Scanning Electrochemical Microscopy Imaging by Means of High

A specific technique for measuring fast variations of the high-frequency impedance of ultramicroelectrodes (UME) under potential control is presented...
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J. Phys. Chem. B 2004, 108, 11620-11626

Scanning Electrochemical Microscopy Imaging by Means of High-Frequency Impedance Measurements in Feedback Mode C. Gabrielli, F. Huet, M. Keddam, P. Rousseau, and V. Vivier* UPR 15 du CNRS, Laboratoire Interfaces et Syste` mes Electrochimiques, UniVersite´ Pierre et Marie Curie, 4, place Jussieu, case courrier 133, 75252 Paris Cedex 05, France ReceiVed: January 22, 2004; In Final Form: May 18, 2004

A specific technique for measuring fast variations of the high-frequency impedance of ultramicroelectrodes (UME) under potential control is presented. It allows real-time electrolyte-resistance Re measurements from an analogue signal, the amplitude of which is inversely proportional to the modulus of the UME impedance, and from calibration curves measured with pure resistors instead of the electrochemical cell. Re-distance approach curves to insulating or conducting substrates show opposite behaviors: Re increased when the tip electrode approached an insulating substrate, while it decreased for a conducting substrate, which apparently precludes scanning electrochemical microscopy (SECM) imaging under Re feedback control. Simultaneous current and electrolyte-resistance measurements have been successfully performed in SECM constant-height imaging of various substrates, which allows local information on both topography and surface reactivity to be obtained.

Introduction The kinetics of ultramicroelectrodes (UME) has been largely described in the literature.1-4 Because of their small dimension, in the range of a micrometer or less, mass transport is controlled totally by hemispherical diffusion between the solution bulk and the electrode surface. The steady-state current flowing through the UME is thus limited to a value I∞ that is reached in a very short time and is proportional to the electrode radius a4

I∞ ) 4nFDc∞a

(1)

where n is the number of electrons involved in the electrochemical reaction, F the Faraday constant, and c∞ and D the bulk concentration and the diffusion coefficient of the reacting species, respectively. The use of UMEs as amperometric probes in scanning electrochemical microscopy (SECM)5-10 makes possible the electrochemical characterization of both insulating and conducting interfaces in the micrometer and sub-micrometer ranges. In the feedback mode, in which a redox mediator is used, the diffusion of the mediator is hindered as the tip-substrate distance diminishes when the substrate is insulating (negative feedback). As a result, when the UME tip is scanned over the surface of the substrate, the tip-current variations iT are ascribed to local changes of the substrate topography. In that case, as the current depends only on the tip-substrate distance, these variations enable the tip position to be controlled above the substrate. On the other hand, if the substrate is conducting (positive feedback), the current variations can be ascribed to local changes of both topography and local reactivity. Since the samples to be characterized are commonly made of both conducting and insulating zones, the tip current cannot be used for regulating the tip-sample distance. The risky juxtaposition of regions with different conductivity can lead first to crash the tip on the sample surface and second to misinterpret the local variations of the tip current. Different techniques have been * To whom correspondence may be addressed. Tel.: 33 1 44 27 41 58. Fax: 33 1 44 27 40 74. E-mail: [email protected].

investigated for imaging such substrates; they consist either in controlling the tip-substrate distance by an external method or in simultaneously measuring another quantity that can reinforce information obtained from the tip-current variations. Several attempts have been made for imaging at a constant tip-substrate distance. Bard and co-workers11 have described a constant current-imaging method to regulate the tip position. This technique is based on the use of a small-amplitude vertical oscillation of the probe to determine the nature of the substrate. However, this tip-position modulation gives no information on the substrate conductivity in the absence of mediator and, therefore, is not useful for imaging in the amperometric generation/collection mode. Schuhmann and co-workers12,13 have developed a method that uses the hydrodynamic forces between the tip and the solution in the vicinity of the substrate similarly to that employed in near-field microscopy. The UME is laterally vibrated using a piezoelectric pusher, and the vibrations of the tip, which are damped as the tip approaches the substrate, are monitored by means of laser-beam deflection. Smyrl and co-workers14-16 have used a shear-force feedback method with a tuning fork transducer to vibrate the electrode in a parallel direction to the substrate. Such a setup allows the tip-substrate distance to be controlled in the 10-nm range. With this technique, the Bard’s group has reported the simultaneous topography and optical imaging of a living unicellular organism.17 Another possibility of constant control of the tip-sample distance is to use the electrochemical impedance spectroscopy (EIS) and measure the electrolyte resistance Re. Bard et al.18 have used a 10-kHz-frequency sinusoidal signal for positioning an amperometric biosensor. Schuhmann et al.19,20 used a 1-10kHz-frequency sinusoidal signal for controlling the position of a platinum tip and imaged localized corrosion. In both cases, the use of such small frequencies was possible because the SECM experiments were performed without any electrochemical mediator; in the absence of a charge-transfer reaction, the electrolyte resistance could be obtained from the real part of the impedance at relatively low frequencies.

