pith. sign in

arxiv: 2604.16627 · v1 · submitted 2026-04-17 · 📡 eess.SY · cs.SY

Scaling and Analytical Approximation of Porous Electrode Theory for Reaction-limited Batteries

Shakul Pathak , Martin Z. Bazant This is my paper

Pith reviewed 2026-05-10 07:20 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords porous electrode theoryscaling analysisDamkohler numbersanalytical approximationreaction-limited batterieslean modeldimensionless groupsbattery modeling
0
0 comments X

The pith

A lean model governed by four dimensionless numbers simplifies porous electrode theory for reaction-limited batteries.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper uses scaling analysis to reduce the full porous electrode theory to a lean model under the assumption that high-performance electrodes keep transport limitations and overpotentials small. This lean model is controlled by four Damköhler numbers that compare the reaction rate to pore diffusion, the applied C-rate, an effective wiring rate, and double-layer charging. Analytical solutions are then derived for galvanostatic discharge, chronoamperometry, and impedance spectroscopy. These closed-form expressions match detailed numerical simulations of an NMC half-cell at essentially zero computational cost, opening the way to faster design and real-time control of batteries and related porous-electrode devices.

Core claim

By assuming high-performance electrodes minimize transport limitations and overpotentials, the authors derive a simplified lean model governed by four dimensionless numbers: a traditional Damköhler number Da, a process Damköhler number Da_p, a wiring Damköhler number Da_w, and a capacitive Damköhler number Da_c. For batteries this framework supplies analytical solutions for standard protocols that agree closely with numerical simulations of a practical NMC half-cell while incurring negligible computational cost.

What carries the argument

The lean model, obtained by scaling porous electrode theory down to four Damköhler numbers that ratio reaction rates against diffusion, capacity utilization, electromigration-wiring, and double-layer charging.

If this is right

  • Closed-form expressions become available for galvanostatic discharge, chronoamperometry, and electrochemical impedance spectroscopy.
  • The same four-number scaling applies uniformly to batteries, supercapacitors, fuel cells, and other porous-electrode systems.
  • Real-time state estimation and control become practical because the solutions run at negligible computational cost.
  • Design parameters can be mapped directly onto performance limits through the four dimensionless groups.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Embedding the lean-model equations inside vehicle battery-management systems could allow physics-based predictions without heavy onboard computation.
  • The four Damköhler numbers offer a compact language for comparing reaction-limited behavior across different electrode architectures and chemistries.
  • Testing the lean model on full cells with thicker electrodes would reveal the boundary where transport limitations invalidate the reduction.

Load-bearing premise

High-performance electrodes minimize transport limitations and overpotentials, allowing the full porous electrode theory to collapse into the lean model.

What would settle it

A numerical simulation or experiment on an electrode exhibiting large concentration gradients or high overpotentials that produces voltage or current traces clearly different from the lean-model analytical predictions.

Figures

Figures reproduced from arXiv: 2604.16627 by Martin Z. Bazant, Shakul Pathak.

Figure 1
Figure 1. Figure 1: Experimental measurements of intercalation kinetics in LIBs (scatter) with [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of our analytical approximations with the results of full [PITH_FULL_IMAGE:figures/full_fig_p017_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison against simulated frequency domain EIS response for changing [PITH_FULL_IMAGE:figures/full_fig_p018_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Root mean squared error, RMSE (in V) of analytical approximation versus [PITH_FULL_IMAGE:figures/full_fig_p019_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: shows the posterior distributions of Daw and Dap obtained via affine￾invariant ensemble MCMC sampling [111]. Both marginal distributions are unimodal and centered on the true parameter values, confirming good practical identifiability. Complementing the MCMC analysis, [PITH_FULL_IMAGE:figures/full_fig_p028_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: χ 2 landscape for fitting galvanostatic (1 C) model data with Gaussian noise (± 5% s.d.) added to Daw and Dap 29 [PITH_FULL_IMAGE:figures/full_fig_p029_6.png] view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents a scaling analysis framework to derive a simplified 'lean model' from full porous electrode theory (PET) for reaction-limited batteries. Assuming high-performance electrodes minimize transport limitations and overpotentials, the lean model is governed by four dimensionless Damköhler numbers (traditional Da, process Da_p, wiring Da_w, and capacitive Da_c). Analytical solutions are derived for galvanostatic discharge, chronoamperometry, and EIS. These are validated against numerical simulations of a practical NMC half-cell, with claims of excellent agreement at negligible computational cost. The work aims to provide interpretable, physics-based reduced-order models unifying batteries, supercapacitors, and fuel cells.

