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Direct Observation of C2O4#– and CO2#– by Oxidation of Oxalate within Nanogap of Scanning Electrochemical Microscope Tianhan Kai, Min Zhou, Sarah Johnson, Hyun S. Ahn, and Allen J. Bard J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b08900 • Publication Date (Web): 02 Nov 2018 Downloaded from http://pubs.acs.org on November 3, 2018
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Direct Observation of C2O4● and CO2● by Oxidation of Oxalate within Nanogap of Scanning Electrochemical Microscope
Tianhan Kai, Min Zhou, Sarah Johnson, Hyun S. Ahn and Allen J. Bard*
Center for Electrochemistry, Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, United States
* Corresponding author. Phone: (512) 471-3761, email:
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Abstract Oxalate oxidation in the presence of different oxidized luminophores leads to the emission of light and has been studied extensively in electrogenerated chemiluminescence (ECL). The proposed mechanism involves the initial formation of the oxalate radical anion, C2O4●. The ensuing decomposition of C2O4● produces a very strong reductant, CO2●, which reacts with the oxidized luminophores to generate excited states that emit light. Although the mechanism has been proposed for decades, the experimental demonstration is still lacking, because of the complexity of the system and the short lifetimes of both radical anions. To address these issues, we studied oxalate oxidation at platinum ultramicroelectrodes (UMEs) in anhydrous N,N-dimethylformamide (DMF) solution by nanoscale scanning electrochemical microscopy (SECM) with the tip generation/substrate collection (TG/SC) mode. A Pt nanoelectrode was utilized as the SECM generator for oxalate oxidation, while another Pt UME served as the SECM collector and was used to capture the generated intermediates. We studied the influence of the gap distance, d, on the substrate current (is). The results indicate that, when 73 nm d 500 nm, the species captured by the substrate were primarily CO2●, while C2O4● was the predominant intermediate measured when d was below 73 nm. A half-life of 1.3 µs for C2O4● was obtained, which indicates a stepwise mechanism for oxalate oxidation. The relevance of these observations to the use of oxalate as the co-reactant in ECL systems is also discussed.
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Introduction Electrogenerated chemiluminescence (ECL) is a redox-induced light emission by an energetic electron transfer (et) reaction between the species generated at electrodes.1 Since the first detailed ECL studies in the 1960s2, two different operation modes for ECL have been developed: direct radical ion annihilation ECL and co-reactant ECL3,4. There is a strong interest in the co-reactant ECL mode since it permits the utilization of this technique in aqueous solutions.3,5 The intermediates generated by oxidation of a co-reactant (e.g., oxalate) decompose to produce a powerful reductant that reacts with the oxidized luminophore to produce excited states and emit light. For example, oxalate ion has been used in ECL systems with different luminophores in aprotic and aqueous solutions.6,7 The suggested reaction mechanism involves the production of oxalate radical species (C2O4) initially through a 1e oxidation electrochemically (reaction 1) and chemically (reaction 2), followed by rapid decomposition of C2O4 yielding CO2 (reaction 3). As a strong reducing species8,9 (E0(CO2/ CO2) = 2.2 V vs SCE), CO2 reacts with oxidized ECL luminophores (e.g., Ru(bpy)33+) to produce an excited state (Ru(bpy)32+) and emit light (Reaction 4-6). C2O42 e ⇋ C2O4
(1)
Ru(bpy)33+ + C2O42 Ru(bpy)32+ + C2O4
(2)
k1
C2O4 CO2 + CO2
(3)
Ru(bpy)32+ e Ru(bpy)33+
(4)
Ru(bpy)33+ + CO2 Ru(bpy)32+ + CO2
(5)
Ru(bpy)32+ Ru(bpy)32+ + hv
(6)
Although the above reaction mechanism has been proposed for decades, CO2 has not yet been identified during oxalate oxidation. It is also not clear, whether the first 1e transfer for oxalate oxidation produces an intermediate, e.g. C2O4, or occurs via concerted bond cleavage.10 Although the reaction mechanism is 2 ACS Paragon Plus Environment
