Feedback-Independent Pt Nanoelectrodes for Shear Force-Based

Sep 12, 2006 - insulated Pt nanoelectrodes used as SECM tips were prepared using the general .... wire was made with a copper wire (0.25-mm diameter) ...
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Anal. Chem. 2006, 78, 7317-7324

Feedback-Independent Pt Nanoelectrodes for Shear Force-Based Constant-Distance Mode Scanning Electrochemical Microscopy Mathieu Etienne,†,‡ Emily C. Anderson,§ Stephanie R. Evans,§ Wolfgang Schuhmann,*,† and Ingrid Fritsch*,§

Analytical Chemistry, Elektroanalytik & Sensorik, Ruhr-Universita¨t Bochum, Universita¨tsstrasse 150, D-44780 Bochum, Germany, and Department of Chemistry and Biochemistry, University of Arkansas, Fayetteville, Arkansas 72701

Scanning electrochemical microscopy (SECM) allows electrochemical measurements to be performed with high spatial resolution by scanning a small electrode at the interface between a solution and a second medium that can be a solid material, a nonmiscible liquid, or a gas.1 The amperometric response of

electroactive species present in solution strongly depends on the (electro)chemical reactivity at the interface or transfer reactions of analytes, the probe-to-interface distance, and the radius of the microelectrode. For a solid/liquid interface, as the electrode probe approaches the surface in the solution, its current, due to reduction or oxidation of freely diffusing electroactive species, decreases over an insulating material (negative feedback) and increases over conductive material (positive feedback). These phenomena are often used in classical SECM to determine the distance between the probe tip and the surface for relatively flat and homogeneously conductive samples. The SECM feedback mode has also been used for high-resolution imaging of topographic changes and conductivity variations.1 However, use of current feedback information for positioning and imaging is only possible for well-defined systems and is inappropriate for surfaces exhibiting complex topography and complex conductivity or for probes that do not consume (and produce) electroactives species (i.e., potentiometric probes).2 The size of the electrode/probe tip is also critical in classical SECM. The gap between the electrode and sample surface must be within one radius of the electrode to achieve enough current feedback to control positioning. Larger electrodes can be positioned farther away from the sample and are therefore less likely to run into protruding features of rough surfaces and more forgiving of sample tilt. However, smaller electrodes required for higher spatial resolution must be positioned closer to the surface, leading to a more delicate and time-consuming sample/tip setup so that tip crashes can be avoided. A 300-nm electrode would have to be 100-150 nm from the surface, making classical SECM analysis virtually impossible with three-dimensional sample structures. For accurate, nonelectrochemical positioning of electrode probes, two different strategies have been used, the use of shear force on a needle-type microelectrode3,4 in constant-distance mode SECM (CD-SECM) and the implementation of the electrode in an atomic force microscopy (AFM) cantilever.5-7

* To whom correspondence should be addressed. E-mail: [email protected]. Phone: +49-234-3226200. Fax: +49-2343214683. E-mail: [email protected]. Phone: 479-575-6499. Fax: 479-575-4049. † Elektroanalytik & Sensorik, Ruhr-Universita¨t Bochum. ‡ Present address: Laboratoire de Chimie Physique et Microbiologie pour l′Environnement, Unite´ Mixte de Recherche UMR 7564, CNRS-Universite´ H. Poincare´ Nancy I, 405, rue de Vandoeuvre, F-54600 Villers-le`s-Nancy, France. § University of Arkansas.

(1) Bard, A. J.; Mirkin, M. V. Scanning Electrochemical Microscopy; Marcel Dekker: New York, 2001. (2) Wei, C.; Bard, A. J.; Nagy, G.; Toth, K. Anal. Chem. 1995, 67, 1346-1356. (3) Hengstenberg, A.; Kranz, C.; Schuhmann, W. Chem. Eur. J. 2000, 6, 15471554. (4) James, P. I.; Garfias-Mesias, L. F.; Moyer, P. J.; Smyrl, W. H. J. Electrochem. Soc. 1998, 145, L64-L66. (5) MacPherson, J. V.; Unwin, P. R. Anal. Chem. 2000, 72, 276-285.

