Forced Convection during Feedback Approach ... - ACS Publications

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Forced Convection during Feedback Approach Curve Measurements in Scanning Electrochemical Microscopy: Maximal Displacement Velocity with a Microdisk R. Cornut, S. Poirier, and Janine Mauzeroll* Laboratory for Electrochemical Reactive Imaging and Detection for Biological Systems, Department of Chemistry, NanoQAM Research Centre, Université du Québec à Montréal, C.P. 8888, Succ. Centre-ville, Montréal, QC, Canada, H3C 3P8 S Supporting Information *

ABSTRACT: In scanning electrochemical microscopy (SECM), an approach curve performed in feedback mode involves the downward displacement of a microelectrode toward a substrate while applying a bias to detect dissolved electroactive species at a diffusion-limited rate. The resulting measured current is said to be at steady state. In order to reduce the required measurement time, the approach velocity can be increased. In this paper, we investigate experimentally and theoretically the combination of diffusion and convection processes related to a moving microdisk electrode during feedback approaches. Transient modeling and numerical simulations with moving boundaries are performed, and the results are compared to the experimental approach curves obtained in aqueous solution. The geometry and misalignment of the microelectrode influence the experimental approach curves recorded at high approach velocities. The effects are discussed through the decomposition of the current into transient diffusional, radial convectional, and axial convectional contributions. Finally a ready-to-use expression is provided to rapidly evaluate the maximal approach velocity for steady state measurements as a function of the microelectrode geometry and the physical properties of the media. This expression holds for the more restrictive case of negative feedback as well as other modes, such as SECM approach curves performed at substrates displaying first order kinetics.

S

measurements, such as impedance, are performed.24 To circumvent the problem during SECM imaging experiments, microelectrode arrays have been developed to increase the substrate area sampled and reduce the imaging time. Barker and co-workers presented a linear array of 16 independent Pt 10 μm-diameter microelectrodes.25 Cortes-Salazar and co-workers developed soft stylus probes fabricated by ablating microchannels on a polyethylene terephthalate film and filling them with carbon ink.26 This fabrication protocol was further improved with the use of a Parylene coating that allows for smaller working distances.27 For SECM applications not targeting high-throughput imaging, a simple improvement to reduce the overall analysis time is to increase the approach velocity of the microelectrode during prepositioning and subsequent quantitative measurements. In the most restrictive case of the approach to an insulating substrate (usually called negative feedback approach curve), the faradaic current recorded at a microelectrode is monitored with decreasing microelectrode to substrate distance. Far away from the substrate, the dissolved redox species undergo an

canning electrochemical microscopy (SECM) has proven effective to locally study in situ a variety of substrates. Since its inception in the late 1980s,1−4 examples of targeted substrates include enzymes deposits,5,6 cells,7 liquid−liquid interfaces,8 alloys,9 thin films,10,11 and catalysts.12 Invariably, the SECM measurements required the prepositioning of a microelectrode in close proximity to the substrate. Prepositioning of the microelectrode can be accomplished using optical means,13 shear force regulation,14 atomic force microscopy,15 electron tunneling,16 solution resistance,17,18 impedance,19,20 or electrochemical measurements based on alternating (ac)21 or direct current (dc)22,23 methods. Once positioned, SECM quantitatively monitors electrochemical reactions, which are affected by the topography and reactivity of the neighboring substrate. Quantitative measurement interpretations require detailed knowledge of the microelectrode geometry and microelectrode to substrate distance. Importantly, the velocity at which they are performed directly affects the overall analysis time. For example, a standard quantitative approach curve would take 300 s if it covered a 300 μm distance using a 1 μm/s velocity. The acquisition time for sequences can increase even further when performing matrix scans, whereby the microelectrode is approached at every point of a matrix and additional © 2012 American Chemical Society