10.1021/jp0496809 CCC: $27.50 © 2004 American Chemical Society Published on Web 07/02/2004

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Alpuche-Aviles and Wipf21 used EIS at higher frequencies (but lower than 100 kHz) to image a small platinum-disk substrate in the presence of Ru(NH3)63+ as the electrochemical mediator. However, in contrast to previous results of the Bard’s group with amperometric biosensors,18 they observed that the electrolyte resistance increased for both conducting and insulating substrates, as the tip-substrate distance decreased. Kashyap and Gratzl22 tried also to regulate the tip-sample distance with EIS measurements by using tip diameters from 250 to 1000 µm. Surprisingly, they found that the electrolyte resistance Re was quite independent of the tip-sample distance whereas the sum Re + Rct (Rct ) charge-transfer resistance) enabled the tip position regulation. In view of the conflicting results reported in the literature concerning the measurement of the electrolyte resistance for UMEs, a detailed investigation of such difficult measurements has been undertaken. It is shown in this paper that valid Re measurements can be carried out by using a specific measurement technique and a calibration procedure. Simultaneously measured tip-current and electrolyte-resistance approach curves to conducting and isolating substrates are presented. These procedures allow the use of the electrolyte-resistance signal for imaging substrates presenting conducting and isolating regions in constant-height and constant-distance modes to be assessed. UME Impedance Modeling Mass transport by diffusion of an electroactive species at a disk UME is described in the cylindrical coordinate system by Fick’s second law

(

)

∂c ∂2c 1 ∂c ∂2c )D 2+ + ∂t r ∂r ∂z2 ∂r

(2)

where c is the concentration of the electroactive species, r the radial coordinate measured from the center of the electrode, and z the direction normal to the disk-electrode surface. In impedance measurements, a small-amplitude sinusoidal perturbation of pulsation ω is applied to the UME potential, allowing the flux at the electrode to be expressed as follows

D

∂c ) Q sin(ωt) ∂z

(3)

where Q is a constant flux (independent of time). Taking into account the average concentration over the microdisk, Fleishmann et al.3,23 have shown that the diffusion part Zd of the impedance Z is the solution of a Bessel-type differential equation that can be expressed as

Re(Zd) )

( ) ( )

a2ω 4RT Φ 4 D πn2F2(Dω)1/2a2c∞

-Im(Zd) )

4RT a2ω Φ 5 D πn2F2(Dω)1/2a2c∞

(4) (5)

where Re(Zd) and Im(Zd) are the real and imaginary parts of Zd, respectively, R the gas constant, T the temperature, i0 the exchanged current density; Φ4 and Φ5 are the tabulated functions in ref 3. The ratio a2ω/D represents a dimensionless frequency. Assuming a Randles-type equivalent circuit to describe the electrochemical interface, the overall impedance Z is then

Z ) Re +

1 1 + jCdlω Zd(ω) + Rct

(6)

where Re is the electrolyte resistance, Cdl the double-layer capacitance, and Rct the charge-transfer resistance RT/πnFi0a2. In the high-frequency range, the diffusion impedance Zd and the charge-transfer resistance can be neglected, so that the overall impedance depends on Re and Cdl only

Z ≈ Re +

1 jCdlω

(7)

