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Redox Cycling in Nanogap Electrochemical Cells. The Role of Electrostatics in Determining the Cell Response Qianjin Chen, Kim McKelvey, Martin A. Edwards, and Henry S. White J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b05483 • Publication Date (Web): 13 Jul 2016 Downloaded from http://pubs.acs.org on July 19, 2016

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The Journal of Physical Chemistry

Redox Cycling in Nanogap Electrochemical Cells. The Role of Electrostatics in Determining the Cell Response Qianjin Chen, Kim McKelvey, Martin A. Edwards and Henry S. White* Department of Chemistry, University of Utah, 315 S 1400 E, Salt Lake City, UT 84112, United States Email: [email protected] Phone: +1 (801) 585-6256

Abstract: Ion transport near interfaces is a fundamental phenomenon of importance in electrochemical, biological and colloidal systems. In particular, electric double layers in highly confined spaces have implications for ion transport in nanoporous energy storage materials. By exploiting redox cycling amplification in lithographically fabricated thin-layer electrochemical cells comprising two platinum electrodes separated by a distance of 140 nm to 400 nm, we observed current enhancement during cyclic voltammetry of the hexaamineruthenium (III) chloride redox couple (Ru(NH3)63/2+) at low supporting electrolyte concentrations, resulting from ion enrichment of Ru(NH3)63/2+ in the electrical double layers and an enhanced ion migration contribution to mass transport. The steady-state redox cycling was shown to decrease to predominately diffusion controlled level with increasing supporting electrolyte concentration. Through independent biasing of the potential on the individual Pt electrodes, the voltammetric transport limited current can be controlled without changing the electrochemical nature at the system. Using finite-element simulations based on numerical solutions to the Poisson and Nernst-Plank equations with Butler-Volmer type boundary conditions, we are able to semiquantitatively predict the voltammetric behavior of the nanogap cell that results from coupling of surface electrostatics and ion transport.

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Introduction Ion transport at electrically charged surfaces is of fundamental importance in a variety of applications, ranging from electrochemistry and electrophoresis,1, 2 to nanofluidics3, 4 and water desalination.5, 6 Nanoscale ion transport occurs in a range of high performance electrochemical energy systems, such as fuel cells,7 batteries,8-10 and supercapacitors,11 where a thorough understanding of transport near charged surfaces and in confined geometries is important in the quest for improved energy and power densities. Several studies have previously investigated the effect of electric double layer on mass transport at micro-/nanoelectrodes,12-19 and thin-layer electrochemical cells.20 In these systems, electrostatic interactions, mass transport and electrode kinetics are highly coupled. Bohn and coworkers21,

22

reported enhanced redox cycling from ion accumulation at recessed ring-disk

nanoelectrode arrays in the absence of supporting electrolyte as a possible mode of signal enhancement for sensors; however, they made no attempt to formally analyze the contribution of electromigration to mass transport. Chen and coworkers23 used finite-element simulations to examine the effect of the electric double layer and the electron-transfer kinetics and the mass transport of charged redox species within thin-layer cells. Voth and coworkers.24 used molecular dynamics simulations to predict inhibited or enhanced charge transport due to high electric field through ultrathin electrolytes layers. Recently, we used lithographically fabricated, nanometer-wide thin-layer electrochemical cells (nanogap cells), first reported by Lemay and coworkers,25-27 to study ion transport phenomena at interfaces in an organic solution using the ferrocenylmethyltrimethylammonium redox couple (FcTMA+/2+). Because of the close spacing between the two planar Pt electrodes in these cells, redox species generated at one electrode can be collected at the other electrode with


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near 100% efficiency, and a significant current enhancement may be achieved through redox cycling (repeated oxidation and reduction of a single redox molecule at closely spaced electrodes). Redox cycling can also be observed in other geometries with closely spaced electrodes, such as thin layer cells,28 scanning electrochemical microscopy near a conducting surface20, 29, 30 and recessed ring-disk nanoelectrodes.21, 22, 31, 32 For the nanogap system, we found nonclassical steady-state peak-shaped voltammograms for redox cycling of the positively charged redox couple (FcTMA+/2+) at low concentrations of supporting electrolyte.33 Moreover, we observed significant decreases in the voltammetric current as the supporting electrolyte concentration was lowered. In contrast, in this report, we report the enhancement in the redox cycling current of a positively charged redox couple hexaamineruthenium (III) chloride (Ru(NH3)63/2+) at low supporting electrolyte concentrations. The remarkable difference in the behavior of the Ru(NH3)63/2+ and FcTMA+/2+ redox systems demonstrates the critical dependence of the electrostatic coupling of the redox ion and surface charges at the electrodes potentials used in redox cycling. Our system, with two independent working electrodes and a combined reference/auxiliary electrode, allows for independent biasing of the two electrodes, providing a means to modulate the ion transport while keeping electron transfer kinetics fast enough that currents are limited by mass transport. Finite-element simulations, which couple the governing equations of ion transport, electric fields and the interfacial redox reactions, are used to provide a quantitative understanding of these phenomena.