A new generation of platinum nanoelectrodes for constantdistance mode scanning electrochemical microscopy (CDSECM) has been prepared, characterized, and used for high spatial resolution electrochemical measurements and visualization of electrochemically induced concentration gradients in microcavities. The probes have long (1-2 cm), narrow quartz tips that were conically polished and have a Pt nanoelectrode that is slightly offset from center. Because of the size and location of the electrode on the probe, it does not exhibit SECM feedback while approaching the analyzed sample surfaces even to distances within a few hundred nanometers. The probe was positioned near the surface while scanning and performing electrochemical measurements through use of nonoptical shear force control of the tip-to-sample distance. Test structures consisted of cylindrically shaped microcavities that are 50 µm in diameter with three individually addressable electrodes: a gold disk at 8-µm depth, a crescent-shaped gold ring at 4-µm depth along the wall, and a top gold electrode at the rim. Different electrodes within the microcavity were used to reduce and oxidize redox species in 250 µL of a solution of 5 mM hexaamineruthenium(III) chloride and 0.1 M potassium chloride, protected from evaporation by mineral oil, while the SECM tip followed the topography of the structures and monitored the current from the oxidation of [Ru(NH3)6]2+. Electrochemically generated concentration profiles were obtained from these complex test structures that are not possible with any other SECM technology at this time.