Received: November 16, 2011 Accepted: March 4, 2012 Published: March 5, 2012 3531

dx.doi.org/10.1021/ac203047d | Anal. Chem. 2012, 84, 3531−3537

Analytical Chemistry

Article

velocity and pressure. The following dimensionless formulation is considered:

electrochemical reaction at a microelectrode surface that is mass-transfer limited. In decreasing the microelectrode to substrate distance, the physical presence of the substrate hinders the diffusion of the redox species, which leads to a progressive decrease in the measured current.28,29 Negative approach curves are typically acquired at approach velocities on the order of a few micrometers per seconds and are generally considered to occur under steady-state conditions. This greatly simplifies the interpretation of results all the more as analytical approximations for this situation are available in the literature.30 Increasing the approach velocity of the microelectrode to reduce analysis time will generate convection in the surrounding electrolyte, which will alter the measured current and limit the quantitative interpretation of data. Convection effects during SECM studies have been previously studied. Natural convection31,32 that stems, for example, from microscopic heterogeneities of the fluid’s density has been investigated. This inherent convection affects, for example, the current measured at a band microelectrode.33 In addition, the convection coupled to diffusion occurring close to a porous membrane34 or a cartilage35 has been investigated. Forced convection occurs as a result of the displacement of the microelectrode or substrate. It has been studied for the displacement of the microelectrode in a plane parallel to that of the substrate,36,37 in a direction normal to the plane of the substrate38 and for a vertically oscillating microelectrode.21 Modeling efforts, which were corroborated with experiments, were performed in SECM studies in deep eutectic solvents39 or in ionic liquids.40,41 In fact, despite the well-established importance of convective effects when performing SECM approach curves in aqueous solvent, to the best of our knowledge, no general and quantitative discussion is available on the subject. This is all the more important as the overall SECM analysis time will be reduced if the maximal approach velocity that can be achieved with a given microelectrode is well-known. In this work, we investigate the influence of the fluid’s property and microelectrode geometry on negative feedback approach curves acquired at approach speeds ranging from 0.3 to 50 μm/s. We investigate experimentally and theoretically the combined effects of diffusion and convection on a moving microdisk electrode during negative feedback. Transient modeling and numerical simulations with moving boundaries are performed, and the results are compared to the experimental approach curves obtained in aqueous solution. The effect of microelectrode alignment is discussed in depth. From this analysis, a ready-to-use expression is provided to rapidly identify the maximal approach speed for steady state measurements as a function of microelectrode geometry and the diffusion coefficient of the redox mediator. In turn, this allows one to maximize the approach velocity while maintaining the ability to quantitatively interpret the approach curve. Finally it is verified that this speed is also appropriate for SECM approach curves performed at substrates displaying any first order kinetics.

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R=

r , rT

V⃗ =

Z=

z , rT

,

pr T P= ηvdisp

v⃗ vdisp

T=

vdispt rT

,

c C = 0, c (1)

where c0 is the initial mediator concentration, η is the viscosity of the fluid, vdisp is the displacement velocity of the microelectrode, rT is the active material radius of the microelectrode, c is the local concentration, p is the local pressure, v is the local fluid velocity, r and z are the radial and axial variables, and t is the time variable. Dimensionless quantities are defined by the corresponding capital letters. Borrowing from Nkuku and LeSuer’s existing model for deep eutectic solvents,39 the dimensionless equations system (Supporting Information) has been modified at the boundary condition expressing the displacement rate of the microelectrode. The equation system we used is in accordance with the chosen dimensionless formulation. The complete equation system is presented in the Supporting Information. In the present study, the conditions for the fluid velocity at the microelectrode are

Vr = 0 Vz = 1

(2)

The resulting current is normalized by the current obtained far from the substrate, leading to a normalized current IN, which depends on the following dimensionless parameters: the Reynolds number, Re (Re = (ρvdisprT)/η), the Péclet number, Pe (Pe = (vdisprT)/D), L0, and RG. During a typical SECM experiments performed in water, Re can be estimated as follows: Re =