Experimental Section Ultramicroelectrodes were made from a 10 µm in diameter platinum wire (Goodfellow) sealed into a soft glass tube, finely polished, rinsed with ethanol, and then ultrasonicated in distilled water. The total diameter of the apex of the UME (tip + insulating material) was 200 µm, which gave a dimensionless radius RG (the ratio of the insulating glass sheath radius to that of the electroactive disk) of 20. Solutions were prepared from analytical-grade chemicals (K4Fe(CN)6, K3Fe(CN)6, and KCl) purchased from Sigma and used as received in deionized and bidistilled water. All experiments were performed with a 3-electrode cell; the reference electrode and the counter electrode were a saturated calomel electrode (SCE) and a small platinum grid (1 cm2 surface area), respectively. The UME tips were daily cycled at a rate of 5 V s-1 in a 0.5 M H2SO4 solution during 10 min to ensure its perfect cleaning. SECM instrumentation was a laboratory-built setup described elsewhere.24 It consisted of a 3-axis positioning system (VP25XA, Newport) driven by a motion encoder (ESP300, Newport) allowing a spatial resolution of 100 nm in the three directions. Preliminary positioning of the tip electrode in the vicinity of the substrate was made with the help of a CCD camera (Sony) equipped with a monozoom (Nachet). The electrochemical impedance measurements in the range (10 mHz, 100 kHz) were performed with a potentiostat/ frequency analyzer (Gamry PC4/300). The other electrochemical measurements were carried out with a homemade bipotentiostat coupled to a low-noise current-voltage converter (Femto DLPCA200, BFI Optilas) with an adjustable gain (103-1011 V/A) and a large bandwidth (up to 500 kHz). For the high-frequency (HF) impedance measurements coupled to the SECM technique, the impedance modulus of the tip electrode was measured with an in-house-made analogue device, similar to that used in the laboratory for measuring electrolyteresistance fluctuations.25,26 A sinusoidal voltage (frequency fHF of 75-150 kHz and peak-peak amplitude Vp-p of 10-50 mV) delivered by a function generator (TG550, TTi) was superimposed to the dc voltage of the potentiostat. The frequency fHF was chosen so as to measure the variations of the electrolyte resistance Re of the cell. The total current I(t) flowing through the working UME was then given by

I(t) ) IHF(t) + Idc

(8)

where IHF(t) and Idc are the HF and dc components of the current, respectively. At the output of the low-noise current-voltage converter, the signal was sampled with a digital voltmeter (Keithley 2000), which gave the dc component of the current. On the other hand, the analogue signal was also sent to the Re measurement channel, in which the dc component was removed by a resistor-capacitor high-pass filter. The HF component of the signal was first amplified and high-pass filtered to eliminate all influence of current variations. It was then rectified by a diode and low-pass filtered. The low-pass filter acting as an analogue integrator circuit, the delivered voltage signal VRe(t)

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Figure 1. Calibration curve giving VRe as a function of 1/R for pure resistances R, measured at fHF ) 100 kHz and Vp-p ) 30 mV.

was proportional to the amplitude of IHF(t) and, therefore, was a linear function of the reciprocal of the impedance modulus Mod(ZHF) at the frequency fHF, according to the relationship

V Re )

b1 Mod(ZHF)

+ b2

(9)

The constants b1 and b2 were estimated from a calibration procedure using variable resistors in place of the electrochemical cell. As an example, the calibration curve in Figure 1 shows a perfect linear behavior of VRe as a function of the reciprocal of the resistance R. The parameters b1 and b2 can be deduced from such curves with a linear fitting procedure. It should be noticed that these parameters depend on the amplitude of the applied HF signal and on the total gain of the measurement channel.

Figure 2. Impedance diagrams of pure resistances: (a) modulus; (b) phase angle.

