Determination of Diffusion Coefficients of Electroactive Species in

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Anal. Chem. 2001, 73, 2468-2475

Determination of Diffusion Coefficients of Electroactive Species in Time-of-Flight Experiments Using a Microdispenser and Microelectrodes Marcus Mosbach,*,† Thomas Laurell,‡ Johan Nilsson,‡ Elisabeth Cso 1 regi,§ and Wolfgang Schuhmann†

Analytische Chemie-Elektroanalytik & Sensorik, Ruhr-Universita¨t Bochum, Universita¨tsstrasse 150, 44780 Bochum, Germany, Department of Electrical Measurements, Lund Institute of Technology, Box 118, 22100 Lund, Sweden, Department of Biotechnology, Lund University, Box 124, 22100 Lund, Sweden

Two novel methods for the determination of diffusion coefficients of redox species combining the special properties of microdispensing devices and microelectrodes are presented. Both are based on the local application of tiny volumes of the redox-active species by means of a dispenser nozzle at a defined distance from the surface of a microelectrode. The microelectrode, which is inserted through the bottom into an electrochemical cell, is held at a constant potential sufficient to oxidize or reduce the electro-active species under diffusional control. The dispenser, which is filled with the electro-active species, can be positioned by means of micrometer screws over the microelectrode. After dispensing a defined number of droplets near the microelectrode surface, the current through the microelectrode is recorded, usually yielding a peak-shaped curve having a defined time delay between the shooting of the droplets and the maximum current. The time that is necessary to attain maximum current, together with the known distance between two dispensing points, can be used to determine the diffusion coefficient of the electroactive species without knowledge of any system parameters, such as concentration of the redox species, diameter of the electroactive surface or number of transferred electrons. A similar method for the determination of diffusion coefficient of redox species involves a second redox species for calibration purposes. A mixture of both species is shot close to the microelectrode surface. Due to the different formal potentials of the redox species that are used, they can be distinguished in sequential experiments by variation of the potentials that are applied to the microelectrode, and it is thus possible to determine the individual transit times of the redox species independently. The difference in the transit times, together with the known diffusion coefficient of one of the redox species, can be used to calculate the unknown diffusion coefficient of the second one. Electrochemical methods are widely used to determine diffusion coefficients of electro-active species by carrying out heterogeneous electron-transfer reactions using experimental conditions 2468 Analytical Chemistry, Vol. 73, No. 11, June 1, 2001

for which the rate of the electron-transfer process is controlled by diffusional mass transfer of the redox species to the electrode surface. However, in most of these experiments, it is indispensably necessary to know additional system parameters, for example, the concentration of the electro-active species, the area of the active electrode surface, and the number of transferred electrons. Recently, microelectrodes have gained increasing attention as a tool for the determination of the diffusion coefficient of electroactive compounds. The diffusion coefficient and the electrontransfer rate constant of an electro-active species could be determined using the dependence of the peak separation and peak current at cylindrical microelectrodes from the scan rate in cyclic voltammetry.1 The evaluation of the rate constant of the electrontransfer reaction and the diffusion coefficient are based on the numerical solution to the integral equation for simple chargetransfer reactions and diffusion of redox species to a microcyclindrical electrode. The calculation effort is quite high and system parameters such as concentration, number of transferred electrons, and electrode geometry have to be known or determined. Steady-state amperometry,2 chronopotentiometry,3 and linearsweep voltammetry4 with stationary microelectrodes have been successfully applied to determine the diffusion coefficient of redoxactive molecules. However, at least the concentration of the electro-active species and the exact electrode surface area have to be known for an accurate determination of the diffusion coefficient. Attempts have been reported to apply chrono-amperometry at disk-shaped microelectrodes to determine simultaneously the concentration and the diffusion coefficient of a redox species5 when the number of transferred electrons and the area of the active electrode surface are known. Because the obtained * Corresponding author. Phone: ++49 (234) 3226202. Fax: ++49 (234) 3214683. E-mail: [email protected]. † Ruhr-Universita ¨t Bochum. ‡ Department of Electrical Measurements, Lund Institute of Technology. § Department of Biotechnology, Lund University. (1) Neudeck, A.; Dittrich J. J. Electroanal. Chem. 1991, 313, 37-59. (2) Baur, J. E.; Wightman, R. M. J. Electroanal. Chem. 1991, 305, 73-81. (3) Aoki, K.; Akimoto, K.; Toduka, K.; Matsuda, H.; Osteryoung, J. J. Electroanal. Chem. 1985, 182, 281-94. (4) Aoki, K.; Akimoto, K.; Toduka, K.; Matsuda, H.; Osteryoung, J. J. Electroanal. Chem. 1984, 171, 219-30. (5) Jung, Y.; Kwak, J. Bull. Korean Chem. Soc. 1994, 15, 209-13. 10.1021/ac0012501 CCC: $20.00