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complicated, a number of indirect measurements (e.g., ECL6,7,11,12 and pulse radiolysis13,14) suggest the existence of such intermediates. Previously reported cyclic voltammetry (CV)15 and fast-scan CV7 failed to detect these intermediates, indicating that CO2 and C2O4, are too short-lived to be detected with the scan rates employed. One can increase the scan rate in an attempt to capture the presumed intermediates, but accurate measurements are prevented in that case by the large contribution from capacitive charging at high scan rates and adsorbed species on the electrode surface.16,17 The advantage of scanning electrochemical microscopy (SECM) for the detection of short-lived intermediates has been demonstrated previously.16,18,19 Most SECM measurements are made at the steady state and not perturbed by factors in fast scan CV. Tip generation/substrate collection (TG/SC) mode is employed for the measurements. In this mode, the tip (generator) is held at the potential where an electrode reaction occurs. The species generated at the tip travels across the gap between the tip and the substrate (collector), and is collected by the substrate. If the species is a reaction intermediate, the collection efficiency (CE) at different gap distances (d), allows for the determination of rate constants for homogeneous reactions.16 The lifetime of the intermediate that can be detected is determined by how small d can be made. This is governed by the size of the electrodes and the stability of the instrument, but can be in the small nm-regime. Recently, SECM at nm resolution has been described with the efforts of Mirkin, Amemiya, Unwin, and our group.20-28 By increasing the positional stability and suppressing thermal drift at nanoscale distances, nm-tip position, and maintenance at nm-distances become possible.21 These improvements allow measurements of fast heterogeneous electron transfer kinetics22-26 and nano-scale imaging20,27,28. Few measurements of rapid homogeneous reactions within the nanogap (below 100 nm) have been carried out. One novel application by Mirkin and coworkers was the measurement of superoxide radical anion (O2) at a liquid-liquid interface during the oxygen reduction reaction (ORR) at a Pt surface in aqueous solution with a nanopipette filled with benzotrifluoride.29 This work is devoted to the investigation of oxalate oxidation in N,N-dimethylformamide (DMF) solution with a gap distance, d of 55 to 500 nm, between the tip and substrate, using the TG/SC mode via 3 ACS Paragon Plus Environment
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nanoscale SECM. Precise control of the separation between the tip and substrate at nm resolution yielded evidence for the reaction mechanism and quantitative information for the reaction kinetics. Varying d allowed the demonstration of the existence of CO2 during oxalate oxidation. C2O4 was also captured directly when the nm gap was below 73 nm. By fitting the experimental results at different d, the half-life of C2O4 and its kinetic parameters were obtained. The experimental and simulated results conclusively demonstrate that oxalate oxidation follows a stepwise mechanism outlined above. This work represents one of the most complicated multistep reactions that have been studied by SECM so far. Furthermore, the approach described here can be extended to the studies of other ECL co-reactants, as well as other reactions involving bond cleavage and bond formation.
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Experimental Chemicals: Oxalic acid dihydrate (H2C2O4; ≥99%) and anhydrous N,N-Dimethylformamide (DMF; 99.9%) were purchased from Fisher Scientific (Pittsburgh, PA). Acetonitrile (CH3CN; 99.8%), Nitrobenzene (NB; ≥99%), Tetrahydrofuran (THF; ≥99%), Tetrabutylammonium hexafluorophosphate (TBAPF6; ≥99%), Tetraethylammonium hydroxide solution (TEAOH, 35 wt.% in H2O) and Ferrocene (Fc; 98%) were obtained from Sigma-Aldrich (St. Louis, MO). Aqueous solutions were prepared with ultrapure water obtained from a Milli-Q Integral system (EDM Millipore, Billerica, MA) with the resistivity of 18.3 M/cm. Synthesis of Bis(tetraethylammonium) oxalate [(TEA)2Ox)]: Bis(tetraethylammonium) oxalate ((TEA)2Ox)]30 was prepared by mixing tetraethylammonium hydroxide and oxalic acid in a 2:1 molar ratio. The solution was dried under vacuum at room temperature overnight. The resulting hygroscopic white solid was rinsed three times with hot THF. The precipitate was separated from the solution and dried using a vacuum. The product was dissolved in acetonitrile, recrystallized with THF, and transferred into a glovebox for storage. Procedure: Electrodes. The fabrication of Pt UMEs (radius (a) = 12.5 µm) has been demonstrated elsewhere.16,17 Pt nanoelectrodes were fabricated using a laser puller (P-2000, Sutter Instruments, Novato, CA), a microforge (MF-0P, Narishige, Japan), and a focused ion beam (FIB) system (FEI STRATA DB235), as described previously.20 The size determination of Pt nanoelectrodes was accomplished by scanning electron microscope (SEM) imaging (Figure S1A) and the diffusion limited current obtained from cyclic voltammogram (CV) in CH3CN containing 1 mM Fc and 0.1 M TBAPF6 at a scan rate of 50 mV•s1 (Figure S1B). For a diskshaped, non-recessed Pt nanoelectrode, a obtained from SEM (310 nm) is in agreement with the one deduced from CV (300 nm). Apparatus. SECM experiments were conducted using a nanoscale SECM. The instrument consists of a bipotentiostat (CHI 760E), a stage (Linear stage series 600, Newport) equipped with micromanipulators (DM25L, Newport) and piezoelectric actuators (P620.2CL and P620.ZCL, PI). The detailed instrumentation has 5 ACS Paragon Plus Environment