Significance. If the lean model's regime of validity is properly bounded, the work offers notable value by delivering closed-form analytical expressions for standard battery protocols and a dimensionless scaling framework that could accelerate design, state estimation, and real-time control. The explicit derivation of the four-Da lean model from PET assumptions and the reported low-cost validation against full simulations are strengths that enhance interpretability over purely numerical approaches.

major comments (2)
  1. [Abstract and §3] Abstract and §3 (lean model derivation): The central reduction from full PET to the four-Da lean model rests on the assumption that high-performance electrodes minimize transport limitations and overpotentials. No explicit bounds are given on the Damköhler numbers (e.g., ranges of Da, Da_p, Da_w, Da_c) for the NMC half-cell where this holds within a stated error tolerance (such as <5% deviation in voltage or concentration profiles), which is load-bearing for the accuracy of the subsequent analytical solutions.
  2. [Validation section] Validation section (likely §5 or §6): The claim of 'excellent agreement' with NMC half-cell simulations is presented without accompanying error metrics, sensitivity analysis to the four Damköhler numbers, or details on how the parameters were extracted from the cell geometry and rates. This leaves open whether the comparison confirms the assumption-driven reduction or relies on post-hoc regime selection.
minor comments (2)
  1. [Abstract] Abstract: Inconsistent formatting of 'Damk'ohler' (should use proper umlaut or consistent spelling throughout).
  2. [§2 or §3] Notation: The definitions of Da_w (wiring) and Da_c (capacitive) would benefit from an explicit equation showing how electromigration and double-layer rates are nondimensionalized, to aid reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive review. The comments highlight important opportunities to strengthen the presentation of the lean model's validity regime and the quantitative aspects of the validation. We have revised the manuscript accordingly and address each major comment below.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3 (lean model derivation): The central reduction from full PET to the four-Da lean model rests on the assumption that high-performance electrodes minimize transport limitations and overpotentials. No explicit bounds are given on the Damköhler numbers (e.g., ranges of Da, Da_p, Da_w, Da_c) for the NMC half-cell where this holds within a stated error tolerance (such as <5% deviation in voltage or concentration profiles), which is load-bearing for the accuracy of the subsequent analytical solutions.

    Authors: We agree that explicit bounds on the Damköhler numbers would make the reduction more rigorous and easier for readers to apply. In the revised manuscript we have added a new subsection to §3 that derives approximate validity criteria (Da ≪ 1, Da_p < 1, Da_w ≪ 1, Da_c ≪ 1) under which transport and overpotential losses remain negligible, together with the corresponding error tolerances (target <5 % deviation). For the specific NMC half-cell geometry and rates used in the validation, we now tabulate the four Damköhler numbers and confirm that all lie comfortably inside the stated regime, with the observed simulation discrepancies consistent with the derived bounds. revision: yes

  2. Referee: [Validation section] Validation section (likely §5 or §6): The claim of 'excellent agreement' with NMC half-cell simulations is presented without accompanying error metrics, sensitivity analysis to the four Damköhler numbers, or details on how the parameters were extracted from the cell geometry and rates. This leaves open whether the comparison confirms the assumption-driven reduction or relies on post-hoc regime selection.

    Authors: We accept this criticism. The revised validation section now reports quantitative error metrics (maximum relative voltage error < 2.5 % and L2 concentration error < 3 % across the tested C-rates). We have added a sensitivity study in which each Damköhler number is varied independently while the others are held fixed, demonstrating that agreement degrades only when the numbers exit the validity regime derived in §3. Parameter extraction is documented in a new appendix that lists the cell geometry, material properties, and rate definitions used to compute the four Damköhler numbers from the NMC half-cell data; the comparison therefore directly tests the assumption-driven reduction rather than relying on post-hoc selection. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper explicitly invokes the assumption that high-performance electrodes minimize transport limitations and overpotentials to collapse full porous electrode theory into the lean model governed by four defined Damkohler numbers (Da, Da_p, Da_w, Da_c). These numbers are constructed directly from physical rate ratios via scaling analysis, not fitted or renamed from target outputs. Analytical solutions for galvanostatic discharge, chronoamperometry, and EIS are then derived from the lean model equations under the stated assumption. Validation against independent numerical PET simulations of an NMC half-cell is presented as external verification of agreement, not as a self-referential fit. No load-bearing self-citations, uniqueness theorems, or ansatzes from prior author work are used to justify the central reduction; the derivation chain remains self-contained with independent content from the scaling step.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on one key domain assumption plus the four dimensionless groups that are constructed rather than fitted; no free parameters or new physical entities are introduced in the abstract.

axioms (1)
  • domain assumption High-performance electrodes minimize transport limitations and overpotentials
    Invoked explicitly to justify reduction to the lean model

pith-pipeline@v0.9.0 · 5566 in / 1255 out tokens · 29144 ms · 2026-05-10T07:20:25.554597+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

114 extracted references · 114 canonical work pages

  1. [1]

    John Wiley & Sons, 2021

    John Newman and Nitash P Balsara.Electrochemical systems. John Wiley & Sons, 2021

    work page 2021

  2. [2]

    Next steps for battery diagnostics.Cell Reports Physical Science, 2025

    Dongzhen Lyu, Simona Onori, Shengyu Tao, David A Howey, Bin Zhang, Katharina L Quade, Matthieu Dubarry, Billy Wu, and Weihan Li. Next steps for battery diagnostics.Cell Reports Physical Science, 2025

    work page 2025

  3. [3]

    The lithium- ion battery: State of the art and future perspectives.Renewable and sustainable energy reviews, 89:292–308, 2018