© 2001 American Chemical Society Published on Web 05/02/2001

experimental data have to be fitted by a nonlinear regression, the mathematical effort for the calculation of the diffusion coefficient is high. An easier approach for the direct determination of diffusion coefficients of electroactive species using the chrono-amperometric response at a microdisk electrode has been proposed by Bard and co-workers.6 Normalizing the time-dependent current with respect to its steady-state value at long times and plotting the resulting current against 1/xt results in a straight line with an intercept of 1 and a slope, S. The diffusion coefficient can be calculated from the slope and the known diameter of the microelectrode. An alternative way to determine diffusion coefficients without any knowledge about the concentration and the number of transferred electrons involves the determination of the time which is necessary for a species that is produced at a generator electrode to diffuse to a collector electrode. From the known distance between the generator and collector electrode and the measured transit time, the diffusions coefficient of the produced species can be estimated. Licht et al.7 used an array of individually addressable microelectrodes to determine the diffusion coefficient of Ru(NH3)62+ generated from Ru(NH3)63+ at one branch of the microelectrode array. Similar approaches made use of the positioning of microelectrodes in a scanning electrochemical microscope (SECM)8 or the application of rotating disk electrodes.9 In addition, interdigitated electrode arrays have been used to determine the diffusion coefficient of electrons in redox polymers using timeof-flight experiments, which is important for the design of related biosensors.10,11 In this communication, a novel method for the determination of diffusion coefficients of electroactive species that is based on the diffusion time of the redox species from a dispensing spot to a microelectrode is proposed. For this, a setup has been developed that consists of a previously described microdispensing device12,13 and a positionable microelectrode as the collector. The dispenser was used to shoot a tiny amount of a redox species to a spot close to the microelectrode, which is poised to a potential that is sufficiently high to invoke a diffusion-controlled heterogeneous electron transfer between the redox species and the electrode surface. The time-dependent current change is recorded, and evaluation of the peak-shaped response curve allows the determination of the diffusion coefficient of the redox species. In contrast to most other methods, this novel method is independent from system parameters like concentration of the redox species, number of transferred electrons, and area of the electrode surface. Although the recently described methods using microband(6) Denuault, G.; Mirkin, M. V.; Bard, A. J. J. Electroanal. Chem. 1991, 308, 27-38. (7) Licht, S.; Cammarata, V.; Wrighton, M. S. J. Phys. Chem. 1990, 94, 613340. (8) Bard, A. J.; Denuault, G.; Dornblaser, B. C.; Friesner, R. A.; Tuckerman, L. S. Anal. Chem. 1991, 63, 1282-88. (9) Albery, W. J.; Hitchman, M. L. Ring-Disc Electrodes; Clarendon Press: Oxford, 1971; p 105. (10) Chidsey, C. E.; Feldman, B. J.; Lundgren, C.; Murray, R. W. Anal. Chem. 1986, 58, 601-7. (11) Feldman, B. J.; Feldberg, S. W.; Murray, R. W. J. Phys. Chem. 1987, 91, 6558-60. (12) O ¨ nnerfjord, P.; Nilsson, J.; Wallmann, L.; Laurell, T.; Marko-Varga, G. Anal. Chem. 1998, 70, 4755-60. (13) Laurell, T.; Wallman L.; Nilsson, J. J. Micromech. Microeng. 1999, 9, 369376.

Figure 1. Ferrocene derivatives 1 and 2. (the Br- counterions are omitted for clarity).

