Toward More Reliable Measurements of Electron-Transfer Kinetics at

Article pubs.acs.org/ac

Toward More Reliable Measurements of Electron-Transfer Kinetics at Nanoelectrodes: Next Approximation Yun Yu, Tong Sun, and Michael V. Mirkin* Department of Chemistry and Biochemistry, Queens College-CUNY, Flushing, New York 11367, United States The Graduate Center, CUNY, New York, New York 10016, United States S Supporting Information *

ABSTRACT: Steady-state voltammetry at nanoelectrodes and scanning electrochemical microscopy (SECM) have recently been used to measure kinetics of several rapid heterogeneous electron transfer (ET) reactions. One problem with those experiments was that the dependence of the shape of the steady-state voltammogram on kinetic parameters becomes weak when the reaction rate approaches the diffusion limit. The possibility to fit the same experimental voltammogram using different combinations of the standard rate constant, transfer coefficient, and standard potential results in significant uncertainties in extracted parameter values. In this article, the reliability of the kinetic analysis was improved by obtaining steady-state voltammograms with both oxidized and reduced forms of redox species initially present in solution. Additional improvements were attained by characterizing the nanoelectrode geometry with the atomic force microscope and using water with a very low level of organic contaminants (TOC ≤ 1 ppb). This approach was used to re-evaluate the ET rate constants measured for several electroactive species, including ferrocene, ferrocenemethanol, 7,7,8,8-tetracyanoquinodimethane (TCNQ), and ferrocyanide at Pt electrodes. The obtained standard rate constants are higher than the values measured earlier at Pt and Au nanoelectrodes but comparable to those obtained in recent nanogap/SECM experiments.

N

reactions at nanometer-sized Pt16 and Au17 tips. For each ET process, the kinetic parameters were extracted from a number of voltammograms obtained at different tip radii and separation distances. In this way, we hoped to minimize the errors resulting from inaccurate evaluation of a and d values, flawed geometry of a particular tip, imperfect tip/substrate alignment, and other factors that could not be fully controlled in nanoelectrochemical experiments. The obtained results were self-consistent, with the standard rate constant (k0) and transfer coefficient (α) values essentially independent of a and d, and the measured rates were significantly higher that most k0 values previously reported for the same ET processes. More recent results suggest that the data reported in ref 16 should be reevaluated. The imperfections in nanoelectrode geometry (including the recess of the electrode surface into the insulator18,19) may result in major errors in measured ET kinetics. Our ability to characterize the geometry improved significantly after the methodology was developed for AFM imaging of nanoelectrodes.20 The importance of thorough characterization became more apparent since the Amemiya group showed that a nanoelectrode can be easily damaged unless appropriate protection is used to avoid the electrostatic discharge (ESD).21 In this article, we used ESD protection and

umerous attempts to measure kinetics of rapid heterogeneous electron transfer (ET) reactions by various electrochemical techniques have been made during the last several decades.1 A heterogeneous ET rate constant can be measured only if it is smaller than or comparable to the mass-transfer coefficient (m) attainable with the employed electrochemical technique.1,2 The introduction of nanometersized electrodes in 1980s−1990s3−11 has led to a significant increase in the mass-transfer rate attainable under the steadystate conditions and alleviated the problems caused by resistive potential drop in solution and double layer charging current, which affected the reliability of earlier kinetic experiments at larger interfaces.1,12,13 To further increase the mass-transfer rate, a nanoelectrode can be used as a tip in the scanning electrochemical microscope (SECM) operated in a feedback mode and brought close to a conductive substrate (Figure 1A).14 With the tip/substrate separation distance (d) significantly smaller than the tip radius (a), positive SECM feedback produced by fast cycling of the redox mediator between the two working electrodes results in a very high m value. The kinetic parameters of the ET reaction occurring at the tip can be extracted from the steady-state voltammogram that is obtained by sweeping the tip potential (ET) while the substrate potential (ES) is fixed at a constant value corresponding to the diffusion-controlled regeneration of the mediator.15 Using this approach, we have previously measured the kinetics of several rapid outer-sphere ET © XXXX American Chemical Society

Received: August 29, 2016 Accepted: November 7, 2016

A

DOI: 10.1021/acs.analchem.6b03392 Anal. Chem. XXXX, XXX, XXX−XXX

Article

Analytical Chemistry

Figure 1. Schematic representation of the (A) ET reaction in a feedback mode SECM experiment and (B) geometric parameters for the SG/TC mode of the SECM operation.