Results and Discussion 1. Difficulties in HF Large-Impedance Measurements. UMEs have impedances of large magnitude at high frequency. First, the electrolyte resistance, which depends on both the electrolyte resistivity F and the electrode radius a through the relationship

Re )

F 4a

(10)

is about 9 kΩ for a 10-µm-diameter Pt UME in a 0.5 M KCl solution, and about 45 kΩ in a 0.1 M KCl solution. Equation 10 also shows that using a smaller UME leads to an increase in Re as a-1. Second, the UMEs have a very low double-layer capacitance, proportional to a2, so that the term 1/(Cdlω) in eq 7 can reach a few tens of kΩ at 100 kHz for a 10-µm-diameter platinum tip, which cannot be neglected in the evaluation of the impedance modulus. In other words the time constant ReCdl is proportional to a. The difficulty of large-impedance measurements at high frequency is illustrated in Figure 2 that gives the impedance diagrams (Bode plot representation) of pure resistances R varying between 10 and 60 kΩ measured at frequencies ranging from 1 Hz to 100 kHz with the Gamry potentiostat/analyzer. Both the modulus Mod(Z) and the phase angle Φ of the impedance varied at high frequency. Below 10 kHz, Mod(Z) was in good agreement with the value of the tested resistance while discrepancies became visible beyond 10 kHz (Figure 2a). For a 15-kΩ resistance, the discrepancy appeared at 50 kHz

and the measured value was only 14.5 kΩ at 100 kHz, which corresponds to an error of about 3%. For a higher resistance, the discrepancy appeared at lower frequencies (10 kHz for R ) 60 kΩ) and the error at 100 kHz was higher (13% for R ) 60 kΩ). Figure 2b shows that the phase angle started varying at lower frequencies: at 1 kHz, its value was -0.7° for R ) 15 kΩ and -2.2° for R ) 60 kΩ and reached -9.2° and -22.4° at 100 kHz, respectively. With other commercial measurement equipments (data not shown), the phase angle was positive, probably because of differences in the analogue circuits in the potentiostat and transfer function analyzer tested. This led to an overevaluation of the resistance, but in absolute value, the phase angle had the same order of magnitude. 2. UME Impedance Measurements. Figure 3 shows a typical impedance diagram (Nyquist representation) of a 10µm-diameter Pt UME in a 10 mM K3Fe(CN)6 + 10 mM K4Fe(CN)6 + 0.5 M KCl solution measured at the equilibrium potential in the 0.01-100 kHz range. Very good agreement was found with the impedance curve (solid line in Figure 3) numerically simulated from eqs 4-6 and the kinetic constants given below, which validates both impedance measurements and simulation. The low-frequency loop was ascribed to the diffusion of the electroactive species in the solution. From numerical simulation, the diffusion coefficient of the reactive species was found to be 6.60 × 10-6 cm2 s-1, which is in good agreement with that determined by cyclic voltammetry at 10 mV s-1 (6.45 × 10-6 cm2 s-1) and with those reported in the literature.27

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Figure 3. Impedance diagram of a 10-µm-diameter Pt UME in a 10 mM K3Fe(CN)6 + 10 mM K4Fe(CN)6 + 0.5 M KCl solution at the equilibrium potential. Symbols: experimental data; solid line: numerical simulation.

The high-frequency loop was ascribed to the electron-transfer process. At 100 kHz, the impedance was reduced to the electrolyte resistance Re ) 9.2 kΩ, which is in good agreement with the previously calculated value. The measurement error in this resistance range is about 2%, thus no correction was necessary. The charge-transfer resistance was estimated to be Rct ) 850 kΩ. The value of the kinetic constant k0 of the electron transfer, determined according to the following equation

k0 )

RT 1 n2F2 Rctc∞

(11)

was 3.6 × 10-2 cm s-1, which is consistent with literature data.28 The double-layer capacitance was ca. 47 pF (60 µF cm-2), which gives 35 kΩ as the imaginary part of the impedance at 100 kHz. This contribution can be slightly different from one set of experiments to the other since Cdl depends on the state of the platinum surface of the UME. The values of Re and Cdl show that the electrolyte-resistance variations can be measured in the high-frequency range (typically 75 kHz or more) with a sufficiently good accuracy. However, the use of a commercially available transfer-function analyzer does not allow more than 3 or 4 data points per second to be measured at a given high frequency (such as 100 kHz). Thus, in the following, the electrolyte-resistance measurements were performed with the specific measurement technique described in the Experimental Section and the electrolyte resistance Re was evaluated from the modulus of the electrochemical impedance and from the parameters b1 and b2 derived from the calibration curves, as that in Figure 1, through the relationship