electrode arrays7,11 show the same advantages with respect to a preknowledge about system parameters, they allow only the determination of the diffusion coefficient of redox species that are generated from the starting compound at one of the electrodes. This diffusion coefficient may not be identical with the diffusion coefficient of the redox species in its initial redox state that is mainly present in the solution; hence, especially for redox species that are not available in both redox states, like ferrocene derivatives, these methods are not applicable. EXPERIMENTAL SECTION Reagents. Ferrocene monocarboxylic acid (Fc-COOH) and [Ru(NH3)6]Cl3 were purchased from Strem Chemicals (Newburyport, MA). Potassium ferrocyanide(II) was obtained from Merck (Darmstadt, Germany). [1,3-Bis(N,N-dimethyl-N-(2-ferrocenylethyl)ammoniummethyl)-5-(N,N-dimethyl-N-(2-hydroxyethyl) ammoniummethyl]benzoltribromid (ferrocene derivative 1) and [1-(N,Ndimethyl-N-(2-ferrocenylethyl)ammoniummethyl)-4-(N,N-dimethylN-(2-hydroxyethyl) ammoniummethyl)] benzoldibromid (ferrocene derivative 2) (see Figure 1) were synthesized by A. Salmon and P. Jutzi, Universita¨t Bielefeld, Germany.14 KCl (Merck; Darmstadt, Germany) was used in 0.1 M concentration as a supporting electrolyte if not otherwise stated. Ferrocene monocarboxylic acid (Fc-COOH) was dissolved in 0.1 M KCl by slightly raising the pH value with 1 M KOH (Merck; Darmstadt, Germany). Dimethyl sulfoxide (DMSO) was from Riedel-de-Haen (Seelze, Germany). Ferrocene derivatives 1 and 2 were dissolved in 0.2 mL of DMSO and then intensively mixed with 1.8 mL of 0.1 M KCl. All of the chemicals were of the highest available purity and were used as received. DI water was distilled in a quartz apparatus 3 times before use. Microdispenser. The microdispenser, which was previously developed for handling liquids in the nanoliter to picoliter range in a flow-through system, has found application in picoliter pipetting and sample injection, for example, for chromatography applications,15 MALDI-TOF mass spectrometry,12,16 or capillary electrophoresis.17 The dispenser is constructed of two joined silicon structures forming a flow-through channel. One channel wall is coupled to a piezo-actor, generating a pressure pulse. Each (14) Salmon, A.; Jutzi, P. unpublished results. (15) Nilsson, J.; Szecsi, P.; Schafer-Nielsen, C. J. Biochem. Biophys. Methods 1993, 27, 181-90. (16) Little, D. P.; Cornish, T. J.; O’Donnell, M. J. Anal. Chem. 1997, 69, 454046. (17) Sziele, D.; Bru ¨ ggemann, O.; Do¨ring, M.; Freitag, R.; Schu ¨ gerl, K. J. J. Chromatogr. A 1994, 669, 254-58.

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pressure pulse results in a single droplet (typical volume, 100 pL) being released from an orifice in the opposing channel wall. High stability and directivity of the droplet formation is attained by a pyramid-shaped nozzle having an orifice size of 40 × 40 µm. The dispenser has an internal volume of 2.6 µL. The exact fabrication procedure and additional information can be found in previously published articles.12,13 Electrodes. Microelectrodes are produced by sealing a platinum wire (diameter, 50 µm or 25 µm; Goodfellow; Cambridge, U.K.) in a borosilicate glass capillary having a diameter of 1.5 mm. Complete details of the fabrication of such microelectrodes have been described previously.18 The electrodes are ground with emery paper and finely polished with alumina slurry (LECO; Kirchheim, Germany) of decreasing particle size (3 µm, 1 µm, and finally, 0.3 µm). Prior to each measurement, the microelectrodes are repolished and cleaned by 10 min of ultrasonification in water. A Ag/AgCl, 3 M Cl- reference electrode (Biometra; Go¨ttingen, Germany) and a platinum wire as a counter electrode are used to complete the three-electrode electrochemical cell. Apparatus. Chronoamperometric measurements have been performed using a BAS LC-4C potentiostat (Bioanalytical Systems; West Lafayette, IN). The position of the microelectrode that is inserted through the bottom of the electrochemical cell can be adjusted relative to the microdispenser by positioning tables using micrometer screws (Owis; Staufen, Germany) for the x, y, and z directions. The angle between the electrolyte surface and the droplet stream from the microdispenser was adjusted to ∼90 degrees. For fast data acquisition of the chronoamperometric response of the microelectrode, a laptop computer was used that was equipped with a 16-bit AD card (PCM-DAS16S; ComputerBoards Inc.; Middleboro, MA) and self-written software programmed in Visual BASIC 3.0 (Microsoft; Redmond, WA). A pulse generator (Philips PM 5786B with burst option) was manually programmed to a predefined number of droplets per experiment, with a typical dispensing frequency of 100 Hz. The driving parameters of the microdispenser were optimized to get a satellite-free droplet stream having a length of ∼2 cm. RESULTS AND DISCUSSION To establish a new method for the determination of diffusion coefficients of electroactive species, we used a setup that combines the specific properties of the microdispenser and of microelectrodes.The electrochemical cell was mounted on positioning tables equipped with micrometer screws that allowed exact movements in all directions. The microelectrode was inserted in the electrochemical cell through the bottom. The cell was filled with 0.1 M KCl solution so that the electrode surface of the microelectrode was just beneath the liquid surface. The dispenser was filled with a redox species dissolved in the same supporting electrolyte as was used in the electrochemical cell. The position of the dispenser was adjusted so that the droplet stream was almost perpendicular to the liquid surface and aiming on the glass surrounding the microelectrode. This perpendicular droplet stream minimized unidirectional convective effects after the droplets hit the liquid phase, thus avoiding preferential movement of the redox species in one direction. To minimize misdirection of the droplet stream (18) Kranz, C.; Ludwig, M.; Gaub, H. E.; Schuhmann, W. Adv. Mater. 1995, 7, 38-40.

