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.

Stochasticity in Single-Entity Electrochemistry.

Most electrochemical processes are stochastic and discrete in nature. Yet experimental observables, e.g., i vs E, are typically smooth and deterministic, due to many events/processes, e.g., electron transfers, being averaged together. However, when the number of entities measured approaches a few or even one, stochasticity frequently emerges. Yet all is not lost! Probabilistic and statistical interpretation can generate insights matching or superseding those from macroscale/ensemble measurements, revealing phenomena that were hitherto averaged over. Herein, we review recent literature examples of stochastic processes in single-entity electrochemistry, highlighting strategies for interpreting stochasticity, contrasting them with macroscale measurements, and describing the insights generated.

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.

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.

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.

Investigation of sp2-Carbon Pattern Geometry in Boron-Doped Diamond Electrodes for the Electrochemical Quantification of Hypochlorite at High Concentrations.

An electrochemical sensor that contains patterned regions of sp2-carbon in a boron-doped diamond (BDD) matrix is presented for the quantitative detection of hypochlorite (OCl-) at high concentrations in the alkaline, chemically oxidizing environment associated with bleach. As BDD itself is unresponsive to OCl- reduction within the solvent window, by using a laser micromachining process, it is possible to write robust electrochemically active regions of sp2-carbon into the electrochemically inert sp3-BDD electrode. In this work, four different laser patterned BDD electrodes are examined, and their response compared across a range of OCl- concentrations (0.02-1.50 M). A single macrospot (0.37 mm diameter disk) electrode and a closely spaced microspot (46 µm diameter disk) hexagonal array electrode, containing the same surface area of sp2-carbon, are shown to provide the most linear response toward OCl- reduction. Finite element modeling (FEM) is employed to better understand the electrochemical system, due to the complexity of the electrode geometry, as well as the need to include contributions from migration and Ohmic drop at these high concentrations. FEM data suggest that only a small percentage (∼1 × 10-3%) of the total laser-machined sp2 area is active toward the OCl- reduction process and that this process is kinetically very sluggish (∼keff = 1 × 10-12 cm s-1). The sensitivity at the array electrode (-0.127 ± 0.004 mA M-1; R2 = 0.992) is higher than that at the single-spot electrode (-0.075 ± 0.002 mA M-1; R2 = 0.996) due to the enhanced effect of transport to the edges of the microspots, shown via simulation. The electrodes returned a relatively stable response over a greater than 3 month period of use in the OCl- solutions, demonstrating these hybrid sp2-BDD electrodes show promise for long-term monitoring applications in the harsh environments associated with bleaching applications.

Electrochemically Controlled Nucleation of Single CO2 Nanobubbles via Formate Oxidation at Pt Nanoelectrodes.

CO2 is an anodic product of many liquid fuel cells. The nucleation of CO2 nanobubbles during cell operation may block the transport of the fuel to the anode, lowering the overall conversion efficiency. Herein, we report the controlled formation of individual CO2 nanobubbles at Pt nanoelectrodes via the electrooxidation of formate. The electrochemical data are used to extract key parameters of CO2 gas nucleation. We determine that CO2 bubbles nucleate when the concentration of CO2 at the Pt electrode is greater than ∼0.6 M, corresponding to supersaturation of ∼18. The critical nucleus required for the formation of a CO2 bubble is measured to have a radius of curvature of ∼100 nm, a contact angle of 173°, and contains ∼70 CO2 molecules.

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.

A synthetic chemist's guide to electroanalytical tools for studying reaction mechanisms.

Monitoring reactive intermediates can provide vital information in the study of synthetic reaction mechanisms, enabling the design of new catalysts and methods. Many synthetic transformations are centred on the alteration of oxidation states, but these redox processes frequently pass through intermediates with short life-times, making their study challenging. A variety of electroanalytical tools can be utilised to investigate these redox-active intermediates: from voltammetry to in situ spectroelectrochemistry and scanning electrochemical microscopy. This perspective provides an overview of these tools, with examples of both electrochemically-initiated processes and monitoring redox-active intermediates formed chemically in solution. The article is designed to introduce synthetic organic and organometallic chemists to electroanalytical techniques and their use in probing key mechanistic questions.

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.

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.

Voltammetric Determination of the Stochastic Formation Rate and Geometry of Individual H2, N2, and O2 Bubble Nuclei.

Herein, we report a general voltammetric method to characterize the electrochemical nucleation rate and nuclei of single nanobubbles. Bubble nucleation is indicated by a sharp peak in the current in the voltammetry of gas-evolving reactions. In contrast to expectations based on the stochastic nature of nucleation events, the peak current signifying a stable nucleus is extremely reproducible over hundreds of cycles (∼3% deviation). By applying classical nucleation theory, this seemingly deterministic behavior can be not only understood but also used to quantify the nucleation rate and size of bubble nuclei. A statistical model is developed whereby properties of single critical nuclei (contact angle, the radius of curvature, activation energy, and Arrhenius pre-exponential factor) can be readily measured from the narrow distribution of peak currents (mean, standard deviation) from hundreds of voltammetric cycles at a nanoelectrode. Single nanobubbles formed from gas-evolving reactions (H2 from H+ reduction, N2 from N2H4 oxidation, O2 from H2O2 oxidation) are analyzed to find that their critical nuclei have contact angles of ∼150, ∼160, and ∼154° for H2, N2, and O2, respectively, corresponding to ∼50, ∼40, and ∼90 gas molecules in each nucleus. The energy barriers for heterogeneous nucleation of H2, N2, and O2 bubbles are, respectively, 2, 0.4, and 0.7% of those required for homogeneous nucleation under the same supersaturation.

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.

The importance of nanoscale confinement to electrocatalytic performance.

Electrocatalytic nanoparticles that mimic the three-dimensional geometric architecture of enzymes where the reaction occurs down a substrate channel isolated from bulk solution, referred to herein as nanozymes, were used to explore the impact of nano-confinement on electrocatalytic reactions. Surfactant covered Pt-Ni nanozyme nanoparticles, with Ni etched from the nanoparticles, possess a nanoscale channel in which the active sites for electrocatalysis of oxygen reduction are located. Different particle compositions and etching parameters allowed synthesis of nanoparticles with different average substrate channel diameters that have varying amounts of nano-confinement. The results showed that in the kinetically limited regime at low overpotentials, the smaller the substrate channels the higher the specific activity of the electrocatalyst. This is attributed to higher concentrations of protons, relative to bulk solution, required to balance the potential inside the nano-confined channel. However, at higher overpotentials where limitation by mass transport of oxygen becomes important, the nanozymes with larger substrate channels showed higher electrocatalytic activity. A reaction-diffusion model revealed that the higher electrocatalytic activity at low overpotentials with smaller substrate channels can be explained by the higher concentration of protons. The model suggests that the dominant mode of mass transport to achieve these high concentrations is by migration, exemplifying how nano-confinement can be used to enhance reaction rates. Experimental and theoretical data show that under mass transport limiting potentials, the nano-confinement has no effect and the reaction only occurs at the entrance of the substrate channel at the nanoparticle surface.