similar to that of reversible ones. Indeed, the irreversible waves at micropipet electrodes as obtained by numerical simulations can be represented approximately by an analytical expression for irreversible reactions at uniformly accessible electrodes, which is given as (see Supporting Information)
E ) E1/2 +
RT 2 ln RnF
s-1
(1 - iRG/id,RG)s iRG/id,RG
(20)
The shape of the irreversible waves, however, also depends on (53) Wilke, S.; Wang, H. J. Electroanal. Chem. 1999, 475, 9-19.
Figure 6. Cyclic voltammograms of (A) Ca2+ and (B) Mg2+ transfers at the water/DCE interface (a) with and (b) without ETH 129 in the organic phase. Scan rate, 20 mV/s. a ) 6.2 and 8.0 µm for (A) and (B), respectively. The closed and open circles represent theoretical curves for reversible reactions based on eq 18 and irreversible reactions based on numerical simulations with R ) 0.50 (see Supporting Information), respectively. s ) (A) 3 and (B) 2. The positions of the theoretical curves are arbitrary. (C) Backgroundcorrected chronoamperometric data for Ca2+ transfer following a step in the potential from 0.1 to -0.2 V. The sampling rate was 1 ms per point. The chronoamperogram was obtained with the same electrode as used for cyclic voltammetry. The transient current, id,RG(t), was normalized with respect to the diffusion-limited steady-state current, id,RG. The solid line represents eq 16 at RG ) 1.5.
the transfer coefficient, R, so that prior determination of the stoichiometry as was done by chronoamperometry here is required for accurate analysis of the irreversible waves limited by ionophore diffusion. Analytical Chemistry, Vol. 76, No. 18, September 15, 2004
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CONCLUSIONS Chronoamperometry at micropipet electrodes was successfully used for the first time to determine directly the diffusion coefficient of a species in the outer solution. The technique is very useful to study complicated charge-transfer reactions at liquid/liquid microinterfaces because it allows subsequent determination of the charge transferred by each species from the diffusion-limited steady-state current. Since the chronoamperometric current is limited by diffusion, the diffusion coefficient and transferred charge thus determined can be used reliably to analyze kinetically controlled voltammograms. The theory of chronoamperometry at micropipet electrodes was developed for accurate determination of diffusion coefficients. Results of our numerical simulations confirmed enhancement of the long-time transient current as predicted theoretically by Shoup and Szabo,36 where diffusion from behind the pipet tip surrounded by a thin glass wall enhances the flux to the electrode. The current enhancement was confirmed also experimentally as deviations from eqs 2 and 15. Our simulation results were provided in the form of an empirical equation (eq 16). Since prolonged charging current due to large cell resistance allows precise identification (54) Josserand, J.; Morandini, J.; Lee, H. J.; Ferrigno, R.; Girault, H. H. J. Electroanal. Chem. 1999, 468, 42-52. (55) Ohde, H.; Uehara, A.; Yoshida, Y.; Maeda, K.; Kihara, S. J. Electroanal. Chem. 2001, 496, 110-117. (56) Bond, A. M.; Luscombe, D.; Oldham, K. B.; Zoski, C. G. J. Electroanal. Chem. 1988, 249, 1-14.
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of the faradic current only at a long-time regime (typically t > 5 ms), eq 16 can be used for more accurate analysis of chronoamperograms at micropipet electrodes. Since cell resistance at microhole-supported interfaces is comparable to that at micropipet electrodes,29 the former interfaces may be used also to determine diffusion coefficients and transferred charges by long-time chronoamperometry. In contrast to silanized micropipets,12,13,30 however, the interface position within the cylindrical microhole is not well-defined.27,54,55 Indeed, chronoamperometry was carried out to demonstrate that microholesupported interfaces were recessed or inlaid depending on the sequence of liquid introduction.27 Information about the interface position is necessary for accurate analysis of chronoamperometric responses at recessed disk electrodes.56 ACKNOWLEDGMENT We thank the Research Corporation for financial support. This work was also supported by the University of Pittsburgh. SUPPORTING INFORMATION AVAILABLE Additional information as noted in text. This material is available free of charge via the Internet at http://pubs.acs.org.
Received for review April 26, 2004. Accepted July 8, 2004. AC0493774