ρvdispr T η

≈

103 × 10−5 × 10−6 10−3

≈ 10−5

Such a small order of magnitude for Re strongly suggests the presence of a laminar flow, which is confirmed by performing unrestricted calculations with the complete equation system. In all cases, a laminar flow is obtained and corroborates the results obtained by Nkuku and LeSuer.39 Re has thus a minimal influence on the present simulations and can be neglected. L0 (typically L0 = 20) also has a negligible impact on the simulations, which implies that IN is mainly governed by Pe and RG. The numerical resolution of the equations has been performed using Comsol Multiphysics 3.5a,42 with a Quad CPU 2.5 GHz Intel Processor having 8 GB of RAM. For the evaluation of the current, instead of integrating the calculated concentration gradient at the active part of the tip, a special function named reacf was used. It provides a direct access to the Lagrange multiplier used during the calculation and leads subsequently to an increased accuracy. In addition, a high mesh density has been imposed at the point of contact between the electrode active and insulating materials. For example, in the 2D calculations, the size of the meshes in the vicinity of this point (Z = 0, R = 1) was fixed to 0.01. Following this optimization, the simulated currents had a relative error less than 0.5%.

THEORY AND SIMULATIONS

In addition to the diffusion equation for the redox mediator concentration, convection effects are described by the incompressible Navier−Stokes equation system for the fluid 3532



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The effect of the vertical misalignment of the microelectrode with the substrate surface was evaluated through the use of a beveled microelectrode, which required 3D calculations. Numerical resolution of the 3D problem involved (i) evaluating the velocity field (involving Vr and Vz) using only the convection equation (eqs S-10−S-17), (ii) inputting this velocity field in the equation system involving the concentration field (eqs S-2−S-9) and calculating the microelectrode current (eq S-18 in the Supporting Information). With this procedure, the number of degrees of freedom of each problem was small enough to allow use of direct solvers (such as UMFPACK) that are faster and more efficient than indirect ones (such as GMRES).

performed using a 100 nm ELPro Scan system (HEKA; model PG 340). Procedures. SECM negative feedback approach curves were performed in an aqueous solution with 1 mM dissolved FcCH2OH and 1 M KCl. The microelectrode was approached to a flat Teflon substrate at approach velocities ranging from 0.3 to 50 μm/s. During the approach, a positive bias (0.45 V vs Ag/ AgCl/KCl 1 M) was applied, leading to a diffusion-limited current coming from the oxidation of FcCH2OH into FcCH2OH+. Each family of curves recorded at different approach velocities was performed using the same geometry such that the positions at the beginning and at the end of the displacement were the same for all curves.

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RESULTS AND DISCUSSION Effect of the Approach Velocity on Negative Feedback at a Disk Microelectrode. To reduce the acquisition time in SECM, the approach velocity can be increased. Increasing the approach velocity of the microelectrode generates convection in the surrounding electrolyte, which alters the measured current (IN,tot). The measured current is a sum of steady state and transient contributions. The steady state current (IN,ss), obtained at small velocity is the quantity usually called the feedback current. To isolate the transient contribution (IN,trans), the experimental and theoretical approach curves (IN,tot) acquired at high velocities have been corrected by the steady state current (IN,ss) over all L (the approach curves recorded at 0.3 μm/s have been used). The experimental approach curve (0.3 μm/s) had been previously fitted to the analytical approximation of the negative feedback44 in order to extract the RG and rT values used to calculate the theoretical curves for different approach velocities. The extracted values (rT = 3.5 μm, RG = 19) were in accordance with the micrographs of the microelectrode. Figure 1 presents the experimental and theoretical transient contributions to the approach curve acquired at 5 μm/s, 20