substrate. This substrate generation/tip collection (SG/TC) setup resulted in negligibly small concentration gradients in the tip proximity (see below) and allowed the “bulk” cO* and cR* values to be varied by changing the ES. In this article, we aim at improving the reliability of nanoelectrochemical kinetic experiments rather than at setting a new record for the fastest measured rate constant. Therefore, we implemented several safeguards to avoid some anticipated pitfalls at the cost of not attaining the highest possible masstransfer rate. These include not using very small nanoelectrodes (a < 15−20 nm) that could not be visualized by AFM and would raise a question about possible deviations from the classical electrochemical theory.25,26 Similarly, the feedback mode of the SECM operation was not used because the geometry of the tip/substrate nanogap is harder to ascertain than that of a single nanoelectrode, and there are additional possibilities of nonclassical behavior27,28 and other experimental issues in such experiments.29,30 The kinetic parameters reported below were obtained from voltammograms that were fitted to

performed AFM imaging to ensure that the electrodes employed in kinetic experiments were properly shaped. A few recent studies indicated that heterogeneous ET kinetics may be faster than those reported in refs 16 and 17. Kim and Bard22 reported k0 = 36 cm/s for the Ru(NH3)63+ reduction at the electrodeposited Pt nanoparticles. The effect of the electrode surface contamination by adsorption of organic impurities on apparent ET rates was investigated, and very fast rate constants were measured in solutions made with highpurity water.23 Although only carbon electrodes were used in ref 23 and no similar issue has been reported for ET at Pt, here we employed a Millipore system equipped with a VOC Pak to decrease the total organic carbon (TOC) in water to ≤1 ppb. Another problem not recognized in previous ET studies is that the shape of a quasi-reversible steady-state voltammogram depends weakly on kinetic parameters. For near-Nernstian processes, the same experimental voltammogram can be fit to the theory using different combinations of kinetic parameters with only minor adjustments of the formal potential (E°′). This issue was revealed in analysis of steady-state voltammograms of ion transfer across the liquid/liquid interface24 whose shape is essentially equivalent to that of quasi-reversible ET voltammograms. In ref 24, the unique fit of the experimental steady-state voltammogram to the theory was obtained by adding transferable ions to both liquid phases and, thus, obtaining two voltammetric waves. A conceptually similar approach to measurements of rapid ET kinetics at nanoelectrodes developed below requires both oxidized (O) and reduced (R) forms of redox species to be simultaneously present in solution. For many redox mediators [e.g., ferrocene (Fc) or ferrocenemethanol (FcMeOH)], one of two forms has to be generated in situ because of its relatively short lifetime in solution. This was done by positioning a nanoelectrode SECM tip at a relatively short distance (d ≈ 2 μm) from the 2 mm diameter Pt disk substrate (Figure 1B). The substrate potential (ES) was adjusted to produce the desired ratio of O and R concentrations (cO*/cR*) near its surface, according to the Nernst equation: ES = E°′ +

c * RT ln O nF cR*

the theory with the dimensionless rate constant (K =

πak0 , 4DO

where DO is the diffusion coefficient of species O) values ≤4, as opposed to the K = 10 reversibility limit used in most previous studies.15,16,23,31 With these safeguards, the k0 values up to ∼15 cm/s could be measured confidently, and we have not tried to re-evaluate the kinetics of Ru(NH3)63/2+ oxidation/reduction at Pt for which a higher k0 value can be expected.16,22

■

EXPERIMENTAL SECTION SECM Setup and Procedures. SECM experiments were carried out using a previously described home-built instrument.32 A Pt disk nanoelectrode was used as an SECM tip, and the reference electrode was an Ag/AgCl (Bioanalytical Systems). The nanoelectrode tip was positioned a few tens of micrometers above the substrate surface with the help of a longdistance video microscope. The tip was then brought closer to the substrate in an automated mode until the monitored tip current changed by 10%. In the negative feedback mode, a bare glass slide was used as an insulating substrate to check the tip geometry. A 2 mm-diameter Pt electrode (CH Instruments) was used as a conductive substrate and a Pt wire served as the counter electrode. The tip/substrate distance scale was established from the approach curve based on positive feedback at the unbiased Pt substrate. The tip voltammograms were obtained at d ≈ 2 μm. The potential sweep began with a 30 s delay after applying the potential to the substrate. All

(1)

where R is the gas constant, T is the temperature, n is the number of transferred electrons, and F is the Faraday constant. The separation distance of ∼2 μm was too long (d ≫ a) for the SECM feedback to contribute to the tip current but very short in comparison to the diffusion layer thickness at a macroscopic B


Article


Figure 2. (A) Anodic (top) and cathodic (bottom) voltammograms of a simple one-step ET at a disk nanoelectrode simulated for different combinations of K, α, and E°′ and (B) corresponding voltammograms calculated for the same reaction with both O and R species simultaneously present in solution. (A) The E and E°′ are related to the same reference potential. (B) The current is normalized by ic,∞ = ia,∞.