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been described elsewhere.21 To prevent contamination of the DMF solution with water and oxygen, the SECM cell was placed inside a chamber kept at a higher pressure than the surrounding air under a cushion of argon gas (5.0 UHP), as shown in Figure 1. This design allows one to conduct SECM experiments under an inert atmosphere without placing it in a glovebox. The tip position was initially adjusted with the micromanipulators, and then the piezo controller was employed for a more accurate position of the tip. The cell and the chamber were tightened with Teflon caps and were made to fix the reference (a Pt/PPy electrode31) and counter electrodes (a Pt wire) through the cell. The potential for the Pt/PPy reference electrode was calibrated to be 0.26 V vs aq. saturated calomel electrode (SCE). The SECM cell was cleaned with piranha solution, ultrapure water, and acetonitrile successively and dried with argon. The alignment of the SECM tip and substrate were accomplished by following a procedure described earlier.32 Nitrobenzene (NB, 1 mM) served as the redox mediator. A “smart approach curve” method33 was utilized to obtain approach curves. This method allows the rapid acquirement of SECM approach curves with a variable approach speed. The closest approach distance for a well-aligned SECM tip (a = 300 nm Pt UME) and substrate (a = 12.5 µm Pt UME) is estimated to be 55 nm (Figure S2). Slight contact of the tip with the substrate was observed, as evidenced by the sluggish increase of tip current (iT). This minimal contact did not result in the apparent crash of the SECM tip, even though nm-sized electrodes are fragile and easily destroyed by physical contact and vibration. This reveals that nanoscale SECM provides a higher spatial stability compared with regular SECM. To prevent interaction between NB and the presumably generated intermediate (CO2), the solution was replaced with DMF solution containing 10 mM (TEA)2Ox and 0.1 M TBAPF6 for the studies of oxalate oxidation. Thus, the SECM cell was modified with an additional solution replacement system (Figure 1). A syringe pump (Orion Sage 362, Thermo-Fisher Scientific) was utilized to replace the solution inside the SECM cell to eliminate vibration during solvent displacement. The cell was rinsed three times to ensure a minimal amount of NB inside the SECM cell. A slight change in the position of the SECM tip with respect to the substrate, which is caused by the inevitable drift of the positioners,
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may affect the accuracy of the d estimations. The absolute value of d, especially at a very small range, can still be evaluated from the decrease of iT for oxalate oxidation, due to the hindered diffusion (vide infra).
Figure 1. Diagram of the SECM cell design for the SECM nanogap experiments under an inert atmosphere. Results and Discussion Strategy of Measurement and Proposed Mechanism Experiments to detect intermediates in the oxidation of oxalate were carried out by using a small gap to collect oxidation products generated at a tip electrode (TG/SC mode of SECM). A schematic diagram of this mode using anhydrous DMF as a solvent with 10 mM (TEA)2Ox and 0.1 M TBAPF6 is shown in Figure 2. A a = 300 nm Pt tip with RG (ratio of the radius of the electrode to that of the metal disk) of 1.6 was employed as the generator for oxalate oxidation. The collector substrate with a a = 12.5 µm Pt UME was used to collect generated intermediates. The generator and the collector were aligned and separated by a distance, d (the SECM gap). The proposed mechanism for oxalate oxidation involves an initial one electron transfer to form C2O4 followed by carbon-carbon bond cleavage to produce CO2, which is also oxidized at the generator tip (for an overall 2e process). In addition, the CO2 can dimerize to form oxalate (Reaction 7). CO2 can also react with C2O4 as shown in Reaction 8. Despite this complicated reaction sequence, some CO2 and C2O4 can still arrive at the substrate when d is extremely small. To elucidate the reaction mechanism and detect CO2 and C2O4, the collector substrate potential was adjusted to oxidize CO2 and to reduce C2O4. Thus, is at different d reflect the amount of C2O4 and CO2• that arrive at the substrate. When the tip is far from the substrate (d is 7 ACS Paragon Plus Environment
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large), CO2 and C2O4 might not reach the substrate because of the rapid homogeneous reactions (reactions 2, 7, and 8) as proposed. When d is smaller, is can show contributions from both of CO2 oxidation and C2O4 reduction, as discussed below.