EXPERIMENTAL SECTION Materials. Electrochemical measurements were performed in nanopure water solutions, purified with a Millipore Milli-Q Biocel Ultrapure water system (Fisher, Ottawa, ON), ferrocenemethanol (FcCH2OH) (97%, Aldrich, Canada), and potassium chloride (KCl). Electrode fabrication materials used were 25 μm diameter Pt-wire (purity 99.9%; hard) (Goodfellow), quartz capillaries (length 150 mm; o.d. 1 mm, i.d. 0.3 mm) (Sutter Instrument), electrically conductive silver epoxy (EPO-TEK H20E) (Epoxy Technology Inc., Canada), and standard copper connection wires (diameter < 0.3 mm). The polishing materials (Buehler, Canada) used were abrasive disks (800 and 1200 grit), diamond lapping film disks (1, 0.3, and 0.05 μm diamond size) and alumina suspensions (1, 0.3, and 0.05 μm particle diameter). Electrodes. A conventional three-electrodes setup was used for the voltammetry and SECM experiments. It involved a platinum (Pt) microdisk working electrode, a Ag/AgCl (1 M KCl) reference electrode, and a 0.5 mm diameter Pt wire auxiliary electrode. The Pt microdisks were produced using an established laser pulling protocol43 that produces microelectrode of controlled geometry. Briefly, quartz capillaries were cleaned with a dilute (10% v/v) nitric acid solution, rinsed with water, and allowed to dry in an oven. The 25 μm diameter Pt wire was cleaned with acetone, rinsed with deionized water, and connected to a 0.2 mm diameter copper wire with silver epoxy before heat curing. The Pt assembly is then inserted in the center of the capillary. Both ends of the capillary are connected to a vacuum pump. During sealing, weak pulling forces on the glass capillary are avoided using two stoppers that fix the puller bars. Sealing of the Pt-wire into the quartz capillary was achieved using a single line program (heat, 540; filament, 5; velocity, 60; delay, 140; pull, 0) and repeated for five cycles. A cycle consists of 40 s of heating followed by a 20 s cooling period. Following the removal of the stoppers and silicon tubes, the pulling program (heat, 780; filament, 12; velocity, 160; delay, 100; pull, 200) is applied. The extremity of the microelectrode was then cut and polished with 0.3 and 0.05 μm diamond lapping film, leading to microdisks with 2−5 μm diameter platinum electrodes and a surrounding glass thickness 20−30 times larger. To simulate the misalignment of the microelectrode, the laser pulled electrodes were beveled with a small angle (typically 2°) and polished with 0.3 and 0.05 μm diamond lapping film. This did not significantly change the observed optical micrograph. Instrumentation. A laser puller (P-2000, Sutter Instrument Company, Novato, CA) was used to produce the microelectrodes. The CVs, SECM images, and approach curves were

Figure 1. Experimental and calculated approach curves obtained with a disk microelectrode (rT = 3.5 μm, RG = 19) at different approach velocities. Theoretical curves ▲, 5 μm/s; □, 20 μm/s; ■, 50 μm/s using D = 7.8 × 10−6 cm2/s. The corresponding experimental curves are plotted as lines without symbols.

μm/s, and 50 μm/s during the oxidation reaction of FcCH2OH. In Figure 1, the steady state current is given by IN,trans = 0 over all L. It must also be mentioned that in order to plot the theoretical curves presented in Figure 1, no parameter adjustment has been performed. This is an important difference with the existing studies available in the literature39 where an adjustment of the Pe value for each approach curve is performed. Figure 1 demonstrates that the model accurately describes the combined diffusion and convection effects on approach curves acquired using approach velocities smaller than 5 μm/s. 3533



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For example, at 5 μm/s, the convective current is reproduced by the model over the entire microelectrode to substrate distance. At large microelectrode substrate distances (L > 1), the convection current positively departs from the expected steady state value. Interestingly, at L < 1 the transient contribution leads to a negative departure from the expected steady state value, yielding a smaller measured current. The origin of this phenomenon is discussed in a later section. Approach curves acquired at approach velocities greater than 5 μm/s, agree with the model at microelectrode to substrate distances (L > 2). At distances L < 2, the measured experimental currents are larger than the calculated ones. With increasing approach velocity and decreasing L, the difference between experimental and theoretical currents is exacerbated. A possible explanation for the enhanced experimental currents is the convection effect resulting from the vertical misalignment of the microelectrode with the substrate. This point is further investigated in the following section. Effect of the Approach Velocity on Negative Feedback at a Misaligned Disk Microelectrode. The vertical misalignment of the microelectrode with the substrate is modeled by a bevelled disk microelectrode (Figure 2a). A family of approach curves for the same microdisk before and after bevelling were recorded during the oxidation reaction of FcCH2OH at approach velocities ranging from 0.3 to 20 μm/s. The steady-state approach curves obtained with the microdisk (0.3 μm/s) were fitted to negative feedback44 in order to extract RG and rT. For each data set, the distance correction