Experimental Methods Reagents. Ferrocene (Fc) (Aldrich) was purified twice by sublimation. Tetrabutylammonium hexafluorophosphate (TBAPF6) (Aldrich) was recrystallized from absolute ethanol and dried


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under vacuum. Hexaamineruthenium (III) chloride (99%) (Strem Chemicals), KNO3 (99%, Aldrich) and CH3CN (HPLC grade, Fisher Chemical) were used as received. Aqueous solutions were prepared from deionized water (Barnstead Smart2Pure, Thermo Scientific). Ru(NH3)6PO4 was prepared by metathesis of Ru(NH3)6Cl3 with K3PO4 and followed by recrystallization from the warm aqueous solution. Electrochemical Measurements. A bipotentiostat Pine AFRDE5 was employed for the threeelectrode voltammetric measurements. The upper/lower Pt electrodes of the thin-layer cell were the two working electrodes. A chloridized Ag wire immersed directly into the aqueous solution was used as a quasi-reference and auxiliary electrode. All potentials reported in this paper are relative to the Ag/AgCl wire. The potentiostat was interfaced to a PC computer running custom written programs (LabVIEW 2010, National Instruments) through a multifunction data acquisition card (PCI-6040, National Instruments). All experiments were performed inside a Faraday cage at room temperature. Solutions was exchanged at least 10 times between experiments to ensure there was no carry-over between measurements. Nanometer Wide Thin-Layer Cell Fabrication. Design and fabrication of the nanometer wide thin-layer electrochemical cells followed a lithographic method similar to that reported by the Lemay group25, 26 and was previously documented.33 The resulting geometry, shown in Figure 1, is of two parallel 20 µm-diameter Pt disk electrodes supported on SiNx/SiO2, and separated by 150 to 450 nm. The top electrode has a 6 µm-diameter hole drilled in it to allow solution access. Finite-Element Simulations of the Voltammetric Response. The voltammetric response of Ru(NH3)63/2+ redox cycling within the thin-layer electrochemical cell was simulated using commercial finite-element software (COMSOL Multiphysics 5.2) as described in the Supporting


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Information section S1. Briefly, the mass transport was described using the Nernst-Planck equation34

J i = − Di∇Ci −

zi F Di Ci ∇Φ RT

(1) where F is the Faraday's constant, R is the molar gas constant, T is the absolute temperature, Φ is the potential, Ji, Di, Ci, and zi, are the flux, diffusivity, concentration, and charge of the species i (Ru(NH3)63+, Ru(NH3)62+, K+, Cl− or NO3−). Poisson’s equation was used to calculate the electric potential

∇ 2Φ = −

∑zCF i

i

εε 0

(2) where ε0 is the vacuum permittivity and ε, the relative dielectric constant, was set to be 80 in bulk solution and 6 within the Helmholtz layer(HL), which was taken to be 0.6 nm thick (dHL). The Butler-Volmer equation was used to describe the rate of the electron-transfer reactions of the redox reaction Ru(NH3)63+ + e− = Ru(NH3)62+. This was deemed to take place at the plane of electron transfer (PET) at the upper and lower electrodes, which was taken to be at the outer Helmholtz plane, 0.6 nm from the electrode surface. The electron flux j (= i/nFA) was described by j = k 0 [ C R exp( α f ∆Φ) − C O exp(1 − α ) f ∆Φ)]

(3)

where, α is the transfer coefficient (set to be 0.5), CR and CO are the concentrations of reduced and oxidized form at the PET, and f = F/(RT).We assume that the PET is located at the edge of


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the HL. ∆Φ corresponds to the reaction over-potential, which equals the potential drop across the HL minus the standard redox potential, E0, i.e., the potential corrected for the Frumkin effect.34, 35

E0 was set to −0.3 V vs. Ag/AgCl. The standard heterogeneous rate constant, k0, was set to be

17 cm/s (unless otherwise stated).36 In addition, the potential of zero charge (PZC) of the Pt electrodes is incorporated into the simulation by biasing the potential of the bulk solution. In the simulations, unless otherwise stated, we assume the PZC is at 0 V vs Ag/AgCl, i.e., the external solution is biased at 0 V. Thus a negative E corresponds to a negatively charged electrode, while a positive E corresponds to a positively charged electrode. In reality, the polycrystalline Pt electrodes used in the experiment do not have a well-defined PZC that is uniform across the entire electrode surface (see the Supporting Information section S1 for details). The faradic current results from the 1-electron reduction of Ru(NH3)63+ at the cathode (scanned between 0 and −0.7 V) and the 1-electron oxidation of Ru(NH3)62+ at the anode (typically held constant at 0 V), and its value was computed by integrating the flux of Ru(NH3)62+ or Ru(NH3)63+ across the electrode surfaces.

