Electric current across the metal–solid electrolyte interface I. Direct current, current–voltage characteristic

Itskovich, E. M.; Kornyshev, A. A.; Vorotyntsev, Mikhail A.

doi:10.1002/pssa.2210390126

Cited by 45 publications

(43 citation statements)

References 12 publications

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“…A common approach is to separate interfacial differential capacitance into a series of capacitances. 371,[389][390][391][392][393] Dividing equation 120 by the metal charge and differentiating it, one obtains…”

Section: 142mentioning

confidence: 99%

A Critical Review of Modeling Transport Phenomena in Polymer-Electrolyte Fuel Cells

Weber

Borup

Darling³

et al. 2014

J. Electrochem. Soc.

498

394

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Polymer-electrolyte fuel cells are a promising energy-conversion technology. Over the last several decades significant progress has been made in increasing their performance and durability, of which continuum-level modeling of the transport processes has played an integral part. In this review, we examine the state-of-the-art modeling approaches, with a goal of elucidating the knowledge gaps and needs going forward in the field. In particular, the focus is on multiphase flow, especially in terms of understanding interactions at interfaces, and catalyst layers with a focus on the impacts of ionomer thin-films and multiscale phenomena. Overall, we highlight where there is consensus in terms of modeling approaches as well as opportunities for further improvement and clarification, including identification of several critical areas for future research. Fuel cells may become the energy-delivery devices of the 21 st century. Although there are many types of fuel cells, polymer-electrolyte fuel cells (PEFCs) are receiving the most attention for automotive and small stationary applications. In a PEFC, fuel and oxygen are combined electrochemically. If hydrogen is used as the fuel, it oxidizes at the anode releasing proton and electrons according toThe generated protons are transported across the membrane and the electrons across the external circuit. At the cathode catalyst layer, protons and electrons recombine with oxygen to generate waterAlthough the above electrode reactions are written in single step, multiple elementary reaction pathways are possible at each electrode. During the operation of a PEFC, many interrelated and complex phenomena occur. These processes include mass and heat transfer, electrochemical reactions, and ionic and electronic transport. * Electrochemical Society Active Member. z E-mail: azweber@lbl.govOver the last several decades significant progress has been made in increasing PEFC performance and durability. Such progress has been enabled by experiments and computation at multiple scales, with the bulk of the focus being on optimizing and discovering new materials for the membrane-electrode-assembly (MEA), composed of the proton-exchange membrane (PEM), catalyst layers, and diffusionmedia (DM) backing layers. In particular, continuum modeling has been invaluable in providing understanding and insight into processes and phenomena that cannot be resolved or uncoupled through experiments. While modeling of the transport and related phenomena has progressed greatly, there are still some critical areas that need attention. These areas include modeling the catalyst layer and multiphase phenomena in the PEFC porous media.While there have been various reviews over the years of PEFC modeling 1-7 and issues, [8][9][10][11][12][13][14] as well as numerous books and book chapters, there is a need to examine critically the field in terms of what has been done and what needs to be done. This review serves that purpose with a focus on transport modeling of PEFCs. This is not meant to be an exhaustive review...

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Section: 142mentioning

confidence: 99%

A Critical Review of Modeling Transport Phenomena in Polymer-Electrolyte Fuel Cells

Weber

Borup

Darling³

et al. 2014

J. Electrochem. Soc.

498

394

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“…Thus, the presence of the Stern layer can be accounted for via a different boundary condition to Equation 4b imposed at the Stern/diffuse layer interface located at x = (L − H ) and substituting Equations 6a and 6b by 95,99,126,127 Figure 3a, the boundary conditions at the Stern/diffuse layer interface accounting for the presence of the Stern layer can be expressed as…”

Section: Equilibrium Modelingmentioning

confidence: 99%

Recent Advances in Continuum Modeling of Interfacial and Transport Phenomena in Electric Double Layer Capacitors

