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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | https://arxiv.org/abs/2604.16627 |
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| _version_ | 1866911603476135936 |
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| author | Pathak, Shakul Bazant, Martin Z. |
| author_facet | Pathak, Shakul Bazant, Martin Z. |
| contents | Porous electrode theory (PET) provides essential insights into electrochemical states, but its computational complexity hinders real-time control and obscures scaling relations. To bridge the gap between high-fidelity simulations and reduced-order models, we present a framework of scaling analysis and analytical approximations. By assuming high-performance electrodes minimize transport limitations and overpotentials, we derive a simplified "lean model" governed by four dimensionless numbers: (i) a traditional Damk"ohler number, Da, scaling the characteristic reaction rate to the diffusion rate in the electrolyte-filled pores; (ii) the "process Damk"ohler number," Da_p, scaling the reaction rate to the applied capacity utilization rate (C-rate); (iii) the "wiring Damk"ohler number," Da_w, scaling the reaction rate to an effective electromigration rate for ions in the pores in series with electrons in the conducting matrix; and (iv) the "capacitive Damk"ohler number," Da_c, comparing the rates of Faradaic reactions and double-layer charging. For batteries, we derive analytical solutions for standard protocols, including galvanostatic discharge, chronoamperometry, and electrochemical impedance spectroscopy. Validated against numerical simulations of a practical NMC half-cell, our formulae show excellent agreement at negligible computational cost. This interpretable, physics-based framework accelerates battery design and state estimation while unifying the modeling of batteries, supercapacitors, fuel cells, and other porous electrode systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_16627 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Scaling and Analytical Approximation of Porous Electrode Theory for Reaction-limited Batteries Pathak, Shakul Bazant, Martin Z. Systems and Control Porous electrode theory (PET) provides essential insights into electrochemical states, but its computational complexity hinders real-time control and obscures scaling relations. To bridge the gap between high-fidelity simulations and reduced-order models, we present a framework of scaling analysis and analytical approximations. By assuming high-performance electrodes minimize transport limitations and overpotentials, we derive a simplified "lean model" governed by four dimensionless numbers: (i) a traditional Damk"ohler number, Da, scaling the characteristic reaction rate to the diffusion rate in the electrolyte-filled pores; (ii) the "process Damk"ohler number," Da_p, scaling the reaction rate to the applied capacity utilization rate (C-rate); (iii) the "wiring Damk"ohler number," Da_w, scaling the reaction rate to an effective electromigration rate for ions in the pores in series with electrons in the conducting matrix; and (iv) the "capacitive Damk"ohler number," Da_c, comparing the rates of Faradaic reactions and double-layer charging. For batteries, we derive analytical solutions for standard protocols, including galvanostatic discharge, chronoamperometry, and electrochemical impedance spectroscopy. Validated against numerical simulations of a practical NMC half-cell, our formulae show excellent agreement at negligible computational cost. This interpretable, physics-based framework accelerates battery design and state estimation while unifying the modeling of batteries, supercapacitors, fuel cells, and other porous electrode systems. |
| title | Scaling and Analytical Approximation of Porous Electrode Theory for Reaction-limited Batteries |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2604.16627 |