10.1021/ac061310o CCC: $33.50 Published on Web 09/12/2006

© 2006 American Chemical Society

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Shear force-based CD-SECM allows application of a wide range of long needle-shaped electrodes such as carbon fiber microelectrodes,8 platinum nanoelectrodes,9,10 biosensors,3 and potentiometric sensors.11 Initially, optical shear force detection was implemented in SECM to achieve simultaneous visualization of sample topography and local electrochemical activity.8,12,13 Later, despite problems related to a very short positioning distance, tuning forks coupled with microelectrodes were used for shear force detection.4,14,15 More recently, a nonoptical shear force control was proposed16 and successfully applied for distance control using nanoelectrodes10 and potentiometric tips.11 Until now, amperometric probes in shear force-based CDSECM or combined AFM-SECM have been predominantly used either in the feedback mode or in the substrate-generation-tipcollection mode with the electrode positioned at a feedback distance. However, for both systems, the capability to follow topography of the analyzed sample can perturb the measured current due to changes in the tip-to-sample distance during an experiment.6,17,18 As a consequence, despite inherent advantages of following both topography and current simultaneously, interpretation of the current response may be difficult. Thus, there is a need for submicrometer-sized electrochemical probes that minimize negative and positive feedback and can be accurately positioned in proximity to the sample surface using CD-SECM. Pt nanoelectrode preparation,19-22 by pulling a quartz capillary containing a Pt wire using a laser puller,22 generally leads to a blunt-ended tip with a disk-shaped nanoelectrode after symmetrical polishing (Figure 1a). In contrast to nanoelectrodes prepared with an insulating layer of a cathodic or anodic paint,23-28 (6) Kranz, C.; Friedbacher, G.; Mizaikoff, B.; Lugstein, A.; Smoliner, J.; Bertagnolli, E. Anal. Chem. 2001, 73, 2491-2500. (7) Abbou, J.; Demaille, C.; Druet, M.; Moiroux, J. Anal. Chem. 2002, 74, 63556363. (8) Hengstenberg, A.; Blo ¨chl, A.; Dietzel, I. D.; Schuhmann, W. Angew. Chem., Int. Ed. 2001, 40, 905-908. (9) Etienne, M.; Schulte, A.; Schuhmann, W. Electrochem. Commun. 2004, 6, 288-293. (10) Ballesteros Katemann, B.; Schulte, A.; Schuhmann, W. Electroanalysis 2004, 16, 60-55. (11) Etienne, M.; Schulte, A.; Mann, S.; Jordan, G.; Dietzel-Meyer, I.; Schuhmann, W. Anal. Chem. 2004, 76, 3682-3688. (12) Ludwig, M.; Kranz, C.; Schuhmann, W.; Gaub, H. E. Rev. Sci. Instrum. 1995, 66, 2857-2860. (13) Kranz, C.; Gaub, H. E.; Schuhmann, W. Adv. Mater. 1996, 8, 634-637. (14) Garay, M. F.; Ufheil, J.; Borgwarth, K.; Heinze, J. Phys. Chem. Chem. Phys. 2004, 6, 4028-4033. (15) Lee, Y.; Ding, Z.; Bard, A. J. Anal. Chem. 2002, 74, 3634-3643. (16) Ballesteros Katemann, B.; Schulte, A.; Schuhmann, W. Chem. Eur. J. 2003, 9, 2025-2033. (17) Schulte, A.; Schuhmann, W., Science, Technology and Education of Microscopy: an Overview. In Formatex Microscopy Book Series; Me´ndezVilas, A., Ed.; Formatex: Badojoz, Spain, 2003; No. 1; Vol. II, pp 753-760. (18) Sklyar, O.; Wittstock, G. J. Phys. Chem. B 2002, 106, 7499-7508. (19) Pendley, B. D.; Abruna, H. D. Anal. Chem. 1990, 62, 782-784. (20) Penner, R. M.; Heben, M. J.; Longin, T. L.; Lewis, N. S. Science 1990, 250, 1118-1121. (21) Shao, Y.; Mirkin, M. V.; Fish, G.; Kokotov, S.; Palanker, D.; Lewis, A. Anal. Chem. 1997, 69, 1627-1634. (22) Ballesteros Katemann, B.; Schuhmann, W. Electroanalysis 2002, 14, 2228. (23) Schulte, A.; Chow, R. H. Anal. Chem. 1996, 68, 3054-3058. (24) Schulte, A.; Chow, R. H. Anal. Chem. 1998, 70, 985-990. (25) Bach, C. E.; Nichols, R. J.; Beckmann, W.; Meyer, H.; Schulte, A.; Besenhard, J. O.; Jannakoudakis, P. D. J. Electrochem. Soc. 1993, 140, 1281-1284. (26) Schulte, A. SPIE Proc. 1998, 3512, 353-357. (27) Slevin, C. J.; Gray, N. J.; Macpherson, J. V.; Webb, M. A.; Unwin, P. R. Electrochem. Commun. 1999, 1, 282-288.

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Figure 1. Schematic drawing showing the effect of polishing procedure on electrode shape and properties. (a) Symmetrical polishing leads to electrode suitable for current feedback mode in SECM; (b) conical and unsymmetrical polishing leads to feedbackindependent nanoelectrodes.