Results and Discussion The schematic of the nanogap cell is shown in Figure 1, with two parallel 20 µmdiameter Pt disk electrodes, separated by a distance of 150 to 450 nm. The top electrode has a 3 µm-radius hole drilled in it to allow solution access. The nanogap cell thickness was initially calibrated from the diffusion limited steady-state redox cycling of the neutral redox molecule, ferrocene (Fc), in an acetonitrile solution. The following expression for a thin-layer cell, was used to convert the diffusion-limited current, ilim, to the distance between the electrodes, L.34

ilim =

nFADC L

(4)


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D(2.4×10-5 cm2/s) is the average diffusion coefficient (2DFc/(1+DFc+/DFc)), where DFc and DFc+ are the diffusion coefficients of ferrocene and ferrocenium, respectively; C (2.6 mM) is bulk concentration of Fc, respectively, while n = 1 is the number of electrons transferred per molecule; A=π(102−32) µm2, is the overlap area between the top and bottom electrodes, where the subtraction of π×32µm2 accounts for the access hole in the top electrode. For the two cell sizes we fabricated, the thicknesses were determined as 147 ± 18 and 438 ± 29 nm, respectively. See Supporting Information section S2 and S3 for more details.

Figure 1. (a) Schematic of the nanogap electrochemical cell and the redox cycling of Ru(NH3)63/2+ with relevant dimensions labeled (not to scale). The left half is a 2D cross-sectional view and the right half is the 3D view of the nanogap cell configuration. A chloridized Ag wire situated in the droplet of solution was used as


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a quasi-reference/auxiliary electrode. During the redox cycling, the bottom Pt electrode was cycled, typically from between 0 and −0.7 V vs Ag/AgCl and acted as the cathode, while the top Pt electrode was held at a potential EAn, more positive than the standard potential for the Ru(NH3)63/2+ redox couple (E0 ~ −0.30 V vs Ag/AgCl), and acted as the anode. (b) Top-view optical image of a device prior to the etching of the Cr layer. The dashed circle indicates the location of the bottom circular electrode. The blue color is due to the photoresist coated on the surface. Following measurement of the cell thickness using ferrocene, the Ru(NH3)63+ + e− = Ru(NH3)62+ system was studied in aqueous solutions containing varying concentrations of supporting electrolyte (0 to 200 mM KNO3). In typical electrochemical experiments, a large excess of supporting electrolyte is added to the solution in order to decrease the undesirable ohmic potential drop in the solution. Excess electrolyte ions also restrict the electric double layer to distances very close to the electrode-solution interface, reducing the effect of electromigration on the mass transport of the redox active species. Conversely, at low supporting electrolyte concentrations these migration effects, which can increase or decrease the observable current, cannot be ignored, as the electric double layer extends well beyond the electrode surface into the solution.37-39 The effect of the electric potential distribution within the double layer on the rate of an electrode reaction is collectively referred to as the Frumkin effect.34 Our experimental thinlayer cell investigations of the Ru(NH3)63/2+ redox chemistry as a function of the electrolyte concentration provide precise evaluation of electric double layer effects on transport. To minimize any effects of electrolyte ion carry-over between experiments, the experiments were performed in a series of increasing KNO3 concentration. Ru(NH3)63+ undergoes a reversible and rapid 1-electron reduction (Ru(NH3)63+ + e− = Ru(NH3)62+, with E0~ −0.30 V vs Ag/AgCl) at the Pt electrode. In a typical experiment, the anode potential was poised at EAn = 0.0 V vs Ag/AgCl while the cathode potential was cycled from ECat = 0 to −0.7 V vs


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Ag/AgCl at 10 mV/s. Figure 1 shows redox cycling that takes place when ECat is sufficiently negative. In this situation, Ru(NH3)63+ is reduced to Ru(NH3)62+ at the cathode, which is then transported to the anode through a combination of diffusion and migration. At the anode, it is oxidized back to Ru(NH3)63+. Transport of the Ru(NH3)63+ back to the cathode completes the redox cycling. As a single molecule can undergo multiple redox reactions in a very short time, the current displays a significant enhancement over that which would be expected from a single disk-shaped electrode with identical dimensions and in the same solution. Typical experimental voltammograms are displayed in Figures 2a and c for 147 and 438 nm-wide cells, respectively. For clarity, here and in the rest of the main text, only a single cycle of the cathodic current is shown. However, as voltammograms show excellent reproducibility between cycles and the anodic and cathodic current were always almost equal and opposite, the cathodic current is sufficient to fully describe the system (example voltammograms showing multiple cycles with both cathodic and anodic currents are available in Supporting Information section S4). The contribution from oxygen dissolved in the aqueous solution to the voltammetric response is negligible, as it does not undergo redox cycling in the experimental conditions employed in this work (detailed description is provided in Supporting Information section S5). Also note that, while we plot the anode as the top electrode in schematics and simulations, in the practice this was not always the case. However, for the aforementioned reasons reversing the polarity of the electrodes does not alter the response.


