Anal. Chem. 2007, 79, 2952-2956
Technical Notes
Scanning Electrochemical Microscopy: Approach Curves for Sphere-Cap Scanning Electrochemical Microscopy Tips Georgina Lindsey, Stuart Abercrombie, and Guy Denuault*
School of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom Salvatore Daniele and Eddy De Faveri
Department of Physical Chemistry, University of Venice, Calle Larga S. Marta 2137, 30123 Venice, Italy
The parameters of functions used to predict diffusioncontrolled scanning electrochemical microscopy approach curves under positive and negative (hindered diffusion) feedback for sphere-cap tips are reported. These functions were obtained by fitting approach curves simulated with an error-bounded adaptive finite element algorithm. Several geometries corresponding to different sphere-cap dimensions were considered including the effect of the tip insulating sheath. The simulated approach curves were successfully compared with experimental ones obtained with mercury sphere caps electrodeposited onto platinum microdisk electrodes. Mercury microelectrodes can be easily fabricated by electrodepositing mercury onto microdisk electrodes. On solid substrates wettable by mercury, e.g., Pt, the deposits adopt a spherical segment geometry and produce sphere-cap microelectrodes which have found applications in cyclic voltammetry and stripping analysis.1,2 These electrodes have also been applied in scanning electrochemical microscopy3-8 (SECM) to probe heavy metal concentrations in the vicinity of solid/liquid interfaces or to study the kinetics of oxygen transfer across monolayers at an air/water * To whom correspondence should be addressed. Phone: +44-23-80592154. Fax: +44-23-80593781. E-mail:
[email protected]. (1) Baldo, M. A.; Daniele, S.; Corbetta, M.; Mazzocchin, G. A. Electroanalysis 1995, 7, 980-986. (2) Baldo, M. A.; Daniele, S.; Ciani, I.; Bragato, C.; Wang, J. Electroanalysis 2004, 16, 360-366. (3) Selzer, Y.; Mandler, D. Anal. Chem. 2000, 72, 2383-2390. (4) Janotta, M.; Rudolph, D.; Kueng, A.; Kranz, C.; Voraberger, H. S.; Waldhauser, W.; Mizaikoff, B. Langmuir 2004, 20, 8634-8640. (5) Rudolph, D.; Neuhuber, S.; Kranz, C.; Taillefert, M.; Mizaikoff, B. Analyst 2004, 129, 443-448. (6) Daniele, S.; Bragato, C.; Ciani, I.; Baldo, M. A. Electroanalysis 2003, 15, 621-628. (7) Ciani, I.; Daniele, S.; Bragato, C.; Baldo, M. A. Electrochem. Commun. 2003, 5, 354-358. (8) Mauzeroll, J.; Buda, M.; Bard, A. J.; Prieto, F.; Rueda, M. Langmuir 2002, 18, 9453-9461.
2952 Analytical Chemistry, Vol. 79, No. 7, April 1, 2007
interface9 or in the substrate generation-tip collection mode.10 For some SECM applications, sphere-cap tips may be more advantageous than disk-shaped tips because the very end of the tip can get closer to the substrate surface; this can be useful for fast kinetic studies and allow a better estimation of the true zero distance.10 SECM theory for sphere-cap tips however is less developed than that for disk electrodes. In particular, no general equation exists that allows the prediction of approach curves, though the latter can be obtained by using simulation procedures.11 With the advent of user-friendly commercial software and very powerful workstations on the desktop, finite element simulations are becoming increasingly popular within the electrochemical community. For the work reported here we used our own steadystate adaptive finite element solver, which provides a guaranteed error bound on the simulated current.12 The solver is based on the seminal contribution of Harriman et al.; see, e.g., refs 13 and 14 and subsequent papers from the same group. The objective of this paper is to provide SECM users with a set of equations and parameters that describe the shape of SECM approach curves (tip-current versus tip-substrate distance) for tips with sphere-cap geometries. Similar parameters we computed for the disk geometry15 have found widespread use within the SECM community. The dataset allows investigators to compare their experimental approach curves to theoretical data without the need to run simulations. To illustrate the point, we use the equations and parameters to analyze experimental approach (9) Ciani, I.; Burt, D. P.; Daniele, S.; Unwin, P. R. J. Phys. Chem. B 2004, 108, 3801-3809. (10) Mauzeroll, J.; Hueske, E. A.; Bard, A. J. Anal. Chem. 2003, 75, 38803889. (11) Bard, A. J., Mirkin, M. V., Eds. Scanning Electrochemical Microscopy; Marcel Dekker, Inc.: New York, Basel, 2001. (12) Abercrombie, S. C. B.; Denuault, G. Electrochem. Commun. 2003, 5, 647656. (13) Harriman, K.; Gavaghan, D. J.; Houston, P.; Suli, E. Electrochem. Commun. 2000, 2, 150-156. (14) Harriman, K.; Gavaghan, D. J.; Houston, P.; Suli, E. Electrochem. Commun. 2000, 2, 157-162. (15) Amphlett, J. L.; Denuault, G. J. Phys. Chem. B 1998, 102, 9946-9951. 10.1021/ac061427c CCC: $37.00