k
2CO2 2 C2O42
(7)
k
(8)
CO2 + C2O4 3 CO2 +C2O42
Figure 2. Schematic description of the proposed mechanism for oxalate oxidation in TG/SC mode of SECM using a a = 300 nm Pt nanoelectrode as SECM tip for oxalate oxidation, and a a = 12.5 µm Pt UME as SECM substrate for the collection of C2O4 and CO2.
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Voltammetric characterization of UMEs
Figure 3. Oxalate oxidation. CVs obtained at a Pt UME (a = 14.5 µm) (A) and a Pt nanoelectrode (a = 300 nm) (B), respectively, in anhydrous DMF containing 0.1 M TBAPF6 in the presence (black) and absence of 10 mM oxalate (red curve). The scan rate was 100 mV/s. The diffusion coefficient (D) of oxalate was obtained from the steady-state voltammogram at a a = 14.5 µm Pt UME, as shown in Figure 3A. A typical sigmoidal voltammogram for 10 mM oxalate oxidation was obtained with the diffusion-limited current (iss) of 30.5 nA (black curve). The background current was negligible in the absence of oxalate (red curve). Assuming 2 et occurs at this UME for oxalate oxidation, D of oxalate was calculated to be 2.7 × 106 cm2·s-1 using equation 9,17 iss = 4nFDca
(9)
where n is the number of electrons transferred (n = 2 for oxalate oxidation), F is the Faraday constant (96500 C·mol1), c is the concentration of oxalate (10 mM), and a is the radius of the UME (14.5 µm). We further studied the voltammetric behavior of oxalate at a Pt nanoelectrode (a = 300 nm), which was later utilized as the SECM tip for nanogap experiments (vide infra). Compared with the one obtained at the larger Pt UME, a more sluggish voltammogram was observed at this Pt nanoelectrode (black curve in Figure 3B) with the half-wave potential (E1/2) of 0.72 V. From iss (0.62 nA) and the D value, n = 2.0 was obtained with this nanoelectrode using equation 9. Since n is essentially 2 at both µm- and nm-size electrodes, the rate of carboncarbon bond homolysis is too fast to be measured by steady-state measurements with different size UMEs.17 9 ACS Paragon Plus Environment
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SECM nanogap investigation
Figure 4. Proposed reactions on the SECM tip and substrate at the given potentials. SECM TG/SC experiments within a nanogap, where oxalate was oxidized at the tip and intermediates were collected at the substrate, were undertaken to detect intermediates (CO2 and C2O4) and estimate their lifetimes. Figure 4 shows a scale of potentials and regimes where the indicated reactions occur to clarify substrate reactions.
Figure 5. TG-SC Experiments. Experimental (black) and the best fit of the simulated results (red dotted curve) of iT (A) at the steady-state under diffusion limited conditions for 10 mM oxalate oxidation and the corresponding iS (B) obtained when Es was held at 0.05 V vs Pt/PPy. (C) shows iS/iT at different d obtained with the experimental (black) and simulated results (red dotted curve). The SECM tip was a a = 300 nm Pt UME (RG = 1.6) and the substrate was a a = 12.5 µm Pt UME.