experiments were carried out at room temperature (23 ± 2 °C) inside a Faraday cage. AFM Imaging. An XE-120 scanning probe microscope (Park Systems) was employed to obtain AFM images of the nanoelectrodes. PPP-NCHR AFM probes (Nanosensors) were used for noncontact imaging. The procedures for AFM imaging of nanoelectrodes were reported previously.20

of magnitude smaller (e.g., for v = 50 mV/s, a = 50 nm, and D = 1 × 10−5 cm2/s, σ ≈ 10−5), and its value does not affect the shape of simulated voltammograms. For kinetic analysis, the steady-state current was normalized by either the anodic (ia,∞) or the cathodic (ic,∞) diffusion limiting current

■

RESULTS AND DISCUSSION Analysis of Steady-State Voltammograms. Considering a simple, quasi-reversible one-step ET reaction at the disk electrode surface kb

(2)

The forward and heterogeneous rate constants for the reduction and oxidation reactions given by the Butler−Volmer model1 are ⎡ ⎤ F k f = k0 exp⎢ −α (E − E°′)⎥ ⎣ RT ⎦

(3)

⎡ ⎤ F k b = k0 exp⎢(1 − α) (E − E°′)⎥ ⎣ ⎦ RT

(4)

where k is the standard rate constant, α is the transfer coefficient, F is the Faraday constant, E is the electrode potential, and E°′ is the formal potential. With the excess supporting electrolyte present in all our experiments, the migration current is negligible and the time-dependent, twodimensional axisymmetric diffusion problem for a disk-shaped nanoelectrode was formulated in cylindrical coordinates and solved using COMSOL Multiphysics v4.4 (see Figure 1B for simulation geometry and Supporting Information). The electrodes used in this work had the insulating glass radius much larger than that of the conductive metal (RG ≥ 10) and were essentially equivalent to an inlaid disk. The diffusion of the redox molecules at the nanoelectrode reaches a steady-state at a moderate potential sweep rate, v. The time required to attain a steady state is determined by the dimensionless sweep rate33 0

σ=

a 2 Fv 4DO RT

(6)

ic, ∞ = 4FDOcO*a

(7)

The difficulties in extracting a unique set of kinetic parameters from a conventional steady-state voltammogram, consisting of a single anodic or cathodic current wave, are illustrated in Figure 2. In two sets of simulated anodic (upper half) and cathodic (lower half) voltammograms shown in Figure 2A, very similar curves were obtained for completely different K and α values (ranging from 0.4 to 4.0 and from 0.3 to 0.7, respectively) with only minor adjustments of the E°′ (±20 mV). The differences between these curves are within the range of uncertainty in experimental nanoelectrode voltammograms caused by capacitive and background currents. The possibility to fit an experimental quasi-reversible voltammogram to the theory using different combinations of E°′, k0, and α results in significant uncertainties in extracted kinetic parameters. The higher the K value the weaker the dependence of the shape of a conventional steady-state voltammogram on kinetic parameters and the larger the uncertainties in k0 and α values extracted from it. When both O and R forms are present in solution, the steady-state voltammogram (Figure 2B) contains a zero-current point, corresponding to the equilibrium potential Eeq,

kf

O + e− ⇆ R

ia, ∞ = 4FDR c R *a

Eeq = E°′ +

c * RT ln O F cR *

(8)

The E°′ value is exactly defined by eq 8 and is no longer an adjustable parameter in fitting an experimental voltammogram to the theory. The steady-state voltammograms in Figure 2B were simulated for the same K and α values as in Figure 2A, but with both O and R forms present in solution (ia,∞ = ic,∞). The differences between the voltammograms in Figure 2B are much larger than the differences between the corresponding curves in Figure 2A, suggesting that the uncertainties in K and α values obtained by fitting the experimental data to the theory should be much lower. An approximate equation for quasi-reversible steady-state voltammograms with both forms initially present was derived to facilitate the extraction of the kinetic parameters from the experimental curves:

(5)

that compares the electrode radius to the diffusion distance for the redox molecules. In general, the mass-transfer process at a microdisk attains a steady state if σ < ∼10−2. In a typical voltammetric experiment at a nanoelectrode, σ is several orders C


Article


Figure 3. Voltammograms obtained from simulations (solid lines) and calculated from eq 9a (symbols), ia,∞ = ic,∞: (A) α = 0.5, (B) K = 2, and (C) K = 5.

