Theory and structure of the metal-electrolyte interface incorporating adsorption and solvation effects

Galilean Bulk-Surface Electrothermodynamics and Applications to Electrochemistry

In this work, the balance equations of non-equilibrium thermodynamics are coupled to Galilean limit systems of the Maxwell equations, i.e., either to (i) the quasi-electrostatic limit or (ii) the quasi-magnetostatic limit. We explicitly consider a volume Ω, which is divided into Ω+ and Ω- by a possibly moving singular surface S, where a charged reacting mixture of a viscous medium can be present on each geometrical entity (Ω+,S,Ω-). By the restriction to the Galilean limits of the Maxwell equations, we achieve that only subsystems of equations for matter and electromagnetic fields are coupled that share identical transformation properties with respect to observer transformations. Moreover, the application of an entropy principle becomes more straightforward and finally helps estimate the limitations of the more general approach based the full set of Maxwell equations. Constitutive relations are provided based on an entropy principle, and particular care is taken in the analysis of the stress tensor and the momentum balance in the general case of non-constant scalar susceptibility. Finally, we summarise the application of the derived model framework to an electrochemical system with surface reactions.

The Role of Energy Scales for the Structure of Ionic Liquids at Electrified Interfaces: A Theory-Based Approach

Ionic liquids offer unique bulk and interfacial characteristics as battery electrolytes. Our continuum approach naturally describes the electrolyte on a macroscale. An integral formulation for the molecular repulsion, which can be quantitatively determined by both experimental and theoretical methods, models the electrolyte on the nanoscale. In this article, we perform a systematic series expansion of this integral formulation, derive a description of chemical potentials in terms of higher-order concentration gradients, and rationalize the appearance of fourth-order derivative operators in modified Poisson equations, as recently proposed in this context. In this way, we formulate a rigorous multiscale methodology from atomistic quantum chemistry calculations to phenomenological continuum models. We apply our generalized framework to ionic liquids near electrified interfaces and perform analytical asymptotic analysis. Three energy scales describing electrostatic forces between ions, molecular repulsion, and thermal motion determine the shape and width of the long-ranging charged double layer. We classify the charge screening mechanisms dependent on the system parameters as dielectricity, ion size, interaction strength, and temperature. We find that the charge density of electrochemical double layers in ionic liquids either decays exponentially, for negligible molecular repulsion, or oscillates continuously. Charge ordering across several ion diameters occurs if the repulsion between molecules is comparable with thermal energy and Coulomb interactions. Eventually, phase separation of the bulk electrolyte into ionic layers emerges once the molecular repulsion becomes dominant. Our framework predicts the exact phase boundaries among these three phases as a function of temperature, dielectricity, and ion size.

Demystifying the Stern layer at a metal-electrolyte interface: Local dielectric constant, specific ion adsorption, and partial charge transfer

Electric double layer (EDL) represents one of the most basic concepts in electrochemistry and is pertinent to diverse engineering applications ranging from electrocatalysis to energy storage. Whereas phenomenological and coarse-grained models have been long established to describe ionic distributions in the diffuse layer, a faithful prediction of the physicochemical properties of the electrode-electrolyte interface from a molecular perspective remains a daunting challenge. In this work, we investigate the charging behavior of an Ag (111) electrode in NaF aqueous solutions leveraging experimental results and theoretical calculations based on the classical density functional theory for ion distributions in the diffuse layer and on the joint density functional theory (JDFT) for the electronic structure. When the Ag electrode is applied with a negative voltage, the surface charge density can be reasonably described by assuming a neutral Stern layer with the dielectric constant dependent on the local electric field as predicted by the Kirkwood equation. However, the specific adsorption of F^- ions must be considered when the electrode is positively charged and the fluoride adsorption can be attributed to both physical and chemical interactions. Qualitatively, F^- binding and partial charge transfer are supported by JDFT calculations, which predict an increased binding energy as the voltage increases. Our findings shed insight on the molecular characteristics of the Stern layer and the charge behavior of adsorbed species not specified by conventional EDL models.

