Simulation of the cyclic voltammetric response of an outer-sphere redox species with inclusion of electrical double layer structure and ohmic potential drop.

A finite-element model has been developed to simulate the cyclic voltammetric (CV) response of a planar electrode for a 1e outer-sphere redox process, which fully accounts for cell electrostatics, including ohmic potential drop, ion migration, and the structure of the potential-dependent electric double layer. Both reversible and quasi-reversible redox reactions are treated. The simulations compute the time-dependent electric potential and ion distributions across the entire cell during a voltammetric scan. In this way, it is possible to obtain the interdependent faradaic and non-faradaic contributions to a CV and rigorously include all effects of the electric potential distribution on the rate of electron transfer and the local concentrations of the redox species Oz and Rz-1. Importantly, we demonstrate that the driving force for electron transfer can be different to the applied potential when electrostatic interactions are included. We also show that the concentrations of Oz and Rz-1 at the plane of electron transfer (PET) significantly depart from those predicted by the Nernst equation, even when the system is characterised by fast electron transfer/diffusion control. A mechanistic rationalisation is also presented as to why the electric double layer has a negligible effect on the CV response of such reversible systems. In contrast, for quasi-reversible electron transfer the concentrations of redox species at the PET are shown to play an important role in determining CV wave shape, an effect also dependant on the charge of the redox species and the formal electrode potential of the redox couple. Failure to consider electrostatic effects could lead to incorrect interpretation of electron-transfer kinetics from the CV response. Simulated CVs at scan rates between 0.1 and 1000 V s-1 are found to be in good agreement with experimental data for the reduction of 1.0 mM Ru(NH3)63+ at a 2 mm diameter gold disk electrode in 1.0 M potassium nitrate.

Finite Element Modeling of the Combined Faradaic and Electrostatic Contributions to the Voltammetric Response of Monolayer Redox Films.

The voltammetric response of electrodes coated with a redox-active monolayer is computed by finite element simulations based on a generalized model that couples the Butler-Volmer, Nernst-Planck, and Poisson equations. This model represents the most complete treatment of the voltammetric response of a redox film to date and is made accessible to the experimentalist via the use of finite element modeling and a COMSOL-generated report. The model yields a full description of the electric potential and charge distributions across the monolayer and bulk solution, including the potential distribution associated with ohmic resistance. In this way, it is possible to properly account for electrostatic effects at the molecular film/electrolyte interface, which are present due to the changing charge states of the redox head groups as they undergo electron transfer, under both equilibrium and nonequilibrium conditions. Specifically, our numerical simulations significantly extend previous theoretical predictions by including the effects of finite electron-transfer rates (k0) and electrolyte conductivity. Distortion of the voltammetric wave due to ohmic potential drop is shown to be a function of electrolyte concentration and scan rate, in agreement with experimental observations. The commonly used Laviron analysis for the determination of k0 fails to account for ohmic drop effects, which may be non-negligible at high scan rates. This model provides a more accurate alternative for k0 determination at all scan rates. The electric potential and charge distributions across an electrochemically inactive monolayer and electrolyte solution are also simulated as a function of applied potential and are found to agree with the Gouy-Chapman-Stern theory.

Visualization of Hydrogen Evolution at Individual Platinum Nanoparticles at a Buried Interface.

Electrochemical processes occurring at solid/solid and solid/membrane interfaces govern the behavior of a variety of energy storage devices, including electrocatalytic reactions at electrode/membrane interfaces in fuel cells and ion insertion at electrode/electrolyte interfaces in solid-state batteries. Due to the heterogeneity of these systems, interrogation of interfacial activity at nanometer length scales is desired to understand system performance, yet the buried nature of the interfaces makes localized activity inaccessible to conventional electrochemical techniques. Herein, we demonstrate nanoscale electrochemical imaging of hydrogen evolution at individual Pt nanoparticles (PtNPs) positioned at a buried interface using scanning electrochemical cell microscopy (SECCM). Specifically, we image the hydrogen evolution reaction (HER) at individual carbon-supported PtNP electrocatalysts covered by a 100 to 800 nm thick layer of the proton exchange membrane Nafion. The rate of hydrogen evolution at PtNP at this buried interface is shown to be a function of Nafion thickness, with the highest activity observed for ∼200 nm thick films.

