Double layer of platinum electrodes: Non-monotonic surface charging phenomena and negative double layer capacitance

Zooming into the Inner Helmholtz Plane of Pt(111)-Aqueous Solution Interfaces: Chemisorbed Water and Partially Charged Ions

The double layer on transition metals, i.e., platinum, features chemical metal-solvent interactions and partially charged chemisorbed ions. Chemically adsorbed solvent molecules and ions are situated closer to the metal surface than electrostatically adsorbed ions. This effect is described tersely by the concept of an inner Helmholtz plane (IHP) in classical double layer models. The IHP concept is extended here in three aspects. First, a refined statistical treatment of solvent (water) molecules considers a continuous spectrum of orientational polarizable states, rather than a few representative states, and non-electrostatic, chemical metal-solvent interactions. Second, chemisorbed ions are partially charged, rather than being electroneutral or having integral charges as in the solution bulk, with the coverage determined by a generalized, energetically distributed adsorption isotherm. The surface dipole moment induced by partially charged, chemisorbed ions is considered. Third, considering different locations and properties of chemisorbed ions and solvent molecules, the IHP is divided into two planes, namely, an AIP (adsorbed ion plane) and ASP (adsorbed solvent plane). The model is used to study how the partially charged AIP and polarizable ASP lead to intriguing double-layer capacitance curves that are different from what the conventional Gouy-Chapman-Stern model describes. The model provides an alternative interpretation for recent capacitance data of Pt(111)-aqueous solution interfaces calculated from cyclic voltammetry. This revisit brings forth questions regarding the existence of a pure double-layer region at realistic Pt(111). The implications, limitations, and possible experimental confirmation of the present model are discussed.

Essays on Conceptual Electrochemistry: I. Bridging Open-Circuit Voltage of Electrochemical Cells and Charge Distribution at Electrode–Electrolyte Interfaces

We ponder over how an electrochemical cell conforms itself to the open-circuit voltage (OCV) given by the Nernst equation, where properties of the electrodes play no role. We first show, via a pedagogical derivation of the Nernst equation, how electrode properties are canceled and then take a closer look into the electrode–electrolyte interface at one electrode by linking charge and potential distributions. We obtain an equilibrium Poisson–Nernst equation that shows how the charge distribution across an electrode–electrolyte interface can be dictated by the chemical potentials of redox species. Taking a H2/O2 fuel cell as an example, we demystify the formal analysis by showing how the two electrodes delicately regulate their “electron tails” to abide by the Nernst equation. In this example, we run into a seemingly counterintuitive phenomenon that two electrodes made of the same transition metal display two distinct potentials of zero charge. This example indicates that the double layer at transition metals with chemisorption can display distinct behaviors compared to ideally polarizable double layers at sp metals.

Continuum Modeling of Porous Electrodes for Electrochemical Synthesis

Electrochemical synthesis possesses substantial promise to utilize renewable energy sources to power the conversion of abundant feedstocks to value-added commodity chemicals and fuels. Of the potential system architectures for these processes, only systems employing 3-D structured porous electrodes have the capacity to achieve the high rates of conversion necessary for industrial scale. However, the phenomena and environments in these systems are not well understood and are challenging to probe experimentally. Fortunately, continuum modeling is well-suited to rationalize the observed behavior in electrochemical synthesis, as well as to ultimately provide recommendations for guiding the design of next-generation devices and components. In this review, we begin by presenting an historical review of modeling of porous electrode systems, with the aim of showing how past knowledge of macroscale modeling can contribute to the rising challenge of electrochemical synthesis. We then present a detailed overview of the governing physics and assumptions required to simulate porous electrode systems for electrochemical synthesis. Leveraging the developed understanding of porous-electrode theory, we survey and discuss the present literature reports on simulating multiscale phenomena in porous electrodes in order to demonstrate their relevance to understanding and improving the performance of devices for electrochemical synthesis. Lastly, we provide our perspectives regarding future directions in the development of models that can most accurately describe and predict the performance of such devices and discuss the best potential applications of future models.