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Figure 2. Schematic drawing of the setup. The microelectrode is screwed through the bottom into the electrochemical cell, which is filled with 0.1 M KCl solution as electrolyte. The microelectrode is positioned just beneath the liquid surface and polarized to a potential sufficiently high to oxidize or reduce the investigated redox species under diffusional control. The position of the dispenser, which is filled with a solution of the redox species, and the droplet stream relative to the microelectrode can be adjusted by moving the electrochemical cell using micrometer screws. The dispenser triggers the data acquisition software, allowing recording of the time-vs-current response of the microelectrode after the dispensing of droplets containing the redox species into the electrolyte in close proximity to the site of the microelectrode.

by air movements, the dispenser and the electrochemical cell were placed in a box. The microelectrode was set to a potential high enough to establish a diffusion-controlled heterogeneous electron transfer reaction, with the redox species filled in the dispenser. The pulse generator was operated in burst mode, allowing the exact number of droplets in each experiment, which is equal to the number of generated pulses, to be defined. Each dispensing experiment was started manually by activating the internal trigger of the pulse generator. The pulse generator triggered the acquisition software of the laptop computer to simultaneously start data acquisition, recording the current-vs-time response of the potentiostat at a rate of 0.3 kHz. The dotted line in Figure 3 represents a typical current-vstime curve of the amperometric response of a microelectrode after dispensing 10 droplets of ferrocyanide(II) (c ) 20 mM) to a spot located close to the electrode surface. At the beginning of the experiment, the current was close to zero, because no redox species was present in front of the electrode surface. After a short delay time the current increased quickly to a maximum peak value, after which the current decreased slowly. This observation is indicative of the time that is needed by the dispensed ferrocyanide(II) ions to diffuse from their dispensing point (the spot where the droplets are entering the electrolyte solution) to reach the microelectrode surface. The current decrease after the peak maximum is caused by dilution of the dispensed ferrocyanide within the bulk of the supporting electrolyte. Because the overall electrolyte volume in the electrochemical cell (∼5 mL) was a factor of 5 × 106 higher than the total volume of the dispensed droplets, the equilibrium concentra-

Figure 3. Current-vs-time response of a 50-µm-diameter platinum microelectrode (+500 mV vs Ag/AgCl/3 M KCl) after the dispensing of 10 droplets of 20 mM ferrocyanide(II) solution. The upper curve represents a situation in which the dispenser is positioned in such a manner that the dispensing point is very close to the electroactive surface of the microelectrode. In this case, a sharp current peak having a peak time of 1.33 s is obtained. The lower curve shows the current response in a subsequent experiment after laterally moving the microdispenser by 100 µm farther away from the microelectrode. The resulting curve shows a broader peak exhibiting a decreased height by a factor of 3 and a delayed peak maximum at t ) 2.44 s.

tion of ferrocyanide in the bulk electrolyte was negligible. Hence, the microelectrode current is decreasing to the baseline. The delay time (which is defined as the time to attain the maximum current) and the peak shape are strongly dependent on the distance between the active microelectrode surface and the spot where the dispensed droplets are shot into the electrolyte solution. The delay time increases with increasing distance; concomitantly, the peak height decreases and the peak becomes broader (see Figure 3, solid line). By plotting the peak time against the distance between the first dispensing spot and subsequent spots after repositioning of the electrochemical cell with respect to the microdispenser, the electroactive surface of the microelectrode can be visualized. A coarse prepositioning was attained by continuously dispensing droplets and recording the resulting current through the microelectrode while moving the electrochemical cell relative to the dispenser by using the micrometer screws. High currents indicated that the dispensing spot was close to the active electrode surface, thus allowing a coarse identification of the site of the microelectrode. After this, the electrochemical cell was moved relative to the dispenser in 100 µm steps, leading to a rectangular grid of 400 × 500 µm. At each position of the grid, the delay time to reach the current peak was recorded after dispensing of 10 droplets (with a single-droplet volume of 100 pL) of ferrocyanide. In Figure 4 these delay times are plotted versus the grid position. Dark areas correspond to short delay times, indicating that the dispenser is positioned in close proximity to the electroactive part of the microelectrode. The black area (showing a diameter of ∼100 µm) indicates the closest possible distance between the dispensing site and the microelectrode. When one considers the influence of the thickness of the electrolyte layer over the microelectrode surface and the rather coarse grid distance of 100 µm, together with the fact that it is a coarse assumption to treat the dispensing site as a point source, the determined size of the microelectrode and the actual size of 50 µm are in good agreement.