Nitrogen Bubbles at Pt Nanoelectrodes in a Nonaqueous Medium: Oscillating Behavior and Geometry of Critical Nuclei.

Gas bubble evolution is present in many electrochemical and photoelectrochemical processes. We previously reported the formation of individual H2, N2, and O2 nanobubbles generated from electrocatalytic reduction of H+ and oxidation of N2H4 and H2O2, respectively, at Pt nanodisk electrodes in an aqueous solution. All the nanobubbles formed display a dynamic stationary state of a three-phase boundary with an invariant residual current. Here, we test the hypothesis that gas nanobubbles can also be electrogenerated in a nonaqueous medium. Interestingly, we found oscillating bubble behavior corresponding to nucleation, growth, and dissolution in dimethyl sulfoxide and methanol. One possible explanation of the oscillation mechanism is provided by the instable dynamic equilibrium between the gas influx due to supersaturation and outflux due to Laplace pressure. Furthermore, the critical gas concentrations for N2 nanobubble nucleation are estimated to be 148, 386, 200, and 16 times supersaturation and the contact angles of the critical nuclei to be 164°, 151°, 160°, and 174° in water, dimethyl sulfoxide, ethylene glycol, and methanol, respectively. This is the first report on electrochemical nucleation of gas bubbles in nonaqueous solvents. Our electrochemical gas bubble study based on a nanoelectrode platform has proven to be a prototypical example of single-entity electrochemistry.

Electrochemical Generation of Individual Nanobubbles Comprising H2, D2, and HD.

The electrochemical reduction of deuterons (2D+ + 2e- → D2) at Pt nanodisk electrodes (radius = 15-100 nm) in D2O solutions containing deuterium chloride (DCl) results in the formation of a single gas nanobubble at the electrode surface. Analogous to that previously observed for the electrochemical generation of H2 nanobubbles, the nucleation and growth of a stable D2 nanobubble is characterized in voltammetric experiments by a highly reproducible and well-resolved sudden drop in the faradaic current, a consequence of restricted mass transport of D+ to the electrode surface following the liquid-to-gas phase transition. D2 nanobubbles are stable under potential control due to a dynamic equilibrium existing between D2 gas dissolution and electrochemical generation of D2 at the circumference of the Pt nanodisk electrode. Remarkably, within the error of the experimental measurement (<6%), the electrochemical current required to nucleate a D2 gas phase in a D2O solution is identical to that for the H2 gas phase in a H2O solutions, indicating that the concentration required for nucleating a D2 nanobubble in D2O (0.29 M) is ∼1.25 times larger than that for a H2 nanobubble (0.23 M), while the supersaturation is ∼300 in each case. We further demonstrate that individual nanobubbles can be electrogenerated in mixed D2O/H2O solutions containing both D+ and H+ at respective individual concentrations well below those required to nucleate a gas phase containing either pure D2 or H2. This latter finding indicates that the resulting nanobubbles comprise a mixture of D2, H2, and HD molecules with the chemical composition of a nanobubble determined by the concentrations and diffusivities of D+ and H+ in the mixed D2O/H2O solutions.

Electric Field-Controlled Synthesis and Characterisation of Single Metal-Organic-Framework (MOF) Nanoparticles.