the quartz-encapsulated Pt nanoelectrodes exhibit improved vibration characteristics for shear force-based CD-SECM due to the stiffness of the insulating sheath. Consequently, successful use of such Pt nanoelectrodes in CD-SECM has been demonstrated;9,10 however, those electrodes exhibit negative and positive feedback currents near the sample surface. Here, a new type of nanoelectrode is described for CD-SECM applications exhibiting a current response that has negligible feedback. A modification of a previous fabrication procedure22 results in a conical shape at the tip with an off-center Pt nanoelectrode (Figure 1b). These tips allow a much higher topographical resolution when used in CD-SECM, and the nanoelectrodes offer high spatial resolution of electrochemical activity. We have used nonoptical shear force SECM to demonstrate the feasibility of the approach by evaluating complex reaction zones of redox species while scanning the probe over an intricate, threedimensional test structure, consisting of an electrochemical microcavity in which electroactive species were consumed and regenerated in a controlled fashion. EXPERIMENTAL SECTION Chemicals and Materials. All chemicals were reagent grade and used without further purification. The redox solution consisted of 5 mM hexaamineruthenium(III) chloride ([Ru(NH3)6]Cl3; 98%, Aldrich) and 0.1 M KCl (analytical reagent, Riedel-de-Hae¨n, Seelze, Germany). Mineral oil (USP) was obtained from Sigma (St. Louis, MO). Water was triply distilled. Fabrication of Pt Nanoelectrode, SECM Tips. Quartzinsulated Pt nanoelectrodes used as SECM tips were prepared using the general procedure reported previously.22 A Pt wire, ∼10 mm long and 25 µm in diameter (purity 99.9%; hard, Goodfellow, Bad Nauheim, Germany), was inserted into the center of a 100mm-long, open-ended, quartz capillary tube, having a 0.9-mm outer diameter and a 0.3-mm inner diameter (Hilgenberg, Malsfeld, Germany). The capillary was placed in a laser puller (P-2000, Sutter Instrument Co., Novato, CA) and connected at each end to a vacuum generated by a water aspirator. The Pt wire and the quartz material were sealed together by a cycle of heating and cooling. This was repeated four times over 4 min. Then, during a heating step, the ends of the capillary were pulled apart, producing (28) Watkins, J. J.; Chen, J.; White, H. S.; Abruna, H. D.; Maisonhaute, E.; Amatore, C. Anal. Chem. 2003, 75, 3962-3971.

Figure 2. Confocal microscope image of a 50-µm-diameter microcavity, showing disk and ring electrodes, and where line scans for Figure 10 were performed.

two separate probes, each with a 40-50-mm-long shaft having a 0.9-mm outer diameter on one end and a ∼10-mm-long section that tapers to a point on the other end. In the tapered section, the quartz forms an excellent seal around the Pt, which has also thinned to a point at the tip. Contact to the backside of the Pt wire was made with a copper wire (0.25-mm diameter) using silver epoxy (Epo-Tek H20S, Polytec, Waldbronn, Germany), which was allowed to cure at 100 °C for 1.5 h. After pulling, the tip was polished conically. In a special holder, the shaft of the quartz-encapsulated Pt was positioned with a tilt of 45° above a rotating disk covered by 1-µm alumina particles. Both electrode and polishing disk were rotated independently of each other. The end of the electrode tip contacted the polishing disk for a few minutes. The off-centered location of the Pt nanoelectrode was obtained by having an angle of only a few degrees between the axis of the electrode holder and the axis of the electrode itself. Scanning electron microscopy (SEM; Gemini 1530 system, LEO, Oberkochen, Germany) was used to characterize the tips. Fabrication of Three-Dimensional Test Structures. A microcavity structure was used for generating local variations in concentration of redox species in three dimensions. Figure 2 shows a confocal microscope image (NanoProbe II Pro, Solarius Corp., Sunnyvale, CA) of one microcavity. It is ∼50 µm in diameter and 8 µm deep in which three, individually addressable, gold electrodes reside so that self-contained electrochemistry is possible on small volumes: a top layer electrode at the rim, a microring that is offset along one side and 4 µm down from the rim, and a recessed microdisk electrode, 8 µm down from the rim. The design and construction of the microcavities were modified from those reported earlier.29 Microcavities were fabricated through the use of photolithography and photoplot masks (Advance Reproductions Corp., North Andover, MA). They consist of five alternating layers of gold and polyimide, each layer sequentially deposited and patterned. The design positions four, 50-µm-diameter microcavities near one edge of each 1.25 × 2.50 cm chip, whereas the opposite end of the chip contains the contact pads to which an edge connector could be attached. Up to 27 such chips were fabricated on a single 5-in.-diameter wafer. A ∼3-µm layer of SiO2 was grown onto silicon wafers (5-in. diameter (100), donated by the High-Density Electronics Center at the University of Arkansas) by thermal oxidation at 650 °C for 8 h. This serves as an initial passivation layer between the first electrode and semiconductive silicon. (29) Henry, C. S.; Fritsch, I. J. Electrochem. Soc. 1999, 146 (9), 3367-3373.