Figure 4. Plot of the dispenser position vs current peak times after the dispensing of 10 droplets of 20 mM ferrocyanide(II) into the electrolyte in defined distances from a 50-µm-diameter Pt microelectrode (+500 mV vs Ag/AgCl/3 M KCl). The distance between two grid points is 100 µm. Dark areas correspond to short peak times and light areas, to long times. The black area indicates the closest possible position of the dispensing point relative to the microelectrode and has a diameter of ∼100 µm.

A similar approach can be used to determine diffusion coefficients of redox active species without any additional knowledge about the concentration of the redox species or the active area of the microelectrode. The following assumptions are necessary: 1. The square in the grid between 100 µm < x < 200 µm and 200 µm < y < 300 µm (the site of the active electrode surface; see Figure 4) is set as the zero position for distance measurements. 2. The distance between two points measured radially from the zero square is equal to the distance that the redox species diffuses from the dispensing point to the electrode surface. This approximation is essential, because the depth of the liquid layer over the microelectrode is unknown, which makes an exact calculation of the diffusion distance impossible. 3. The dispensing points and electrode surface can be treated as a point source and a point collector, respectively. 4. Convective effects can be neglected. 5. The Einstein-Smoluchowsky equation19

d ) x(2Dt)

(1)

describing the correlation between diffusion distance d and diffusion time t for one dimension is valid. The distance between a first dispensing point and the electrode surface is x. The redox species needs a time t1 after dispensing to reach the electrode surface indicated by the maximum current. The distance between a second dispensing spot which is lying on the same radial line from the 0 position as the first spot and the electrode surface is d + x. After dispensing the redox species, current peak height is attained after time t2, which is somewhat larger than t1. The distance x is not known; however, the distance d between dispensing spots 1 and 2 can be exactly determined from the grid. Using the prerequisites listed above, the following (19) Atkins, P. W. Physical Chemistry, 3rd ed.; Oxford University Press: Oxford, 1986; p 692.

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Table 1. Calculated Values for the Diffusion Coefficient of Ferrocyanide(II) in 0.1 M KCl Using Different Points of the Grid Defining the Distance between Dispensing Point and Electrode Surfacea dispensing point 1

dispensing point 2

grid coord

t1, s

grid coord

t2, s

d, µm

D, 10-6 cm2 s-1

100, 100 200, 100 300, 100 300, 200 300, 300 300, 400 200, 400

1.33 1.05 1.90 1.38 1.13 1.85 1.09

100, 0 200, 0 400, 0 400, 100 400, 300 400, 500 200, 500

4.40 4.08 8.64 4.13 2.95 7.5 4.54

100 100 141 100 100 141 100

4.73 5.39 5.33 4.87 6.47 5.92 4.96

a

Compare to Figure 4.

equations are derived from the Einstein-Smoluchowsky equation.

D ) x2/2t1

(2)

D ) (x + d)2/2t2

(3)

and

Equations 2 and 3 can be combined and solved, leading to an equation for the diffusion coefficient.

(

D) -

dx2t1

2(t1 - t2)

-

x(

dx2t1

2(t1 - t2)

)

2

d2 2(t1 - t2)

)

2

(4)

Table 1 shows calculated values for the diffusion coefficient of ferrocyanide(II) using different points of the grid. The average value of 5.38 ( 0.58 × 10-6 cm2 s-1 is close to the values reported in the literature. Stackelberg et al.20 reported a value for ferrocyanide(II) in 0.1 M KCl of 6.50 × 10-6 cm2 s-1. Taking a deeper look into literature shows that the reported values for the same electroactive species differ over quite a large range. Depending on the method of determination and the calculation algorithm, values for the diffusion coefficient of ferrocyanide(II) in 1 M KCl from 5.19 × 10-6 cm2 s-1 up to 7.98 × 10-6 cm2 s-1 can be found4,6. The deviation of the value for the diffusion coefficient of ferrocyanide(II) from the values reported in the literature can be explained by the assumptions made above. We have assumed that the diffusion pathway of the redox species is equal to the movements of the electrochemical cell; however, the real diffusion path is given by the rectangular triangle between the dispensing point, the active electrode surface, and the height of the liquid layer above the microelectrode. Obviously, as a consequence, the distance d used for the calculation is too small. Because in eq 5 the distance d is only present in the numerator, the calculated value of the diffusion coefficient will be too low. On the other hand, convective effects, which are not considered in this approach, result in a positive error. Convective effects are mainly attributed (20) v. Stackelberg, M.; Pilgram, M.; Toome, V. Z. Elektrochem. 1953, 57, 34250.