applied during the fitting procedure was applied to approach curves measured at higher velocities. The steady state (0.3 μm/s) experimental and theoretical approach curves obtained at a microdisk (0°) and bevelled microdisk (2.3°) perfectly overlapped, which implies that bevelling has a negligible effect on the RG and rT of the microdisks. Perfectly overlapping theoretical curves at 0.3 μm/s are expected45,46 because the tilt of the microelectrode under conventional (steady state) negative feedback has a minor impact on the measured current, as long as the reference tip to substrate position is adequately chosen. Figure 2b presents the difference between the experimental currents obtained at a 2.3° bevelled microelectrode with that obtained at a microdisk (assumed 0°), as a function of the microelectrode-to-substrate distance. At approach velocities superior to 0.5 μm/s, a noticeable effect of microelectrode misalignment is observed. A tilt variation of a few degrees has thus a significant impact on the measured current acquired at high approach velocities and small microelectrode-to-substrate distances. This difference may even be more significant than the expected departure from steady state, as observed in Figure 1. For example, for the approach curves recorded at 20 μm/s, the difference in current between the 2.3° and 0° curves reaches 0.15 at L = 1 (Figure 2b), while the difference with the steady state is maximally equal to 0.1 in Figure 1. In turn, this implies that at a high approach velocity, it is difficult to interpret quantitatively the measured currents because the microelectrode is never approaching the substrate in a perfectly perpendicular fashion. The contribution of the microelectrode misalignment to the convection current was not considered in the model used in Figure 1, which dealt with a microdisk approaching the substrate in a perfectly perpendicular orientation. The revised model accounted for the misalignment of the microelectrode through the addition of the bevelled geometry in the simulation space, which resulted in a departure from cylindrical symmetry. Using the extracted RG and rT from the experimental approach curves, a family of simulated approach curves with the desired approach velocities were calculated using this revised model. Figure 2c presents the difference between the simulated currents obtained at a 2.3° bevelled microelectrode with that obtained at a microdisk, as a function of the microelectrode-tosubstrate distance. The same previous trend (Figure 2b) is observed: a positive departure of the current obtained with the bevelled electrode, and an increase of this departure with the velocity. Decomposition of the Diffusion and Convection Contributions to the Current of a Negative Feedback Approach Curve. During a negative feedback approach curve performed at a high approach velocity, several phenomena with contradictory impacts on the resulting current occur simultaneously. Potential contributions to the feedback current include transient diffusion, axial convection, and radial convection as presented Figure 3. Their calculation is detailed in the following. Transient diffusion comes from the increased concentration gradients at high velocities relative to that observed at steady state when convection effects are neglected. Axial convection is the result of the decrease of the diffusion layer thickness due to the moving microelectrode. Radial convection is defined as the outward flux of solution as a result the incompressibility of the fluid. It is equivalent to a squeezing effect. In order to individually quantify and discuss each contribution, approach curves with a specific equation system

Figure 2. Effect of the tilt angle of the microelectrode on the experimental and theoretical feedback approach curves. (a) Scheme of a microelectrode polished without and with a tilt angle. (b and c) Difference in the experimental (b) and theoretical (c) normalized currents between a 2.3° and a 0° tilted microelectrode for RG = 26, rT = 3 μm. Approach velocities: ■, 0.5 μm/s; ○, 5 μm/s; ▲, 20 μm/s. 3534