Layer 1 forms the disk electrodes at the bottom of the cavities and the contact pads to those electrodes. It consists of an adhesion layer of 10-nm Cr (from a Cr-plated W rod (Lesker)) and 500-nm Au (from a Canadian maple leaf gold coin), deposited with an Edwards Auto 306 thermal evaporator. This layer was patterned using positive photoresist (AZ4330RS) and photoresist developer (AZ400K) (Hoechst-Celanese) with an image defined by the first mask. The Au was etched for ∼2 min with KI (50 g) and I2 (12 g) in water (500 mL), and the Cr was etched for ∼1 min with CEP200 chrome etchant (Microchrome Technology, San Jose, CA). The photoresist was removed with acetone. Layers 2 and 4 serve as insulators between the metal layers. Wafers were spin-coated with 4 µm of polyimide (Pyralin PI-2721, DuPont). The polyimide was cured at 150 °C for 30 min, followed by 250 °C for 30 min. Layer 3 forms the middle microring electrodes and their corresponding contact pads. A layer consisting of 10-nm Cr and 40-nm Au was deposited by thermal evaporation. Photoresist was deposited and patterned according to the second mask, allowing the metals to be selectively etched, with the same etchants used for layer 1, resulting in the desired pattern. The mask results in the etching away of 50-µm-diameter circles that will ultimately serve as the middle ring electrode. The remaining photoresist was removed with acetone. Layer 5 forms the top rim electrode. Thermal evaporation was used to deposit 10-nm Cr and 100-nm Au. Photoresist was deposited and patterned using a third mask. This mask results in the etching of 50-µm-diameter circles, which will form the top layer rim around the microcavity. The remaining photoresist was removed with acetone. The polyimide (layers 2 and 4) was etched away to form microcavities by reactive ion etching (RIE) with a mixture of O2 (36 sccm) and SF6 (4 sccm) at 150 mTorr and 150-W rf power (Unaxis PlasmaTherm SLR 720). An etching time of 30-35 min was sufficient to remove the polyimide in the cavity and expose all three cavity electrodes and their contact pads. The RIE parameters chosen were selective for polyimide etching. Thus, the gold rim electrode remained intact. Because of the different approach in fabricating the microcavities from that used previously, the opening through the middle gold layer may be offset from the opening of the microcavity and thus produces a step with a crescent shape, instead of a nanoband flush with the wall. We refer to this electrode as a “ring” electrode throughout this paper. The extent of the offset depends on the alignment of the mask above a photoresist film over the top layer of gold with the opening that had been etched in the middle layer of gold. Because the top layer of gold blocks the view of the opening in the middle layer and because of the use of transparency masks that slightly warp over time, the alignment is challenging and not highly reproducible from wafer to wafer. Figure 2 illustrates an intermediate offset for the ring electrode. The benefit of this fabrication procedure is that the yield is much higher than in the previous approach where all layers (both gold and polyimide) are etched through to form the microcavity using the pattern in the photoresist over the top gold layer from a single mask. Experimental Setup. Figure 3 illustrates the general experimental setup for the SECM tip and the chip-containing microAnalytical Chemistry, Vol. 78, No. 20, October 15, 2006

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Figure 3. Diagram of experimental setup. Both the top gold layer of chip and silver wire can be used as pseudoreference/auxiliary electrodes. Microcavities cannot be seen on this scale. They are located near the edge of the chip inside the reservoir.

