Removing 65 Years of Approximation in Rotating Ring Disk Electrode Theory with Physics-Informed Neural Networks.

The rotating Ring Disk Electrode (RRDE), since its introduction in 1959 by Frumkin and Nekrasov, has become indispensable with diverse applications in electrochemistry, catalysis, and material science. The collection efficiency (N) is an important parameter extracted from the ring and disk currents of the RRDE, providing valuable information about reaction mechanism, kinetics, and pathways. The theoretical prediction of N is a challenging task: requiring solution of the complete convective diffusion mass transport equation with complex velocity profiles. Previous efforts, including by Albery and Bruckenstein who developed the most widely used analytical equations, heavily relied on approximations by removing radial diffusion and using approximate velocity profiles. 65 years after the introduction of RRDE, we employ a physics-informed neural network to solve the complete convective diffusion mass transport equation, to reveal the formerly neglected edge effects and velocity corrections on N, and to provide a guideline where conventional approximation is applicable.

Rotating Disk Electrodes beyond the Levich Approximation: Physics-Informed Neural Networks Reveal and Quantify Edge Effects.

Physics-informed neural networks are used to characterize the mass transport to the rotating disk electrode (RDE), the most widely employed hydrodynamic electrode in electroanalysis. The PINN approach was first quantitatively verified via 1D simulations under the Levich approximation for cyclic voltammetry and chronoamperometry, allowing comparison of the results with finite difference simulations and analytical equations. However, the Levich approximation is only accurate for high Schmidt numbers (Sc > 1000). The PINN approach allowed consideration of smaller Sc, achieving an analytical level of accuracy (error <0.1%) comparable with independent numerical evaluation and confirming that the errors in the Levich equation can be as high as 3% when Sc = 1000 for rapidly diffusing species in aqueous solution. Entirely novel, the PINNs permit the solution of the 2D diffusion equation under cylindrical geometry incorporating radial diffusion and reveal the rotating disk electrode edge effect as a consequence of the nonuniform accessibility of the disc with greater currents flowing near the extremities. The contribution to the total current is quantified as a function of the rotation speed, disk radius, and analyte diffusion coefficient. The success in extending the theory for the rotating disk electrode beyond the Levich equation shows that PINNs can be an easier and more powerful substitute for conventional methods, both analytical and simulation based.

Experimental Voltammetry Analyzed Using Artificial Intelligence: Thermodynamics and Kinetics of the Dissociation of Acetic Acid in Aqueous Solution.

Artificial intelligence (AI) is used to quantitatively analyze the voltammetry of the reduction of acetic acid in aqueous solution generating thermodynamic and kinetic data. Specifically, the variation of the steady-state current for the reduction of protons at a platinum microelectrode as a function of the bulk concentration of acetic acid is recorded and analyzed giving data in close agreement with independent measurements, provided the AI is trained with accurate and precise knowledge of diffusion coefficients of acetic acid, acetate ions, and H+.

The application of physics-informed neural networks to hydrodynamic voltammetry.

Electrochemical problems are widely studied in flowing systems since the latter offer improved sensitivity notably for electro-analysis and the possibility of steady-state measurements for fundamental studies even with macro-electrodes. We report the exploratory use of Physics-Informed Neural Networks (PINNs) as potentially simpler, and easier way to implement alternatives to finite difference or finite element simulations to predict the effect of flow and electrode geometry on the currents observed in channel electrodes where the flow is constrained to a rectangular duct with the electrode embedded flush with the wall of the cell. Several problems are addressed including the evaluation of the transport limited current at a micro channel electrode, the transport of material between two adjacent electrodes in a channel flow and the response of an electrode where the electrode reaction follows a preceding chemical reaction. The approach is shown to give quantitative agreement in the limits for which existing solutions are known whilst offering predictions for the case of the previously unexplored CE reaction at a micro channel electrode.

Predicting Voltammetry Using Physics-Informed Neural Networks.

We propose a discretization-free approach to simulation of cyclic voltammetry using Physics-Informed Neural Networks (PINNs) by constraining a feed-forward neutral network with the diffusion equation and electrochemically consistent boundary conditions. Using PINNs, we first predict one-dimensional voltammetry at a disc electrode with semi-infinite or thin layer boundary conditions. The voltammograms agree quantitatively with those obtained independently using the finite difference method and/or previously reported analytical expressions. Further, we predict the voltammetry at a microband electrode, solving the two-dimensional diffusion equation, obtaining results in close agreement with the literature. Last, we apply a PINN to voltammetry at the edges of a square electrode, quantifying the nonuniform current distribution near the corner of electrode. In general, we noticed the relative ease of developing PINNs for the solution of, in particular, the higher dimensional problem, and recommend PINNs as a potentially faster and easier alternative to existing approaches for voltammetric problems.

Use of Artificial Intelligence in Electrode Reaction Mechanism Studies: Predicting Voltammograms and Analyzing the Dissociative CE Reaction at a Hemispherical Electrode.