Achieving control over the size distribution of metal-organic-framework (MOF) nanoparticles is key to biomedical applications and seeding techniques. Electrochemical control over the nanoparticle synthesis of the MOF, HKUST-1, is achieved using a nanopipette injection method to locally mix Cu2+ salt precursor and benzene-1,3,5-tricarboxylate (BTC3- ) ligand reagents, to form MOF nanocrystals, and collect and characterise them on a TEM grid. In situ analysis of the size and translocation frequency of HKUST-1 nanoparticles is demonstrated, using the nanopipette to detect resistive pulses as nanoparticles form. Complementary modelling of mass transport in the electric field, enables particle size to be estimated and explains the feasibility of particular reaction conditions, including inhibitory effects of excess BTC3- . These new methods should be applicable to a variety of MOFs, and scaling up synthesis possible via arrays of nanoscale reaction centres, for example using nanopore membranes.

Coupled Electron- and Phase-Transfer Reactions at a Three-Phase Interface.

Coupled electron- and phase-transfer reactions are fundamentally important in electrochemical energy conversion and storage, e.g., intercalation of Li+ in batteries and electrochemistry at the three-phase boundary in fuel cells. The mechanism, energetics, and kinetics of these complex reactions play an important role in device performance. Herein, we describe experimental methodology to quantitatively investigate coupled electron- and phase-transfer reactions at an individual, geometrically well-defined, three-phase interface. Specifically, a Pt-Ir wire electrode is placed across a H2O/1,2-dichloroethane (DCE) interface, creating a Pt-Ir/H2O/DCE boundary that is defined mathematically by a line around the surface of the wire. We investigated the oxidation of ferrocene (Fc), initially present in DCE (but essentially insoluble in water), at the three-phase boundary, and the transfer of its charged reaction product ferrocenium (Fc+) across the interface into the aqueous phase. In cyclic voltammetry, a reversible wave at E1/2 ∼ 0.58 V is observed for Fc oxidation in DCE on the first scan. The Fc+ produced near the H2O/DCE interface transfers into the aqueous phase. On the second and subsequent cycles, a second reversible wave at more negative potentials, E1/2 ∼ 0.33 V, is observed, corresponding to the reduction of Fc+ (and reoxidation back to Fc) in the aqueous phase. Finite-element simulations quantitatively capture the voltammetric response of coupled electron and phase transfer at the three-phase interface and indicate that the electrochemical response observed in the aqueous phase occurs within ∼200 µm of the Pt-Ir/H2O/DCE boundary. Finally, we demonstrate that the rate of transfer of Fc+ is strongly dependent on the concentration of supporting electrolyte, reaching a maximum at an intermediate electrolyte concentration, suggesting a critical role of the electric field distribution in determining the reaction rates at the three-phase interface.

Electrochemically Driven, Ni-Catalyzed Aryl Amination: Scope, Mechanism, and Applications.

C-N cross-coupling is one of the most valuable and widespread transformations in organic synthesis. Largely dominated by Pd- and Cu-based catalytic systems, it has proven to be a staple transformation for those in both academia and industry. The current study presents the development and mechanistic understanding of an electrochemically driven, Ni-catalyzed method for achieving this reaction of high strategic importance. Through a series of electrochemical, computational, kinetic, and empirical experiments, the key mechanistic features of this reaction have been unraveled, leading to a second generation set of conditions that is applicable to a broad range of aryl halides and amine nucleophiles including complex examples on oligopeptides, medicinally relevant heterocycles, natural products, and sugars. Full disclosure of the current limitations and procedures for both batch and flow scale-ups (100 g) are also described.

Observing Transient Bipolar Electrochemical Coupling on Single Nanoparticles Translocating through a Nanopore.

