Quantitative Electroanalysis in Ionic Liquids Using Scanning Electrochemical Cell Microscopy

Abstract

Steady-state voltammetry of the redox mediator ferrocene in the room temperature ionic liquid, 1-ethyl-3-methylimidazolium tetrafluoroborate was carried out using scanning electrochemical cell microscopy (SECCM) on a glassy carbon substrate. The measured linear sweep voltammograms (LSVs) were analyzed using recently developed analytical expressions, and validated using numerical modeling, to extract the diffusion coefficient, D, and heterogeneous rate constant, k ⁰, where only the pipet half angle and pipet radius, measured using electron microscopy, were needed to determine the kinetic and transport parameters. Sufficient data were collected to quantify these parameters using statistical analysis providing values for D of 4.1 × 10^–7 cm² s^–1, and k ⁰ of 1.0 × 10^–2 cm s^–1, which were in good agreement with literature values. Through the use of several different pipet diameters, it was possible to adjust the rate of mass transport of ferrocene, and it was shown that Koutecký–Levich analysis could be used to extract the kinetic current using SECCM, providing a value of k ⁰ of 1.0 × 10^–2 cm s^–1, matching the results obtained using the analytical expression. Finally, individual LSVs exhibiting ultralow currents in the femtoampere and picoampere range were successfully fit using the analytical expression to map k ⁰ across a carbon surface.

Introduction

Room temperature ionic liquids (RTILs) are electrolytes composed entirely of organic cations and inorganic or organic anions that form a liquid at or near room temperature. They exhibit wide potential windows, low vapor pressures, and chemical tunability, motivating their development for a variety of electrochemical applications such as charge storage and electrodeposition. − An ongoing challenge in the electrochemical analysis of RTILs arises from their inherently high viscosities, which limit mass transport and decrease the diffusivity of electroactive species. Although RTILs consist entirely of ions, their elevated viscosity can reduce ionic conductivity and redox mediator diffusivity, resulting in non-negligible iR drops that can complicate the analysis of electrochemical measurements. One strategy to overcome these limitations is the use of microelectrodes. Their reduced dimensions enhance the rate of mass transport of redox species through radial diffusion, and the correspondingly small currents minimize iR effects, allowing for more reliable measurements. While microelectrodes offer significant advantages for electroanalysis in room-temperature ionic liquids, their fabrication is typically restricted to noble metals or carbon. However, as RTILs are increasingly employed in electrocatalysis and battery systems that use diverse and often heterogeneous substrates, there is a growing need for new methodologies capable of measuring transport and kinetic parameters on a wide range of surfaces.

Scanning electrochemical cell microscopy (SECCM), uses a glass pipet filled with an electrolyte to form a meniscus confined electrochemical cell, where the electrode dimensions are determined by the droplet contact area with the working electrode. − This droplet-based configuration requires only minimal solvent volumes, making SECCM valuable for studies in RTILs, where electrolytes are often expensive. SECCM offers additional advantages for electrochemical studies in ionic liquids, including high rates of mass transport of reactants to the electrode surface and the measurement of small currents to minimize iR effects. In addition, the probe can be positioned over virtually any surface, facilitating measurements of complex and heterogeneous substrates. As a consequence, SECCM has been used to map an array of electrochemical processes across a multitude of substrate surfaces in RTILs including (photo)­electrocatalytic reactions at platinum electrodes and conjugated polymers, battery electrode materials, as well as ultrasensitive analytical measurements such as single molecule electrochemical detection.

A common practice in the quantitative analysis of SECCM data is the use of finite element modeling to account for the quasi-radial mass-transport that depends on the geometry of the pipet. While this is a useful approach for analyzing individual voltametric measurements such as linear sweep voltammograms (LSV) and cyclic voltammograms (CV), it is not amenable to analyzing large data sets. For example, in the hopping mode operation of SECCM, the droplet cell is repeatedly approached to different locations across a substrate surface, tens, hundreds or even thousands of times, where at each location an individual measurement, such as an LSV, is carried out. This has enabled remarkable advances in visualizing the flux of electroactive species across heterogeneous substrate surfaces, including the generation of potential dependent electrochemical movies. At the same time, these large data sets are rich in information that could be further analyzed using analytical expressions to rapidly fit individual measurements to extract kinetic and transport parameters. While analytical expressions have been widely applied to analyze the steady state response of microelectrodes to determine D, k ⁰, n the number of electrons transferred, and α the charge transfer coefficient, , they were only recently developed to analyze voltammograms obtained using SECCM and have not yet been applied to experimental data.