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complete model (eqs S-2−S-18 in the Supporting Information, without any modification) and that previously calculated with the radial component of V⃗ set to 0 in the concentration field equation system (eq S-2 in the Supporting Information). Importantly, if a similar procedure is followed but with a radial convective contribution that is calculated first followed by the evaluation of the axial contribution, consistent results are obtained. This commutativity, in addition to the fact that by construction the sum of all the contributions gives the expected current, increases the reliability of the method. As seen in Figure 3c, the radial convection mostly tends to decrease the measured current. This comes from the fact that the radial convection occurs in the direction opposite to the diffusion (i.e., out of the center), so that the overall mass transport to the electrode decreases. For nontilted microelectrodes (0°), the comparison between parts b and c of Figure 3 shows that the two convective contributions have opposite effects and similar amplitudes so that they tend to cancel out. The contribution that is mainly responsible for the departure from steady state is then the transient diffusion for L > 2 as presented Figure 3a. At smaller distances (L < 2), the occurrence of each contribution’s maxima is important. The maxima of the transient diffusion (Lmax = 1.1) and axial convection (Lmax = 1.7) contributions are reached at larger distances than that of the radial convection contribution (Lmax = 0.6). Thus at small microelectrode-substrate distances, the radial convection contribution may become the dominant factor, leading to an overall current that is smaller than that obtained at steady state. This is what had been observed experimentally and theoretically in Figure 1 for L < 1 at 5 μm/s. For longer distances or higher velocities, the transient diffusion and axial convection dominate, which leads to a positive departure from the steady state current. For misaligned microelectrodes (2.3°), Figure 3a,b demonstrates that the tilt angle has no influence on the transient diffusion or axial convection. However, the radial convection is highly influenced by a tilt in the approach, as shown Figure 3c. At small microelectrode to substrate distances, the radial convection contribution tends to be significantly less negative. This explains the results presented in Figure 3: the current measured with the 2.3° beveled electrode, despite the very small change in geometry of the microelectrode, has a very different radial convection contribution. It is larger, leading to an overall current that is larger. This enhanced impact of the tilt on the radial convection contribution can be explained as follows. If during the approach the surface of the microdisk is perfectly parallel to the substrate, then the source of the radial convective flow is the center of the microelectrode.23 This flow tends then to push the reactants away from the active surface, leading to a negative contribution as observed Figure 3c. However, in the case of a tilted approach, the source of the radial convective flow is no longer the center of the microelectrode, but the position where the distance between the microelectrode and the substrate is the smallest. A part of the lateral flow goes then from this point in the direction of the active part of the probe. This flow carries reactive species that may then react and positively contribute to the current. In fact, the high impact of the microelectrode substrate misalignment is similar to the previously mentioned importance of a well centered active part within the insulating sheet.23 To sum up, a radial flow is very sensitive to any geometric default of the microelectrode and to any topological feature of the substrate. As such, a perfect axisymmetric approach should be seen as a

Figure 3. Contributions to feedback currents IN: (a) transient diffusion, (b) axial convection, and (c) radial convection. The impact on the current of each contribution is presented for a microelectrode of RG = 10 having a 0° tilt (●) and a 2.3° tilt (▽), for Pe = 0.3.

have been calculated using RG = 10 and Pe = 0.3. This Pe value corresponds to a 10 μm diameter microelectrode approached at 23 μm/s in a FcCH2OH solution (D = 7.8 × 10−6 cm2/s). To isolate the transient diffusion contribution to the current, convection effects were removed by solving the equation system for the concentration field (eqs S-2−S-9 in the Supporting Information) with a velocity field equal to 0 (V⃗ = 0 in eq S-2 in the Supporting Information). Figure 3a demonstrates that transient diffusion tends to increase the feedback current relative to steady state conditions. There are more reactive species in the vicinity of the active part of the microelectrode because the consumption reaction has occurred during a smaller amount of time. In order to evaluate the convection contributions, a two-step procedure has been followed. Importantly, the equation determining the velocity field does not contain concentration dependent variables allowing one to evaluate the fluid movement independently of the concentration. First, an approach curve is calculated by solving the complete equation system for the velocity field (Eqs S-10−S-17 in the Supporting Information). Then, to evaluate the axial contribution, the axial convective term in the diffusion equation is injected: in eq S-2 in the Supporting Information, the radial component of V⃗ is set to 0. The axial convective contribution is then given by the difference of this curve with the one obtained for transient diffusion (Figure 3b). This contribution also tends to increase the current, as the axial fluid flow brings additional reactive species to the active part of the electrode. Finally, the radial convective contribution is given by the difference between the approach curve calculated using the 3535