cavities. Scanning took place at any one of the four, 50-µmdiameter microcavities that were addressable through an edge connector. An alligator clip made the connection to the top layer of gold. The reservoir was formed from a 6-mm-wide section that was cut from a plastic 1 cm × 1 cm cuvette designed for UV-visible absorption spectroscopy. The cut edges were sanded to smoothness, and the reservoir was cleaned from particulates by sonicating in water and then methanol for a few minutes. A glass slide, cut to the same width of the chip and approximately the same length, was epoxied (Plus Endfest 300, UHU) to the back of the chip so that it was set back from the edge that connects to the edge connector and provided a support for the reservoir on the side of the chip containing the microcavities. The reservoir was then glued with epoxy along its edge onto the chip so that the microcavities were located halfway between two opposing sides. The entire assembly was allowed to cure overnight. The reservoir could contain ∼600 µL of solution. When used for the SECM studies, 250 µL of aqueous solution was placed in the reservoir and covered by 250 µL of mineral oil of lower density, which prevents water evaporation. Thus, the concentration of [Ru(NH3)6]3+ remained unchanged during the experiments. It is also important to maintain a constant solution level because shear force could be lost due to changes in frequency when the level drops. We did not observe a change in volume, even after 36 h. Instrumentation. A bipotentiostat/galvanostat (PG100, Jaissle Elektronik, Waiblingen, Germany) permitted control of potential and measurement of current at the ring and disk electrodes of the microcavity, independently, while the top layer of the chip served as an auxiliary/pseudoreference electrode. For generation-collection experiments, the generator electrode was held at -0.5 V and the collector electrode was held at 0 V versus the top Au layer. A highly sensitive potentiostat (VA-10, NPI electronic, Tamm, Germany) was used for monitoring the electrochemical reaction at the Pt nanoelectrode. To prevent perturbations between the potentiostat and the bipotentiostat, the latter was powered by batteries. An external silver wire coated with AgCl was placed in the reservoir where it would not short to the top layer of gold and served as the auxiliary/pseudoreference electrode for the SECM tip. 7320

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The electrode was coarsely positioned in x, y, and z directions using stepper motors (0.625 nm/half-step; OWIS, Germany) and finely positioned using a precise piezoelement (Nanocube, P-611.35, 100-µm maximal scanning range, LVPZT Position Servo Controller, Physik Instrumente, Waldbronn, Germany). The electrode positioning and data acquisition were performed using a PC equipped with 16-bit AD/DA cards (CIO-DAS 1602/16, CIO-DAC02/16, Plug-In Electronic, Eichenau, Germany) and controlled by software programmed in-house (Sensolytics, Bochum, Germany). A digital camera allowed viewing of positioning of the Pt nanoelectrode in proximity to the sample. Initial positioning of the probe near the microcavity, but not in contact with the sample, was best performed without the solution in the reservoir. This is because the reflections off the mineral oil/air interface and at the mineral oil/solution interface, as well as the change in refractive indices made initial positioning difficult. The aqueous solution and mineral oil were added. Then the light and location of the objective lens were readjusted, resulting in subsequent trouble-free viewing of the tip. The constant-distance mode was operated by nonoptical shear force control of the distance between the tip and the sample.9-11,16 In brief, two piezoelectric plates (Piezomechanik Pickelmann, Mu¨nchen, Germany) were glued on brass holders and mechanically attached on the quartz capillary with set screws just above the tapered region of the tip (see Figure 3). A function generator (HP 33120A, Hewlett-Packard, Bo¨blingen, Germany) was used as an external reference for a dual-phase analog lock-in amplifier (PAR5210, Perkin-Elmer, Bad Wildbad, Germany) and connected to the upper piezoelectric element for stimulating resonance vibration of the SECM tip. The second piezoelectric element was connected to the input of the lock-in amplifier. The resonant frequencies of the electrode tip were determined by comparing frequency spectra obtained when the tip was free of interaction with a solid surface and when the tip was interacting with the top gold layer of the analyzed sample.11 At the resonance frequencies of the vibrating SECM tip, the response of the lock-in amplifier was strongly affected by the interaction between the tip and the analyzed surface. After determination of a set point and calibration of the shear force signal at a suitable frequency, a computercontrolled loop allowed automatic adjustment of the electrode height while scanning in x and y directions. This CD-SECM permits simultaneous acquisition of both topographic and electrochemical information. Because distance of the SECM tip from the sample is kept constant using the shear force-based distance regulation, the tip’s scan rate can vary throughout a single line scan. The rate depends on the tolerance, the dampening factor, the steepness of the approach curve, the topography of the sample, and the number of measurements taken along the x or y direction. For example, when the tip passes over steep changes in surface topography, the horizontal translation slows down. For high-resolution scanning, the software allows selection of a shear force priority mode. In this mode, incremental scanning in the x or y direction is only performed once the tip-to-sample distance is within a predefined deviation from the shear force set point. Thus, the scanning is fast as long as the SECM tip is over the top layer; however, it may be very slow while being positioned within the microcavity. On average, a typical single line scan of 90 µm with 1-µm