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Figure 2. Experimental (a, c) and simulated (b, d) voltammetric responses of 1.0 mM Ru(NH3)6Cl3 in H2O with KNO3 concentrations as labeled. Cell thicknesses were (a, b) 147 nm, and (c, d) 438 nm. The scan rate was 10 mV/s. Arrows indicate the forward potential scan. EAn = 0 V. At a high concentration of supporting electrolyte (500 mM KNO3), the sigmoidal shaped voltammetric response has a limiting current consistent with predictions from classic diffusion limited transport thin-layer electrochemistry (Equation 4). As the KNO3concentration decreases, the limiting current increases in magnitude, which is a consequence of increasing effect of the electrical double layer on ion transport, vide infra. In the voltammograms for the 147 nm wide cell, shown in Figure 2a, an approximately two-fold increase in the limiting current is observed in the absence of KNO3 when compared to 500 mM KNO3 (ilim = 102 nA vs ilim = 202 nA). As predicted by Equation 4, these voltammograms show smaller currents for the thicker cell due to increased transport distance and, thus, diminished redox cycling.


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All the experimental voltammograms display some hysteresis between the forward and reverse scans. This hysteresis is more significant for the thinner nanogap cell (L = 147 nm) and at lower supporting electrolyte concentrations. As the 10 mV/s scan rate is sufficiently slow that any mass transport phenomena should be at steady state, this suggests that a slower physical process is the cause, as will be discussed in more detail later. The extension of electric double layer into the solution can be characterized by the Debye length, λD

λD =

ε 0ε kT e

2

(5)

∑C z

2 i i

where ε and ε0 are the relative electric permittivity of the solvent and permittivity of vacuum, respectively, k is the Boltzmann constant, zi is the charge number of the ion i, and e is the elementary charge. In particular, for our system as the supporting electrolyte concentration is decreased from 500 mM to 200, 10, 2.0 and 0 mM, λD increases from 0.42 nm to 0.66, 2.34, 3.32, and 3.83 nm, respectively. Note the small change in λD when the KNO3 concentration is decreased from 2.0 to 0 mM, which is due to the contributions of 1.0 mM Ru(NH3)63+ (assumed to be in the 3+ form for calculation of λD) and 3.0 mM Cl− (counter ion). Thus, by varying the supporting electrolyte concentration, we are able to tune the thickness of the electric double layer (95% decay of the potential assumed to be at a distance of ~3λD), and consequently, affect the electrostatic interaction between charged redox molecules and charged electrodes, as well as the ion transport across the thin-layer electrochemical cell. Simulated voltammograms corresponding to the experiments shown in Figure 2a and c described above are shown in Figure 2b and d. While the absolute values of the simulated voltammetric currents differ slightly from the experiments, the voltammograms reproduce the


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experimentally observed trend of increasing current with decreasing concentrations of supporting electrolyte. Also note that in the experiments, the currents arise more gradually with the overpotential, which might infer that slow electrode kinetics are responsible; however, based on simulation results (see Supporting Information section S6), a rate constant three orders of magnitude (0.01 cm/s vs 17 cm/s) less than that generally accepted40 would be required for the Ru(NH3)63/2+ redox couple in order to observe the effects of slow electron-transfer kinetics.

Figure 3. Simulations of 1.0 mM Ru(NH3)6Cl3 in a 147 nm thick cell undergoing oxidation at the top electrode (0 V) and reduction at the bottom electrode (−0.7 V). (a) Color plot of the simulated Ru(NH3)63+ concentration distribution in the presence of excess supporting electrolyte (500 mM KNO3) and a zoom-in of concentration distribution at the electrode center (red-dashed box). (b) Potential


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profiles, and (c, d) concentration profiles of Ru(NH3)63+ and Ru(NH3)62+, respectively, taken across the center of the cell in the same system for 500 mM and 0 mM KNO3 (along the black dashed vertical line in part a). (e) Total average concentration of redox molecules (Ru(NH3)63+ and Ru(NH3)62+) between the two electrodes as a function of cathode potential. The concentration distributions of Cl−, K+ and NO3− for each of these situations is available in the Supporting Information section S7. To understand the voltammetric response, it is necessary to observe how the potential, concentrations and fluxes vary throughout the nanogap cell. Figure 3 presents the results of finite element simulations of the nanogap cells. In these simulations electron transfer occurs at the plane of electron transfer (PET) which is anticipated to be of thickness equivalent to the outer Helmholtz plane. We take this distance to be 0.6 nm (see Methods and Supplementary Information for more details). The precise thickness used for the Helmholtz layer does not significantly alter the simulated results. However, omitting the potential drop across the Helmholtz layer produces non-physical potential distributions and i-V behavior inconsistent with experimental observations. In part a, the simulated concentration distribution of Ru(NH3)63+ in a 147 nm thin-layer cell in the presence of excess supporting electrolyte (500 mM KNO3) is shown. At this high ionic strength, the electric double layer is highly compressed (λD = 0.42 nm). In the zoom-in plot, which shows the region between the electrodes, far away from the access hole or electrode edges, we see the surface concentration of Ru(NH3)63+ are 0 and 1 mM at the cathode and anode, respectively, indicating that the potentials (ECat = −0.7 V, EAn = 0 V) are sufficient to reduce Ru(NH3)63+ or oxidize Ru(NH3)62+ at a transport-limited rates. A hemispherical diffusion profile is seen at the access hole, where the bottom electrode has no electrode above it; however, as we have previously shown,33 the current contribution of this region is insignificant as it cannot undergo redox cycling. As can be seen in the zoom-in, in the region far away from the electrode


