Diffuse Layer Effect on Electron-Transfer Kinetics Measured by

Mar 13, 2017 - Recent theoretical and experimental studies revealed strong effects of the electrical double layer (EDL) on mass transfer at nanometer-...
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Diffuse Layer Effect on Electron-Transfer Kinetics Measured by Scanning Electrochemical Microscopy (SECM) Je Hyun Bae,† Yun Yu,†,‡ and Michael V. Mirkin*,†,‡ †

Department of Chemistry and Biochemistry, Queens College, Flushing, New York 11367, United States The Graduate Center of CUNY, New York, New York 10016, United States

‡

S Supporting Information *

ABSTRACT: Recent theoretical and experimental studies revealed strong effects of the electrical double layer (EDL) on mass transfer at nanometer-sized electrodes and in electrochemical nanogaps. Although the EDL effect is much stronger in weakly supported media, it can significantly influence the kinetics of electron-transfer processes involving multicharged ionic redox species, even at high concentrations of supporting electrolyte. We measured the kinetics of Fe(CN)64− oxidation in 1 M KCl solution at the Pt nanoelectrode used as a tip in the scanning electrochemical microscope. The apparent standard rate constant values extracted from tip voltammograms without double-layer correction increased markedly with the decreasing separation distance between the tip and substrate electrodes. The same steady-state voltammograms were fitted to the theory including the EDL effect and yielded the rate constant essentially independent of the separation distance.

T

recently measured with the ferrocenylmethyltrimethylammonium (FcTMA+/2+) redox mediator in 5 mM KCl could only be fitted to the theory using extremely high standard rate constant values (k0 ≥ 100 cm/s) indicative of a very strong EDL effect.13 To accurately model such a system, one needs the exact values of the compact layer thickness, PZC, and dielectric constant within the double layer, which are not currently available. We used the SECM to investigate the oxidation of Fe(CN)64− in 1 M KCl, that is, a relatively slow ET reaction whose kinetic parameters can be easily measured at not very small nanoelectrodes and the EDL effect on the k0 is moderately strong. To increase the reliability of the measured k0, we characterized the tip geometry by the atomic force microscopy (AFM) to ensure that the Pt surface was not recessed into glass26 and used water with a low level of organic contaminants (TOC ≤ 1 ppb) that can significantly affect rapid heterogeneous ET rates.22 In Figure 1A, a 130 nm radius Pt disk electrode characterized by the AFM and voltammetry (Supporting Information) was used as an SECM tip to approach a flat macroscopic Au film substrate. The experimental current versus distance curve (black circles in Figure 1A) fits well the conventional SECM theory for diffusion-controlled positive feedback (solid red curve; eq 1 in ref 27). The same experimental curve fits well the blue dashed curve generated by numerical simulations taking into account the EDL effect (Supporting Information). This result is different from that reported in ref 13, where the

he effects of the electrical double layer (EDL) on heterogeneous electron-transfer (ET) kinetics through the changes in concentrations of the ionic redox species at the electrode surface and the potential driving the ET reaction (Frumkin correction) were postulated several decades ago.1 Strong EDL effects on the shape of voltammograms at nanometer-sized electrodes and in electrochemical nanogaps were predicted theoretically and observed experimentally.2−14 However, the evidence of double-layer effects on electrode kinetics reported to date is scarce because of experimental difficulties in measuring the rates of rapid outer-sphere ET reactions and the uncertainties in EDL parameter values required for predicting these effects theoretically.4,15,16 In recent kinetic studies at nanoelectrodes,17−25 the double-layer effects have not been taken into account. The EDL effect should be most significant for ionic redox species bearing multiple charges whose formal potential (E0′) is far from the electrode potential of zero charge (PZC). Its magnitude is expected to increase with decreasing electrolyte concentration, nanoelectrode radius (a), and nanogap thickness (or tip/substrate separation distance in scanning electrochemical microscopy (SECM), d). Most redox species employed in previous SECM and nanogap kinetic studies (e.g., ferrocene, ferrocenemethanol, TCNQ, and tetrathiafulvalene) were either neutral or single-charged, and the standard potential of the multicharged Ru(NH3)63/2+ couple is not very far from the PZC of Pt in KCl solution.12 The rate constant values measured for these species in the presence of excess supporting electrolyte (≥0.1 M) were essentially independent of a and d, thus pointing to the negligible EDL effect.18,19,23 By contrast, the voltammograms and SECM approach curves © XXXX American Chemical Society