Multiscale Lithium-Battery Modeling from Materials to Cells

New experimental technology and theoretical approaches have advanced battery research across length scales ranging from the molecular to the macroscopic. Direct observations of nanoscale phenomena and atomistic simulations have enhanced the understanding of the fundamental electrochemical processes that occur in battery materials. This vast and ever-growing pool of microscopic data brings with it the challenge of isolating crucial performance-decisive physical parameters, an effort that often requires the consideration of intricate interactions across very different length scales and timescales. Effective physics-based battery modeling emphasizes the cross-scale perspective, with the aim of showing how nanoscale physicochemical phenomena affect device performance. This review surveys the methods researchers have used to bridge the gap between the nanoscale and the macroscale. We highlight the modeling of properties or phenomena that have direct and considerable impact on battery performance metrics, such as open-circuit voltage and charge/discharge overpotentials. Particular emphasis is given to thermodynamically rigorous multiphysics models that incorporate coupling between materials' mechanical and electrochemical states.

Corrector estimates in homogenization of a nonlinear transmission problem for diffusion equations in connected domains

This paper is devoted to the homogenization of a nonlinear transmission problem stated in a two-phase domain. We consider a system of linear diffusion equations defined in a periodic domain consisting of two disjoint phases that are both connected sets separated by a thin interface. Depending on the field variables, at the interface, nonlinear conditions are imposed to describe interface reactions. In the variational setting of the problem, we prove the homogenization theorem and a bidomain averaged model. The periodic unfolding technique is used to obtain the residual error estimate with a first-order corrector.

A continuum model for yttria-stabilized zirconia incorporating triple phase boundary, lattice structure and immobile oxide ions

A continuum model for yttria-stabilized zirconia (YSZ) in the framework of non-equilibrium thermodynamics is developed. Particular attention is given to (i) modeling of the YSZ-metal-gas triple phase boundary, (ii) incorporation of the lattice structure and immobile oxide ions within the free energy model and (iii) surface reactions. A finite volume discretization method based on modified Scharfetter-Gummel fluxes is derived in order to perform numerical simulations. The model is used to study the impact of yttria and immobile oxide ions on the structure of the charged boundary layer and the double layer capacitance. Cyclic voltammograms of an air-half cell are simulated to study the effect of parameter variations on surface reactions, adsorption and anion diffusion.

Bulk-Surface Electrothermodynamics and Applications to Electrochemistry

We propose a modeling framework for magnetizable, polarizable, elastic, viscous, heat conducting, reactive mixtures in contact with interfaces. To this end, we first introduce bulk and surface balance equations that contain several constitutive quantities. For further modeling of the constitutive quantities, we formulate constitutive principles. They are based on an axiomatic introduction of the entropy principle and the postulation of Galilean symmetry. We apply the proposed formalism to derive constitutive relations in a rather abstract setting. For illustration of the developed procedure, we state an explicit isothermal material model for liquid electrolyte|metal electrode interfaces in terms of free energy densities in the bulk and on the surface. Finally, we give a survey of recent advancements in the understanding of electrochemical interfaces that were based on this model.

Analytical Interfacial Layer Model for the Capacitance and Electrokinetics of Charged Aqueous Interfaces

We construct an analytical model to account for the influence of the subnanometer-wide interfacial layer on the differential capacitance and the electro-osmotic mobility of solid-electrolyte interfaces. The interfacial layer is incorporated into the Poisson-Boltzmann and Stokes equations using a box model for the dielectric properties, the viscosity, and the ionic potential of mean force. We calculate the differential capacitance and the electro-osmotic mobility as a function of the surface charge density and the salt concentration, both with and without steric interactions between the ions. We compare the results from our theoretical model with experimental data on a variety of systems (graphite and metallic silver for capacitance and titanium oxide and silver iodide for electro-osmotic data). The differential capacitance of silver as a function of salinity and surface charge density is well reproduced by our theory, using either the width of the interfacial layer or the ionic potential of mean force as the only fitting parameter. The differential capacitance of graphite, however, needs an additional carbon capacitance to explain the experimental data. Our theory yields a power-law dependence of the electro-osmotic mobility on the surface charge density for high surface charges, reproducing the experimental data using both the interfacial parameters extracted from molecular dynamics simulations and fitted interfacial parameters. Finally, we examine different types of hydrodynamic boundary conditions for the power-law behavior of the electro-osmotic mobility, showing that a finite-viscosity layer explains the experimental data better than the usual hydrodynamic slip boundary condition. Our analytical model thus allows us to extract the properties of the subnanometer-wide interfacial layer by fitting to macroscopic experimental data.

A new perspective on the electron transfer: recovering the Butler–Volmer equation in non-equilibrium thermodynamics

Butler–Volmer equations can be recovered from a complete non-equilibrium thermodynamic model by application of asymptotic analysis. Thereby we gain insight into the coupling of different physical phenomena and can derive Butler–Volmer equations for very different materials and electrochemical systems.