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edges, there is linear concentration gradient in the vertical direction and no gradient in the radial direction. Thus for the remainder of this work, we consider only quantities in a cross-section of the cell perpendicular to the electrodes and far from their edges, as denoted by the black dashed vertical line in the left hand portion of Figure 3a. As expected, for both 0 and 500 mM KNO3, the majority of the potential drop occurs within the HL as is indicated in Figure 3b. At 500 mM KNO3 (λD = 0.42 nm), the potential at the plane of electron transfer is −33 mV, and decays rapidly to 0 mV around 2 nm from the cathode. At 0 mM KNO3 (λD = 3.83 nm), the potential is −86 mV at the PET and decays quickly within the first ~40 nm; however, there is still an appreciable, but small, potential gradient across the entire width of the cell. Note, in these simulations the PZC is assumed to be 0 V, so there is no double layer at the anode; discussion of the choice of PZC will be presented later. Figure 3c and d show the cross-sectional concentrations in the center of the cell for Ru(NH3)63+ and Ru(NH3)62+, respectively. At high ionic strength, both concentration distributions are essentially linear between the electrodes, apart from a large increase in the concentration of Ru(NH3)62+ within a ~0.3 nm region close to the cathode. The ion enrichment in this region (surface concentration of ~13.6 mM for the red curve in Figure 3d) is due to the Ru(NH3)62+, which is produced at this electrode, being electrostatically attracted to the negatively charged cathode. When no extra supporting electrolyte is added to the solution, the ionic strength is determined entirely by the redox species and the counter ions (1.0 mM Ru(NH3)6Cl3) and a deviation from linearity of the concentration of the redox molecules is observed within the electric double layer (3λD = 11.5 nm). Compared to the distribution in 500 mM KNO3 shown in Figure 3c, one can observe that the concentration profile of Ru(NH3)63+ is slightly sub-linear and


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this effect extends ~50 nm from the cathode surface. This small diminishment is due to electrostatic attraction of Ru(NH3)63+ to cathode, where it is rapidly consumed. In Figure 3d we can see that in the absence of extra supporting electrolyte, the concentration of Ru(NH3)62+ is also enhanced at the cathode surface, with a surface concentration (848 mM) that is ~60-fold higher than that in the presence of 500 mM KNO3. Moreover, while the concentration gradient of Ru(NH3)62+ is linear beyond around 40 nm from the cathode, it is steeper than for 500 mM KNO3, which indicates enhanced diffusional transport and thus, enhanced current. Figure 3e shows the average concentration of redox molecules between the electrodes (the sum of Ru(NH3)63+ and Ru(NH3)62+ concentrations) as a function of the cathode potential at 0 and 500 mM KNO3. No enrichment is observed in the presence of excess supporting electrolyte at any cathode potential and the average concentrations of each redox form is equal to half of the bulk concentration, i.e., 0.5 mM. In contrast, in the absence of supporting electrolyte, enrichment of Ru(NH3)63/2+ is observed, which increases with decreasing values of ECat to a maximal 3-fold enhancement at ECat = −0.7 V. As we can infer from parts c and d, the ion accumulation is localized to the region close to the cathode surface and the average concentration of the two redox species are unequal. At ECat = −0.7 V, the average concentration of Ru(NH3)62+ is 2.51 mM, while the concentration of Ru(NH3)63+ is ~5-fold lower (0.49 mM). This indicates that the transport of Ru(NH3)62+ to the top electrode is indeed the rate limiting step for the cell redox cycling. Note that, while unequal average concentrations have previously been reported when the two halves of the redox couple have unequal diffusion coefficients,41, 42 the diffusion coefficients were taken to be equal in our simulations.


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Figure 4. Individual diffusional and migrational fluxes (red curves) and total fluxes (black lines) of Ru(NH3)62+ within the cells with (a) 500 mM KNO3, and (b) 0 mM KNO3 in a 1.0 mM Ru(NH3)6Cl3 solution at EAn = 0 V and ECat = −0.7 V. Figure 4 shows the fluxes for the rate-limiting transport Ru(NH3)62+ in both the high (500 mM KNO3) and no supporting electrolyte conditions, parts a and b, respectively. Large diffusional and migrational fluxes are observed in the region close to the cathode, which are almost equal but opposite in their values. Their sum, which is the total flux, is at least 10000-fold smaller than the maximum individual values of the components. The enhanced diffusional flux near the cathode is due to the concentration gradient being many orders of magnitude greater than in the rest of the cell (see Figure 3d). The flux on the surface of the cathode (z = 0 nm) without supporting electrolyte is ~ 50-fold higher than the case with 500 mM KNO3, indicating the much stronger concentration gradient in the former. In each case, the diffusional flux ( −D∇C ) rapidly decreases and levels off to a constant value equal to the total flux (see insets). A significant difference in the distance over which the diffusional flux decays is observed, as a function of the electrolyte concentration, which results from the differences in the Debye length. With 500 mM KNO3, the drop occurs over the first ~4 nm from the cathode, whereas for the 0 mM system, the drop occurs mostly by ~40 nm. The enhanced migrational flux ( −