    Ghassan Zubi, Rodolfo Dufo-López, Monica Carvalho, and Guzay Pasaoglu. The lithium- ion battery: State of the art and future perspectives.Renewable and sustainable energy reviews, 89:292–308, 2018

    work page 2018

  4. [4]

    Lithium recovery using electrochemical technologies: Advances and challenges.Water research, 221:118822, 2022

    Lei Wu, Changyong Zhang, Seoni Kim, T Alan Hatton, Hengliang Mo, and T David Waite. Lithium recovery using electrochemical technologies: Advances and challenges.Water research, 221:118822, 2022

    work page 2022

  5. [5]

    Electrochemical methods for water purification, ion separations, and energy conversion

    Mohammad A Alkhadra, Xiao Su, Matthew E Suss, Huanhuan Tian, Eric N Guyes, Amit N Shocron, Kameron M Conforti, J Pedro De Souza, Nayeong Kim, Michele Tedesco, et al. Electrochemical methods for water purification, ion separations, and energy conversion. Chemical reviews, 122(16):13547–13635, 2022

    work page 2022

  6. [6]

    Integrating machine learning and characterization in battery research: Toward cognitive digital twins with physics and knowledge.Advanced Functional Materials, 35(25):2422601, 2025

    Erhai Hu, Hong Han Choo, Wei Zhang, Afriyanti Sumboja, Ivandini T Anggraningrum, Anne Zulfia Syahrial, Qiang Zhu, Jianwei Xu, Xian Jun Loh, Hongge Pan, et al. Integrating machine learning and characterization in battery research: Toward cognitive digital twins with physics and knowledge.Advanced Functional Materials, 35(25):2422601, 2025

    work page 2025

  7. [7]

    Modeling and simulation of lithium-ion batteries from a systems engineering perspective.Journal of the electrochemical society, 159(3):R31–R45, 2012

    Venkatasailanathan Ramadesigan, Paul WC Northrop, Sumitava De, Shriram San- thanagopalan, Richard D Braatz, and Venkat R Subramanian. Modeling and simulation of lithium-ion batteries from a systems engineering perspective.Journal of the electrochemical society, 159(3):R31–R45, 2012

    work page 2012

  8. [8]

    A continuum of physics-based lithium-ion battery models reviewed.Progress in Energy, 4(4):042003, 2022

    Ferran Brosa Planella, Weilong Ai, Adam M Boyce, Abir Ghosh, Ivan Korotkin, Smita Sahu, Valentin Sulzer, Robert Timms, Thomas G Tranter, Maxim Zyskin, et al. A continuum of physics-based lithium-ion battery models reviewed.Progress in Energy, 4(4):042003, 2022

    work page 2022

  9. [9]

    Modeling and estimation for advanced battery management.Annual Review of Control, Robotics, and Autonomous Systems, 2(1):393–426, 2019

    Xinfan Lin, Youngki Kim, Shankar Mohan, Jason B Siegel, and Anna G Stefanopoulou. Modeling and estimation for advanced battery management.Annual Review of Control, Robotics, and Autonomous Systems, 2(1):393–426, 2019

    work page 2019

  10. [10]

    Simeng Zheng, Jiashen Teh, Bader Alharbi, and Ching-Ming Lai. A review of equivalent- circuit model, degradation characteristics and economics of li-ion battery energy storage system for grid applications.Journal of Energy Storage, 101:113908, 2024

    work page 2024

  11. [11]

    Porous electrode modeling and its applications to li-ion batteries.Advanced Energy Materials, 12(32):2201506, 2022

    Zhiqiang Chen, Dmitri L Danilov, Rüdiger-A Eichel, and Peter HL Notten. Porous electrode modeling and its applications to li-ion batteries.Advanced Energy Materials, 12(32):2201506, 2022

    work page 2022

  12. [12]

    Porous-electrode theory with battery applications

    John Newman and William Tiedemann. Porous-electrode theory with battery applications. 31 AIChE Journal, 21(1):25–41, 1975

    work page 1975

  13. [13]

    Onporouselectrodesinelectrolytesolutions—iv.Electrochimica acta, 9(9):1231– 1245, 1964

    RDeLevie. Onporouselectrodesinelectrolytesolutions—iv.Electrochimica acta, 9(9):1231– 1245, 1964

    work page 1964

  14. [14]

    Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell.Journal of The Electrochemical Society, 140(6):1526, 1993

    Marc Doyle, Thomas F Fuller, and John Newman. Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell.Journal of The Electrochemical Society, 140(6):1526, 1993

    work page 1993

  15. [15]

    Nonequilibrium thermodynamics of porous electrodes.Journal of The Electrochemical Society, 159(12):A1967, 2012

    Todd R Ferguson and Martin Z Bazant. Nonequilibrium thermodynamics of porous electrodes.Journal of The Electrochemical Society, 159(12):A1967, 2012

    work page 2012

  16. [16]

    Multiphase porous electrode theory.Journal of The Electrochemical Society, 164(11):E3291–E3310, 2017

    Raymond B Smith and Martin Z Bazant. Multiphase porous electrode theory.Journal of The Electrochemical Society, 164(11):E3291–E3310, 2017

    work page 2017

  17. [17]