Figure 4. (A) Steady-state voltammogram of 5 mM Fe(CN)64− and 5 mM Fe(CN)63− in 1 M KCl and (B) the same curve in the normalized form (blue symbols) fitted to the theory (eq 9; red line). a = 185 nm. v = 50 mV/s. ic,∞ = 265 pA.

i ic, ∞

⎡ ⎤ ia, ∞ = ⎢(θ − 1) − 1⎥ ⎢⎣ ic, ∞ ⎦⎥

⎛ π 2κθ + 3π ⎞ ⎜θ + ⎟ ⎝ κ 4κθ + 3π 2 ⎠

ET Kinetics from Steady-State Voltammograms of Fe(CN)63−/Fe(CN)64−. Because both forms of hexacyanoferrate are stable in water, the ET kinetics could be extracted from steady-state voltammograms obtained with oxidized and reduced forms simultaneously present in the bulk solution (Figure 4). The voltammogram in Figure 4A was obtained at a 185 nm-radius Pt electrode in solution containing 5 mM of both Fe(CN)64− and Fe(CN)63− and 1 M KCl. The ia,∞/ic,∞ ratio, 240 pA/265 pA = 0.91 is consistent with the literature values of DR = 6.7 × 10−6 cm2/s and DO = 7.3 × 10−6 cm2/s,35 corresponding to DR/DO = 0.92. The zero-current potential, Eeq = 162 mV. In Figure 4B, the current was normalized by ic,∞ = 265 pA and the experimental voltammogram was fitted to the theory calculated from eq 9. The kinetic parameter values extracted from this and similar voltammograms recorded at 15 different Pt nanoelectrodes are summarized in Table 1. The k0 and α values obtained over the range of a from 91 to 625 nm show modest variation (k0 = 0.82 ± 0.11 cm/s and α = 0.44 ± 0.02; the uncertainties are 95% confidence intervals) and no strong correlation with the electrode size. The determined rate constant can be compared to the previously reported results. Several k0 values 3−4 times lower than ours (i.e., 0.2−0.3 cm/s) were measured for Fe(CN)63−/4− in KCl and other electrolytes at macroscopic36−38 or micrometer-sized39,40 Pt electrodes. The k0 values obtained at macroscopic electrodes are likely to be affected by uncompensated resistive potential drop in solution. The mass-transfer limit ∼0.5 cm/s in refs39 and 40 may have resulted in the underestimated k0. The rate constants measured at nanometersized electrodes, i.e., either etched Pt wire41 or a single flake of reduced graphene oxide supported by an UME42 were close to

(9a)

where θ=1+

ic, ∞ ia, ∞

⎡ F ⎤ exp⎢ (E − Eeq )⎥ ⎣ RT ⎦

⎛ c * ⎞α ⎡ ⎤ F κ = K ⎜ R ⎟ exp⎢ −α (E − Eeq )⎥ ⎣ RT ⎦ ⎝ cO* ⎠

(9b)

(9c)

The dimensionless current is normalized by the cathodic diffusion limiting current ic,∞. One should notice that all variables in eqs 9 are expressed in terms of directly measurable experimental quantities, i.e., ia,∞, ic,∞, and Eeq. The cR*/cO* value is either known or can be found from the ia,∞/ic,∞ ratio. When only one form of redox species is initially present (e.g., cR* = 0), eq 9a can be reduced to the Oldham-Zoski equation for a steady-state voltammogram at the inlaid disk electrode.34 The numerical results obtained by COMSOL Multiphysics simulations (solid lines in Figure 3; see the Supporting Information for details) fit eq 9a (symbols) within 10 4.55 3.42 2.69 2.54 2.04 2.05 1.80 1.65 1.67 2.05 1.25 1.18 1.60 0.84

reversible 0.68 0.68 0.63 0.86 0.82 0.88 0.87 0.82 0.84 1.03 0.77 0.74 1.05 0.86

0.46 0.42 0.42 0.43 0.43 0.46 0.42 0.45 0.41 0.45 0.43 0.41 0.47 0.44

c R (z , t ) = c R * −

⎛ z ⎞ c R *ξ ⎟⎟ erfc⎜⎜ 1 + ξθ ⎝ 2 DOt ⎠

(10b)

where θ = exp[F(E°′ − ES)/RT], ξ = DR /DO , z is the vertical distance from the substrate surface, and t is the time after applying the potential to the substrate. The time dependences of cO and cR computed for ES = E°′, DO = DR, and z = 2 μm (the tip/substrate separation distance in our experiments) are shown in Figure 5A. From Figure 5A, one can see that both concentrations reach their steady-state values at t < 10 s that is significantly shorter than the 30 s delay time in our experiments. The concentration profiles computed from eq 10 for t = 30 s (Figure 5B) are essentially flat over the entire range of z, 0 < z < 3 μm. The effective thickness of the diffusion layer for a 100 nm-radius tip electrode is ∼10a = 1 μm. Figure 5B suggests that the variations in cO and cR within ±1 μm distance (along z axis) from the surface of the nanoelectrode tip positioned at d = 2 μm should be 100 nm, the voltammograms were essentially Nernstian. The kinetic parameters listed in Table 2 were obtained at 10 Pt

potentials. Only reduction wave (red curve in Figure 7A) and oxidation wave (purple) were recorded at the tip with ES = 200 i mV and ES = −250 mV, respectively. The c,∞ ratio is 1.03, and ia, ∞

