Overcoming the shortcomings of the Nernst–Planck model

Dreyer, Wolfgang; Guhlke, Clemens; Müller, Rüdiger

doi:10.1039/c3cp44390f

Cited by 109 publications

(186 citation statements)

References 15 publications

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“…Flux relation.-The most simple relation between the diffusional flux j α and the chemical potentials μ α in order to ensure a non-negative entropy production is 23,35 …”

Section: Journal Of the Electrochemical Society 164 (11) E3671-e3685mentioning

confidence: 99%

Boundary Conditions for Electrochemical Interfaces

Landstorfer

2017

J. Electrochem. Soc.

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Consistent boundary conditions for electrochemical interfaces, which cover double layer charging, pseudo-capacitive effects and transfer reactions, are of high demand in electrochemistry and adjacent disciplines. Mathematical modeling and optimization of electrochemical systems is a strongly emerging approach to reduce cost and increase efficiency of super-capacitors, batteries, fuel cells, and electro-catalysis. However, many mathematical models which are used to describe such systems lack a real predictive value. Origin of this shortcoming is the usage of oversimplified boundary conditions. In this work we derive the boundary conditions for some general electrode-electrolyte interface based on non-equilibrium thermodynamics for volumes and surfaces. The resulting equations are widely applicable and cover also tangential transport. The general framework is then applied to a specific material model which allows the deduction of a current-voltage relation and thus a comparison to experimental data. Mathematical modeling of electrochemical systems is a strongly growing subject with many applications in science and industry. Applications range from fundamental single crystal systems 2 to plating and metal deposition, 3 lithium ion batteries, 4-8 fuel cells, 9 super caps, 10 and many further. Continuum models are the very basis of interpreting experimental results and widely used in chemical engineering to estimate cell dimensioning and heat generation, utilized in computed aided optimization of charging profiles or material compositions, and applied to many more issues of electrochemical systems.But the development of new electrochemically active materials and subsequent reaction mechanisms proceeds rapidly, e.g. with lithium air 11 or sulfur batteries, 12 solid electrolytes 13 or ionic liquids 14 and new electro-catalytic materials. 15 The adaption of existing mathematical models to new materials or material combinations is quite often not straight forward, if at all possible, and could even lead to a misinterpretation of experimental results. A systematic modeling approach which is applicable to various new electrochemical systems is hence of great importance, including reaction intermediates which can form at the electrode-electrolyte interface.The continuum mechanical modeling procedure generally spreads in two parts, (i) the derivation or prescription of volumetric balance equations, and (ii) stating the corresponding boundary conditions. The volumetric balance equations account for ion diffusion in the electrolyte phase, solid state diffusion in intercalation materials, mechanical deformation and stress, viscosity effects, heat transport, and others. Their derivation is mainly based on the modern framework of nonequilibrium thermodynamics, which provides some guidance through the actual modeling procedure. A core advantage of this framework is the stringent separation between general, material independent relations (expressed in chemical potentials μ α of some species A) and the actual material modeling (expr...

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“…Flux relation.-The most simple relation between the diffusional flux j α and the chemical potentials μ α in order to ensure a non-negative entropy production is 23,35 …”

Section: Journal Of the Electrochemical Society 164 (11) E3671-e3685mentioning

confidence: 99%

Boundary Conditions for Electrochemical Interfaces

Landstorfer

2017

J. Electrochem. Soc.

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“…Nonequilibrium thermodynamics [13] suggests that the chemical potentials of the species have to be regarded as driving forces, allowing to describe finite ion size effects in the constitutive relationship between chemical potential and concentration. The authors of [14] recently confirmed that in order to derive a thermodynamically consistent model it is necessary to include the dependency on the pressure into this relationship [4].…”

Section: Introductionmentioning

confidence: 99%

“…In Section 2, the Nernst-Planck-Poisson-Navier-Stokes system for an ideal incompressible mixture is introduced in a formulation equivalent to that provided in [14]. Then, constitutive relationships between chemical potential, pressure and concentration are introduced for four cases: the classical Nernst-Planck equations leading to the Gouy-Chapman double layer model, the excluded volume models after Bikerman and Freise [3,4], the ideal incompressible mixture [14], and -as it is closely related -Fermi-Dirac statistics for semiconductor problems.…”

Section: Introductionmentioning

confidence: 99%

“…Then, constitutive relationships between chemical potential, pressure and concentration are introduced for four cases: the classical Nernst-Planck equations leading to the Gouy-Chapman double layer model, the excluded volume models after Bikerman and Freise [3,4], the ideal incompressible mixture [14], and -as it is closely related -Fermi-Dirac statistics for semiconductor problems. It is shown that in thermodynamical equilibrium and for the case of equal molar masses, the ideal incompressible mixture model [14] is equivalent to a multispecies generalisation of the Bikerman-Freise model.…”

Section: Introductionmentioning

confidence: 99%

“…Appendix B provides the link of the model described in Section 2 to the formulation used in [14]. In order to support the proposal to formulate the equations in activities as primary variables, Appendix C discusses the consequences of using concentrations as basic unknowns.…”

Section: Introductionmentioning

confidence: 99%

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Ciucci

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Solid‐state batteries (SSBs) have gained lots of attention recently due to its availability to work with Li metal anode and the safety concerns arisen from conventional lithium‐ion batteries (LIBs). However, solid electrolyte that possesses high ionic conductivity and acceptable electrochemical stability against high potential difference is still under investigation. Also the interfacial resistance at the electrode|electrolyte interface may be significant due to the space charge layer formation, phase and mechanical instability. To address these problems, one needs a thorough understanding on the physics and electrochemistry of the SSB system, which can be acquired from both atomistic and continuum simulations. In this article, we review the theoretical framework for both atomistic and continuum modeling of SSBs. Also, we elucidate the usage of modeling for understanding various physical phenomena and illustrate how these understanding can lead to new SSB designs with better performance.

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Overcoming the shortcomings of the Nernst–Planck model

Cited by 109 publications

References 15 publications

Boundary Conditions for Electrochemical Interfaces

Boundary Conditions for Electrochemical Interfaces

Comparison and numerical treatment of generalised Nernst–Planck models

Modeling Solid State Batteries

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