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REVIEW 2 major objections 5 minor 68 references

Kinetic Cellular Model of Corrosion

T0 review · 2 major / 5 minor · reviewed 2026-07-13 · grok-4.5

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Pith's one-line read A cell-based kinetic model of corrosion bridges atomistic detail and continuum length and time scales.

desk verdict Solid early methods paper that cleanly packages rate equations recovering NP/BV/PF/CA, with good analytic matches on diffusion and Gouy–Chapman; the Mg demo is unstable and the multi-scale claim is still aspirational. read the letter →

arxiv 2607.09292 v1 pith:Z6AOHMDW submitted 2026-07-10 cond-mat.mtrl-sci

Orkan Sezer , Andrew Horsfield This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords corrosionmodellingkineticcellularmodelNernst–PlanckButler–Volmerphasefieldautomataelectrochemicalpotentialmulti-scalesimulation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Aqueous corrosion couples electron transfer, ion dissolution, diffusion, electrostatics and chemical reactions across many length and time scales, so pure atomistic simulation cannot cover the whole process. This paper introduces a Kinetic Cellular Model that divides the system into cells that exchange particles according to generalised rate equations driven by electrochemical potentials, while allowing local rearrangements such as reactions inside cells. In appropriate limits the same equations reduce to the Nernst–Planck and Butler–Volmer continuum descriptions or to phase-field and cellular-automata update rules. Illustrative one- and two-dimensional calculations (diffusion, Gouy–Chapman double layers, hydrogen evolution, magnesium dissolution) recover analytic or expected physical behaviour, showing that the framework can already capture the essential coupled physics while remaining open to free-energy models taken from more detailed calculations.

What carries the argument

The Kinetic Cellular Model: each cell is assigned particle numbers and electrochemical potentials; inter-cell transfer obeys the master rate equation (1) with hop rates of the form (2); the electrostatic potential is obtained from Poisson’s equation; local free-energy derivatives supply the chemical potentials that drive both transport and internal rearrangements.

What would settle it

A quantitative comparison, for the same free-energy parameters, of the KCM magnesium-dissolution profile against a fully continuum Nernst–Planck/Butler–Volmer finite-element solution (or a lattice kinetic Monte Carlo trajectory) that shows systematic mismatch in interface position or charge-layer thickness once the time-step and mesh are refined.

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Extended reading notes

Core claim

Generalised kinetic equations written on a cellular mesh, with hop rates set by differences of electrochemical potential, simultaneously reproduce the continuum Nernst–Planck and Butler–Volmer equations, reduce to phase-field or cellular-automata dynamics in stated limits, and accommodate explicit local chemical rearrangements, thereby extending the accessible scales of corrosion modelling beyond pure atomistics.

Load-bearing premise

Each cell is assumed to be nearly in internal equilibrium so that particle exchange is completely determined by cell electrochemical potentials and a single attempt frequency; accuracy falls when rearrangement and transfer rates become comparable.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The manuscript introduces a Kinetic Cellular Model (KCM) that partitions a system into cells exchanging particles according to generalised rate equations (Eqs. 1–2) driven by electrochemical potentials, while allowing local rearrangements (chemical reactions or phase change) inside cells. It shows that the transfer rule recovers the Nernst–Planck equation under small potential differences and is closely related to Butler–Volmer kinetics; cellular automata and phase-field dynamics appear as stated limits. Illustrative 1D tests (analytic diffusion, Gouy–Chapman double layer, hydrogen evolution, Mg dissolution) and a 2D diffusion comparison are presented, with good agreement to analytics where available. The authors position KCM as a bridge that can incorporate free-energy models (e.g. from DFT) while reaching longer length and time scales than pure atomistics.