Cation Overcrowding Effect on the Oxygen Evolution Reaction

The influence of electrolyte ions on the catalytic activity of electrode/electrolyte interfaces is a controversial topic for many electrocatalytic reactions. Herein, we focus on an effect that is usually neglected, namely, how the local reaction conditions are shaped by nonspecifically adsorbed cations. We scrutinize the oxygen evolution reaction (OER) at nickel (oxy)hydroxide catalysts, using a physicochemical model that integrates density functional theory calculations, a microkinetic submodel, and a mean-field submodel of the electric double layer. The aptness of the model is verified by comparison with experiments. The robustness of model-based insights against uncertainties and variations in model parameters is examined, with a sensitivity analysis using Monto Carlo simulations. We interpret the decrease in OER activity with the increasing effective size of electrolyte cations as a consequence of cation overcrowding near the negatively charged electrode surface. The same reasoning could explain why the OER activity increases with solution pH on the RHE scale and why the OER activity decreases in the presence of bivalent cations. Overall, this work stresses the importance of correctly accounting for local reaction conditions in electrocatalytic reactions to obtain an accurate picture of factors that determine the electrode activity.

Modelling electrocatalytic reactions with a concerted treatment of multistep electron transfer kinetics and local reaction conditions

A physicochemical model is developed for electrocatalytic reactions involving multiple electron transfer steps occurring in the electric double layer (EDL). The local reaction conditions are calculated using a mean-field EDL model, which is derived from a comprehensive grand potential that considers the steric effects, solvent polarization, and chemisorption-induced surface dipoles. Macroscopic mass transport in the so-called diffusion layer is controlled by the same set of controlling equations of the EDL model, without imposing the electroneutrality assumption as usual. The Gerischer's formulation of electron transfer theory, corrected with local reaction conditions, is used to describe the kinetics of elementary steps. Multistep kinetics of the electrocatalytic reaction is treated using microkinetics modelling, without resorting to the usual rate-determining step approximation. In formal analysis of the model, we retrieve canonical models with additional assumptions. Self-consistent numerical implementation of the model is demonstrated for oxygen reduction reaction (ORR) at Pt(111) in acidic solution, and the aptness of the model is verified by comparison with experimental data. A comparative study of the full model and its simplified versions allows us to examine how the ORR is influenced by asymmetric steric effects, finite concentration of ions, solvent polarization, surface charge effects, and metal electronic structure effects. We find that the difference in terms of the overpotential between the full model and the simplest model can be up to ∼0.1 V at a current density of -6 mAcm-2.

Properties of the Pt(111)/electrolyte electrochemical interface studied with a hybrid DFT-solvation approach

Self-consistent modeling of the interface between solid metal electrode and liquid electrolyte is a crucial challenge in computational electrochemistry. In this contribution, we adopt the effective screening medium reference interaction site method (ESM-RISM) to study the charged interface between a Pt(111) surface that is partially covered with chemisorbed oxygen and an aqueous acidic electrolyte. This method proves to be well suited to describe the chemisorption and charging state of the interface at controlled electrode potential. We present an in-depth assessment of the ESM-RISM parameterization and of the importance of computing near-surface water molecules explicitly at the quantum mechanical level. We found that ESM-RISM is able to reproduce some key interface properties, including the peculiar, non-monotonic charging relation of the Pt(111)/electrolyte interface. The comparison with independent theoretical models and explicit simulations of the interface reveals strengths and limitations of ESM-RISM for modeling electrochemical interfaces.