© 2007 American Chemical Society Published on Web 02/22/2007
curves obtained for positive and negative feedback currentdistance plots recorded with mercury sphere cap deposited on microdisk SECM tips. EXPERIMENTAL CONDITIONS All chemicals employed were of analytical-reagent grade. Ruthenium(III) hexaammine trichloride was purchased from Aldrich and used as received. All aqueous solutions were prepared with Milli-Q water. Cathodic electrophoresis paint Stollaquid D 1330 was from Herberts (Germany). All measurements requiring no oxygen were carried out in solutions that had been purged with pure nitrogen (99.99%) from SIAD, Italy. The platinum microdisks, which served as the substrate for mercury deposition, were prepared either by sealing wires, 1 and 12.5 µm radius, into glass capillaries or by coating the cylindrical length of 12.5 µm radius Pt wires with a cathodic electrophoretic paint as described previously,16 depending on the desired thickness of the insulating shield surrounding the disk electrode. The thicker electrode tips were then tapered to form a truncated conical shape analogous to that of a conventional SECM tip.11 Prior to mercury deposition, the microdisks were polished with graded alumina powder of different sizes (1, 0.3, and 0.05 µm) on a polishing microcloth. For each microdisk, the radius of the insulating sheath, as is customary, was determined with an optical microscope while the microtips were being prepared. The value was further confirmed by fitting theoretical SECM approach curves15 to experimental ones recorded under purely diffusion controlled conditions. Moreover, for the thin shielded microdisks the cyclic voltammetric procedure described in ref 16 was also employed. Sphere-cap mercury microelectrodes of different sizes were prepared ex situ by cathodic deposition of mercury onto the platinum microdisks, as reported elsewhere.1,17 The deposition was performed under potentiostatic conditions at -0.1 V against a Ag/AgCl reference electrode in a plating solution consisting of 5 mM Hg2(NO3)2 in 1 M KNO3 acidified with nitric acid to pH < 1. Increasing deposition times were employed to obtain mercury deposits of different heights. The effective radius and aspect ratio of the sphere caps produced were estimated by recording the steady-state limiting currents in a 1 mM Ru(NH3)63+ + 0.1 M KCl aqueous solution (D(Ru(NH3)63+) ) 7.0 × 10-6 cm2 s-1)18 and comparing them with the theoretically predicted limiting current.19 The SECM micropositioning device consisted of a set of three stepper motor stages with a 0.1 µm resolution (MICOS) and an optical encoder (ZEISS), and the motion was controlled by a closed loop motion controller board, PCI-7324 (National Instruments). The data acquisition was performed by a PCI-6035E Multifunction I/O board controlled with Lab View (National Instruments). A CH700B workstation (CH Instruments) was employed for SECM measurements and for other electrochemical experiments including those for the characterization of platinum disks and the preparation of mercury sphere-cap microelectrodes. For positive and negative feedback measurements a 3 mm diameter smooth Pt disk and the Teflon sheath surrounding the conducting disk, (16) Ciani, I.; Daniele, S. Anal. Chem. 2004, 76, 6575-6581. (17) Corbetta, M.; Baldo, M. A.; Daniele, S.; Mazzocchin, G. A. Ann. Chim. 1996, 86, 77-86. (18) Sun, P.; Zhang, Z. Q.; Guo, J. D.; Shao, Y. H. Anal. Chem. 2001, 73, 53465351.
Figure 1. Schematic representation of the axisymmetric simulation domain (delimited by the thick black line) with a sphere-cap SECM tip. Boundary conditions: 1, 3, and 4, zero flux; 2, zero surface concentration; 5 and 6, unity concentration; 7, zero flux for insulating substrates or unity concentration for conducting substrates. a is the microdisk radius, h the sphere-cap height, d the tip-substrate distance, rg the insulating glass radius, rd the domain radius, and tl the tip length. Family of sphere caps: H ) 0.1 (smallest cap), 0.2, 0.5, 1, and 2 (largest cap).