In this work, we carry out steady state voltammetry measurements of ferrocene in the RTIL 1-ethyl-3-methylimidazolium tetrafluoroborate [EMIM]­[BF₄], which was selected as a model system as its low vapor pressure and moderate viscosity enable stable droplet formation to carry out electroanalytical measurements under well-defined conditions. The hopping mode of SECCM was used to acquire LSVs across a glassy carbon substrate using four different pipet sizes and the results were analyzed using the recently developed analytical expressions to extract transport and kinetic parameters. While good agreement was found across all pipet sizes for the determination of k ⁰, there was a larger spread in the values for the determination of D, that was attributed to a pipet geometry that may not be perfectly conical. The use of four different pipet geometries enabled the rate of mass transport to be systematically adjusted, enabling Koutecký–Levich analysis for the determination of k ⁰ and α, with the results matching those obtained using the analytical fitting procedure. Finally, individual LSVs were fit using the analytical equations, enabling LSVs in the femtoampere range to be analyzed with high fidelity, leading to the generation of electrochemical maps of k ⁰. The results presented here demonstrate that voltammograms measured using SECCM can be analyzed using complementary steady-state approaches that show good agreement in the determination of kinetic parameters. This work presents the integration of SECCM with analytical modeling and offers a new route to quantify charge-transfer and diffusion processes in RTILs, opening up new opportunities for mapping heterogeneous substrate surfaces.

Experimental Section

Chemical Reagents and Electrode Materials

1-Ethyl-3-methylimidazolium tetrafluoroborate >98% [EMIM]­[BF₄] and ferrocene 98% (C₅H₅)₂Fe were purchased from Io.li.tec GmbH and Sigma-Aldrich, respectively. A glassy carbon substrate was used as a working electrode, and a silver wire served as a quasi-reference counter electrode (QRCE). The surface of the glassy carbon electrode was sequentially polished using monocrystalline diamond suspensions with particle sizes of 3.0, 1.0, 0.5, and 0.25 μm. Following each polishing step, the electrode was sonicated for 1 min in a 1:1 ethanol–water solution and subsequently for 5 min in deionized water. Finally, the electrode was dried under argon before use. The QRCE was prepared by cutting approximately 10 cm of high-purity silver wire. The wire was lightly polished using a polishing pad, rinsed with a 1:1 ethanol–water solution, and then dried before use. Pipets varying in diameter (220 nm, 270 nm, 510 and 760 nm) were fabricated using quartz capillaries (0.8 mm ID x 1.00 mm OD VitroCom) and a laser puller (P2000, Sutter instrument). Pulling parameters are available in the Supporting Information (Section S1). A JEOL JSM-IT800 scanning electron microscope was used to characterize the geometry of the pulled pipets. The distribution and arrangement of the SECCM droplet footprints on the substrate surface were visualized using an optical microscope (Olympus DSX1000).

Electrochemical Measurements with Scanning Electrochemical Cell Microscopy (SECCM)

Each pipet was filled with an electrolyte solution containing [EMIM]­[BF₄] with 2 mM ferrocene. An Ag wire quasi-reference counter electrode was located in the pipets to form a local electrochemical cell in contact with the glassy carbon electrode substrate. The pipet positioning, localized electrochemical measurements, and data collection were conducted using a HEKA ElProScan scanning electrochemical microscope. The voltammetric hopping mode of SECCM was used to carry out linear sweep voltammograms (LSVs) for the oxidation of ferrocene at each landing site across the glassy carbon electrode surface with a scan rate of 100 mV s^–1. The total scanned area was 50 μm × 50 μm, with 25 data points collected for each pipet size.

Finite Element Modeling

SECCM steady state voltammograms for ferrocene oxidation in [EMIM]­[BF₄] using a nanopipette were simulated using a two-dimensional axisymmetric model in COMSOL Multiphysics v5.4, based on finite element analysis. Additional simulation details are provided in the Supporting Information.