DO/DR = 1.06 obtained from eq 11 agrees well with the literature data.50 From TCNQ voltammograms obtained at well characterized microelectrodes, DO = 1.6 × 10−5 cm2/s and DR = DO/1.06 = 1.5 × 10−5 cm2/s in very good agreement with previously reported values of 1.66 × 10−5 cm2/s and 1.47 × 10−5 cm2/s.51 The voltammograms obtained at intermediate ES values (black, blue, and green curves in Figure 7A) were normalized by ic,∞ and fitted to eq 9 (Figure 7B). The kinetic parameter values, K = 2.75 and α = 0.49 were found from the blue curve with cO*/cR* = 0.95 and Eeq = −71 mV. Very similar parameter values, K = 2.76, α = 0.48 and K = 2.80, α = 0.49 were obtained from the black and green curves, respectively. The kinetic parameters for TCNQ/TCNQ− determined at different Pt nanoelectrodes (Table 3; the mean values, k0= 8.2 ± 1.5 cm/s and α = 0.47 ± 0.03) show no apparent correlation with a. The determined standard rate constant is significantly higher than the values obtained previously for this ET reaction at macroscopic or micrometer-sized electrodes (0.005−2.9 cm/ s50−52). The k0 = 1.1 cm/s measured at nanoelectrodes in our previous SECM study16 was also significantly smaller, pointing to the importance of the AFM characterization and analysis of steady-state voltammograms comprising both the cathodic and anodic waves. An estimate obtained in the recent study employing nanogap SECM voltammetry (k0 ≤ 7 cm/s)53 was close to the results reported here. The ET kinetics of FcMeOH/FcMeOH+ in aqueous solution was investigated using the same SG/TC approach to generate the unstable FcMeOH+ species in situ. Figure 8A shows the voltammograms of FcMeOH at a 26 nm-radius tip nanoelectrode corresponding to different substrate potentials. Only reduction wave (red curve in Figure 8A) and oxidation wave (black curve) were recorded at ES = 400 mV and ES = 0 mV, respectively, and ic,∞/ia,∞ = 1.08 was found from these curves. The corresponding DO/DR value is 1.16. From voltammograms obtained at well-shaped disk microelectrodes, DR = 7.6 × 10−6 cm2/s and DO = 1.16 × DR = 8.8 × 10−6 cm2/s were evaluated in very good agreement with previously reported values of 7.8 × 10−6 cm2/s and 8.8 × 10−6 cm2/s.53 Using DO/DR = 1.16, cO*/cR* = 0.63 and 0.91 for the blue and green curves in Figure 8A, respectively. The same formal potential value E°′ = 189 mV was found by substituting cO*/cR* = 0.63 and Eeq = 177 mV (blue curve) and cO*/cR* = 0.91 and Eeq = 187 mV (red curve) in eq 1. Both experimental voltammograms were fitted to the

Table 2. Kinetic Parameters of Fc/Fc+ Oxidation/Reduction at Pt Nanoelectrodes in 0.5 M TBAPF6 Acetonitrile Solution a (nm)

K

k0 (cm/s)

α

119 64 63 58 53 47 44 40 38 37 35

≥8 3.98 3.78 3.88 3.45 2.84 2.91 2.65 2.25 2.20 2.21

reversible 12.9 12.2 13.6 13.2 12.3 13.5 13.5 12.1 12.1 12.8

0.52 0.49 0.49 0.55 0.49 0.50 0.50 0.51 0.48 0.50

nanoelectrodes (35 nm ≤ a ≤ 64 nm) and show very low uncertainties (k0 = 12.8 ± 0.6 cm/s and α = 0.50 ± 0.02). The determined rate constant is ∼50% higher than the values previously determined for this ET by SECM with either Pt16 or Au17 tip nanoelectrodes (k0 = 8.0−8.4 cm/s). It is also close to the upper limit of the range of k0 values (3.4−13.4 cm/s) measured by steady-state voltammetry at Pt nanoelectrodes whose radii (1.6 nm ≤ a ≤ 183.5 nm) were calculated from the diffusion limiting currents.46 The rate constants obtained at micrometer-sized electrodes were several times lower.15,47−49 Kinetics of TCNQ and Ferrocenemethanol. The ET kinetics of the TCNQ/TCNQ− in acetonitrile solution was measured in the SG/TC mode of the SECM operation. Figure 7A shows steady-state voltammograms of 2 mM TCNQ obtained with a 67 nm-radius tip at different substrate F


Article


Figure 7. Steady-state voltammograms of 2 mM TCNQ in 0.5 M TBAPF6 obtained at the 67 nm-radius Pt tip. (A) d = 2 μm. ES (mV) = 200 (red), −40 (green), −70 (blue), −100 (black), and −250 (purple); v = 50 mV/s. (B) Experimental voltammograms (symbols) fitted to the theory (solid red curves). The current was normalized by ic,∞= 21 pA (black), 38 pA (blue), and 48 pA (green). The symbol colors correspond to those of solid lines in panel A.