respectively, were employed as substrates. All measurements were carried out in a two-electrode cell maintained in a Faraday cage made with aluminum sheets. In all cases, the reference electrode was Ag/AgCl saturated with KCl. RESULTS AND DISCUSSION 1. Sphere-Cap Geometry and Simulation Domain. Spherecap tips were characterized by the parameter h, the height of the spherical segment,19 which depends on the amount of mercury deposited, Figure 1. To allow comparison with the disk, the tipsubstrate distance, d, was not taken from the end but from the base of the sphere cap. As usual in SECM theory, all dimensions were normalized with respect to the microdisk radius, a, while the tip current, itip, was normalized by its value in the bulk, itip,∞. The dimensionless quantities used to define the tip geometry and simulation domain were H ) h/a, L ) d/a, RG ) rg/a, RD ) rd/a, and TL ) tl/a; see Figure 1 for a description of these quantities and detailed boundary conditions. Note that there was no initial condition as the simulation was performed by a steadystate solver. Each simulation produced the steady-state diffusioncontrolled tip current for a given domain, i.e., for a given tip geometry, tip-substrate distance, and type of substrate (insulating or conducting depending on the type of feedback considered). To ensure the results were not affected by the location of the bulk solution, the far-field boundaries were set at RD ) 500 and TL ) 500. Simulations performed with these boundaries located further yielded very similar results, well within the error tolerance. The perimeter of the sphere cap was constructed with 10 linear segments whatever the H value. Simulations run with more segments yielded identical results within the error tolerance. To generate approach curves, simulations were repeated over a range of L values, typically from L ) H + 0.1 to L ) 20. Similarly, to investigate the effect of the tip geometry, a family of sphere caps was generated by varying H from 0.1, where the tip essentially works as a flat disk, to 2, where the tip effectively behaves as a (19) Myland, J. C.; Oldham, K. B. J. Electroanal. Chem. 1990, 288, 1-14.
Analytical Chemistry, Vol. 79, No. 7, April 1, 2007
2953
Figure 3. Sphere-cap tip current in the bulk, itip,∞Sc, normalized by the corresponding microdisk tip current, itip,∞Md, against the spherecap height, H. The theoretical curve is RnFDcba/4nFDcba, with R a function of H given by eq 3 in ref 17; all other parameters have their usual meaning.
Figure 2. Simulated approach curves for a family of sphere-cap tips for positive feedback (upper curves) and hindered diffusion (lower curves). The legend gives the corresponding H values. The inset shows the same data but plotted against L - H.
hanging mercury microdrop, Figure 1. For comparison with experimental approach curves, simulations were run for the H values determined experimentally. 2. Fitting of Simulated Approach Curves. The simulated approach curves were fitted to expressions defined by four adjustable parameters. No attempt was made to have fewer parameters as the intention was to use expressions similar to those for microdisk tips.15 Current-distance curves controlled by negative feedback (hindered) diffusion were successfully fitted to the equation for a microdisk approaching an insulating substrate:11
itip 1 ) itip,∞ k1 + k2/L + k3 exp(k4/L)
(1)
where k1, k2, k3, and k4 are the adjustable parameters. However, simulated positive feedback approach curves could only be fitted to the corresponding microdisk equation15 at low H values where the sphere cap is analogous to a “swollen” microdisk. Instead the following equation was found to fit the simulated approach curves over the whole range of sphere-cap heights considered:
itip itip,∞
) k1 +
k3 k4 k2 + + L - H/3 L - 2H/3 L - H
(2)
This expression, derived from mathematical intuition, was constructed assuming the sphere-cap/substrate system is equivalent to a combination of three concentric thin layer cells with thicknesses equal to L - H for the innermost disk, L - 2H/3 for the middle ring, and L - H/3 for the outermost ring. This very crude (the aim being to retain four adjustable parameters, no attempt was made to refine it further) but intuitively pleasing discretization of the sphere cap was found to work extremely well. 3. Simulation Results. Figure 2 shows the shape of the approach curves for feedback and hindered diffusion simulated 2954 Analytical Chemistry, Vol. 79, No. 7, April 1, 2007
Table 1. Dependence of the Adjustable Coefficients k1, k2, k3, and k4 for Approach Curves Controlled by Hindered Diffusion and by Positive Feedback against the Sphere-Cap Height H, RG ) 10a H
k1
0.1 0.2 0.48 0.5 0.78 1 1.03 1.41 1.88 2
0.5242 0.5053 0.4367 0.4249 0.3081 0.1725 0.1536 -0.2430 -0.9720 -1.277
0.1 0.2 0.5 1 2
0.9758 0.9774 0.9808 0.981 0.9828
error (%)
L validity range
Hindered Diffusion (Eq 1) 1.5277 0.4754 -2.9363 1.5919 0.4949 -2.9518 1.8196 0.5641 -2.9927 1.8440 0.5753 -2.9625 2.1772 0.6931 -2.9374 2.5203 0.8293 -2.8574 2.5690 0.8482 -2.8472 3.3956 1.2451 -2.5772 4.7528 1.9753 -2.2981 5.2349 2.2808 -2.2026