Received: January 21, 2017 Accepted: March 8, 2017

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DOI: 10.1021/acs.jpclett.7b00161 J. Phys. Chem. Lett. 2017, 8, 1338−1342

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The Journal of Physical Chemistry Letters

Software was used for curve fitting.) Unlike the transfer coefficient value (α = 0.42 ± 0.02), which was similar for all fitted voltammograms and very close to the value found recently for the same ET reaction using a different technique (0.44 ± 0.0225), the k0 value increased significantly with decreasing separation distance. While the k0 = 1.02 cm/s measured at the tip positioned far away from the substrate is within the range of values reported in ref 25 (0.68 to 1.05 cm/s; these values were extracted from steady-state voltammograms recorded in the bulk solution that contained both oxidized and reduced forms of redox species and 1 M KCl), much larger rate constants were found at shorter d. This trend is not related to the increase in the mass-transfer coefficient with decreasing d because the measured ET kinetics are far from the diffusion limit. The dimensionless kinetic parameter λ = 1.97 (λ = k0 a/D, where D = 6.7 × 10−6 cm2/s is the diffusion coefficient of ferrocyanide25) measured in the bulk solution is much lower than the reversibility limit of 10,15 and the process is even further from the Nernstian regime at shorter d. It was noticed previously25,29 that the lack of the unique fit between the theoretical and experimental quasi-reversible voltammograms (i.e., the possibility to fit an experimental curve to the theory using different combinations of E°′, k0, and α) may result in significant uncertainties in the extracted kinetic parameters. However, the fit uncertainty is not a major issue here because of the very small variations of α and E°′ (227 ± 3 mV) in Table 1. Similar results were obtained with different tip electrodes (Figure S2 and Table S1 in the Supporting Information). To check the possibility that the increase in the apparent k0 value at shorter d is due to the EDL effect, the voltammograms of Fe(CN)64− oxidation at the disk nanoelectrode (Figure 2; curve 1, solid line) and in the SECM nanogap (curve 2, solid line) were simulated by solving the Nernst−Planck and Poisson equations using a commercial simulation package (COMSOL Multiphysics 5.2a; Supporting Information). Comparing these curves to the voltammograms calculated for the same process without taking the double-layer effect into account (the dotted lines in Figure 2A18,28), one can see that the EDL effect on the ET involving multicharged ions (e.g., Fe(CN)64‑/3‑) is expected to be significant even for a concentration of supporting electrolyte as high as 1 M, especially at a short tip/substrate separation distance (e.g., 65 nm in curve 2). By contrast, the EDL effect should be negligible for the same ET reaction occurring at the 5 μm radius electrode (Figure S3 in Supporting Information). The approximate values of several EDL parameters used in our simulations were taken from refs 9−12. Specifically, the PZC for the polycrystalline Pt in KCl was taken as 0 V versus Ag/AgCl based on the −50 ± 50 mV versus Ag/AgCl range suggested in ref 12. The 0 V PZC is also close to the previously reported value of +40 mV versus Ag/AgCl.30 The electron transfer is assumed to occur with the redox species located at the outer Helmholtz plane whose coordinate corresponds to the thickness of the compact layer, 0.6 nm (ε = 6 within this layer).10,12 Because ES = 0 V in Figure 2 (and in our experiments) is equal to the PZC value, the concentrations of both Fe(CN)64− (Figure 2B) and Fe(CN)63− (Figure 2C) at the substrate surface (z = 65 nm) computed with (solid curves) and without (dotted curves) considering the EDL are not very different. By contrast, the ET = 0.4 V is more positive than PZC, resulting in significant accumulation of both anionic species at the tip. Consequently, the simulations including the EDL effect produced the steady-state voltammograms (solid curves in