Table 3. Kinetic Parameters of TCNQ/TCNQ− in 0.5 M TBAPF6 Acetonitrile Solution a (nm) 155 130 128 102 81 75 75 69 67 61 57 45 33

K

k0 (cm/s)

3.80 6.15 3.90 3.30 3.98 2.25 2.30 2.75 2.65 2.58 2.28 1.01

reversible 5.9 9.8 7.8 8.3 10.8 6.1 6.8 8.4 8.8 9.2 10.3 6.2

Table 4. Kinetic Parameters of FcMeOH/FcMeOH+ Oxidation/Reduction at Pt Nanoelectrodes in 0.2 M KCl Solution

α

a (nm) 0.47 0.50 0.55 0.50 0.43 0.44 0.47 0.49 0.46 0.48 0.46 0.41

83 42 40 36 28 26 23 17

K

k0 (cm/s)

α

3.6

reversible reversible reversible reversible reversible reversible reversible 21

0.44

appeared to be quasi-reversible (K = 3.6) was obtained with a 17 nm-radius electrode and yielded k0 = 21 cm/s, which is close to the lower limit for rate constant of this ET reaction. To confidently measure such rapid ET kinetics under steadystate conditions, one has to use smaller electrodes (a ≤ 10 nm) or very small d that would likely produce unreliable results because of imperfect electrode geometry and significant double layer effects.25−28 The determined lower limit for k0 is much higher than the standard rate constant previously reported for FcMeOH oxidation at Pt nanoelectrodes (6.8 cm/s16). Similar estimates were recently obtained for this reaction at graphene (k0 ≥ 25 cm/s)54 and for FcTMA+ oxidation at HOPG (k0 ≥ 17 cm/s),23 using ultrapure water to prevent contamination of the electrode surface with organic impurities. Like in most previous kinetic studies at nanoelectrodes,16,17,22,23,47 the double layer effects have not been taken

theory (Figure 8B) with K > 10 indicative of Nernstian behavior, i.e., the k0 is too fast to measure at a 26 nm electrode under steady-state conditions. Similar results were obtained at the nanoelectrodes of different radii (Table 4). The voltammograms were reversible at all nanoelectrodes with a ≥ 23 nm. The upper limit for the standard rate constant measurable under steady-state conditions, was often defined as K = 10.15,16,23 For the 23 nmradius electrode in Table 4, K > 10 corresponds to k0 > 40 cm/ s. Using a more conservative value for the upper limit of quasireversibility, K = 5, the results in Table 4 suggest k0 > 20 cm/s. The only voltammogram of FcMeOH/FcMeOH + that

Figure 8. Steady-state voltammograms of 1 mM FcMeOH in 0.2 M KCl obtained at the 26 nm-radius tip. d = 2 μm; v = 10 mV/s. (A) ES (mV) = 0 (black curve), 175 (blue), 185 (green), and 400 (red). (B) Experimental voltammograms (symbols) fitted to the theory (solid red curves). The current was normalized by ic,∞ = 3.5 pA (blue) and 4.5 pA (green). The symbol colors correspond to those of solid lines in panel A. G



■

into account here. In addition to Frumkin correction,1 the apparent ET kinetic parameters measured at a nanoelectrode with the dimensions comparable to the thickness of the diffuse layer may be distorted by double layer effects on mass transfer and other deviations from classical electrochemical theory.25,26,55 These effects are expected to be most significant for multicharged ions, at low ionic strength, and especially in nanogap experiments. In this work, we used high electrolyte concentrations and performed voltammetry at relatively large nanoelectrodes (a > 20 nm) placed at a significant distance from the substrate surface (d ≫ a). Except multicharged Fe(CN)64−/3−, all employed redox couples consisted of a neutral molecule and an ion with a ±1 charge. Under these conditions, our results are not expected to be strongly influenced by double layer effects.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: 718-997-5531. Notes

The authors declare no competing financial interest.