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to the hitting of the droplets into the liquid phase. Because the time period between the dispensing of the redox species and the detection at the microelectrode is quite long, convective effects that are induced by the shooting should play a minor role. To overcome these limitations, we made use of a second redox species for calibration purposes. The microdispenser was filled with a solution containing both redox species. At first, we used a mixture of ferrocyanide(II) and ferrocene monocarboxylic acid. By applying a potential of 500 mV to the microelectrode, both of the redox species would be simultaneously oxidized under diffusional control. If the difference of the diffusion coefficient of both species were large enough, two separated peaks in the current-vs-time curves caused by the different diffusion times of both redox species should occur. Unfortunately, only a peak broadening could be observed, which does not allow accurate separation of the peak heights. Thus, the diffusion coefficients of ferrocyanide(II) and Fc-COOH could not be determined (graph not shown). To circumvent this problem, for calibration we used a second redox species that is not electrochemically converted at the electrode potential necessary to oxidize the first one. As a prerequisite, however, both redox species have to be stable in the same supporting electrolyte without affecting each other. A mixture of Fc-COOH and ruthenium hexamine ([Ru(NH3)6]3+) in 0.1 M KCl meets these requirements. The dispenser was filled with a solution containing 10 mM [Ru(NH3)6]3+ and 10 mM Fc-COOH, and the setup was completed as described above. In contrast to the experiment described for dispensing one redox species, here two measurements had to be made at each grid point, thus changing the microelectrode potential to the setpoints dictated by the dispensed redox species. At first, the potential of the microelectrode was adjusted to +500 mV, allowing the oxidation of Fc-COOH under diffusional control. An exact number of droplets was dispensed and the resulting current-vs-time curve was recorded. Then the microelectrode was polarized to -300 mV in order to reduce [Ru(NH3)6]3+ under diffusional control. The same number of droplets was dispensed again and a second current-vs-time curve was recorded. After this, the electrochemical cell was displaced by a defined distance, and the measurements were repeated similarly for the other grid points. The obtained peak time of the current was evaluated. Figure 5 shows an example for current-vs-time curves of Fc-COOH and [Ru(NH3)6]3+ dispensed at the same position (the currents are normalized with respect to the respective peak current). In the current-vs-time curve of Fc-COOH, the current reaches its maximum at t ) 1.33 s, but for [Ru(NH3)6]3+, the peak current is reached at t ) 1.15 s. Because all system parameters remained unchanged, the different peak times reflect the different diffusion coefficients of [Ru(NH3)6]3+ and Fc-COOH. The dispenser position relative to the 0 position is changed gradually, the described measurements are repeated at each position, and the peak times for both of the redox species are derived. Solid curve 1 in Figure 6 shows a plot of the peak times obtained for Fc-COOH at different dispensing spots vs the peak times for [Ru(NH3)6]3+ at the same locations. The points are fitted with a linear regression, and the resulting straight line shows an expected intercept close to zero (i ) 0.03) and a slope of 0.90.

Figure 5. Plot of the current response at a 25-µm-diameter Pt microelectrode after dispensing 5 droplets of a solution containing both 10 mM Fc-COOH and 10 mM Ru(NH3)63+. The obtained current values are normalized by the respective peak current. The upper curve shows the response at an electrode potential of +500 mV vs Ag/AgCl/3 M KCl, hence, allowing only the diffusion-limited oxidation of Fc-COOH. The lower curve shows the current response in a subsequent experiment after adjusting the microelectrode potential to -300 mV vs Ag/AgCl/3 M KCl. At this potential, only the reduction of Ru(NH3)63+ takes place. Because of the different diffusion coefficients of the two redox species, the current for the Ru(NH3)63+ reduction has a peak maximum at t ) 1.33 s, and the current for the Fc-COOH oxidation shows a peak maximum at t ) 1.08 s.