We report the observation of transient bipolar electrochemical coupling on freely moving 40 nm silver nanoparticles. The use of an asymmetric nanoelectrochemical environment at the nanopore orifice, for example, an acid inside the pipette and halide ions in the bulk, enabled us to observe unusually large current blockages of single Ag nanoparticles. We attribute these current blockages to the formation of H2 nanobubbles on the surface of Ag nanoparticles due to the coupled faradaic reactions, in which the reduction of protons and water is coupled to the oxidation of Ag and water under potentials higher than 1 V. The appearance of large current blockages was strongly dependent on the applied voltage and the choice of anions in the bulk solution. The correlation between large current blockages with the oxidation of Ag nanoparticles and their nanopore translocation was further supported by simultaneous fluorescence and electric recordings. This study demonstrates that transient bipolar electrochemistry can take place on small metal nanoparticles below 50 nm when they pass through nanopores where the electric field is highly localized. The use of a nanopore and the resistive-pulse sensing method to study transient bipolar electrochemistry of nanoparticles may be extended to future studies in ultrafast electrochemistry, nanocatalyst screening, and gas nucleation on nanoparticles.

Nanoscale Fluid Vortices and Nonlinear Electroosmotic Flow Drive Ion Current Rectification in the Presence of Concentration Gradients.

Ion current rectification (ICR) is a transport phenomenon in which an electrolyte conducts unequal currents at equal and opposite voltages. Here, we show that nanoscale fluid vortices and nonlinear electroosmotic flow (EOF) drive ICR in the presence of concentration gradients. The same EOF can yield negative differential resistance (NDR), in which current decreases with increasing voltage. A finite element model quantitatively reproduces experimental ICR and NDR recorded across glass nanopipettes under concentration gradients. The model demonstrates that spatial variations of electrical double layer properties induce the nanoscale vortices and nonlinear EOF. Experiments are performed in conditions directly related to scanning probe imaging and show that quantitative understanding of nanoscale transport under concentration gradients requires accounting for EOF. This characterization of nanopipette transport physics will benefit diverse experimentation, pushing the resolution limits of chemical and biophysical recordings.

Critical Nuclei Size, Rate, and Activation Energy of H2 Gas Nucleation.

Electrochemical measurements of the nucleation rate of individual H2 bubbles at the surface of Pt nanoelectrodes (radius = 7-41 nm) are used to determine the critical size and geometry of H2 nuclei leading to stable bubbles. Precise knowledge of the H2 concentration at the electrode surface, CH2surf, is obtained by controlled current reduction of H+ in a H2SO4 solution. Induction times of single-bubble nucleation events are measured by stepping the current, to control CH2surf, while monitoring the voltage. We find that gas nucleation follows a first-order rate process; a bubble spontaneously nucleates after a stochastic time delay, as indicated by a sudden voltage spike that results from impeded transport of H+ to the electrode. Hundreds of individual induction times, at different applied currents and using different Pt nanoelectrodes, are used to characterize the kinetics of phase nucleation. The rate of bubble nucleation increases by four orders of magnitude (0.3-2000 s-1) over a very small relative change in CH2surf (0.21-0.26 M, corresponding to a ∼0.025 V increase in driving force). Classical nucleation theory yields thermodynamic radii of curvature for critical nuclei of 4.4 to 5.3 nm, corresponding to internal pressures of 330 to 270 atm, and activation energies for nuclei formation of 14 to 26 kT, respectively. The dependence of nucleation rate on H2 concentration indicates that nucleation occurs by a heterogeneous mechanism, where the nuclei have a contact angle of ∼150° with the electrode surface and contain between 35 and 55 H2 molecules.

The Nucleation Rate of Single O2 Nanobubbles at Pt Nanoelectrodes.