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curve may be obtained for velocities 3 times higher with RG = 2 than with RG = 20: for rT = 3 μm (and D = 7.8 × 10−6 cm2/s), it is equal to 2.6 μm/s for RG = 2 and to 0.8 μm/s for RG = 20. Finally, the maximal approach velocity can be analytically expressed as a function of D, rT, and RG:

unique situation where the radial flow exactly comes from the center of the microelectrode. In practice, this situation is very difficult to achieve, as observed in Figure 1, and a quantitative interpretation of the experimental data recorded at high velocity and small distances is not possible without a very precise control of the geometry of the configuration. Maximal Approach Velocities for Steady State Measurements. There is a maximum velocity at which one can move the microelectrode near the substrate and still retain the ability to quantitatively extract information using steady state developed models. This can be useful, for example, in a negative feedback situation, for the evaluation of the microelectrode substrate distance or for the local characterization of the substrate’s reactivity using an available analytical approximation.47 Figure 4 shows the approach velocity leading to a

vdisp,2% =

D RG r T 115 + 22RG1.9

(3)

Equation 3 proposes an expression for the optimum approach velocity: lower velocities would increase the analysis time, while higher velocities would lead to significant deviations from the steady state behavior. It is accurate for RGs ranging from 2 to 30. Equation 3 has been established for negative feedback using results such as those presented Figure 4a. Figure 4b presents the maximal approach velocity as a function of the kinetics of regeneration of the mediator (an irreversible first order has been considered). Results are presented for different RG, rT = 2 μm, and D = 7.8 × 10−6 cm2/s. This figure shows that the maximal approach velocity strongly increases with the reactivity at the substrate. This is in accordance with a previous study that has observed a smaller influence of the approach velocity on the positive feedback than on the negative feedback.39 As such, in the case of unknown kinetics at the substrate, a sufficient condition for a guaranteed less than 2% deviation from the steady state is obtained considering the results for the negative feedback. Equation 3 can then be applied to substrates of any reactivity, with a guaranteed accuracy of at least 2%.

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CONCLUSIONS We have investigated experimentally and theoretically the combined effects of diffusion and convection on a moving microdisk electrode during feedback experiment acquired at variable velocities (0.3−50 μm/s). The effects of microelectrode alignment are discussed in depth. From this analysis, a ready-to-use expression is provided to rapidly identify the maximal approach velocity for steady state measurements as a function of microelectrode geometry and the diffusion coefficient of the redox mediator. In turn, this allows one to maximize the approach velocity while maintaining the ability to quantitatively interpret the approach curve. The next logical step to this study would be the incorporation of a substrate having topological heterogeneities.

Figure 4. Approach velocity for a 2% deviation from steady state conditions, for D = 7.8 × 10−6 cm2/s. (a) For the negative feedback (kcin = 0), as a function of the microelectrode radius rT. (b) As a function of the kinetics constant of mediator regeneration at the substrate, for rT = 2 μm. ■, RG = 2; ○, RG = 10; ▲, RG = 20.

maximal 2% deviation from the steady state measurement, as a function of rT, for different RG and D = 7.8 × 10−6 cm2/s. The 2% deviation from steady state conditions is a tolerance level that is representative of the normal experimental error associated with SECM measurements. Practically, the 2% threshold was verified at every point over the entire distance of the calculated approach curve acquired at increasing velocities and for a given set of rT and RG. If a single current value exceeded (in the positive or negative direction) the 2% tolerance level, the maximum velocity was reached. In all cases, the observed maximal deviation was negative, coming from a dominant radial contribution. It must be mentioned that for the same parameters, at this maximum velocity, a tilt in the approach would lead to a smaller deviation than 2% because the radial contribution would be smaller, as previously investigated. As shown in Figure 4, the maximal approach velocity is inversely proportional to the radius of the microelectrode: small microelectrodes can be moved much faster than large ones. This comes from the expression of Pe (Pe = rT vdisp/D). For the same reason, the maximal approach velocity is proportional to D. Concerning RG, the maximal approach velocities significantly decreases with RG. For example, a steady-state approach

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ASSOCIATED CONTENT

S Supporting Information *

Additional information as noted in text. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Address: Professor Janine Mauzeroll, Chemistry Department, McGill University, 3420 University Street, Montréal, QC, Canada, H3A2A7. Phone: 514-398-3898. Fax: 514-398-8254. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Canadian Foundation for Innovative (CFI) for their financial support. Laurence Danis is acknowledged for technical assistance. 3536



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