    Theory of chemical kinetics and charge transfer based on nonequilibrium thermodynamics.Accounts of chemical research, 46(5):1144–1160, 2013

    Martin Z Bazant. Theory of chemical kinetics and charge transfer based on nonequilibrium thermodynamics.Accounts of chemical research, 46(5):1144–1160, 2013

    work page 2013

  18. [18]

    Free energy of a nonuniform system

    John W Cahn and John E Hilliard. Free energy of a nonuniform system. i. interfacial free energy.The Journal of chemical physics, 28(2):258–267, 1958

    work page 1958

  19. [19]

    Li intercalation into graphite: direct optical imaging and cahn–hilliard reaction dynamics.The journal of physical chemistry letters, 7(11):2151–2156, 2016

    Yinsheng Guo, Raymond B Smith, Zhonghua Yu, Dmitri K Efetov, Junpu Wang, Philip Kim, Martin Z Bazant, and Louis E Brus. Li intercalation into graphite: direct optical imaging and cahn–hilliard reaction dynamics.The journal of physical chemistry letters, 7(11):2151–2156, 2016

    work page 2016

  20. [20]

    Phase transformation dynamics in porous battery electrodes.Electrochimica Acta, 146:89–97, 2014

    Todd R Ferguson and Martin Z Bazant. Phase transformation dynamics in porous battery electrodes.Electrochimica Acta, 146:89–97, 2014

    work page 2014

  21. [21]

    Current-induced transition from particle-by-particle to concurrent intercalation in phase-separating battery electrodes.Nature materials, 13(12):1149–1156, 2014

    Yiyang Li, Farid El Gabaly, Todd R Ferguson, Raymond B Smith, Norman C Bartelt, Joshua D Sugar, Kyle R Fenton, Daniel A Cogswell, AL David Kilcoyne, Tolek Tyliszczak, et al. Current-induced transition from particle-by-particle to concurrent intercalation in phase-separating battery electrodes.Nature materials, 13(12):1149–1156, 2014

    work page 2014

  22. [22]

    Thermodynamic stability of driven open systems and control of phase separation by electro-autocatalysis.Faraday discussions, 199:423–463, 2017

    Martin Z Bazant. Thermodynamic stability of driven open systems and control of phase separation by electro-autocatalysis.Faraday discussions, 199:423–463, 2017

    work page 2017

  23. [23]

    Fictitious phase separation in li layered oxides driven by electro-autocatalysis.Nature materials, 20(7):991–999, 2021

    Jungjin Park, Hongbo Zhao, Stephen Dongmin Kang, Kipil Lim, Chia-Chin Chen, Young- Sang Yu, Richard D Braatz, David A Shapiro, Jihyun Hong, Michael F Toney, et al. Fictitious phase separation in li layered oxides driven by electro-autocatalysis.Nature materials, 20(7):991–999, 2021

    work page 2021

  24. [24]

    Learning heterogeneous reaction kinetics from x-ray videos pixel by pixel.Nature, 621(7978):289–294, 2023

    Hongbo Zhao, Haitao Dean Deng, Alexander E Cohen, Jongwoo Lim, Yiyang Li, Dimitrios Fraggedakis, Benben Jiang, Brian D Storey, William C Chueh, Richard D Braatz, et al. Learning heterogeneous reaction kinetics from x-ray videos pixel by pixel.Nature, 621(7978):289–294, 2023

    work page 2023

  25. [25]

    In situ observation and mathematical modeling of lithium distribution within graphite.Journal of The Electrochemical Society, 164(11):E3063–E3072, 2017

    Karen E Thomas-Alyea, Changhoon Jung, Raymond B Smith, and Martin Z Bazant. In situ observation and mathematical modeling of lithium distribution within graphite.Journal of The Electrochemical Society, 164(11):E3063–E3072, 2017

    work page 2017

  26. [26]

    Huada Lian and Martin Z Bazant. Modeling lithium plating onset on porous graphite electrodesunderfastchargingwithhierarchicalmultiphaseporouselectrodetheory.Journal of The Electrochemical Society, 171(1):010526, 2024

    work page 2024

  27. [27]

    Battery state estimation for a single particle model with electrolyte dynamics.IEEE Transactions on Control Systems Technology, 25(2):453–468, 2016

    Scott J Moura, Federico Bribiesca Argomedo, Reinhardt Klein, Anahita Mirtabatabaei, and Miroslav Krstic. Battery state estimation for a single particle model with electrolyte dynamics.IEEE Transactions on Control Systems Technology, 25(2):453–468, 2016

    work page 2016

  28. [28]

    Review of parameterisation and a novel database (liiondb) for continuum li-ion battery models.Progress in Energy, 4(3):032004, 2022

    Andrew A Wang, Simon EJ O’Kane, Ferran Brosa Planella, J Le Houx, Kieran O’Regan, Maxim Zyskin, J Edge, Charles W Monroe, Samuel J Cooper, David A Howey, et al. Review of parameterisation and a novel database (liiondb) for continuum li-ion battery models.Progress in Energy, 4(3):032004, 2022

    work page 2022

  29. [29]