Nanobubble nucleation is a problem that affects efficiency in electrocatalytic reactions since those bubbles can block the surface of the catalytic sites. In this article, we focus on the nucleation rate of O2 nanobubbles resulting from the electrooxidation of H2O2 at Pt disk nanoelectrodes. Bubbles form almost instantaneously when a critical peak current, inbp, is applied, but for lower currents, bubble nucleation is a stochastic process in which the nucleation (induction) time, tind, dramatically decreases as the applied current approaches inbp, a consequence of the local supersaturation level, ζ, increasing at high currents. Here, by applying different currents below inbp, nanobubbles take some time to nucleate and block the surface of the Pt electrode at which the reaction occurs, providing a means to measure the stochastic tind. We study in detail the different conditions in which nanobubbles appear, concluding that the electrode surface needs to be preconditioned to achieve reproducible results. We also measure the activation energy for bubble nucleation, Ea, which varies in the range from (6 to 30) kT, and assuming a spherically cap-shaped nanobubble nucleus, we determine the footprint diameter L = 8-15 nm, the contact angle to the electrode surface θ = 135-155°, and the number of O2 molecules contained in the nucleus (50 to 900 molecules).

Single Ag nanoparticle collisions within a dual-electrode micro-gap cell.

An adjustable width (between 600 nm and 20 µm) gap between two Au microelectrodes is used to probe the electrodissolution dynamics of single Ag nanoparticles. One Au microelectrode is used to drive the oxidation and subsequent dissolution of a single Ag nanoparticle, which displays a multi-peak oxidation behavior, while a second Au microelectrode is used to collect the Ag+ that is produced. Careful analysis of the high temporal resolution current-time traces reveals capacitive coupling between electrodes due to the sudden injection of Ag+ ions into the gap between the electrodes. The current-time traces allow measurement of the effect of citrate concentration on the electrodissolution dynamics of a single Ag nanoparticle, which reveals that the presence of 2 mM citrate significantly slows down the release of Ag+. Intriguingly, these experiments also reveal that only a portion (ca. 50%) of the oxidized Ag nanoparticle is released as free Ag+ regardless of citrate concentration.

Collision Dynamics during the Electrooxidation of Individual Silver Nanoparticles.

Recent high-bandwidth recordings of the oxidation and dissolution of 35 nm radius Ag nanoparticles at a Au microelectrode show that these nanoparticles undergo multiple collisions with the electrode, generating multiple electrochemical current peaks. In the time interval between observed current peaks, the nanoparticles diffuse in the solution near the electrolyte/electrode interface. Here, we demonstrate that simulations of random nanoparticle motion, coupled with electrochemical kinetic parameters, quantitatively reproduce the experimentally observed multicurrent peak behavior. Simulations of particle diffusion are based on the nanoparticle-mass-based thermal nanoparticle velocity and the Einstein diffusion relations, while the electron-transfer rate is informed by the literature exchange current density for the Ag/Ag+ redox system. Simulations indicate that tens to thousands of particle-electrode collisions, each lasting ∼6 ns or less (currently unobservable on accessible experimental time scales), contribute to each experimentally observed current peak. The simulation provides a means to estimate the instantaneous current density during a collision (∼500-1000 A/cm2), from which we estimate a rate constant between ∼5 and 10 cm/s for the electron transfer between Ag nanoparticles and the Au electrode. This extracted rate constant is approximately equal to the thermal collisional velocity of the Ag nanoparticle (4.6 cm/s), the latter defining the theoretical upper limit of the electron-transfer rate constant. Our results suggest that only ∼1% of the surface atoms on the Ag nanoparticles are oxidized per instantaneous collision. The combined simulated and experimental results underscore the roles of Brownian motion and collision frequency in the interpretation of heterogeneous electron-transfer reactions involving nanoparticles.

Observation of Multipeak Collision Behavior during the Electro-Oxidation of Single Ag Nanoparticles.

The dynamic collision behavior of the electro-oxidation of single Ag nanoparticles is observed at Au microelectrodes using stochastic single-nanoparticle collision amperometry. Results show that an Ag nanoparticle collision/oxidation event typically consists of a series of 1 to ∼10 discrete "sub-events" over an ∼20 ms interval. Results also show that the Ag nanoparticles typically undergo only partial oxidation prior to diffusing away from the Au electrode into the bulk solution. Both behaviors are characterized and shown to exist under a variety of experimental conditions. These previously unreported behaviors suggest that nanoparticle collision and electro-dissolution is a highly dynamic process driven by fast particle-electrode interactions and nanoparticle diffusion.