Figure 4. SEM images at increasing magnification of a probe tip made from a pulled quartz capillary with a Pt nanowire inside. The Pt electrode can be observed at the edge of the quartz cone.

Figure 5. Typical CV response of a Pt nanoelectrode probe in a solution of 5 mM [Ru(NH3)6]3+ and 0.1 M KCl (potential vs Ag/AgCl wire). The CV was performed just before starting constant-distance mode SECM experiments.

increments across the center of the microcavity would take ∼20 min. RESULTS AND DISCUSSION Electrode Characterization and Properties. The shape and size, electrochemical behavior, and utility of the long, narrow Pt/ quartz probes as SECM tips were investigated. Figure 4 shows SEM images of one probe. The conically shaped end of the flexible and tapered, ∼1-cm-long tip can be clearly seen. The width of the base of the cone is ∼6 µm in diameter, the length of the cone is ∼4-5 µm, and the point is of submicrometer dimensions in width. The Pt electrode’s off-center location relative to the quartz point is easily visible and its diameter can be measured (∼100 nm). Initial electrochemical characterization of the Pt nanoelectrodes was carried out by CV in a solution of 5 mM [Ru(NH3)6]3+ containing 0.1 M KCl. As shown in Figure 5, a sigmoidally shaped voltammogram was obtained, as expected. The steady-state diffusion-limited current, i, for a disk-shaped microelectrode can be expressed by i ) knFCDr,30,31 where k is the geometrydependent coefficient, n is the number of moles of electrons transferred per mole of redox molecules (n ) 1 for [Ru(NH3)6]3+), F is the Faraday constant (96 485 C/mol electrons), C is the concentration of redox species, D is the diffusion coefficient of the redox species (D ) 7.7 × 10-6 cm2 s-1 for [Ru(NH3)6]3+, as estimated under similar conditions using a 5-µm-radius Pt disk electrode), and r is the radius of the electrode. The value of k is 4 for the case of a disk embedded in an infinite insulating plane.30,32 As the thickness of the insulator decreases relative to the electrode radius, the value of k can increase,23,33-37 because radial diffusion draws from the solution volume around the tip and up its length. (30) Wightman, R. M.; Wipf, D. O. In Electroanalytical Chemistry; Bard, A. J. Ed.; Marcel Dekker: New York, 1989; Vol. 15, pp 267-353. (31) Montenegro, M. I.; Queiros, M. A.; Daschbach, J. L. In Microelectrodes: Theory and Applications; Montenegro, M. I., Quieres, M. A., Daschbach, J. L., Eds.; NATO ASI Series E197; Kluver Academic: Dordrecht, The Netherlands, 1991. (32) Heinze, J. Angew. Chem., Int. Ed. Engl. 1993, 32, 1268-1288.

Figure 6. Electrochemical (open circles) and shear force (solid squares) responses of probe tip during approach toward the gold surface at the rim of a microcavity, showing no current feedback. The Pt probe electrode was held at reducing voltages (-0.5 V vs Ag/ AgCl wire).

We do not know the exact value of k for the Pt nanoelectrode on the side of a conical probe tip. This value is likely to vary from probe tip to probe tip because the extent of polishing and the angle of the cone were not precisely controlled. However, if we assume that k is 4, we can calculate from this equation and the steady-state current the maximum possible radius, which is less than 150 nm (