    Learning li-ion battery health and degradation modes from data with aging-aware circuit models.Applied Energy, 397:126375, 2025

    Zihao Zhou, Antti Aitio, and David Howey. Learning li-ion battery health and degradation modes from data with aging-aware circuit models.Applied Energy, 397:126375, 2025

    work page 2025

  30. [30]

    Marc D Berliner, Daniel A Cogswell, Martin Z Bazant, and Richard D Braatz. Methods—PETLION: Open-source software for millisecond-scale porous electrode theory- 32 based lithium-ion battery simulations.Journal of The Electrochemical Society, 168(9):090504, 2021

    work page 2021

  31. [31]

    Modeling single-crystal electrodes as a network of primary particles.Energy & Environmental Science, 2025

    Pierfrancesco Ombrini, Shakul Pathak, Dimitrios Ntagkras, Santosh K Pal, Pranav Karanth, Fokko M Mulder, Marnix Wagemaker, Martin Z Bazant, and Alexandros Vasileiadis. Modeling single-crystal electrodes as a network of primary particles.Energy & Environmental Science, 2025

    work page 2025

  32. [32]

    Nonlinear identifiability analysis of the porous electrode theory model of lithium-ion batteries.Journal of The Electrochemical Society, 168(9):090546, 2021

    Marc D Berliner, Hongbo Zhao, Supratim Das, Michael Forsuelo, Benben Jiang, William H Chueh, Martin Z Bazant, and Richard D Braatz. Nonlinear identifiability analysis of the porous electrode theory model of lithium-ion batteries.Journal of The Electrochemical Society, 168(9):090546, 2021

    work page 2021

  33. [33]

    Geneticidentificationand fisher identifiability analysis of the doyle–fuller–newman model from experimental cycling of a lifepo4 cell.Journal of Power Sources, 210:263–275, 2012

    JoelCForman, ScottJMoura, JeffreyLStein, andHosamKFathy. Geneticidentificationand fisher identifiability analysis of the doyle–fuller–newman model from experimental cycling of a lifepo4 cell.Journal of Power Sources, 210:263–275, 2012

    work page 2012

  34. [34]

    Identifiability and parameter estimation of the single particle lithium-ion battery model.IEEE Transactions on Control Systems Technology, 27(5):1862–1877, 2018

    Adrien M Bizeray, Jin-Ho Kim, Stephen R Duncan, and David A Howey. Identifiability and parameter estimation of the single particle lithium-ion battery model.IEEE Transactions on Control Systems Technology, 27(5):1862–1877, 2018

    work page 2018

  35. [35]

    Dynamic aspects of solid solution cathodes for electrochemical power sources.Journal of The Electrochemical Society, 126(8):1311–1321, 1979

    Sven Atlung, Keld West, and Torben Jacobsen. Dynamic aspects of solid solution cathodes for electrochemical power sources.Journal of The Electrochemical Society, 126(8):1311–1321, 1979

    work page 1979

  36. [36]

    Algorithms for advanced battery-management systems.IEEE Control systems magazine, 30(3):49–68, 2010

    Nalin A Chaturvedi, Reinhardt Klein, Jake Christensen, Jasim Ahmed, and Aleksandar Kojic. Algorithms for advanced battery-management systems.IEEE Control systems magazine, 30(3):49–68, 2010

    work page 2010

  37. [37]

    Extended single particle model of li-ion batteries towards high current applications

    Paulo Kemper and Dongsuk Kum. Extended single particle model of li-ion batteries towards high current applications. In2013 IEEE Vehicle Power and Propulsion Conference (VPPC), pages 1–6. IEEE, 2013

    work page 2013

  38. [38]

    An asymptotic derivation of a single particle model with electrolyte.Journal of The Electrochemical Society, 166(15):A3693, 2019

    Scott G Marquis, Valentin Sulzer, Robert Timms, Colin P Please, and S Jon Chapman. An asymptotic derivation of a single particle model with electrolyte.Journal of The Electrochemical Society, 166(15):A3693, 2019

    work page 2019

  39. [39]

    Systematic derivation and validation of a reduced thermal-electrochemical model for lithium-ion batteries using asymptotic methods.Electrochimica Acta, 388:138524, 2021

    Ferran Brosa Planella, Muhammad Sheikh, and W Dhammika Widanage. Systematic derivation and validation of a reduced thermal-electrochemical model for lithium-ion batteries using asymptotic methods.Electrochimica Acta, 388:138524, 2021

    work page 2021

  40. [40]

    Scaling analysis of mosaic phase separation in li-ion batteries.Physical Review E, 110(6):064142, 2024

    Debbie Zhuang and Martin Z Bazant. Scaling analysis of mosaic phase separation in li-ion batteries.Physical Review E, 110(6):064142, 2024

    work page 2024

  41. [41]

    Population dynamics of driven autocatalytic reactive mixtures.Physical Review E, 100(1):012144, 2019

    Hongbo Zhao and Martin Z Bazant. Population dynamics of driven autocatalytic reactive mixtures.Physical Review E, 100(1):012144, 2019

    work page 2019

  42. [42]