Voltage-Rectified Current and Fluid Flow in Conical Nanopores.

Ion current rectification (ICR) refers to the asymmetric potential-dependent rate of the passage of solution ions through a nanopore, giving rise to electrical current-voltage characteristics that mimic those of a solid-state electrical diode. Since the discovery of ICR in quartz nanopipettes two decades ago, synthetic nanopores and nanochannels of various geometries, fabricated in membranes and on wafers, have been extensively investigated to understand fundamental aspects of ion transport in highly confined geometries. It is now generally accepted that ICR requires an asymmetric electrical double layer within the nanopore, producing an accumulation or depletion of charge-carrying ions at opposite voltage polarities. Our research groups have recently explored how the voltage-dependent ion distributions and ICR within nanopores can induce novel nanoscale flow phenomena that have applications in understanding ionics in porous materials used in energy storage devices, chemical sensing, and low-cost electrical pumping of fluids. In this Account, we review our most recent investigations on this topic, based on experiments using conical nanopores (10-300 nm tip opening) fabricated in thin glass, mica, and polymer membranes. Measurable fluid flow in nanopores can be induced either using external pressure forces, electrically via electroosmotic forces, or by a combination of these two forces. We demonstrate that pressure-driven flow can greatly alter the electrical properties of nanopores and, vice versa, that the nonlinear electrical properties of conical nanopores can impart novel and useful flow phenomena. Electroosmotic flow (EOF), which depends on the magnitude of the ion fluxes within the double layer of the nanopore, is strongly coupled to the accumulation/depletion of ions. Thus, the same underlying cause of ICR also leads to EOF rectification, i.e., unequal flows occurring for the same voltage but opposite polarities. EOF rectification can be used to electrically pump fluids with very precise control across membranes containing conical pores via the application of a symmetric sinusoidal voltage. The combination of pressure and asymmetric EOF can also provide a means to generate new nanopore electrical behaviors, including negative differential resistance (NDR), in which the current through a conical pore decreases with increasing driving force (applied voltage), similar to solid-state tunnel diodes. NDR results from a positive feedback mechanism between the ion distributions and EOF, yielding a true bistability in both fluid flow and electrical current at a critical applied voltage. Nanopore-based NDR is extremely sensitive to the surface charge near the nanopore opening, suggesting possible applications in chemical sensing.

The Dynamic Steady State of an Electrochemically Generated Nanobubble.

This article describes the dynamic steady state of individual H2 nanobubbles generated by H+ reduction at inlaid and recessed Pt nanodisk electrodes. Electrochemical measurements coupled with finite element simulations allow analysis of the nanobubble geometry at dynamic equilibrium. We demonstrate that a bubble is sustainable at Pt nanodisks due to the balance of nanobubble shrinkage due to H2 dissolution and growth due to H2 electrogeneration. Specifically, simulations are used to predict stable geometries of the H2/Pt/solution three-phase interface and the width of exposed Pt at the disk circumference required to sustain the nanobubble via steady-state H2 electrogeneration. Experimentally measured currents, iss, corresponding to the electrogeneration of H2, at or near the three-phase interface, needed to sustain the nanobubble are between 0.2 and 2.4 nA for Pt nanodisk electrodes with radii between 2.5 and 40 nm. However, simple theoretical analysis shows that the diffusion-limited currents required to sustain such a single nanobubble at an inlaid Pt nanodisk are 1-2 orders larger than the observed values. Finite element simulation of the dynamic steady state of a nanobubble at an inlaid disk also demonstrates that the expected steady-state currents are much larger than the experimental currents. Better agreement between the simulated and experimental values of iss is obtained by considering recession of the Pt disk nanoelectrode below the plane of the insulating surface, which reduces the outward flux of H2 from the nanobubble and results in smaller values of iss.