zF DC∇Φ ) RT

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close to the cathode is a function of both the relatively high concentration and the high electric field in this region. Both the concentration and electric field decreases with distance away from the cathode, and the migration flux decreases rapidly over the same length scale as the diffusional flux; however, the migrational limiting flux value far from the cathode is zero due to the negligible electric field (potential gradient) far away from the electrode surfaces. Summation of the diffusional and migrational components leads to the total flux, which is constant across the cell, indicating that the system is in a dynamic steady state. As shown in Figure 4a and b and their zoom-ins, despite the great difference in the magnitudes of diffusional and migrational flux components between the two systems, the difference in current, which is proportional to the total flux, is much smaller. In particular, the total flux for the 0 mM KNO3 system (5.6 × 10−3 mol/(m2 s)) is only 1.25 times that for the 500 mM KNO3 system (4.4 × 10−3 mol/(m2 s)), leading to the limiting current of 157 to 125 nA, respectively. The difference in the limiting diffusional fluxes is reflected by the differences in the concentration gradients of Ru(NH3)62+ observed far from the surface in Figure 3d. The previous section explained the effect of supporting electrolyte on the voltammetric responses, as the cathode potential was cycled and anode potential was held at 0 V; however, EAn presents an additional independent control of the voltammetric response. Comparing the potential window for aqueous solution with the E0 for Ru(NH3)63/2+ couple (E0 = −0.30 V vs Ag/AgCl), it is apparent that we can bias the anode at other potentials while keeping the electrode kinetics for Ru(NH3)62+ oxidation at a transport-limited rate. In all cases, the cathode was scanned over the same potential range (from 0 to −0.7 V). Figure 5a and c show experimental voltammograms for the redox cycling of 1.0 mM Ru(NH3)6Cl3 in the absence of extra supporting electrolyte at EAn = −0.1, 0, 0.1 and 0.2 V for the two different cell thicknesses.


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When EAn = −0.1 V, the limiting current is very slightly higher than the EAn = 0 V case. However, when the anode is held at 0.1 V or 0.2 V, a significant decrease of the redox cycling current is observed. Simulated voltammetric responses (part b and d) display comparable changes in current, indicating that the simulations will prove useful in determining the source of this effect. The significant hysteresis between the forward and reverse scans of the experimental voltammograms, which is absent in the simulated voltammograms and which seems to strongly depend on the anode potential, is discussed below. The voltammetric sensitivity to the anode potential decreases as the supporting electrolyte concentration is increased (see Supporting Information section S8). Surprisingly, experimental voltammograms with 200 mM concentration of KNO3 display a significant current inhibition at EAn = 0.2 V when compared with EAn = −0.1 V. In this configuration we would expect the effects of the electrostatics and ion migration to be fully suppressed as is seen in the simulation of this system. (See Supporting Information section S9).


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Figure 5. Experimental (a, c) and simulated (b, d) voltammetric responses of 1.0 mM Ru(NH3)6Cl3 in H2O in the absence of KNO3 at various anode potentials as labeled. Cell thicknesses were respectively (a, b) 147 nm, and (c, d) 438 nm. The scan rate was 10 mV/s. Arrows indicate the direction of forward potential scan. To understand these trends, we again look at the potential and concentrations distributions and the fluxes from simulations, which are presented in Figure 6. For all values of EAn, the potential increases gradually from −86 mV at the cathode PET to 0 mV at the midpoint between the electrodes. The different biases of EAn = −0.1, 0 and 0.2 V result in potentials at the PET of the anode of −23, 0, and 68 mV, respectively. The concentration profiles of Ru(NH3)63+ and Ru(NH3)62+ across the nanogap cell are shown in Figure 6b and c, respectively. For all values of EAn, the concentration of Ru(NH3)63+ close to the cathode shows a similar concentration distribution to that shown in Figure 3c (the EAn = 0 V curve is precisely that shown in Figure 3c). For non-zero values of EAn, there is either enrichment or depletion of Ru(NH3)63+ in the region close to the anode. When EAn = −0.1 V, the concentration of Ru(NH3)63+ at the anode surface is nearly 16 times higher than the bulk concentration, due to its electrostatic accumulation at the anode after production. At EAn = 0.2 V, the Ru(NH3)63+ concentration at the anode surface is zero as it is electrostatically repelled as soon as it is electrogenerated.


