Abstract
Porous electrode theory, pioneered by John Newman and collaborators, provides a macroscopic description of battery cycling behavior, rooted in microscopic physical models. Typically, the active materials are described as solid solution particles with transport and surface reactions driven by concentration fields, and the thermodynamics are incorporated through fitting of the open circuit potential. However, this approach does not apply to phase separating materials, for which the voltage is an emergent property of inhomogeneous concentration profiles, even in equilibrium. Here, we present a general framework, “multiphase porous electrode theory”, based on nonequilibrium thermodynamics and implemented in an open-source software package called “MPET”. Cahn-Hilliard-type phase field models are used to describe the active materials with suitably generalized models of interfacial reaction kinetics. Classical concentrated solution theory is implemented for the electrolyte phase, and Newman’s porous electrode theory is recovered in the limit of solid solution active materials with Butler-Volmer kinetics. More general, quantum-mechanical models of faradaic reactions are also included, such as Marcus-Hush-Chidsey kinetics for electron transfer at electrodes, extended for concentrated solutions. The full model and implementation are described, and a variety of example calculations are presented to illustrate the novel features of the software compared to existing battery models.
Highlights
We have presented an opensource software package called MPET (Multiphase Porous Electrode Theory), which builds on foundations laid by John Newman and many others by describing the active materials with variational nonequilibrium thermodynamics[76,77] applied to porous electrodes.[40,44]
Despite the prevalence of this modeling approach, few open source options are available for simulating the model, ones that are easy to modify with new thermodynamic models based on the powerful phase field formalism,[193] adapted for electrochemical systems.[76]
With MPET, we aimed to address this gap by providing a software platform implementing nonequilibrium thermodynamics of porous electrodes with an open source code, written with a modular design to encourage use, modifications, and improvements
Summary
The derivation of the Butler-Volmer equation[76] and the approach followed above both lead to some prefactor related to the excess chemical potential of the transition state, we suggest that the two terms are not capturing the same physical phenomena and may differ in their functional forms In this approach to the microscopic Marcus theory, there is some separation between the energetic contributions accounted for in the microscopic reorganization and the “approach”. We will simulate the individual particles by describing neutral species transport within them and their mass exchange with the electrolyte via the electrochemical reactions This assumes that electron mobility within the active materials is much larger than that of the inserted species.[114] Homogeneous.—When transport within the solid particles is fast, it can be computationally beneficial to approximate the particles with an average concentration, cs.[44] given a reacting surface area, Ap, and volume, Vp, the dynamics of intercalant i can be described by the average intercalation rate from the electrochemical reaction, j p,. Solid solution.—If the free energy can be described as a function of only the concentration (disregarding the effect of gradients and other contributions), Eq 54 can be rewritten as ci
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