■ ■

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

(1) Bard, A. J.; Faulkner, L. R.Electrochemical Methods: Fundamentals and Applications, 2nd ed.; Wiley: New York, 2001. (2) Mirkin, M. V. In Handbook of Electrochemistry; Zoski, C. G., Ed.; Elsevier: Amsterdam, The Netherlands, 2006; pp 639−660. (3) Wehmeyer, K. R.; Deakin, M. R.; Wightman, R. M. Anal. Chem. 1985, 57, 1913−1916. (4) Morris, R. B.; Franta, D. J.; White, H. S. J. Phys. Chem. 1987, 91, 3559−3564. (5) Pendley, B. P.; Abruña, H. D. Anal. Chem. 1990, 62, 782−784. (6) Penner, R. M.; Heben, M. J.; Longin, T. L.; Lewis, N. S. Science 1990, 250, 1118−1121. (7) Mirkin, M. V.; Fan, F.-R. F.; Bard, A. J. J. Electroanal. Chem. 1992, 328, 47−62. (8) Mirkin, M. V.; Fan, F.-R. F.; Bard, A. J. Science 1992, 257, 364− 366. (9) Shao, Y.; Mirkin, M. V.; Fish, G.; Kokotov, S.; Palanker, D.; Lewis, A. Anal. Chem. 1997, 69, 1627−1634. (10) Slevin, C. J.; Gray, N. J.; MacPherson, J. V.; Webb, M. A.; Unwin, P. R. Electrochem. Commun. 1999, 1, 282−288. (11) Campbell, J. K.; Sun, L.; Crooks, R. M. J. Am. Chem. Soc. 1999, 121, 3779−3780. (12) Wang, Y.; Velmurugan, J.; Mirkin, M. V. Isr. J. Chem. 2010, 50, 291−305. (13) Oja, S. M.; Fan, Y.; Armstrong, C. M.; Defnet, P.; Zhang, B. Anal. Chem. 2016, 88, 414−430. (14) Amemiya, S. In Electroanalytical Chemistry: A Series of Advances; Bard, A. J., Zoski, C. G., Eds.; CRC Press/Taylor & Francis: Boca Raton, FL, 2015; Vol. 26, pp 1−72. (15) Mirkin, M. V.; Richards, T. C.; Bard, A. J. J. Phys. Chem. 1993, 97, 7672−7677. (16) Sun, P.; Mirkin, M. V. Anal. Chem. 2006, 78, 6526−6534. (17) Velmurugan, J.; Sun, P.; Mirkin, M. V. J. Phys. Chem. C 2009, 113, 459−464. (18) Baranski, A. S. J. Electroanal. Chem. Interfacial Electrochem. 1991, 307, 287−292. (19) Oldham, K. B. Anal. Chem. 1992, 64, 646−651. (20) Nogala, W.; Velmurugan, J.; Mirkin, M. V. Anal. Chem. 2012, 84, 5192−5197. (21) Nioradze, N.; Chen, R.; Kim, J.; Shen, M.; Santhosh, P.; Amemiya, S. Anal. Chem. 2013, 85, 6198−6202. (22) Kim, J.; Bard, A. J. J. Am. Chem. Soc. 2016, 138, 975−979. (23) Nioradze, N.; Chen, R.; Kurapati, N.; Khvataeva-Domanov, A.; Mabic, S.; Amemiya, S. Anal. Chem. 2015, 87, 4836−4843. (24) Rodgers, P. J.; Amemiya, S.; Wang, Y.; Mirkin, M. V. Anal. Chem. 2010, 82, 84−90. (25) Liu, Y.; He, R.; Zhang, Q.; Chen, S. J. Phys. Chem. C 2010, 114, 10812−10822. (26) Lan, W.-J.; White, H. S.; Chen, S. in Nanoelectrochemistry; Mirkin, M. V., Amemiya, S., Eds.; CRC Press/Taylor & Francis: Boca Raton, FL, 2015; pp 29−69. (27) Fan, L.; Liu, Y.; Xiong, J.; White, H.; Chen, S. ACS Nano 2014, 8, 10426−10436. (28) Xiong, J.; Chen, Q.; Edwards, M. A.; White, H. S. ACS Nano 2015, 9, 8520−8529. (29) Kim, J.; Shen, M.; Nioradze, N.; Amemiya, S. Anal. Chem. 2012, 84, 3489−3492.

■

CONCLUSIONS The described experiments aimed at improving the reliability of ET kinetic measurements at nanoelectrodes by obtaining steady-state voltammograms with both oxidized and reduced forms of redox species initially present in solution (for more reliable curve fitting), characterizing the nanoelectrode geometry with the AFM, and using water with a low level of organic contaminants. Compared to our previous nanoelectrode experiments, these improvements resulted in higher measured rate constants and more reproducible α, closer to the theoretically expected value of 0.5. For ETs in acetonitrile, the increase in the measured k0 value was moderate (∼50%) for Fc and very significant (by the factor of ∼7) for TCNQ. A large difference was observed for the oxidation of aqueous FcMeOH, in contrast to moderately fast rate constants (7−8 cm/s) measured previously at Pt16 and Au17 nanoelectrodes, our present data suggests that the k0 is >20 cm/s. This dramatic difference may be in part due to the decreased TOC in water, which was previously found to significantly affect rapid heterogeneous ET rates at carbon electrodes.23 As can be inferred from the title of this article, the presented results should be seen as another step toward more accurate measurement of fast electrochemical rate constants. Among the factors not taken into account in this study are the effects of the electrode double layer and glass surface charge on the mass/ charge-transfer. The exact values of several parameters required for modeling these effects (e.g., the potential of zero charge of Pt, dielectric constant in the compact double layer, and the surface charge density on glass) are currently unavailable. In discussed experiments, most kinetic information was contained in the middle portion of the steady-state voltammogram corresponding to E°′ ±∼50 mV. For such a narrow potential range, and the α values very close to 0.5, the Butler−Volmer model is a good approximation for the more general (and physically meaningful) Marcus theory.