Cross-Sphere Electrode Reaction: The Case of Hydroxyl Desorption during the Oxygen Reduction Reaction on Pt(111) in Alkaline Media

Hydroxide ion is a common electrolyte when electrode reactions take place in alkaline media. In the case of oxygen reduction reaction on Pt(111), we demonstrate by ab initio molecular dynamics calculations that the desorption of hydroxyl (OH*) from the electrode surface to form a solvated OH^- is a cross-sphere process, with the OH* reactant in the inner sphere and the OH^- product directly generated in the aqueous outer sphere. Such a mechanism is distinct from the typical inner sphere and outer sphere reactions. It is dictated by the strong hydrogen bonding interactions between a hydroxide ion and water molecules and is facilitated by proton transfer through solvation layers. It should play a significant role whenever OH* desorption, or its reverse, OH^- adsorption, is involved in an electrochemical reaction.

Impedance response of electrochemical interfaces: part II-chemisorption

Physical modeling helps to acquire fundamental insights from experimental data when electrochemical impedance spectroscopy is employed for mechanistic understandings of electrocatalytic reactions. Herein, we report an analytical model for chemisorption impedance with a consistent treatment of ion transport in the solution and electron transfer on the electrode surface. Our formulation avoids botha prioridecoupling of double-layer charging and electron transfer reaction, and a strict separation of double-layer charging and ion transport. Ion transport in the entire solution region is described by the Poisson-Nernst-Planck theory and electron transfer kinetics on the electrode surface by the Frumkin-Butler-Volmer theory. Surface dipoles caused by partially charged chemisorbates are considered. The classical Frumkin-Melik-Gaikazyan model for chemisorption is retrieved as a limiting case. The obtained formula is validated using experimental data of hydrogen adsorption at Pt(111). Characteristic frequencies and asymptotic behaviors of chemisorption impedance are analyzed.

Grand-Canonical Model of Electrochemical Double Layers from a Hybrid Density-Potential Functional

A hybrid density-potential functional of an electrochemical interface that encompasses major effects in the contacting metal and electrolyte phases is formulated. Variational analysis of this functional yields a grand-canonical model of the electrochemical double layer (EDL). Specifically, metal electrons are described using the Thomas-Fermi-Dirac-Wigner theory of an inhomogeneous electron gas. The electrolyte solution is treated classically at the mean-field level, taking into account electrostatic interactions, ion size effects, and nonlinear solvent polarization. The model uses parametrizable force relations to describe the short-range forces between metal cationic cores, metal electrons, and electrolyte ions and solvent molecules. Therefore, the gap between the metal skeleton and the electrolyte solution, key to properties of the EDL, varies consistently as a function of the electrode potential. Partial charge transfer in the presence of ion specific adsorption is described using an Anderson-Newns type theory. This model is parametrized with density functional theory calculations, compared with experimental data, and then employed to unravel several interfacial properties of fundamental significance in electrochemistry. In particular, a closer approach of the solution phase toward the metal surface, for example, caused by a stronger ion specific adsorption, decreases the potential of zero charge and elevates the double-layer capacitance curve. In addition, the ion specific adsorption can lead to surface depolarization of ions. The present model represents a viable framework to model (reactive) EDLs under the constant potential condition, which can be used to understand multifaceted EDL effects in electrocatalysis.

Molecular origin of negative component of Helmholtz capacitance at electrified Pt(111)/water interface

Electrified solid/liquid interfaces are the key to many physicochemical processes in a myriad of areas including electrochemistry and colloid science. With tremendous efforts devoted to this topic, it is unexpected that molecular-level understanding of electric double layers is still lacking. Particularly, it is perplexing why compact Helmholtz layers often show bell-shaped differential capacitances on metal electrodes, as this would suggest a negative capacitance in some layer of interface water. Here, we report state-of-the-art ab initio molecular dynamics simulations of electrified Pt(111)/water interfaces, aiming at unraveling the structure and capacitive behavior of interface water. Our calculation reproduces the bell-shaped differential Helmholtz capacitance and shows that the interface water follows the Frumkin adsorption isotherm when varying the electrode potential, leading to a peculiar negative capacitive response. Our work provides valuable insight into the structure and capacitance of interface water, which can help understand important processes in electrocatalysis and energy storage in supercapacitors.