Figure 6. Plot of the peak times of the amperometric response at a 25-µm-diameter Pt microelectrode after dispensing 5 droplets of solutions containing both Ru(NH3)63+ and Fc-COOH or Ru(NH3)63+ and ferrocene derivative 1 at different distances of the dispensing point from the microelectrode surface. The peak time of Ru(NH3)63+ was determined at a potential of -300 mV vs Ag/AgCl/3 M KCl, and the peak time of ferrocene derivative 1 and Fc-COOH, at a potential of +500 mV vs Ag/AgCl/3 M KCl. The squares show the peak times, obtained after dispensing a solution containing both 10 mM Ru(NH3)63+ and 10 mM Fc-COOH, with a linear regression (solid line) having slope, 0.90; intercept, 0.03; and r, 0.995. The slope represents the ratio of the diffusion coefficients of Ru(NH3)63+ and Fc-COOH. The circles show the peak times of an analogous experiment using concentrations of 10 mM Fc-COOH and 5 mM Ru(NH3)63+. The linear regression (dashed line) shows slope, 0.88; intercept, 0.04; and r, 0.986. The triangles show a plot of the peak times after dispensing a solution of 5.3 mM Ru(NH3)63+ and 5.8 mM ferrocene derivative 1. The dotted line shows the resulting linear regression (slope, 0.63; intercept, 0.13; r, 0.990).

This slope gives the direct correlation between the diffusion coefficients of both redox species. If one knows the diffusion coefficient of one of the redox species, the unknown diffusion coefficient of the second redox species can be easily calculated.

A control experiment was performed to prove that the proposed measuring principle is independent from the concentration of the redox species. While keeping all other parameters constant, the concentration of [Ru(NH3)6]3+ was reduced to 50%, and a series of analogous measurements was carried out again. The dashed curve in Figure 6 shows a plot of the resulting peak times for Fc-COOH vs the peak times for [Ru(NH3)6]3+. The linear regression of the data points has a slope of 0.88 and an intercept of nearly zero (i ) 0.04). As expected, no significant deviation from the slope of the solid curve in Figure 6 can be found, thus proving the hypothesis that the measured peak times are independent from the concentration of the redox species. As already pointed out above, the slope of the linear regression of a plot correlating the peak times of one redox species to the peak times of another redox species depends on the ratio of their diffusion coefficients. Substitution for Fc-COOH by a ferrocene derivative having a higher molecular weight and, therefore, a lower diffusion coefficient should, hence, result in a decreased slope in its correlation curve vs [Ru(NH3)6]3+. The dotted curve in Figure 6 shows a plot of the peak times of ferrocene derivative 1 (compare Figure 1) vs the peak times of [Ru(NH3)6]3+. The slope of the linear fit is 0.63 and the intercept is i ) 0.13. The diffusion coefficient of a second ferrocene derivative, 2, (see Figure 1) was evaluated in the same way. The plot of the peak times of ferrocene derivative 2 vs the peak times of [Ru(NH3)6]3+ shows a straight line with a slope of 0.87 and an intercept of -0.07 (not shown). Ferrocene derivative 2 has a molecular weight comparable to Fc-COOH, and hence, a similar diffusion coefficient is expected. In fact, both compounds show similar relative diffusion coefficients with respect to [Ru(NH3)6]3+ (ferrocene monocarboxylic acid, 0.89; ferrocene derivative 2, 0.87). Until now, we have demonstrated that it is possible to determine the relative diffusion coefficients of different ferrocene derivatives with respect to [Ru(NH3)6]3+ on the basis of the presupposition that it is possible to determine independently the diffusion time of two redox species having different formal potentials and oxidation states. However, it should also be possible to determine the relative diffusion coefficients of redox species having similar formal potentials but a large difference in their diffusion coefficients. It should be possible to measure the transit time of both species at a microelectrode potential that is sufficiently high to oxidize both redox species under diffusional control. If the difference between the diffusion coefficients were large enough, the current-vs-time curve should show two single peaks or at least a split peak with two detectable peak maxima. To confirm this hypothesis, a mixture of ferrocene derivative 1 and Fc-COOH was dispensed with the microelectrode polarized to +500 mV. For most combinations of the parameters, such as distance between dispensing spot and microelectrode, number of dispensed droplets, and height of the electrolyte layer above the microelectrode, no peak separation could be observed. If the distance between electrode surface and dispensing spot was short, the transit times for both species was similar and no peak separation was observed. If the distance between dispensing point and electrode surface was very long, the current peaks became broad so that a clear peak identification was very difficult. However, with an optimized set of parameters, the expected peak separation could be detected. A corresponding current-vs-time Analytical Chemistry, Vol. 73, No. 11, June 1, 2001

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By means of linear regression, a slope of 0.132 and an intercept of i ) 0.677 has been determined (r ) 0.992) for ferrocene derivative 1, and a slope of 0.113 and an intercept of 0.973 (r ) 0.993) for ferrocene derivative 2. As can be derived from eq 5, the ratio of the inverse square roots of the slopes of ferrocene derivatives 1 and 2 corresponds to the ratio of their diffusion coefficients. By comparing the resulting value of 0.733 with the value calculated from the time-of-flight experiments, a good agreement is obtained

D(Fc derivative 1) D(Ru(NH3)3+ 6 ) Figure 7. Plot of the current response at a 25-µm-diameter Pt microelectrode after dispensing 90 droplets of a solution of 5.2 mM ferrocene derivative 1 and 10 mM Fc-COOH. The current-vs-time response shows a split peak with two maxima at t ) 0.92 s and t ) 1.40 s.