■

Article

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.analchem.6b03392. Chemicals, electrodes and voltammetry, characterization of nanoelectrodes, diffusion problem formulation, and the COMSOL model report (PDF) H


Article

Analytical Chemistry (30) Tan, S.-y.; Zhang, J.; Bond, A. M.; Macpherson, J. V.; Unwin, P. R. Anal. Chem. 2016, 88, 3272−3280. (31) Miao, W.; Ding, Z.; Bard, A. J. J. Phys. Chem. B 2002, 106, 1392−1398. (32) Hu, K.; Gao, Y.; Wang, Y.; Yu, Y.; Zhao, X.; Rotenberg, S. A.; Gökmeşe, E.; Mirkin, M. V.; Friedman, G.; Gogotsi, Y. J. Solid State Electrochem. 2013, 17, 2971−2977. (33) Bond, A. M.; Oldham, K. B.; Zoski, C. G. J. Electroanal. Chem. Interfacial Electrochem. 1988, 245, 71−104. (34) Oldham, K. B.; Zoski, C. G. J. Electroanal. Chem. Interfacial Electrochem. 1988, 256, 11−19. (35) Konopka, S. J.; McDuffie, B. Anal. Chem. 1970, 42, 1741−1746. (36) Goldstein, E. L.; Van de Mark, M. R. Electrochim. Acta 1982, 27, 1079−1085. (37) Daum, P. H.; Enke, C. G. Anal. Chem. 1969, 41, 653−656. (38) Angell, D. H.; Dickinson, T. J. Electroanal. Chem. Interfacial Electrochem. 1972, 35, 55−72. (39) Beriet, C.; Pletcher, D. J. Electroanal. Chem. 1993, 361, 93−101. (40) Huang, W.; McCreery, R. J. Electroanal. Chem. 1992, 326, 1−12. (41) Slevin, C. J.; Gray, N. J.; Macpherson, J. V.; Webb, M. A.; Unwin, P. R. Electrochem. Commun. 1999, 1, 282−288. (42) Zhang, B.; Fan, L.; Zhong, H.; Liu, Y.; Chen, S. J. Am. Chem. Soc. 2013, 135, 10073−10080. (43) Zhang, Y.; Zhou, J.; Lin, L.; Lin, Z. Electroanalysis 2008, 20, 1490−1494. (44) Zotti, G.; Schiavon, G.; Zecchin, S.; Favretto, D. J. Electroanal. Chem. 1998, 456, 217−221. (45) Zoski, C. G.; Luman, C. R.; Fernández, J. L.; Bard, A. J. Anal. Chem. 2007, 79, 4957−4966. (46) Li, Y.; Bergman, D.; Zhang, B. Anal. Chem. 2009, 81, 5496− 5502. (47) Wipf, D. O.; Kristensen, E. W.; Deakin, M. R.; Wightman, R. M. Anal. Chem. 1988, 60, 306−310. (48) Bond, A. M.; Henderson, T. L. E.; Mann, D. R.; Mann, T. F.; Thormann, W.; Zoski, C. G. Anal. Chem. 1988, 60, 1878−1882. (49) Clegg, A. D.; Rees, N. V.; Klymenko, O. V.; Coles, B. A.; Compton, R. G. J. Electroanal. Chem. 2005, 580, 78−86. (50) Rongfeng, Z.; Evans, D. J. Electroanal. Chem. 1995, 385, 201− 207. (51) Bano, K.; Nafady, A.; Zhang, J.; Bond, A. M. J. Phys. Chem. C 2011, 115, 24153−24163. (52) Ekanayake, C. B.; Wijesinghe, M. B.; Zoski, C. G. Anal. Chem. 2013, 85, 4022−4029. (53) Nioradze, N.; Kim, J.; Amemiya, S. Anal. Chem. 2011, 83, 828− 835. (54) Chen, R.; Nioradze, N.; Santhosh, P.; Li, Z.; Surwade, S. P.; Shenoy, G. J.; Parobek, D. G.; Kim, M. A.; Liu, H.; Amemiya, S. Angew. Chem., Int. Ed. 2015, 54, 15134−15137. (55) Smith, C. P.; White, H. S. Anal. Chem. 1993, 65, 3343−3353.

I


Toward More Reliable Measurements of Electron-Transfer Kinetics at

Recommend Documents