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.

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.

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.

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.

Nanoscale Electrochemical Sensor Arrays: Redox Cycling Amplification in Dual-Electrode Systems.

Micro- and nanofabriation technologies have a tremendous potential for the development of powerful sensor array platforms for electrochemical detection. The ability to integrate electrochemical sensor arrays with microfluidic devices nowadays provides possibilities for advanced lab-on-a-chip technology for the detection or quantification of multiple targets in a high-throughput approach. In particular, this is interesting for applications outside of analytical laboratories, such as point-of-care (POC) or on-site water screening where cost, measurement time, and the size of individual sensor devices are important factors to be considered. In addition, electrochemical sensor arrays can monitor biological processes in emerging cell-analysis platforms. Here, recent progress in the design of disease model systems and organ-on-a-chip technologies still needs to be matched by appropriate functionalities for application of external stimuli and read-out of cellular activity in long-term experiments. Preferably, data can be gathered not only at a singular location but at different spatial scales across a whole cell network, calling for new sensor array technologies. In this Account, we describe the evolution of chip-based nanoscale electrochemical sensor arrays, which have been developed and investigated in our group. Focusing on design and fabrication strategies that facilitate applications for the investigation of cellular networks, we emphasize the sensing of redox-active neurotransmitters on a chip. To this end, we address the impact of the device architecture on sensitivity, selectivity as well as on spatial and temporal resolution. Specifically, we highlight recent work on redox-cycling concepts using nanocavity sensor arrays, which provide an efficient amplification strategy for spatiotemporal detection of redox-active molecules. As redox-cycling electrochemistry critically depends on the ability to miniaturize and integrate closely spaced electrode systems, the fabrication of suitable nanoscale devices is of utmost importance for the development of this advanced sensor technology. Here, we address current challenges and limitations, which are associated with different redox cycling sensor array concepts and fabrication approaches. State-of-the-art micro- and nanofabrication technologies based on optical and electron-beam lithography allow precise control of the device layout and have led to a new generation of electrochemical sensor architectures for highly sensitive detection. Yet, these approaches are often expensive and limited to clean-room compatible materials. In consequence, they lack possibilities for upscaling to high-throughput fabrication at moderate costs. In this respect, self-assembly techniques can open new routes for electrochemical sensor design. This is true in particular for nanoporous redox cycling sensor arrays that have been developed in recent years and provide interesting alternatives to clean-room fabricated nanofluidic redox cycling devices. We conclude this Account with a discussion of emerging fabrication technologies based on printed electronics that we believe have the potential of transforming current redox cycling concepts from laboratory tools for fundamental studies and proof-of-principle analytical demonstrations into high-throughput devices for rapid screening applications.

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.

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.

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 .

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.

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.

Fluorescence Monitored Voltammetry of Single Attoliter Droplets.

The lipid soluble fluorophore Nile Red (9-diethylamino-5-benzo[α]phenoxazinone) is used to fluorescently and electrochemically label an organic-in-water emulsion, where the organic phase is an ionic liquid [P6,6,6,14][FAP]/toluene mixture. The optical detection of the individual droplets is enabled facilitating the in situ tracking and sizing of the suspended particles (average diameter = 530 nm, interquartile range = 180 nm). Through the use of a combined thin-layer optical/electrochemical cell, the irreversible accumulation of the droplets at an optically opaque carbon fiber electrode (diameter ∼7.5 µm) can be monitored. Potentiostatic control of the system enables the fluorescence of the surface bound particles to be electrochemically switched via control of the redox state of the dye. Subsequent measurements of the individual particle fluorescence intensities as a function of the applied electrode potential enables construction of an effective, dynamically recorded cyclic voltammogram of an individual particle. The confined volume voltammetry (∼tens of attoliters) yields insight into the asymmetry of the kinetics of the redox switching process, where it is proposed that the reformation of the fluorescent Nile Red becomes chemically "gated" in the organic phase.

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.

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.

Testing and validating electroanalytical simulations.

Digital simulations are a commonly used tool in electrochemical and electroanalytical research. However, even though the employed computational methods often feature significant complexity, testing routines are rarely specified or discussed in literature. In this work, we address this topic and describe approaches towards testing electrochemical simulation software. While focussing on simple systems featuring Nernstian reactions in 1 : 1 stoichiometries, we guide through rigorous testing processes of one- and two dimensional simulations with regard to applications in cyclic voltammetry. To this end, we compile expressions for the calculation of key values as references, discuss the conduction of convergence studies, and suggest approaches to automated software testing.

How many molecules are required to obtain a steady faradaic current from mediated electron transfer at a single nanoparticle on a supporting surface?

We investigate the chronoamperometric noise characteristics of electron-transfer reactions occurring on single nanoparticles (NPs) and assemblies of well-separated NPs on a supporting surface. To this end, we combine a formerly described expression for the steady-state current of a single particle with the shot-noise model and derive an expression for the signal-to-noise ratio as a function of bulk concentration and particle radius. Our findings are supported by random-walk simulations, which closely match the analytical results.

Nanoparticles in sensing applications: on what timescale do analyte species adsorb on the particle surface?

The recent decade saw much interest in sensors based on nanoparticles. Such sensors typically employ sensing mechanisms that utilise the adsorption of analyte species on the nanoparticle surfaces, while adsorption induces changes in the physical properties of the nanoparticles. In this work, we introduce an analytical model for the rate of adsorption of analyte species on the nanoparticle surface. Expressions for the fractional surface coverage and the number of adsorbed molecules as a function of time are derived assuming spherical nanoparticles. Moreover, we provide values for common experimental conditions and show that for small nanoparticles (r < 10 nm) a surface coverages of 30% can be reached in less than 1 s at adsorbent concentrations as low as 50 nM.

Sensing with nanopores--the influence of asymmetric blocking on electrochemical redox cycling current.

Nanoporous redox cycling devices are highly efficient tools for the electrochemical sensing of redox-active molecules. By using a redox-active mediator, this concept can be exploited for the detection of molecular binding events via blocking of the redox cycling current within the nanopores. Here, we investigate the influence of different blocking scenarios inside a nanopore on the resulting redox cycling current. Our analysis is based on random walk simulations and finite element calculations. We distinguish between symmetric and asymmetric pore blocking and show that the current decrease is more pronounced in the case of asymmetric blocking reflecting the diffusion-driven pathway of the redox-active molecules. Using random walk simulations, we further study the impact of pore blocking in the frequency domain and identify relevant features of the power spectral density, which are of particular interest for sensing applications based on fluctuation analysis.

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.