D(Fc derivative 2) D(Ru(NH3)3+ 6 ) w

curve is shown in Figure 7. Plotting the time of the first peak versus the time of the second peak results in a straight line with a slope of 1.37 and an intercept of 0.04 (not shown). To prove that the developed method for the determination of the diffusion coefficient of redox-active compounds is self-consistent, the relative values of the diffusion coefficient of Fc-COOH vs [Ru(NH3)6]3+ and of ferrocene derivative 1 vs [Ru(NH3)6]3+ can be compared with the relative value of Fc-COOH vs ferrocene derivative 1.

D(Fc derivative 1) D(Ru(NH3)3+ 6 ) D(Fc-COOH) D(Ru(NH3)3+ 6 ) w

) 0.63

) 0.89

D(Fc-COOH) 0.89 ) 1.41 ) D(Fc derivative 1) 0.63

The calculated value for the quotient of the diffusion coefficients of Fc-COOH and ferrocene derivative 1 of 1.41 is close to the experimentally determined value of 1.37. This good accordance demonstrates the self-consistency and generality of the described method for determining diffusion coefficients. To prove the consistency of the proposed method using an independent method, we determined the diffusion coefficients of ferrocene derivatives 1 and 2 by following a method previously described by Bard et al.6 Chronoamperometric experiments with a potential pulse from 0 mV to 500 mV vs Ag/AgCl with diskshaped microelectrodes were performed. The resulting current was normalized with respect to its steady-state value and plotted versus the inverse square root of the time. The diffusion coefficient of the redox species can be calculated from the slope of the resulting straight line and the radius of the microelectrode

D ) 0.0625πr2 s-2 (s ) slope, r ) radius of the microelectrode) 2474

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(5)

) 0.63

) 0.87

D(Fc - derivative 1) 0.87 ) 0.72 ) 0.63 D(Fc derivative 2)

Thus, the consistency of our novel method could be clearly confirmed. CONCLUSION AND OUTLOOK A novel method for the determination of diffusion coefficients of electroactive species has been presented using a microdispenser to shoot a very small amount of redox species close to a collector microelectrode. By measuring the transit time needed by the redox species to diffuse from the dispensing spot to the microelectrode, it is possible to estimate the diffusion coefficient of the redox species. Two methods proved to be suitable for that purpose. The first method relies on the Einstein-Smoluchowsky equation and needs knowledge of the position of the electroactive surface relative to the dispenser position. Because the position of the active microelectrode surface can be obtained by evaluating current-vs-time curves while continuously dispensing a redox species at different positions, it is possible to calculate the diffusion coefficient directly from the transit time at two different dispensing points. As a result of necessary approximations, the calculated values show a systematic error. The second method makes use of a second redox species with a known diffusion coefficient for calibration purposes. The diffusion coefficient of the unknown species is determined relative to the redox species by using the known diffusion coefficient. This method eliminates all unknown system parameters, and even an exact positioning of the dispenser relative to the active electrode surface is not necessary. Both methods are independent from system parameters such as concentration of the redox species, area of the electroactive electrode surface, and number of transferred electrons. Because of a complete dilution of the negligible amounts of dispensed redox species in the supporting electrolyte of the electrochemical cell, the setup can be operated for a long time without changing the solution in the electrochemical cell. Because the microdispenser that is used is designed for use in a flow-through mode, the filling of the dispenser with segments of different redox species is possible, and hence, the diffusion coefficients of several redox species can be determined sequentially. By replacing the manual micrometer screws with computer-controlled step motors, all prerequisites for an automation are fulfilled.

ACKNOWLEDGMENT The authors are grateful to Alexander Salmon and Prof. Peter Jutzi (Universita¨t Bielefeld) for the generous supply of ferrocene derivatives 1 and 2 and to Dr. Andreas Hengstenberg for programming the data acquisition software. M.M. is grateful for a stipend from the Graduiertenfo¨rderung des Landes NRW. The

traveling expenses between Germany and Sweden were financed by the DAAD and the Swedish Institute (AZ 313-S-PP-7/98). Received for review October 23, 2000. Accepted February 28, 2001. AC0012501

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