Results and Discussion

Steady-State Voltammetry of Ferrocene in [EMIM]­[BF₄]

Linear sweep voltammetry was carried out using the hopping mode of SECCM across a glassy carbon substrate using 2 mM ferrocene as a redox mediator in the RTIL 1-ethyl-3-methylimidazolium tetrafluoroborate [EMIM]­[BF₄]. Ferrocene was used as a redox mediator, as it shows a well-defined redox potential across a variety of organic solvents, as well as room-temperature ionic liquids (RTILs), making it widely used as an internal standard in nonaqueous electrochemistry. − A challenge in carrying out voltametric measurements in RTILs is obtaining a steady-state response. Often, peak-shaped responses, characteristic of a time-dependent response are obtained at higher scan rates. To balance a steady-state response and the throughput of the hopping mode operation of SECCM, a series of cyclic voltammograms were carried out between 5 mV s^–1 and 100 mV s^–1 for a 510 nm pipet diameter (Figures S1 and S2). LSVs recorded for all scan rates in the positive scan direction showed a well-defined plateau, as well as a similar waveshape and limiting current. To optimize throughput, a scan rate of 100 mV s^–1 was used for all measurements and analysis. Specifically, the pipet was approached at a potential of −0.6 V, then potential was swept in a positive direction to +0.6 V until the tip was retracted from the surface and moved to a new location. Figure A presents an average LSV (solid black line) based on 25 individual measurements (solid gray lines) using the same pipet at different locations on a glassy carbon substrate. Specifically, a pipet with a radius (r _p) of 380 nm was used and showed a stable limiting current value of 1.58 pA and standard deviation of 0.072 pA. Similar to microelectrodes, the limiting current depends on the redox mediator concentration, diffusion coefficient and electrode area. In addition, for SECCM measurements, the limiting current depends on the pipet geometry, including the pipet radius and the pipet half angle (γ), meniscus height (h), and droplet wetting radius (r _a) formed with the working electrode (Figure B). Both the pipet radius and half angle can be determined from electron microscopy measurements (Figure C). The droplet contact area can, in some cases, be determined ex situ using optical and/or electron microscopy measurements. Optical microscopy measurements were used as a qualitative measurement to visualize the droplet across the surface, which showed similar sizes (Figure D). The droplet contact area depends on several factors including the relative humidity, the solvent used, , and the electrode–electrolyte surface energy. , Optimization of these parameters is critical to enable high-fidelity measurements and quantitative analysis. RTILs are ideal solvents for controlling contact area as the low vapor pressure combined with elevated viscosity enable stable droplet formation. It has been shown using AFM and SEM that the droplet footprint for SECCM corresponds closely to pipet diameter. ,, In this work, the droplet diameter during contact with the substrate is taken to be equal to the pipet outer diameter when analyzing the electrochemical data. Comparing the droplet size across the electrode surface for each measurement, it was found that they are nearly identical in size at each location (Figure D). The consistency of the droplet size between individual landing sites is consistent with the small deviation of the limiting current (Figure E) and half-wave potential (Figure F). The reversibility of the ferrocene voltammetry was assessed using the Tomeš criterion (E _3/4 – E _1/4), which for a one electron transfer process, should be 56.4 mV. A value of 62 mV for a pipet radius of 380 nm was found for the Tomeš criterion indicating that the average LSV is slightly quasi-reversible (Table ).

1.

(A) SECCM linear sweep voltammograms (25 independent LSVs) and their average (solid black line) for the oxidation of 2 mM ferrocene in [EMIM]­[BF₄] at a glassy carbon electrode with a pipet tip radius of 380 nm at a scan rate of 100 mV s^–1. (B) Schematic representation of the conical SECCM pipet, indicating the half an gle (γ) and tip radius (r _p). The droplet meniscus is defined by its contact radius (r _a) and height (h). (C) Scanning electron microscopy (SEM) image of the SECCM pipet with r _p = 380 nm. (D) Optical image of the droplet footprint on the glassy carbon surface corresponding to the 25 SECCM measurement sites shown in A. (E) Electrochemical maps of the limiting current (I _lim) obtained from 25 localized linear sweep voltammograms in A at (E – E ^0′ = 0.15 V). (F) Corresponding electrochemical map related to half-wave potential (E _1/2) for the same set of LSVs.