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The SECM tip (a = 300 nm Pt UME with RG=1.6) and the substrate (a = 12.5 µm Pt UME) were held at potentials indicated in Figure 4 (tip at 1.25 V vs Pt/PPy and substrate at 0.05 V vs Pt/PPy). Oxalate is oxidized at the tip. The situation at the substrate is unique for SECM TG/SC, since, at the same Es, one species is oxidized and the other is reduced, generating either an anodic or cathodic current, depending upon which species predominates (Figure 4). At this Es (0.05 V), CO2 is oxidized (E0CO2/CO2• = 2.2 V vs SCE)8,9 and C2O4 is reduced (E0(C2O4/ C2O42) = 0.06 V vs SCE)15. As the tip approached the substrate, a decrease of tip current (iT) was observed, because the diffusion of oxalate toward the SECM tip was hindered (black curve in Figure 5A). The black curve in Figure 5B shows the substrate current (is) depends on d. When d was 500 nm, no apparent collection current was observed on the substrate. An anodic current was seen, which increased with decreasing d (500 to 140 nm). When d was 140 nm, the anodic substrate current started to decrease after reaching a maximum anodic value (5.4 pA). As d fell below 73 nm, a steep increase of the cathodic collector current was seen. The observed results in is at different d can be rationalized as follows. We search for the two intermediates: the product of the first 1e transfer, that we assume is a fast outer sphere process, C2O4 and CO2, that was previously investigated in this medium. Since CO2 is a strong reductant, it is oxidized over most of the potential range of interest. The C2O4 is reduced at potentials negative of the oxalate oxidation wave. Over most of the potential region, the collector substrate will have the possibility of both anodic and cathodic currents. In addition to these electrode reactions, the C2O4 will undergo a bond cleavage to produce CO2, which can dimerize. The reaction between CO2 and C2O4 will also need to be considered. (see Figure 2) When d 500 nm, the intermediates generated from oxalate oxidation were consumed before they arrived at the substrate. Thus, no obvious anodic or cathodic current was observed on the substrate. A gradually increasing anodic current at the substrate was observed when 140 nm d 500 nm, indicating that fractional CO2 was captured by the substrate without further reaction. The anodic current started to decrease and “0” collection current was 11 ACS Paragon Plus Environment
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observed when d was about 73 nm, meaning that C2O4 started to contribute more on iS and the same amount of CO2 and C2O4 was captured on the substrate at d = 73 nm. When d is below 73 nm, the product, C2O4, was captured as the primary intermediate, without bond breakage, as evidenced by a very steep increase of the cathodic current. The plot of iS/iT vs. d reveals the CE for both of CO2 and C2O4, as shown in the black curve in Figure 5C. The maximum CE for CO2 (1.4%) and C2O4 (2.2%) was obtained at d values of 112 nm and 55 nm, respectively. The small CE for both of the intermediates is due to the fast bond breakage of C2O4 (reaction 3), the fast dimerization of CO2 (reaction 8)9, and the reaction between CO2 and C2O4 (reaction 9). Moreover, during the anodic collection of CO2 and cathodic collection of C2O4, the collection currents compensate and cancel each other in part, which also contributes to this low CE. As the dimerization rate constant of CO2 (k2) of 6.0 × 108 M1·s1 was obtained in our previous work9, the simulation of the experimental results with Comsol Multiphysics V5.2a software was carried out to obtain rate constants of other homogeneous reactions in the system, as described in the supporting information (SI). All simulations in this study assumed diffusion as the sole means of mass transfer. Recent studies24,25,34 indicate migration could also make a contribution, where it occurs over a distance that is an appreciable fraction of the nanogap. However, given the high concentration of the electrolyte, the double layer effect on the mass transfer probably makes a negligible contribution compared to other uncertainties in the measurements. The best fits of the iT (red dotted curve, Figure 5A), iS, (red dotted curve, Figure 5B) and iS/iT (red dotted curve, Figure 5C) as a function of d, results in the bond breaking rate constant (k1) of 0.55 × 106 s1 and k3 of 1.5×1011 M1·s1. The half-life of C2O4, thus, was estimated to be 1.3 µs using the equation t1/2 = ln 2/k1.17 The reaction layer thickness, µ, for C2O4 was estimated to be about 22 nm using the equation µ = (D/k1)1/2 (D of C2O4 was assumed to be the same as that of oxalate).17 This value is much smaller than the diffusion layer thickness () on the Pt nanoelectrode (a = 300 nm) in the steady-state region. Thus, the earlier assumption of 2e reaction for oxalate oxidation at this nanoelectrode is reasonable. 12 ACS Paragon Plus Environment
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Figure 6. Simulated concentration profiles for the C2O4 (A) and CO2 (B) at steady state under diffusion limited conditions with a a = 300 nm Pt nanoelectrode using the simulated kinetic parameters obtained in Figure 5. Next, we extract the simulated results to obtain the concentration profiles for C2O4 (Figure 6A) and CO2 (Figure 6B) at the SECM tip (a = 300 nm Pt UME). Oxalate oxidation results in a significant amount of C2O4 near the nanoelectrode surface, then a very steep decrease (0 nm d 50 nm) of CC2O4 was observed in Figure 6A, primarily due to the fast bond breakage (0.55 × 106 s1), during the diffusion of C2O4 into the bulk solution. The dissociation of C2O4 results in CO2, which was oxidized at the electrode surface under diffusion limited conditions, thus the surface concentration of CO2 was zero, as indicated in Figure 6B. As CO2 diffused into the solution, it was consumed by the dimerization reaction (reaction 7) and a small amount of reaction with C2O4 (reaction 8). As a result, the concentration of CO2 reached a maximum value of 3.6 µM at d of 46 nm.