(

Re ) (Mod(ZHF))2 -

(

1 Cdl2πfHF

((

))

2 1/2

)

) (

2 b1 1 b2 - V R e Cdl2πfHF

Figure 4. Simultaneous current-distance and Re-distance curves for a 10-µm-diameter Pt UME over an insulating substrate (ET ) -0.2 V/SCE for all curves) in a 10 mM K3Fe(CN)6 + 0.5 M KCl solution. RG ) 20, approach rate ) 1 µm s-1. Excitation signal: b, Vp-p ) 30 mV, fHF ) 75 kHz; 4, Vp-p ) 50 mV, fHF ) 100 kHz; 0, Vp-p ) 50 mV, fHF ) 125 kHz. g, numerical FEM simulation of the negative feedback current.

))

2 1/2

(12)

It must be noticed that in this approach the double-layer capacitance was assumed to be independent of the tip-substrate distance so that the variations of the impedance modulus directly reflected those of Re. 3. Approach Curves. Figures 4 and 5 show dimensionless current-distance and Re-distance curves measured in various conditions of voltage excitation amplitude Vp-p, frequency fHF, and approach rate Vz to an insulating and a potential unbiased conducting substrate (platinum plate), respectively. L, INorm, and

Figure 5. Simultaneous current-distance Re-distance curves for a 10-µm-diameter Pt UME over a conducting substrate (platinum plate, 1 cm2) in a 10 mM K3Fe(CN)6 + 0.5 M KCl solution (ET ) -0.2 V/SCE for all curves, the substrate was not polarized). RG ) 20. Excitation signal and approach rate: b, Vp-p ) 50 mV, fHF ) 100 kHz, Vz ) 0.5 µm s-1; 4, Vp-p ) 50 mV, fHF ) 125 kHz, Vz ) 2 µm s-1; 0, Vp-p ) 30 mV, fHF ) 125 kHz, Vz ) 20 µm s-1.

RNorm represent the ratios d/a, I/I∞, and Re/R∞, respectively, where d is the tip-substrate distance and R∞ is the value of the electrolyte resistance far from the substrate. No significant variation in the electrolyte resistance-distance curves was observed when varying the amplitude Vp-p of the HF signal from 30 to 50 mV peak-peak, the frequency fHF of the HF signal from 75 to 125 kHz, or the approach rate Vz from 0.5 to 20 µm s-1. For each experiment, R∞ was between 9.1 and 9.2 kΩ, which was in good agreement with the value previously determined by impedance measurements. The variations of the current with the tip-substrate distance were also in good agreement with the theory, as shown in Figure 4 in which the approach curve simulated numerically with a finite element method (FEM) for a dimensionless parameter RG ) 20 was reported. In all experiments, the electrolyte resistance was shown to increase when the tip-substrate distance decreased in the negativefeedback mode (Figure 4), whereas it decreased with the tipsubstrate distance in the positive feedback mode (Figure 5). Similar behavior of both electrolyte resistance and tip current were observed for a biased conducting substrate (data not