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Figure 6. Simulated (a) potential profiles; concentration profiles of (b) Ru(NH3)63+ and (c) Ru(NH3)62+ at different anode potential as labeled. (d) Diffusional, migrational and total fluxes of Ru(NH3)62+ across the center of the cell at EAn = 0.2 V, ECat = −0.7 V for 1.0 mM Ru(NH3)6Cl3 in H2O in the absence of extra KNO3. Cell thickness is 147 nm. The inset in part b, c and d are the zoom-ins of concentration and the flux distributions. The fluxes of Ru(NH3)63+ across the center of the cell at the same condition as part d, and concentration profiles of Cl− are available in the Supporting Information sections S10 and 11, respectively. In all cases, it is the transport of Ru(NH3)62+ which is the limiting factor in the nanogap current. The concentration near the cathode surface is essentially the same for all value of EAn, with a large enrichment (~0.84 M) near the electrode surface. In all cases, the concentration of Ru(NH3)62+ is at the anode surface is zero, as Ru(NH3)62+ oxidation is rapid for all values of EAn considered. The Ru(NH3)62+ concentration distributions near the anode are almost identical at EAn = −0.1 and 0 V, with the EAn = −0.1 V case showing very slightly lower values due to


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migration enhanced mass transport to the electrode. When EAn = 0.2 V, a markedly different distribution is observed as Ru(NH3)62+ ions are repelled away from the anode and the concentration enhancement occurs in the central region between the two electrodes. This presents an additional barrier to the mass transport of Ru(NH3)62+ from the cathode to anode, which is reflected in a lower current compared to the EAn = −0.1/0 V systems. Figure 6d presents the diffusional, migrational and total fluxes of Ru(NH3)62+ across the cell for EAn = 0.2 V and ECat = −0.7 V. For most of the domain, the diffusional and migrational fluxes show a similar trend when compared with the fluxes for EAn = 0 V shown in Figure 4b; however, in the region near the anode (z = 110 to 147 nm), a peaked feature is observed. This feature is due to migration, −

zF DC∇Φ , being dependent on the product of the Ru(NH3)62+ RT

concentration, which decays to zero, and the electric field, which is highest on the anode surface. The details are very similar to our previous report on FcTMA+/2+ redox cycling in the nanogap cells, where we saw diminished current due to a similar transport barrier at the cathode.33 The total flux, which is calculated from the summation of two components, is only 2.0 × 10−3 mol/(m2 s)) at EAn = 0.2 V, which is much lower than that (5.6 × 10−3 mol/(m2 s)) at EAn = 0 V. This equates a 64% reduction in the limiting current as presented in Figure 5b. Note, the change in current can also be inferred by observing differences in Ru(NH3)63/2+ concentration gradient in the region where diffusion is the only contribution to mass transport (z = 40 to 100 nm). The results presented so far assumed the potential of zero charge (PZC) for the Pt electrodes was 0 V vs Ag/AgCl. We have seen that the enhancement or attenuation of the limiting current as a function of EAn is strongly related to the potential and concentration distributions close to the anode, which was poised at potentials around the PZC. This suggests


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that the limiting current as a function of EAn may be a sensitive measure of the PZC. We confirmed this hypothesis with further finite element simulations at a range of PZC values, which are presented in Figure 7. Note that, in contrast to the other plots, in this figure it is the anode potential, EAn, that is varied along the x-axis, with ECat = −0.7 V kept constant at a potential sufficient for mass transport limited reduction.

Figure 7. Simulated cathodic limiting current taken at ECat = −0.7 V as a function of the potential of the anode, EAn, for different values of the PZC. Cell thickness of 147 nm. 1.0 mM Ru(NH3)6Cl3 in H2O in the absence of KNO3. The inset shows the limiting current normalized by that at EAn = −0.1 V, with the four experimental points as solid stars for comparison. As shown in Figure 7, for each value of the PZC, a sigmoidal response in the simulated limiting current is observed as EAn is varied. For all values of the PZC, there is a noticeable current drop as EAn is poised at potentials more positive than the PZC. Generally, there is a potential offset in the current response that scales with the PZC. For example, in Figure 7 the


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−50 mV PZC current curve is offset by ca. −50 mV from the 0 V PZC current response. Interestingly, this allows us to assess the PZC of the Pt electrodes under our experimental conditions by comparing the experimental and simulation current response normalized to the maximum current with changing anode potential. The inset in Figure 7 shows the normalized limiting currents from the experimental voltammograms shown in Figure 5a overlaid onto the simulation data. The experimental limiting current remains constant between EAn = −0.1 and 0 V, before it decreases by approximately 38% at EAn = +0.1 V, decreasing further to approximately 10% at EAn = +0.2 V. This suggests that the PZC for the Pt electrodes in our experimental system is −50 ± 50 mV vs Ag/AgCl. While our simulation results offer an explanation for the experimental observations, the significant hysteresis associated with experimental voltammograms (Figures 2 and 5) was not predicted by simulations. Figures 2a and b show the hysteresis for the redox cycling of 1.0 mM Ru(NH3)6Cl3 in aqueous solution increases with decreasing supporting electrolyte concentration and is more profound for the 147 nm electrochemical cell. As our simulations were time dependent we can be confident that the hysteresis is not due to the time necessary for the nanogap to equilibrate with bulk solution. We conjecture that the hysteresis is due to adsorption/desorption of analyte molecules onto the electrodes, a phenomenon that has added importance due to the high surface-to-volume ratio for nanogap cells.43 As hysteresis was observed in the absence of supporting electrolyte, we can be confident that K+ and NO3− are not the primary causes. We also conducted redox cycling of Ru(NH3)6PO4 in the nanogap cell in order to assess if the Cl− adsorption was the source for the observed hysteresis. The choice of Ru(NH3)6PO4 was based on the weak affinity of PO43- for the Pt electrode and its suitability for preparation through metathesis of the commercially available