Stepwise vs. Concerted Oxalate Decomposition The results shown above suggest that the 1e oxidation of oxalate and the bond cleavage to produce CO2 and CO2 occurs by a stepwise reaction with an intermediate lifetime of the order of a µs. However, it is appropriate to consider the possibility of a concerted process as discussed in detail by Savéant,35 who shows that 13 ACS Paragon Plus Environment
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one can pass from a stepwise to a concerted process with changes in the driving force of the heterogeneous et reaction. The situation in this case is rather complicated, but would be worth considering when more accurate thermodynamic data are available. ECL Implications We first studied the reaction of interest, oxidation of oxalate to produce CO2 in connection with studies of ECL in aqueous solution.6 In this work, Ru(bpy)33+ had to react with a strong reductant to produce the excited state. Electro-generation of such a reductant is difficult in aqueous solution because of its limited cathodic range.3 The experiment showed that simultaneous oxidation of Ru(bpy)32+ and oxalate produced the strong emission of light characteristic of the ECL reactions. The presumably generated CO2 is less stable in water than it is in DMF, and as we showed above, CO2 in DMF does not diffuse very far from the electrode before it is exhausted by the dimerization. However, in the ECL experiment, CO2 is surrounded by the strongly oxidizing species generated at the same electrode and hence can react before it diffuses very far. This is probably true for other reductants generated in the same way.36 The present study does confirm the intermediacy of CO2 in an oxidative reduction reaction. Although the CO2 only exists in a small region below the electrode, the Ru(bpy)33+ is produced at the electrode surface and so acts as a “virtual substrate electrode” at a very small distance from the tip surface. It also contributes to the oxidation of oxalate with a driving force for et that may be different than that at the tip, thus affecting the stepwise/concerted ratio. However, in the ECL, the concerted path could also lead to excited state formation.
Conclusions We report the application of nanoscale SECM for the study of oxalate, in anhydrous DMF using the TG/SC mode. By using an extremely small gap, d (50 to 500 nm), between the tip and the substrate, we demonstrate the 14 ACS Paragon Plus Environment
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existence of CO2 during oxalate oxidation experimentally. Moreover, although the bond cleavage following et is rapid, C2O4 was captured when d was below 73 nm, demonstrating that it was not a concerted reaction. This evidence indicates oxalate oxidation follows a stepwise mechanism. The bond breaking rate (0.55 × 106 s1) and half-life of C2O4 (1.3 µs) were obtained, by fitting the experimental data with simulations. The relevance of the observed phenomenon to the use of oxalate ions as the co-reactants for ECL studies was also discussed. The present study suggests nanoscale SECM can be a useful tool for the elucidation of ECL co-reactant mechanisms. More broadly, this analytical technique can be expanded to the studies of other et processes in bond cleavage and formation reactions.
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ASSOCIATED CONTENT Supporting Information
Pt nanoelectrode SEM image and corresponding CV, approach curve, and COMSOL simulation parameters. This supporting information is available free of charge via the Internet at http://pubs.acs.org.
AUTHOR INFORMATION
Corresponding Author *
[email protected] Acknowledgements T. H. K. would like to acknowledge Z. Y. Duan and F. H. Cao for the discussion. We acknowledge the support of this research from the AFOSR MURI (FA9550-14-1-0003) and the Robert A. Welch Foundation (F-0021).
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