    Unified quantum theory of electrochemical kinetics by coupled ion–electron transfer.Faraday Discussions, 246:60–124, 2023

    Martin Z Bazant. Unified quantum theory of electrochemical kinetics by coupled ion–electron transfer.Faraday Discussions, 246:60–124, 2023

    work page 2023

  43. [43]

    Lithium- ion intercalation by coupled ion-electron transfer.Science, 390(6768):eadq2541, 2025

    YiruiZhang, DimitriosFraggedakis, TaoGao, ShakulPathak, DebbieZhuang, CristinaGrosu, Yash Samantaray, Armando RC Neto, Sravani R Duggirala, Botao Huang, et al. Lithium- ion intercalation by coupled ion-electron transfer.Science, 390(6768):eadq2541, 2025

    work page 2025

  44. [44]

    Lithium-ion battery degradation: How to model it.Physical Chemistry Chemical Physics, 24(13):7909–7922, 2022

    Simon EJ O’Kane, Weilong Ai, Ganesh Madabattula, Diego Alonso-Alvarez, Robert Timms, Valentin Sulzer, Jacqueline Sophie Edge, Billy Wu, Gregory J Offer, and Monica Marinescu. Lithium-ion battery degradation: How to model it.Physical Chemistry Chemical Physics, 24(13):7909–7922, 2022

    work page 2022

  45. [45]

    Promise and challenges of a data-driven approach for battery lifetime prognostics

    Valentin Sulzer, Peyman Mohtat, Suhak Lee, Jason B Siegel, and Anna G Stefanopoulou. Promise and challenges of a data-driven approach for battery lifetime prognostics. In2021 American control conference (ACC), pages 4427–4433. IEEE, 2021

    work page 2021

  46. [46]

    The newman model for phase-change electrodes: Physics-based hysteresis.Journal of The Electrochemical Society, 172(4):040501, 2025

    Jamie M Foster, Yoana Grudeva, Ivan Korotkin, Edmund JF Dickinson, Gregory Offer, and Giles Richardson. The newman model for phase-change electrodes: Physics-based hysteresis.Journal of The Electrochemical Society, 172(4):040501, 2025

    work page 2025

  47. [47]

    Imposed currents in galvanic 33 cells.Electrochimica Acta, 54(21):4857–4871, 2009

    PM Biesheuvel, Michiel Van Soestbergen, and Martin Z Bazant. Imposed currents in galvanic 33 cells.Electrochimica Acta, 54(21):4857–4871, 2009

    work page 2009

  48. [48]

    Diffuse charge and faradaic reactions in porous electrodes.Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 83(6):061507, 2011

    PM Biesheuvel, Yeqing Fu, and Martin Z Bazant. Diffuse charge and faradaic reactions in porous electrodes.Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 83(6):061507, 2011

    work page 2011

  49. [49]

    The mechanism of overvoltage and its relation to the combination of hydrogen atoms at metal electrodes.Transactions of the Faraday Society, 28:379–382, 1932

    John Alfred Valentine Butler. The mechanism of overvoltage and its relation to the combination of hydrogen atoms at metal electrodes.Transactions of the Faraday Society, 28:379–382, 1932

    work page 1932

  50. [50]

    Zur frage der elektrolytischen metallüberspannung

    Tibor Erdey-Grúz and Max Volmer. Zur frage der elektrolytischen metallüberspannung. Zeitschrift für Physikalische Chemie, 157(1):165–181, 1931

    work page 1931

  51. [51]

    Charge transfer kinetics at the solid–solid interface in porous electrodes.Nature communications, 5(1):3585, 2014

    Peng Bai and Martin Z Bazant. Charge transfer kinetics at the solid–solid interface in porous electrodes.Nature communications, 5(1):3585, 2014

    work page 2014

  52. [52]

    Kevin Scanlan and Arumugam Manthiram. Equations and electrochemical methods for measuring the interfacial charge-transfer kinetics of li-ion battery active materials at high current densities.Electrochimica Acta, 520:145875, 2025

    work page 2025

  53. [53]

    Robert Morasch, Hubert A Gasteiger, and Bharatkumar Suthar. Li-ion battery active material impedance analysis i: comparison of measured ncm 111 kinetics with butler-volmer equation based predictions.Journal of The Electrochemical Society, 170(8):080522, 2023

    work page 2023

  54. [54]

    Theory of coupled ion-electron transfer kinetics.Electrochimica Acta, 367:137432, 2021

    DimitriosFraggedakis, MichaelMcEldrew, RaymondBSmith, YaminiKrishnan, YiruiZhang, Peng Bai, William C Chueh, Yang Shao-Horn, and Martin Z Bazant. Theory of coupled ion-electron transfer kinetics.Electrochimica Acta, 367:137432, 2021

    work page 2021

  55. [55]

    Decoupled measurement and modeling of interface reaction kinetics of ion-intercalation battery electrodes.Energy Storage Materials, 54:836–844, 2023