Figure 1. Approach curves (A) and steady-state voltammograms obtained at different tip/substrate separation distances (B). Solution contained 5 mM Fe(CN)64− and 1 M KCl. The tip current is normalized by the diffusion limiting current in the bulk solution, iT,∞ = 174 pA. a = 130 nm; RG = 8; ES = 0 V. (A) ET = 0.4 V. The experimental data (black circles) were fitted to the theory for pure positive feedback (red line) and simulated approach curve (blue dashed line) that included EDL effects on mass transfer. (B) Experimental (symbols) and theoretical (solid lines) voltammograms correspond to d, nm = 61 (1), 65 (2), 88 (3), 126 (4), 186 nm (5), and ∞ (6). v = 50 mV/s.

approach curves simulated with and without EDL effect were substantially different. Figure 1B shows a family of voltammograms of the Fe(CN)64− oxidation obtained with the same Pt tip positioned at different distances from the conductive Au film substrate. (The d values were found from the approach curve in Figure 1A.) The experimental voltammograms (symbols in Figure 1B) were fitted to theoretical curves (solid lines) calculated from the equation for quasi-reversible tip voltammograms (eq 3 in ref 18) that does not include EDL effects. When d/a → ∞, the aforementioned equation is reduced to the Oldham−Zoski equation28 for a steady-state voltammogram at the inlaid disk electrode, which was used to fit curve 6 in Figure 1B. The kinetic parameters and E0′ values extracted from the fit are summarized in Table 1. (TableCurve 2D, v. 5.01, Systat Table 1. Kinetic Parameters of the Oxidation of 5 mM Fe(CN)64− at 130 nm Radius Pt Nanoelectrode in 1 M KCl d (nm)

k0 (cm/s)

α

E0′ (V)

λ

∞ 186 126 88 65 61

1.02 1.27 1.46 1.64 1.83 1.85

0.40 0.40 0.40 0.44 0.44 0.44

0.226 0.224 0.227 0.228 0.228 0.229

1.97 2.46 2.84 3.18 3.55 3.58 1339

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Figure 2. EDL effect on nanoelectrode voltammograms in the bulk solution and in the SECM nanogap. Solid and dotted lines were computed with and without the EDL effect taken into account, respectively. k0 = 0.5 cm/s; E0′ = 0.226 V; α = 0.44. (A) Simulated voltammograms of 5 mM Fe(CN)64− in 1 M KCl solution at a 130 nm radius tip (1) in the bulk solution and (2) at d = 65 nm from conductive substrate. v = 50 mV/s. (B,C) Concentration profiles of Fe(CN)64− and Fe(CN)63− in the nanogap at the center of the tip electrode (r = 0; Figure S5). ET = 0.4 V; ES = 0 V.