1. Summary of Electrochemical Parameters Measured for Each Pipet Diameter Using SECCM.

r p (nm)	half angle (γ)	I lim (pA)	D (cm2 s–1)	E 1/2 (V)	E 3/4 – E 1/4 (mV)	m (cm s–1)	k 0 (cm s–1)
110	8	0.45	5 × 10–7	0.398	74	0.0062	0.009
135	11	0.64	4.2 × 10–7	0.391	70	0.0058	0.012
255	13	1.32	3.8 × 10–7	0.385	66	0.0034	0.010
380	12	1.58	3.3 × 10–7	0.387	62	0.0018	0.009

Figure A presents LSVs that correspond to four different pipet radii (110, 135, 255, and 380 nm). Each LSV presents the average of 25 independent measurements (solid line) and the corresponding standard deviation (shaded area). Optical images of the surface and SEM images of the pipet are presented in the Supporting Information (Figure S3). Analysis of the average LSVs enabled determination of E _3/4 – E _1/4, E _1/2 and I _lim for each pipet radius (Table ). A slight shift in E _3/4 – E _1/4 with decreasing pipet diameter suggest the shape of the LSVs could be affected by changes in the rates of mass transport. In addition to changes in the geometry of the pipet (diameter and half angle), there are several factors that can influence the position and shape of the LSV. For example, unequal values of the diffusion coefficients of the uncharged form of ferrocene in the reduced state and the charged form of ferrocenium in the oxidized state could cause a shift in the position of the half-wave potential. Rogers et al. previously measured the diffusion coefficient for ferrocene and ferrocenium in a related ionic liquid that had the same anion used here and a slightly different cation, specifically, [BMIM]­[BF₄], and found that the diffusion coefficient of ferrocenium was approximately 30% lower than ferrocene. This could lead to an offset (about 20 mV) that would be constant and independent of tip diameter and contained within the E ^0′ value. Time-dependent effects could affect the wave-shape. However, as shown in Figures S1 and S2, for LSVs carried out in the positive scan direction, a significant effect was not observed. On the other hand, an iR drop would be expected to lead to systematic changes in the shape of the LSV. The resistance of the pipet is determined by the size of the tip opening and the conductivity of the electrolyte. A decreasing pipet diameter would give a larger resistance, and larger iR drop, leading to a broadening of the LSV. Blount et al. developed an analytical equation for evaluating the resistance of pipets based on their geometry

$$R_{\mathrm{s}}=\frac{h}{\kappa \pi r^2}+\frac{1}{\kappa \pi r\tan \gamma }$$ 1

where h is the height of the droplet, which is assumed to be equal to the radius of the pipet, and κ is the electrolyte conductivity. For [EMIM]­[BF₄], the electrolyte conductivity is 1.55 S m^–1, giving a resistance of 3 MΩ to 15 MΩ for tip radii from 380 to 110 nm. Considering a limiting current of 1.62 pA for a 380 nm radius pipet and a limiting current of 0.46 pA for a 110 nm radius pipet, the potential drop would be less than 1 mV in both cases and would not affect the shape of the LSV. This reinforces the benefits of using SECCM for nanoscale measurements in ionic liquids, where iR drops are not significant due to the small currents measured. For these reasons, we suggest that the broadening of the waveshape with decreasing pipet diameter is due to an increase in mass transport. Overall, for each pipet radius, the small value of the standard deviation in the limiting current value, reproducible current waveshape for a given pipet diameter, and consistent droplet size at each individual landing site enable high fidelity steady state voltammetric measurements to be obtained on a glassy carbon substrate using ferrocene as a redox mediator in [EMIM]­[BF₄].

2.

(A) Average SECCM LSVs with standard deviations for the oxidation of 2 mM ferrocene in [EMIM]­[BF₄] on a glassy carbon electrode. Each curve is the average of 25 individual LSVs obtained using pipets with tip radii of 380 nm (black), 255 nm (red), 135 nm (blue), and 110 nm (green) at a scan rate of 100 mV s^–1. (B) Plot of the average limiting current from (A) as a function of an equivalent hemispherical microelectrode geometry. (C) Fit of the average LSVs using eq .