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Ru(NH3)6Cl3. The results of these experiment, shown in Supporting Information section S12, display hysteresis of comparable size to the Ru(NH3)6Cl3, absolving Cl− from being the primary cause of the hysteresis. This finding leaves Ru(NH3)63/2+ as the likely species involved in adsorption/desorption processes leading the observed hysteresis. Lemay et al. have previously reported the adsorption of many redox species in the nanogap devices.44-47 Pertinent to this work are their reports on the transient current responses for Ru(NH3)63/2+ redox cycling in a Pt nanogap cell upon stepping the electrode potential.44, 45 The transients reported lasted several seconds, far longer than would be predicted by diffusion alone. They attributed the phenomena to two inter-related effects of adsorption/desorption. Firstly, changing the potential changes the equilibrium adsorption, which results in desorption (transiently increasing the concentration) or adsorption (transient decrease). Secondly, adsorption considerably lowers the apparent rate of lateral diffusion (direction parallel to the plane of the electrode), slowing down the time for equilibration. The second effect is due to the diffusing species spending a proportion of the time adsorbed as a new equilibrium surface concentration is established; similar reports of binding causing a drop in the apparent diffusion coefficient have been reported for brain extracellular systems.48,

49

Lemay and co-workers also showed that

cations adsorb more strongly to an electrode as its potential is made more positive, which is highly counter-intuitive when one considers electrostatics. The combination of these observations explains our observations of increased hysteresis when the anode is more positive (strongly adsorbing) and the higher currents on the forward versus the reverse scan. Conclusion This report of redox cycling of the Ru(NH3)63/2+ between two Pt electrodes separated by 147 and 438 nm, coupled with our previous investigation of the FcTMA+/2+ system,33


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demonstrate the importance of quantitatively understanding the electrostatic interactions between the redox species and electrode surface in determining the voltammetric response in highly confined spaces. While both redox systems are characterized by positively charged redox species, the Ru(NH3)63/2+ cycling currents are enhanced at lower electrolyte concentrations, while the currents for FcTMA+/2+ cycling are diminished. Physically, these remarkably different behaviors can be qualitatively explained by the fact that Ru(NH3)63/2+ cycling requires at least one electrode to be biased at potentials negative of the PZC of Pt, while FcTMA+/2+ cycling requires at least one electrode to be biased at potentials positive of the PZC of Pt. In the former case, electrostatic attraction between the cathode and Ru(NH3)63/2+ occurs, resulting in an enhanced current, while in the latter, electrostatic repulsion between FcTMA+/2+ and the anode is operative, resulting in a diminished current. The electrostatic relationships between species charge, the electrode potential and the PZC, as well as the thickness of the cell and Debye length, and how these impact electrochemical cell currents, are very complex, but as shown here and previously, can be captured with semi-quantitative agreement by finite element simulations. In the current study, we demonstrated that the concentration of Ru(NH3)62+ maybe enriched by ~850 times at the surface of the cathode, compared with its value in bulk solution due to ion migration opposing diffusion. The current enhancement phenomenon becomes less significant as the electric double layer thickness decreases at higher ionic strength. We also demonstrated that redox cycling current can be gated (enhanced or attenuated vs diffusion limited) by changing the potential of the opposing anode, while maintaining the system under purely transport control. This study, using a well-defined geometry, provides a basis to understand related electrochemical systems with more complex geometries. In particular, we believe that these fundamental studies are particularly germane to understanding transport near


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charged surfaces associated with energy storage systems, where redox chemistry and ion transport are strongly coupled within confined geometries. Acknowledgements. This work was supported by the Office of Naval Research (N000141211021).This work made use of University of Utah shared facilities of the Micron Technology Foundation Inc. Microscopy Suite and the Utah Nanofab. The authors thanks Dr. David P. Hickey’s assistance in preparation of Ru(NH3)6PO4 and Jiewen Xiong for help with the fabrication of the nanogap cells. Supporting Information. Geometry, meshes and boundary conditions of the finite-element simulations, and further simulation and experimental results are included in supporting information. Supporting information is available free of charge via the Internet at http://pubs.acs.org.


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