Artificial intelligence (AI) is used to learn the key voltammetric characteristics of the dissociative CE mechanism via training from multiple simulations using bespoke code. This allows first for the prediction of voltammograms without the need for further simulations, given knowledge of the relevant experimental parameters (rate and equilibrium constants, electrode geometry, and diffusion coefficients). Second, it is applied to analyze noisy experimental voltammetry to characterize the mechanistic type and to successfully extract the key kinetic and thermodynamic parameters.

Theoretical prediction of a transient accumulation of nanoparticles at a well-defined distance from an electrified liquid-solid interface.

The Brownian motion of nanoparticles near liquid-solid interfaces is at the heart of evolving technologies: recent developments in the sensing of nano-objects and energy storages based on electro-active colloidal solutions crucially rely on the understanding and, even more, on the control of particle transport near charged surfaces. On the basis of the Nernst-Planck equation, the Gouy-Chapman model, and an established model of near-wall hindered diffusion, this work predicts transient and highly-localised accumulations of nanoparticles at a well-defined distance from an electrified surface following a potential being applied. The interplay of electrostatics and near-wall hindered diffusion yields entirely unexpected effects: nanoobjects temporarily accumulate near the interface while even small electric potentials applied at the surface can dramatically enhance the mass transport of nano-objects towards it.

A quantitative methodology for the study of particle-electrode impacts.

Herein we provide a generic framework for use in the acquisition and analysis of the electrochemical responses of individual nanoparticles, summarising aspects that must be considered to avoid mis-interpretation of data. Specifically, we threefold highlight the importance of the nanoparticle shape, the effect of the nanoparticle diffusion coefficient on the probability of it being observed and the influence of the used measurement bandwidth. Using the oxidation of silver nanoparticles as a model system, it is evidenced that when all of the above have been accounted for, the experimental data is consistent with being associated with the complete oxidation of the nanoparticles (50 nm diameter). The duration of many single nanoparticle events are found to be ca. milliseconds in duration over a range of experiments. Consequently, the insight that the use of lower frequency filtered data yields a more accurate description of the charge passed during a nano-event is likely widely applicable to this class of experiment; thus we report a generic methodology. Conversely, information regarding the dynamics of the nano redox event is obscured when using such lower frequency measurements; hence, both data sets are complementary and are required to provide full insight into the behaviour of the reactions at the nanoscale.

Electrochemistry of Single Enzymes: Fluctuations of Catalase Activities.

Dynamic fluctuations of the catalytic ability of single catalase enzymes toward hydrogen peroxide decomposition are observed via the nanoimpact technique. The electrochemical signals of single enzymes show that the catalytic ability of single enzymes can temporarily be much higher than expected from the classical, time-averaged Michaelis-Menten description. By combination of experimental data with a new theoretical model, we interpret the unusual enhancement of the single catalase signal and find that single catalases show large fluctuations of the catalytic ability.

Understanding single enzyme activity via the nano-impact technique.

To evaluate the possible detection of single enzyme activity via electrochemical methods, a combined finite difference and random walk simulation is used to model individual enzyme-electrode collisions where such events are monitored amperometrically via the measurement of products formed by the enzyme in solution. It is found that the observed signal is highly sensitive to both the enzyme turnover number, the size of the electrode and the bandwidth of the electronics. Taking single catalase impacts as an example, simulation results are compared with experimental data. Our work shows the requirement for the detection of electrochemically active product formed by individual enzymes and gives guidance for the design of experiments.

Non-linear sweep voltammetry of adsorbed species: theory and a method to determine formal potentials.

Recent literature revealed the hitherto unexploited opportunities offered by unconventional cyclic voltammetry with non-triangular potential sweeps. We here investigate the implications of such techniques for the equilibrium voltammetry of surface-bound analytes and expose rather counter-intuitive effects: if only slightly different potential waveforms are applied, distinct and characteristic features arise in the voltammogram that can be readily exploited for quantitative analysis. Our work comprises a theoretical analysis and suggests initially a simple method to determine formal potentials.

Immobilised Electrocatalysts: Nafion Particles Doped with Ruthenium(II) Tris(2,2'-bipyridyl).

Nafion particles doped with ruthenium(II) tris(2,2'-bipyridyl) are synthesized by using a re-precipitation method. Characterization including SEM sizing and quantification of Ru(bpy)32+ in the Nafion particles using UV/Vis spectroscopy was conducted. The synthesized Ru-Nafion particles were investigated electrochemically at both ensemble and single particle levels. Voltammetry of the drop-cast Ru-Nafion particles evidences the successful incorporation of Ru(bpy)32+ into the Nafion particle but only a small fraction of the incorporated Ru(bpy)32+ was detected due at least in part to the formation of the likely agglomerated and irregular "mat" associated with the dropcast technique. In contrast, nano-impact experiments provided a quantitative determination of the amount of Ru(bpy)32+ in single Ru-Nafion particles. Finally, oxidation of solution-phase oxalate mediated by Ru(bpy)32+ within individual Nafion particles was observed, showing the electrocatalytic properties of the Ru-Nafion particles.

Improving Single-Carbon-Nanotube-Electrode Contacts Using Molecular Electronics.