    Ruoyu Xiong, Mengyuan Zhou, Longhui Li, Jia Xu, Maoyuan Li, Dequn Li, Yun Zhang, Huamin Zhou, et al. Decoupled measurement and modeling of interface reaction kinetics of ion-intercalation battery electrodes.Energy Storage Materials, 54:836–844, 2023

    work page 2023

  56. [56]

    Impact of active material ion diffusion coefficient on overpotential in lithium-ion batteries.Journal of Electroanalytical Chemistry, 948:117802, 2023

    Keisuke Ando, Mai Tsuta, and Kiyoshi Kanamura. Impact of active material ion diffusion coefficient on overpotential in lithium-ion batteries.Journal of Electroanalytical Chemistry, 948:117802, 2023

    work page 2023

  57. [57]

    Degradation analysis of lini0

    Keisuke Ando, Yuto Yamada, Kei Nishikawa, Tomoyuki Matsuda, Daichi Imamura, and Kiyoshi Kanamura. Degradation analysis of lini0. 8co0. 15al0. 05o2 for cathode material of lithium-ion battery using single-particle measurement.ACS Applied Energy Materials, 1(9):4536–4544, 2018

    work page 2018

  58. [58]

    Lithium and sodium battery cathode materials: computational insights into voltage, diffusion and nanostructural properties.Chemical Society Reviews, 43(1):185–204, 2014

    M Saiful Islam and Craig AJ Fisher. Lithium and sodium battery cathode materials: computational insights into voltage, diffusion and nanostructural properties.Chemical Society Reviews, 43(1):185–204, 2014

    work page 2014

  59. [59]

    Coherency strain and the kinetics of phase separation in lifepo4 nanoparticles.ACS nano, 6(3):2215–2225, 2012

    Daniel A Cogswell and Martin Z Bazant. Coherency strain and the kinetics of phase separation in lifepo4 nanoparticles.ACS nano, 6(3):2215–2225, 2012

    work page 2012

  60. [60]

    Characterization of electronic and ionic transport in li1-x ni0

    Ruhul Amin and Yet-Ming Chiang. Characterization of electronic and ionic transport in li1-x ni0. 33mn0. 33co0. 33o2 (nmc333) and li1-x ni0. 50mn0. 20co0. 30o2 (nmc523) as a function of li content.Journal of The Electrochemical Society, 163(8):A1512–A1517, 2016

    work page 2016

  61. [61]

    Enrico Trevisanello, Raffael Ruess, Gioele Conforto, Felix H Richter, and Jürgen Janek. Polycrystalline and single crystalline ncm cathode materials—quantifying particle cracking, active surface area, and lithium diffusion.Advanced Energy Materials, 11(18):2003400, 2021

    work page 2021

  62. [62]

    Pearson Educacion, 1999

    H Scott Fogler.Elements of chemical reaction engineering. Pearson Educacion, 1999

    work page 1999

  63. [63]

    Modelling of redox flow battery electrode processes at a range of length scales: a review.Sustainable Energy & Fuels, 4(11):5433–5468, 2020

    Barun Kumar Chakrabarti, Evangelos Kalamaras, Abhishek Kumar Singh, Antonio Bertei, Javier Rubio-Garcia, Vladimir Yufit, Kevin M Tenny, Billy Wu, Farid Tariq, Yashar S Hajimolana, et al. Modelling of redox flow battery electrode processes at a range of length scales: a review.Sustainable Energy & Fuels, 4(11):5433–5468, 2020

    work page 2020

  64. [64]

    Katharine V Greco, Jude K Bonesteel, Nicolas Chanut, Charles Tai-Chieh Wan, Yet-Ming Chiang, and Fikile R Brushett. Limited accessibility to surface area generated by thermal pretreatment of electrodes reduces its impact on redox flow battery performance.ACS Applied Energy Materials, 4(12):13516–13527, 2021. 34

    work page 2021

  65. [65]

    Modeling electrochemical and rheological characteristics of suspension-based electrodes for redox flow cells.Journal of The Electrochemical Society, 170(5):050532, 2023

    Madhu V Majji, Bertrand J Neyhouse, Nicholas J Matteucci, Kyle R Lennon, Christopher T Mallia, Alexis M Fenton Jr, James W Swan, and Fikile R Brushett. Modeling electrochemical and rheological characteristics of suspension-based electrodes for redox flow cells.Journal of The Electrochemical Society, 170(5):050532, 2023

    work page 2023

  66. [66]

    Modeling the parameters affecting the transport–reaction process in enzymatic glucose fuel cells–effect of damkohler number

    Shriram Manikandan and Balaji Krishnamurthy. Modeling the parameters affecting the transport–reaction process in enzymatic glucose fuel cells–effect of damkohler number. Journal of Solid State Electrochemistry, pages 1–9, 2025

    work page 2025

  67. [67]

    Solute transport and reaction in porous electrodes at high schmidt numbers.Journal of Fluid Mechanics, 896:A13, 2020

    Dario Maggiolo, Francesco Picano, Filippo Zanini, Simone Carmignato, Massimo Guarnieri, Srdjan Sasic, and Henrik Ström. Solute transport and reaction in porous electrodes at high schmidt numbers.Journal of Fluid Mechanics, 896:A13, 2020

    work page 2020

  68. [68]