11624 J. Phys. Chem. B, Vol. 108, No. 31, 2004 shown). These Re variations for both insulator and potentialbiased or unbiased conductor are consistent with those previously obtained by Bard and co-workers18 for the positioning of a biosensor tip with an excitation-signal frequency fHF of 10 kHz, whereas they differ from those obtained by Alpuche-Aviles and Wipf,21 for whom the impedance modulus varied in the same way when approaching the tip electrode to an insulator or a conductor. They also differ from those obtained by Kashyap and Gratzl,22 who found that the electrolyte resistance was quite independent of the tip-substrate distance when the tip approached a monolayer of biological cells. The present results can be interpreted in the following way: when the microelectrode approached a conducting substrate, the current lines were sidetracked to follow the least-resistive pathway on the substrate, which led to the reduction of the electrolyte resistance. Conversely, when the UME approached an insulating substrate, the lines of potential and current were crushed, which resulted in increasing the electrolyte resistance. A close examination of the approaching curves to a conducting substrate (Figure 5) reveals that, while the current increased monotonically with decreasing distance, Re did not strictly decrease monotonically; Re increased slightly (2% in amplitude) first to reach a maximum at around L ) 10 and then decreased with the distance. No clear explanation was found for this phenomenon; additional experiments and numerical simulations are required to explain this slight effect. As mentioned above, there was no influence of the velocity Vz of the tip displacement from 0.5 to 20 µm s-1 (Figure 5). This important result shows that electrolyte-resistance measurements can be performed during the tip displacement, and therefore, the electrolyte resistance and the tip current can be simultaneously measured in constant-height substrate imaging. 4. Simultaneous Imaging by Impedance and Current Measurements. Figure 6 presents the SECM images of a scratch of about 100-µm width and 50-µm depth in a glass plate in a 10 mM K3Fe(CN)6 + 0.5 M KCl solution. The tip potential was set to a reducing potential (-0.2 V/SCE) and the HFperturbation amplitude and frequency were Vp-p ) 30 mV and fHF ) 100 kHz, respectively. In Figure 6a, in which an increase in current (in absolute value) corresponds to a larger tipsubstrate distance, the scratch is clearly evidenced. For the deepest part of the scratch (x ) 650 µm), the current reached the maximum value I∞ that can be measured far from any substrate, indicating that the tip-substrate distance was sufficient to ensure that the diffusion of the electroactive species was not hindered by the substrate. Figure 6b shows the image of the scratch obtained by recording the variations of the electrolyte resistance. It clearly appears that this technique is also very sensitive since the image is quite similar to that obtained from the current variations. Moreover, when the tip scanned the deepest part of the scratch, RNorm was found to be close to 1, which also corresponds to a value far from any substrate. Both current and electrolyte-resistance values were coherent with those observed on the approach curves. Figure 7 shows SECM images of a 100-µm-diameter Pt microelectrode in a substrate generator/tip collector configuration in a 10 mM K3Fe(CN)6 + 0.5 M KCl solution (ES ) -0.2 V/SCE, ET ) 0.5 V/SCE). The variations of the current (Figure 7a) and of the electrolyte resistance (Figure 7b) were completely similar. However, the nature of the information obtained in both cases was different. In this configuration, the current allowed detecting species formed at the substrate, which informs on the reactivity of the substrate surface, whereas the electrolyte resistance allowed the insulator/conductor transition to be evidenced.

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Figure 6. SECM images of a scratch of about 100-µm width and 50-µm depth in a glass plate measured with a 10-µm-diameter Pt UME in a 10 mM K3Fe(CN)6 + 0.5 M KCl solution (ET ) -0.2 V/SCE): (a) 3D feedback image and top view in the (x,y) plane; (b) 3D Re image and top view in the (x,y) plane (Vp-p ) 30 mV; fHF ) 100 kHz). Tip scan rate: 10 µm s-1.

Figures 8 and 9 present a scheme and the SECM images of a microelectrode with a cavity. The substrate consisted in a 60-µm-diameter platinum microelectrode in which a small hole (40 µm in diameter, 25 µm in depth) was drilled by laser ablation (Figure 8). The wall of the cavity was thus a conducting surface. The tip was polarized at a potential of -0.2 V/SCE, while the substrate was potential unbiased. The feedback image (Figure 9a) shows a current increase (in absolute value) when the tip approached the platinum ring, which corresponds to positive feedback. On the other hand, the zone corresponding to the cavity itself was poorly imaged. Conversely, the image obtained from the electrolyte-resistance variations shows the different zones clearly (Figure 9b): Re decreased when the tip was over a conducting zone (corresponding to the 10-µm-width ring), whereas it increased when the tip was scanned over the hole. Figure 10 shows the variations of the current and of the electrolyte resistance during a single scan over a diameter of the cavity. It appears that RNorm was lower than 1 over the whole cavity surface, indicating that the edge effect due to the ring was not negligible. The decrease in both current intensity and electrolyte resistance outside the cavity shows that the substrate