Quantitative Analysis of the Limiting Current and Waveshape

Recently, Anderson and Edwards developed analytical expressions for the evaluation of steady-state LSVs obtained using SECCM where it was shown that the limiting current could be expressed as a combination of an equivalent sized hemisphere electrode and the fraction of its area that is contacted by the droplet at the end of the pipet through the following expression

$$I_{\lim }=2\pi nFCD{R}_{\mathrm{e}\mathrm{q}}(1-\cos \gamma )$$ 2

where n is the number of electrons transferred, F is Faraday’s constant, C is the bulk redox mediator concentration, D is the diffusion coefficient, and R _eq is a geometrical parameter that corresponds to a hemisphere with an equivalent radius that can be defined using the pipet radius and pipet half angle through the expression, R _eq = (r _p/tan γ). The final term (1 – cos γ) represents the fraction of an equivalent size hemisphere electrode surface that is in contact with the droplet of the SECCM pipet. The values for the pipet radius, r _p, and pipet half angle, γ, that make up R _eq, were determined from SEM images enabling the use of eq to calculate the diffusion coefficient, D, for each pipet based on the limiting current from the average LSV (Table ). Diffusion coefficient values, D, between 3.3 × 10^–7 cm² s^–1 and 4.9 × 10^–7 cm² s^–1 were obtained, with an average value of D _avg = 4.1 × 10^–7 ± 0.6 cm² s^–1. While current variations for a given pipet size are minor, a larger variation between D values was obtained between different pipet diameters. The diffusion coefficient is a constant that is independent of the pipet geometry and variations in this value reflects uncertainty in the pipet geometry that affects the limiting current and the value of D extracted. The pipet geometry, pipet diameter and half angle were determined using a representative side-view image obtained using SEM (Figures C and S3). The use of a side-view image assumes that the pipet is perfectly conical. However, this is not always the case, and if the geometry is not perfectly conical, the effective electrode geometry, which is contained within the term R _eq(1 – cos γ) will have some uncertainty as the side-view SEM image could overestimate or underestimate the apparent half angle and radius of the pipet. Figure S4 illustrates the changes in the relative uncertainty for different values of the half angle and pipet radius. Even modest deviations in the assumed half an gle (e.g., 0.5°–1°) can lead to relatively large uncertainties, especially for smaller half angles. This could explain the larger value of the diffusion coefficient for the smallest pipet radius of 110 nm, where the half angle measured was only 8°, compared to the other pipets that had half angles in the range of 11°–13°. For a pipet half angle of this size, even a 1° error can lead to over 20% error in R _eq. For such small pipets, transmission electron microscopy has been used to resolve the inner tip radius and the conical geometry of the pipet to improve quantitative precision for scanning ion conductance microscopy probes, and future work could include this type of analysis of the SECCM probe to improve the precision in the determination of D for an individual pipet. Time-dependent finite element modeling of CVs measured at different scan rates were also carried out (Figure S2) as the analytical equations are based on a steady-state model. As shown in Figure S2, the same value of k ⁰ was used as the steady state model, whereas D was found to be 10% larger for the time-dependent model. Overall, the similarity in the results obtained using the time-dependent model and the analytical model suggest that the use of a steady-state model to analyze the data is acceptable. An alternative approach to extracting the diffusion coefficient is through the relationship between the limiting current measured using SECCM and the value R _eq(1 – cos γ), which considers the specific geometry of the pipet in contact with the electrode surface (Figure B). A linear relationship is observed, as given by eq , and was used to determine the diffusion coefficient, D _fit, using least-squares fitting of the linear plot, giving a value across all pipet measurements of (3.1 ± 0.2) × 10^–7 cm² s^–1. The linear fit of Figure B has a nonzero offset of 0.15 pA, which is slightly larger than the background noise. An intercept of zero is expected based on eq and a positive offset reduces the slope, leading to an underestimation of the diffusion coefficient. Nevertheless, previous reports of measured values of the diffusion coefficient of ferrocene in [EMIM]­[BF₄] were (1.6–3.2) × 10^–7 cm² s^–1 and 5.1 × 10^–7 cm² s^–1, , placing the values reported here within these ranges.

The limiting current can also be used to determine the mass transport coefficient, m, for each pipet diameter

$$m=\frac{I_{\lim }}{nFAC}$$ 3

where A is the droplet contact area, and the other parameters are as defined previously. The average limiting current value was used for I _lim while the outer pipet diameter was used to calculate A, which approximates the droplet contact area to calculate m values (Table ).