very small within the entire range of d values. The k0 values in Table 2 are lower than in Table 1, but the most important difference is that after taking into account the double-layer effect, the standard rate constant (k0 = 0.45 ± 0.05 cm/s) became essentially independent of the nanogap thickness. Although it was possible to fit all experimental voltammograms in Figure 3 to the theory using very similar values of thermodynamic and kinetic parameters, one should notice that the employed model is approximate. In addition to uncertainties in the PZC and several other parameters (see above), the surface roughness of Pt and possible effect of glass surface charge on the mass/charge transfer at the nanoelectrode were not taken into account. Another factor not included in our analysis is the recently suggested effect of adsorption of the redox mediator on the electrode or glass surface in the nanogap cell.31 However, the degree of adsorption of Fe(CN)63− on Pt is relatively low,32 and these anionic species are not supposed to adsorb on the negatively charged glass surface. The Butler− Volmer equation was used instead of Marcus theory because the reorganization energy could not be evaluated from our voltammograms obtained within the narrow potential range and at the same temperature. Because most kinetic information is contained in the middle portion of the steady-state voltammogram corresponding to E°′ ± ∼50 mV,33 this approximation should be sufficiently accurate for such a narrow potential range and the α values close to 0.5. In 1 M KCl, the potential drop within the diffuse layer is very small (only ∼8 mV for ET = 250 mV; Figure S4) and practically independent of the separation distance. (Three potential profiles in Figure S4 computed for different d values are indistinguishable.) With the high electrolyte concentration, EDL affects k0 primarily through the concentration of redox species. This is the reason why the rate constants measured previously by SECM with excess electrolyte for neutral/singlecharged redox species and those with the standard potential close to the PZC were essentially independent of d and showed no signs of the EDL effect. In conclusion, the effective standard rate constant of the Fe(CN)64− oxidation extracted from steady-state SECM voltammograms at a Pt nanoelectrode increased significantly with decreasing tip/substrate separation distance. By contrast, the k0 value essentially independent of d was obtained by fitting the same experimental voltammograms to the theory that included the EDL effect on ET kinetics. The combination of relatively slow k0 of Fe(CN)64− oxidation that could be confidently measured at a relatively large (e.g., a = 130 nm) nanoelectrode with the high ionic charge and the formal

Figure, 2A) that appear to be more reversible than the corresponding curves calculated with the same parameter values and no EDL effect (dotted curves in Figure 2A). This difference suggests that fitting the same experimental voltammogram to the theory including the EDL effect should yield a lower k0 for Fe(CN)6 3−/4− than that obtained without double-layer correction. As expected from previous publications,9−13 the SECM/nanogap voltammograms (red curves in Figure 2A) are more strongly affected by EDL than those obtained at the same tip electrode in the bulk solution (black curves in Figure 2A). In Figure 3, the same experimental voltammograms as in Figure 1B are fitted to the theoretical curves generated by

Figure 3. Experimental (symbols) steady-state voltammograms obtained at different separation distances between the 130 nm Pt tip and Au film substrate fitted to the simulated curves (sold lines). For parameters, see Figure 1.

finite-element simulations including EDL (Supporting Information). The kinetic parameters extracted from these voltammograms are summarized in Table 2. Similar to Table 1, the variations in α (0.47 ± 0.03) and E°′ (224 ± 3 mV) are Table 2. Kinetic Parameters of Fe(CN)64− Oxidation at a 130 nm Pt Electrode Corrected for the EDL Effect d (nm)

k0 (cm/s)

α

E0′(V)

∞ 535 186 126 88 65 61

0.40 0.45 0.48 0.45 0.45 0.50 0.48

0.44 0.44 0.44 0.44 0.44 0.5 0.5

0.227 0.227 0.223 0.224 0.223 0.220 0.220 1340

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potential significantly different from the PZC of Pt allowed us to detect the EDL effect on ET kinetics in 1 M KCl. This effect was not evident in the previous SECM/nanogap ET experiments at nanoelectrodes with a high concentration of supporting electrolyte.18,19,21,23

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.7b00161. Experimental methods, characterization of the SECM tip, additional experimental and simulated steady-state tip voltammograms, simulated potential profiles, diffusion problem formulation, and the COMSOL model report. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: 718-997-4111. Fax: 718997-5531. ORCID

Michael V. Mirkin: 0000-0002-3424-5810 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The support of this work by the National Science Foundation (CHE-1300158) is gratefully acknowledged. REFERENCES

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DOI: 10.1021/acs.jpclett.7b00161 J. Phys. Chem. Lett. 2017, 8, 1338−1342

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