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Figure 7. SECM images of a 100-µm-diameter UME substrate measured with a 10-µm-diameter Pt UME in a generator/tip collector configuration in a 10 mM K3Fe(CN)6 + 0.5 M KCl solution (ES ) -0.2 V/SCE, ET ) 0.5 V/SCE): (a) 3D current image and top view in the (x,y) plane (the substrate was biased at -0.2 V/SCE, ET ) 0.5 V/SCE); (b) 3D Re image and top view in the (x,y) plane (Vp-p ) 30 mV, fHF ) 100 kHz). Tip scan rate: 20 µm s-1. Figure 9. SECM images of a 60-µm-diameter microelectrode with a 40-µm-diameter cavity measured with a 10-µm-diameter Pt UME in a 10 mM K3Fe(CN)6 + 0.5 M KCl solution (ET ) -0.2 V/SCE, ES imposed by the solution): (a) feedback image; (b) Re image (Vp-p ) 30 mV, fHF ) 125 kHz). Tip scan rate: 20 µm s-1.

Figure 8. Schematic representation of a 60-µm-diameter microelectrode with a cavity of diameter 40 µm and depth 25 µm.

Figure 10. Current and Re variations during a single scan over the cavity electrode (data from Figure 9).

was tilted. This figure also highlights the resolution improvement obtained by carrying out electrolyte-resistance imaging. However, the resolution in the feedback image is only apparently

poorer since the presence of the cavity is in fact detected by the small current hump above it; this hump would not exist over a planar microdisk of the same dimension.

11626 J. Phys. Chem. B, Vol. 108, No. 31, 2004 Conclusions Impedance measurements on pure resistors with a transferfunction analyzer have been carried out to evaluate the relative error when measuring resistances of a few tens of kΩ at high frequency (typically 100 kHz) in the purpose of validating electrolyte-resistance measurements for ultramicroelectrodes. For faster and more precise Re measurements, a specific measurement technique allowing simultaneous measurements of the current and electrolyte-resistance variations was devised. This technique, based on impedance-modulus measurements, has been shown to give exact values of Re inasmuch as calibration curves obtained with pure resistors were used. Approach curves to insulating and conducting substrates have shown opposite Re variations: Re increased when the tip electrode approached an insulating substrate, whereas it decreased for a conducting substrate. This apparently precludes constant-distance SECM imaging under electrolyte-resistance feedback control. In contrast, constant-height SECM imaging with both current and electrolyte-resistance measurements was successfully performed. In negative-feedback and in substrate generator/tip collector modes, the image resolution appears to be similar with both current and Re variations, whereas the resolution appears to be better with the electrolyte resistance when imaging a conducting cavity embedded in an insulator. Moreover, local information on both topography and surface reactivity can be obtained from the simultaneous analysis of the current and electrolyte-resistance variations. As a result, this simultaneous measurement of current and electrolyte resistance variations seems very promising for constant-height SECM imaging. In particular, this coupling is well adapted for the study of interfaces showing both topography and surface reactivity evolutions, such as those encountered, for instance, in various types of corrosion where the size of localized or heterogeneous attacks (pits, crevices, grains and grains boundaries, developed cracks) is in the micrometer range. Symbols a b1 and b2 c Cdl c∞ d D ES ET f fHF F I Idc IHF INorm i0 I∞ Im(Z) k0 L Mod(Z) n Q

tip-electrode radius constants used in eq 9 concentration double-layer capacitance bulk concentration tip-substrate distance diffusion coefficient substrate potential tip potential frequency frequency at which Re was measured Faraday constant tip-electrode current dc component of I sine-wave component of I at frequency fHF normalized tip-electrode current exchanged current density steady-state diffusion-controlled current imaginary part of the impedance Z standard rate constant of the electron transfer normalized tip-substrate distance modulus of the impedance number of exchanged electrons flux amplitude

Gabrielli et al. r R RG RNorm Rct Re Re(Z) R∞ t T Vp-p VRe Vz Z Zd ZHF z Φ F ω

radial coordinate measured from the center of the electrode gas constant normalized radius of the tip-insulating material normalized electrolyte resistance charge-transfer resistance electrolyte resistance real part of the impedance Z electrolyte resistance measured far from any substrate time temperature peak-peak amplitude of the HF perturbation output voltage of the analogue device for the evaluation of Re velocity of the tip displacement normal to the substrate impedance diffusion impedance impedance at frequency fHF direction normal to the disk-electrode surface phase angle of the impedance electrolyte resistivity angular frequency

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