Quantitative Analysis of the Waveshape

In addition to the steady-state current, Anderson and Edwards also introduced an analytical expression to evaluate the current as a function of potential to extract k ⁰ through the following equation

$$I=\frac{I_{\lim }{\mathrm{e}}^{\alpha f(E-E^{0^{\prime }})}}{\frac{m}{k^0}+{\mathrm{e}}^{\alpha f(E-E^{0^{\prime }})}+{\mathrm{e}}^{-(1-\alpha )f(E-E^{0^{\prime }})}}$$ 4

where E ^0′ is the formal potential, and f = F/RT, R is the universal gas constant and T is the temperature. Ferrocene is used an internal redox standard and the value of apparent formal potential, E ^0′, used for ferrocene was 0.387 V, which corresponds to the E _1/2 for the 760 nm pipet, which showed a nearly reversible response among the four different pipet geometries used in this work. Figure C presents average LSVs obtained for each pipet diameter and the fit to the data using eq , while the mass transfer coefficient was determined using eq . The only parameter that was adjusted to fit the data was the heterogeneous rate constant, with the constraint that the value of E _3/4 – E _1/4 for the fitted LSV could not be less than the value of the average LSV. The value of the charge transfer coefficient, α, was assumed to be 0.5. Using this approach, k ⁰ was found to be between 0.9 × 10^–2 cm s^–1 and 1.2 × 10^–2 cm s^–1 for the different pipet diameters used as summarized in Table . Reported values of k ⁰ in the literature can vary widely, with solvent viscosity being a primary factor for the observed differences. Previous reports of k ⁰ in the same RTIL, [EMIM]­[BF₄], are 1.2 × 10^–2 cm s^–1 and 1.6 × 10^–2 cm·s^–1, , which closely match our results. Analysis of the average steady-state LSVs using analytical expressions enabled determination of D and k ⁰, which were found to be (4.1 ± 0.4) × 10^–7 cm² s^–1 and (1.0 ± 0.1) × 10^–2 cm s^–1, respectively (Table ). In addition, using eq to determine D across all pipet sizes (Figure B) using linear fitting provided a slightly smaller value of (3.1 ± 0.2) × 10^–7 cm² s^–1.

Koutecký–Levich Analysis

Comparison of the mass transport coefficient and the standard heterogeneous rate constant shows that they are similar in magnitude, consistent with the observed quasi-reversible behavior. This observation is supported by steady-state finite element modeling (Figure A). The geometry for the numerical simulation and further details are provided in the Supporting Information (Section S6). Figure A presents LSVs obtained using three different values of the standard heterogeneous rate constant (k ₁ = 1 cm s^–1, k ₂ = 0.012 cm s^–1, and k ₃ = 0.0055 cm s^–1). The numerical simulations show a Nernstian response for the largest k ⁰ value and a slight broadening with decreasing k ⁰, consistent with the quasi-reversible response for the k ⁰ values measured above. Figure B plots the experimental steady-state LSVs as a current density illustrating the effect of increasing mass transport, which leads to a broadening of the LSVs that becomes more pronounced with decreasing pipet diameter (Figure S5).

3.

(A) Simulated steady-state voltammograms for the oxidation of 2 mM ferrocene in [EMIM]­[BF₄] using COMSOL Multiphysics, illustrating the effect of electron transfer kinetics on wave shape. Curves with E _3/4 – E _1/4 values of 56 mV (black), 64 mV (red), and 72 mV (blue) correspond to increasing kinetic limitations (decreasing standard rate constants, k ⁰). All voltammograms are normalized to their respective mass transport limiting currents. (B) Experimentally obtained average current density LSVs (using pipets of tip radii 110, 135, 255, and 380 nm). (C) Koutecký–Levich plots derived from the LSVs in part B, showing 1/j vs 1/mC at varying overpotentials (E – E ^0′). (D) Linear plot of ln­(1/j _k ) versus E – E ^0′, enabling extraction of the standard rate constant k ⁰ and transfer coefficient α from the intercept and slope, respectively.