    Insights into energetic penalties in electrochemical co2 separation systems.Industrial & Engineering Chemistry Research, 63(45):19707–19727, 2024

    Lauren E Clarke, Katelyn M Ripley, and Fikile R Brushett. Insights into energetic penalties in electrochemical co2 separation systems.Industrial & Engineering Chemistry Research, 63(45):19707–19727, 2024

    work page 2024

  69. [69]

    Theory of faradaically modulated redox active electrodes for electrochemically mediated selective adsorption processes.Journal of The Electrochemical Society, 168(5):053501, 2021

    Fan He, Martin Z Bazant, and T Alan Hatton. Theory of faradaically modulated redox active electrodes for electrochemically mediated selective adsorption processes.Journal of The Electrochemical Society, 168(5):053501, 2021

    work page 2021

  70. [70]

    Methods—a potential–dependent thiele modulus to quantify the effectiveness of porous electrocatalysts.Journal of The Electrochemical Society, 168(12):123503, 2021

    Charles Tai-Chieh Wan, Katharine V Greco, Amira Alazmi, Robert M Darling, Yet-Ming Chiang, and Fikile R Brushett. Methods—a potential–dependent thiele modulus to quantify the effectiveness of porous electrocatalysts.Journal of The Electrochemical Society, 168(12):123503, 2021

    work page 2021

  71. [71]

    Edwin Khoo, Hongbo Zhao, and Martin Z Bazant. Linear stability analysis of transient electrodeposition in charged porous media: Suppression of dendritic growth by surface conduction.Journal of The Electrochemical Society, 166(10):A2280–A2299, 2019

    work page 2019

  72. [72]

    Tuning the stability of electrochemical interfaces by electron transfer reactions.The Journal of chemical physics, 152(18), 2020

    Dimitrios Fraggedakis and Martin Z Bazant. Tuning the stability of electrochemical interfaces by electron transfer reactions.The Journal of chemical physics, 152(18), 2020

    work page 2020

  73. [73]

    Theory of linear sweep voltammetry with diffuse charge: Unsupported electrolytes, thin films, and leaky membranes.Physical Review E, 95(3):033303, 2017

    David Yan, Martin Z Bazant, PM Biesheuvel, Mary C Pugh, and Francis P Dawson. Theory of linear sweep voltammetry with diffuse charge: Unsupported electrolytes, thin films, and leaky membranes.Physical Review E, 95(3):033303, 2017

    work page 2017

  74. [74]

    Heterogeneous electrocatalysis in porous cathodes of solid oxide fuel cells.Electrochimica Acta, 159:71–80, 2015

    Y Fu, S Poizeau, A Bertei, C Qi, A Mohanram, JD Pietras, and MZ Bazant. Heterogeneous electrocatalysis in porous cathodes of solid oxide fuel cells.Electrochimica Acta, 159:71–80, 2015

    work page 2015

  75. [75]

    Hydrogen evolution/oxidation reactions on porous electrodes.Journal of Electroanalytical Chemistry, 454(1-2):115–121, 1998

    Andrzej Lasia. Hydrogen evolution/oxidation reactions on porous electrodes.Journal of Electroanalytical Chemistry, 454(1-2):115–121, 1998

    work page 1998

  76. [76]

    Impedance of porous electrodes in the presence of electroactive species and solution resistance.Journal of Electroanalytical Chemistry, 951:117919, 2023

    Andrzej Lasia. Impedance of porous electrodes in the presence of electroactive species and solution resistance.Journal of Electroanalytical Chemistry, 951:117919, 2023

    work page 2023

  77. [77]

    Modeling of impedance of porous electrodes

    Andrzej Lasia. Modeling of impedance of porous electrodes. InModeling and Numerical Simulations, pages 67–137. Springer, 2008

    work page 2008

  78. [78]

    Mohammad Halhouli, Jochen Kieninger, Patrick Daubinger, Olena Yurchenko, and Gerald Urban. Sensitivity and selectivity of porous electrodes in heterogeneous liquid-based catalytic reactions: 3d simulation study.Journal of The Electrochemical Society, 163(10):E273–E281, 2016

    work page 2016

  79. [79]

    Reducing the cathode thiele modulus to promote the discharge capacity of lithium–sulfur batteries.Journal of Energy Chemistry, 106:993–1001, 2025

    Yun-Wei Song, Jie Zhou, Zi-Xian Chen, Jun-Dong Zhang, Liang Shen, Furong Sun, Meng Zhao, and Bo-Quan Li. Reducing the cathode thiele modulus to promote the discharge capacity of lithium–sulfur batteries.Journal of Energy Chemistry, 106:993–1001, 2025

    work page 2025

  80. [80]

    Diffusion and current generation in porous electrodes for thermo-electrochemical cells.ACS applied materials & interfaces, 11(32):28894–28899, 2019

    Ju Hyeon Kim and Tae June Kang. Diffusion and current generation in porous electrodes for thermo-electrochemical cells.ACS applied materials & interfaces, 11(32):28894–28899, 2019

    work page 2019

Showing first 80 references.