Pilon

Wang

d’Entremont

2015

J. Electrochem. Soc.

117

105

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This paper reviews recent advances in physical modeling of interfacial and transport phenomena in electric double layer capacitors (EDLCs) under both equilibrium and dynamic cycling. The models are based on continuum theory and account for (i) the Stern layer at the electrode/electrolyte interface, (ii) finite ion sizes, (iii) steric repulsions, (iv) asymmetric electrolytes featuring ions with different valencies, effective diameters, or diffusion coefficients, (v) electric-field-dependent dielectric permittivity of the electrolyte, and/or (vi) porous three-dimensional morphology of the electrodes. Typical characterization methods such as electrochemical impedance spectroscopy, cyclic voltammetry, and galvanostatic cycling were reproduced numerically to identify the dominant physical phenomena and to gain insight into experimental observations. In addition, recent thermal models derived from first principles for EDLCs under constant-current cycling accounting for irreversible Joule heating and reversible heat generation rates due to ion diffusion, steric effects, and changes in entropy are discussed. Scaling analyses of both equilibrium and dynamic models are also presented as a way to identify self-similar and asymptotic behaviors as well as to develop design rules for electrodes and electrolytes of next generation EDLCs. Electrical double layer capacitors (EDLCs) store energy by ion adsorption in the electrical double layer (EDL) forming at the electrode/electrolyte interfaces.1,2 This process is highly reversible and the cycle life of EDLCs exceeds 100,000 cycles.2,3 EDLCs can operate in a wide range of specific energy and power densities. This versatility is a key feature for electrical energy storage, energy harvesting, and energy regeneration applications. 2The performance of EDLCs is determined by the combination of the electrode material and morphology and of the electrolyte. In general, the key attributes of a good electrode include 1,3-7 (i) large surface area accessible to ions to maximize charge storage, (ii) optimum pore size, short pore length, and good pore connectivity to facilitate ion transport, (iii) large electrical conductivity to enable fast charging and discharging and low ohmic resistance, (iv) thin electrodes and current collectors to reduce the total resistance of the device, (v) small leakage current, (vi) small self-discharge, (vii) environmentally friendly materials, and (viii) low price. However, satisfying all these criteria simultaneously is challenging. For example, increasing surface area often results in larger electrode electrical resistivity.1 Micropores with diameter less than 2 nm contribute greatly to EDLCs capacitance.2 But pores smaller than the ion size are typically inactive and do not contribute to charge storage. 1,8 Porous electrodes must also be electrochemically accessible to ions. Then, interconnected mesopores with diameter ranging from 2 to 50 nm are necessary for fast charging thanks to their easier accessibility to ions. 1,6,[9][10][11] In practice, electrode...

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“…To describe the kinetics of the Faradaic reaction, we apply the generalized Frumkin-Butler-Volmer equation, which, for a one-electron reaction, can be represented in dimensional form as [47][48][49][50][51][52][53][60][61][62][63][64][65][66][67][68][69][70][71][72][73] …”

Section: Faradaic Reactions In the Dlsmentioning

confidence: 99%

Diffuse charge and Faradaic reactions in porous electrodes

2011

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Porous electrodes instead of flat electrodes are widely used in electrochemical systems to boost storage capacities for ions and electrons, to improve the transport of mass and charge, and to enhance reaction rates. Existing porous electrode theories make a number of simplifying assumptions: (i) The charge-transfer rate is assumed to depend only on the local electrostatic potential difference between the electrode matrix and the pore solution, without considering the structure of the double layer (DL) formed in between; (ii) the charge-transfer rate is generally equated with the salt-transfer rate not only at the nanoscale of the matrix-pore interface, but also at the macroscopic scale of transport through the electrode pores. In this paper, we extend porous electrode theory by including the generalized Frumkin-Butler-Volmer model of Faradaic reaction kinetics, which postulates charge transfer across the molecular Stern layer located in between the electron-conducting matrix phase and the plane of closest approach for the ions in the diffuse part of the DL. This is an elegant and purely local description of the charge-transfer rate, which self-consistently determines the surface charge and does not require consideration of reference electrodes or comparison with a global equilibrium. For the description of the DLs, we consider the two natural limits: (i) the classical Gouy-Chapman-Stern model for thin DLs compared to the macroscopic pore dimensions, e.g., for high-porosity metallic foams (macropores >50 nm) and (ii) a modified Donnan model for strongly overlapping DLs, e.g., for porous activated carbon particles (micropores <2 nm). Our theory is valid for electrolytes where both ions are mobile, and it accounts for voltage and concentration differences not only on the macroscopic scale of the full electrode, but also on the local scale of the DL. The model is simple enough to allow us to derive analytical approximations for the steady-state and early transients. We also present numerical solutions to validate the analysis and to illustrate the evolution of ion densities, pore potential, surface charge, and reaction rates in response to an applied voltage.

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Electric current across the metal–solid electrolyte interface I. Direct current, current–voltage characteristic

Cited by 45 publications

References 12 publications

A Critical Review of Modeling Transport Phenomena in Polymer-Electrolyte Fuel Cells

A Critical Review of Modeling Transport Phenomena in Polymer-Electrolyte Fuel Cells

Recent Advances in Continuum Modeling of Interfacial and Transport Phenomena in Electric Double Layer Capacitors

Diffuse charge and Faradaic reactions in porous electrodes

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