Koutecký–Levich analysis is a useful approach to isolate the kinetic component of the current from steady-state voltammograms. It was originally developed for hydrodynamic voltammetric measurements where the rate of mass transport is adjusted by controlling the convective flux toward the working electrode’s surface by varying its rotation rate. Through systematic variation of the mass transport using different rotation rates, a series of steady state voltammograms with different limiting current densities can be obtained and Koutecký–Levich analysis can be used to extract k ⁰. Recently, Kim and Bard, have shown that this analysis can be extended to microelectrodes, whereby the dimensions of several microelectrodes were systematically adjusted to vary the mass transport rates. In an analogous fashion to rotating disk electrode measurements, analysis of the current as a function of mass transport enables determination of kinetic parameters. In the case of a quasi-reversible reaction for a one electron transfer oxidation, it was shown that the inverse of the total current density could be separated into their mass transport and kinetic components in through the following expression

$$\frac{1}{j}=\frac{1}{nFmC}+\frac{1}{nF{k}^{0}C{b}^{\alpha }}$$ 5

where j is the current density, b = e ^{F/RT(E–E 0′)}, and the other variables are as defined previously. The first term on the right-hand side is the mass transport limited contribution, while the second term on the right-hand side represents the kinetic component of the current as a function of potential. Based on the observations above, Koutecký–Levich analysis was carried out using the average LSVs for each pipet diameter. Figure C presents 1/j at a given overpotential, E – E ^0′, as a function of 1/mC, which depends on the pipet geometry. Values of E – E ^0′ ≥ 60 mV and less than potentials corresponding to the limiting current were selected, which extrapolate to small, positive kinetic current density values, 1/j _k , that are free from mass transport effects and depend on the value of E – E ^0′. In addition, eq predicts a slope nearly equal to 1/F for a one electron oxidation of ferrocene. Individual plots (R ² > 0.99) are presented in the Supporting Information (Figure S7) and give values of F from 96,300 C mol^–1 for E – E ^0′ = 0.15 V down to 87,489 C mol^–1 for E – E ^0′ = 0.06 V, which is a change of less than 10% over the entire potential range considered here. Figure D presents the values of ln­(1/j _k ) as a function of E – E ^0′, where extrapolation to zero overpotential enables determination of the exchange current density, j ₀. Through the relationship j ₀ = k ⁰ CFn, the heterogeneous rate constant k ⁰, was found to (0.01 ± 0.001) cm·s^–1. This value is in good agreement with the average value of k ⁰ measured for the different pipet diameters using the analytical expression. Analysis of the slope enabled determination of the transfer coefficient α, which was found to be 0.58. The same results were obtained, with an R ² > 0.99 for all plots, when constraining the slope to 1/F and maintaining the same intercept as obtained in Figure S7 suggesting the shift in F with potential did not introduce significant error into the calculated values of k ⁰ and α.

Analysis of Individual Landing Sites

The magnitude of the current values measured here are in the femto- and picoampere range, where instrumental noise can become a limiting factor when analyzing the waveshape of the individual LSVs. This problem is removed when using the average current from all LSV measurements, which smooths out fluctuations in the current values. In order to analyze the waveshape of the individual LSVs, the data were initially filtered using a Savitzky–Golay filter to reduce the effects of instrumental noise when fitting the data. The filtered data were then fit using eqs and to determine m and k ⁰ at each location for each pipet diameter. Figure A–D present the raw experimental data overlaid with the fit based on eq for an individual LSV for each pipet diameter, along with the residual current, which shows a negligible value across the entire potential range, indicating a good fit between the experimental data and eq despite the instrumental noise, particularly for the smaller pipet sizes. Figure E,F present electrochemical maps for the Tomeš criterion and k ⁰, respectively, at each location for a 380 nm pipet radius. The individual values measured here match closely the average values reported above. Electrochemical maps for the other pipets are presented in the Supporting Information (Figures S8) along with fits for each LSV (Figures S9–S12). Figure G presents histograms of the Tomeš criterion for all pipet diameters, which increase in value with decreasing pipet size, consistent with an increase in the quasi-reversible response with increasing mass transport. Finally, histograms presenting the individual values of k ⁰ for all pipet diameters at each location are presented in Figure H, where most values of k ⁰ fall in the range of 0.5 × 10^–2 cm s^–1 to 3 × 10^–2 cm s^–1. Overall, fitting of the histogram for all LSVs measured across four different pipet diameters, provides a mean value of (0.98 ± 0.3) × 10^–2 cm s^–1, which matches the values obtained using the average response for an individual pipet diameter, Koutecký–Levich analysis, as well as literature values. In this work, a glassy carbon surface was used in [EMIM]­[BF₄], with ferrocene as an outer-sphere redox mediator to minimize the influence of surface heterogeneity on the electrochemical response. This approach enabled the acquisition of data sets using four different pipet sizes, allowing both the average and individual responses to be analyzed and subjected to statistical evaluation as a function of pipet geometry. As the electrochemical mapping measurements demonstrate, a single value of the rate constant was obtained using four different pipets at different substrate locations, which is consistent with ferrocene being an outer-sphere redox mediator. In the future, inner-sphere redox mediators and more complex electrode surfaces could be investigated using SECCM in combination with analytical fitting.