We report the use of an electroactive species, acetaminophen, to modify the electrical connection between a carbon nanotube (CNT) and an electrode. By applying a potential across two electrodes, some of the CNTs in solution occasionally contact the electrified interface and bridge between two electrodes. By observing a single CNT contact between two microbands of an interdigitated Au electrode in the presence and absence of acetaminophen, the role of the molecular species at the electronic junction is revealed. As compared with the pure CNT, the current magnitude of the acetaminophen-modified CNTs significantly increases with the applied potentials, indicating that the molecule species improves the junction properties probably via redox shuttling.

Reaction Layer Imaging Using Fluorescence Electrochemical Microscopy.

The chemical confinement of a pH sensitive fluorophore to a thin-reaction layer adjacent to an electrode surface is explored as a potentially innovative route to improving the spatial resolution of fluorescence electrochemical microscopy. A thin layer opto-electrochemical cell is designed, facilitating the visualization of a carbon fiber (diameter 7.0 µm) electrochemical interface. Proton consumption is driven at the interface by the reduction of benzoquinone to hydroquinone and the resulting interfacial pH change is revealed using the fluorophore 8-hydoxypyrene-1,3,6-trisulfonic acid. It is demonstrated that the proton depletion zone may be constrained and controlled by the addition of a finite acid concentration to the system. Simulation of the resulting fluorescence intensity profiles is achieved on the basis of a finite difference model, with excellent agreement between the theoretical and experimental results.

Catalytic activity of catalase-silica nanoparticle hybrids: from ensemble to individual entity activity.

We demonstrate the electrochemical detection and characterization of individual nanoparticle-enzyme hybrids. Silica nanoparticles were functionalized with catalase enzyme and investigated spectroscopically and electrochemically. The catalytic activity of the hybrids towards hydrogen peroxide decomposition was comparable to the activity of a freely diffusing enzyme in solution, exhibiting a Michaelis-Menten constant of KM = 74 mM and a turnover number of kcat = 8 × 107 s-1 per NP. The fast turnover number of the hybrid further enabled the electrochemical detection of individual nanoparticle-enzyme hybrid via a novel method: the hydrogen peroxide substrate was generated at a microelectrode which enabled enzymatic activity exclusively within the diffusion layer of the electrode. The method is the first electrochemical approach for measuring hybrid nanoparticles, at the single entity level.

The Influence of Supporting Ions on the Electrochemical Detection of Individual Silver Nanoparticles: Understanding the Shape and Frequency of Current Transients in Nano-impacts.

We report the influence of electrolyte composition and concentration on the stochastic amperometric detection of individual silver nanoparticles at microelectrode arrays and show that the sensor response at certain electrode potentials is dependent on both the conductivity of the electrolyte and the concentration of chloride ions. We further demonstrate that the chloride concentration in solution heavily influences the characteristic current spike shape of recorded nanoparticle impacts: While typically too short to be resolved in the measured current, the spike widths are significantly broadened at low chloride concentrations below 10 mm and range into the millisecond regime. The analysis of more than 25 000 spikes reveals that this effect can be explained by the diffusive mass transport of chloride ions to the nanoparticle, which limits the oxidation rate of individual silver nanoparticles to silver chloride at the chosen electrode potential.

Lithium-Ion-Transfer Kinetics of Single LiMn2 O4 Particles.

A stochastic investigation of lithium deinsertion from individual 200-nm-sized particles of LiMn2 O4 reveals the rate-determining step at high overpotentials to be the transfer of the cation across the particle-electrolyte interface. Measurement of the (electro)chemical behavior of the spinel is undertaken without forming a conductive composite electrode. The kinetics of the interfacial ion transfer defines a theoretical upper limit for the discharge rates of batteries using LiMn2 O4 in an aqueous environment.

The Role of Entropy in Nanoparticle Agglomeration.

Agglomeration processes in non-interacting particle systems can be understood from a thermodynamic point of view. If the enthalpy of agglomeration is negligible, the distribution of agglomeration states adopts the state of highest entropy. Herein, we provide the exact analytical solution to the mole fractions of agglomerates comprising i monomers, xi =2-i .

Electrode-particle impacts: a users guide.

We present a comprehensive guide to nano-impact experiments, in which we introduce newcomers to this rapidly-developing field of research. Central questions are answered regarding required experimental set-ups, categories of materials that can be detected, and the theoretical frameworks enabling the analysis of experimental data. Commonly-encountered issues are considered and presented alongside methods for their solutions.

When does near-wall hindered diffusion influence mass transport towards targets?

The diffusion of a particle is slowed as it moves close to a surface. We identify the conditions under which this hindered diffusion is significant and show that is strongly dependant on the sizes of both the particle and the target. We focus particularly on the transport of nano-particles to a variety of targets including a planar surface, a sphere, a disc and a wire, and provide data which allows the frequency of impacts to be inferred for a variety of experimental conditions. Equations are given to estimate the particle fluxes and we explain literature observations reported on the detected frequency of impacts. Finally we observe a drastic effect on the calculation of the mean first passage time of a single particle impacting a sub-micron sized target, showing the importance of this effect in biological systems.