4.

Analytical fit (red line) to a representative voltammogram (black line) selected from 25 individual linear sweep voltammograms (LSVs) for the oxidation of 2 mM ferrocene in [EMIM]­[BF₄] on a glassy carbon electrode at a scan rate of 100 mV s^–1, using a SECCM pipet with tip radii of (A) 380 nm, (B) 255 nm, (C) 135 nm, and (D) 110 nm. Residuals (blue line) from each fit are included to evaluate the fit accuracy. (E,F) Electrochemical maps of the Tomeš criterion and the heterogeneous electron transfer rate constant (k ⁰), derived from 25 independent SECCM measurements using a 380 nm radius pipet. The white regions in the map correspond to locations where fitting analysis were not successful due to external noise. Histograms of Tomeš criterion (G) and k ⁰ (H) collected from 97 total measurements.

Conclusions

In conclusion, LSVs on a glassy carbon surface using four different pipet radii ranging in size from 110 to 380 nm in the RTIL [EMIM]­[BF₄], containing ferrocene as a redox mediator were measured using SECCM. For each pipet diameter, using the hopping mode of SECCM, 25 separate LSVs were obtained providing a statistical average and standard deviation of the current response. Fitting of the averaged voltammograms using recently developed analytical expressions enabled determination of D and k ⁰ values that are in good agreement with literature reports for ferrocene in [EMIM]­[BF₄] using other techniques. The mass-transport coefficient, m, and k ⁰ were found to be of similar magnitude, which was confirmed using finite-element numerical modeling. Moreover, the use of different pipet diameters, enabled the systematic control of the mass transport of ferrocene allowing for Koutecký–Levich analysis to be used to remove the effects of mass transport when determining the heterogeneous rate constant. Recent examples in aqueous solutions have shown that kinetic analysis, including Tafel analysis, can reveal new insights into the intrinsic activity of well-known materials such as platinum as well as new high entropy alloys. , In the future, variations in surface activity could be correlated with crystallographic orientation to map surface kinetics for electrocatalytic reactions in RTILs. This approach could be particularly useful for the kinetic analysis of electrocatalytic materials at the single particle level, , or in combination with hybrid SECM-SECCM probes. ,

New methodology for the accurate determination of k ⁰ and D in ionic liquids is of ongoing importance where these solvent systems continue to be of broad interest due to their wide electrochemical windows, negligible vapor pressure, and tunable properties for electrochemical applications. In this regard, SECCM presents several advantages, including high rates of mass transport that can be challenging to obtain using other methods due to complications from the higher viscosities of ionic liquids. Moreover, SECCM’s droplet-based approach uses minimal solvent volume allowing for reduced sample consumption of often expensive ionic liquids. Finally, the hopping mode of SECCM, enabling high-throughput analysis of electrode surfaces, combined with the recently developed analytical equations enables the generation of spatially resolved maps of k ⁰. While this work focused on ferrocene, an outer-sphere redox species, the approach could be extended to the study of inner-sphere electrocatalytic reactions for the mapping of local variations in k ⁰ at a material’s surface where differences in active sites and electrode inhomogeneities could be visualized.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.analchem.5c03671.

• The Supporting Information includes detailed procedures for pipet fabrication and characterization, additional electrochemical map, SECCM cyclic voltammograms at different scan rates, time-dependent finite element modeling, individual Koutecký–Levich plots, individual LSVs overlaid with analytical expressions, and the finite element modeling with the COMSOL reports (PDF)

• SECCM-steady-state (PDF)

• SECCM-time dependent (PDF)

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

The authors declare no competing financial interest.