Significance. If the framework can be made numerically robust for multi-process electrochemical dissolution and product formation, it would offer a useful intermediate-scale tool that unifies continuum transport, interface kinetics, and local chemistry without the geometric bookkeeping of pure FEM or the restricted state space of classical CA. The reductions to NP/BV and the independent analytic benchmarks (error-function diffusion, Gouy–Chapman) are correctly stated and strengthen the foundations. Explicit free-energy construction for Mg (Eqs. 27–42) and the phase-parameter definition are transparent and falsifiable. The work is early-stage but the conceptual architecture is sound and of interest to the corrosion-modelling community.

major comments (2)
  1. §III.D (Mg dissolution): the only corrosion-relevant demonstration requires an explicit Euler step of 10^{-4} fs and becomes unstable after 0.7 fs. The authors note charge build-up may stall further dissolution and defer product-formation reactions. Because the multi-scale claim rests on cells remaining near internal equilibrium while transfer and rearrangement rates can be comparable (§II), a stable multi-process trajectory (or a clear demonstration that an implicit/Crank–Nicolson integrator restores stability at corrosion-relevant times) is needed before the central claim is fully supported.
  2. §II and §III.D: the spontaneous reaction Mg ⇌ Mg++ + 2e− is triggered by a hard phase-field threshold (φ < 0.95) rather than by a continuous free-energy-derived rate. This ad-hoc switch sits outside the rate-equation framework of Eqs. 1–2 and weakens the claim that local rearrangements are treated consistently with inter-cell transfer. Either a rate form derived from the same free energy or a quantitative justification of the threshold is required.
minor comments (5)
  1. Fig. 5 caption and surrounding text: the extremely short simulation time (0.7 fs) should be stated more prominently so readers do not misinterpret the result as a quasi-steady corrosion profile.
  2. Eq. (2) and the subsequent NP reduction: the identification ν_α,i = D_α,i / a² is correct but would benefit from an explicit statement that this holds only when the chemical-potential difference is small (already noted later); a single clarifying sentence near Eq. (6) would help.
  3. §III.E: the 2D diffusion comparison is convincing, yet the finite-box versus infinite-domain discrepancy at late times is mentioned only briefly; a short quantitative residual or a larger-domain check would strengthen the figure.
  4. Notation: both ˜n and n are used for particle numbers/concentrations; a brief glossary or consistent use of areal versus volumetric densities would reduce ambiguity.
  5. References: the similarity to Watanabe & Fujita (2022) is noted; a short paragraph contrasting algorithmic choices would help readers place the contribution.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: continuum limits and free-energy parameters are independent of the numerical targets they are checked against.

full rationale

The paper’s central derivation is the rate equation (Eq. 1) together with the Arrhenius-like hop rate (Eq. 2). From these it recovers the Nernst–Planck continuum limit by a small-potential-difference expansion (Eq. 6) and notes the formal kinship with Butler–Volmer; both recoveries are standard continuum limits, not self-fitted predictions. Equilibrium ion distributions are obtained by free-energy minimization whose stationary condition is exactly the Poisson–Boltzmann relation already assumed in Gouy–Chapman theory; the numerical potential is then compared with the independent analytic Gouy–Chapman formula, not with a quantity that was fitted into the free energy. Diffusion profiles are compared with the closed-form error-function / Gaussian solutions. Chemical-potential parameters for the Mg-dissolution demonstration are assembled from tabulated cohesive, ionization and solvation energies plus a band-gap estimate; they are not adjusted to force a desired dissolution curve. The only residual self-reference is ordinary methods development (the authors’ own 1-D code and the observation that the method reduces to phase-field or cellular-automata forms in stated limits). No load-bearing uniqueness theorem, fitted-input-called-prediction, or definitional identity of the form “Eq. X = Eq. Y by construction” appears. Circularity burden is therefore minimal.

Assumptions & free parameters 6 free parameters · 6 assumptions · 1 invented entities

The central claim is a methods claim: that the stated cellular rate equations plus free-energy-derived chemical potentials suffice to recover known continuum limits and to simulate simple corrosion-related processes. Load-bearing content is therefore the local-equilibrium cell assumption, the symmetric exponential hop rate, the free-energy interpolations for multi-phase cells, and many hand-set kinetic and energy parameters. No new physical particle or force is postulated; the invented entity is the KCM framework itself as an organizing computational object.

free parameters (6)
  • Attempt frequencies ν_α (electrons, Mg, Mg++)
    Set by hand (e.g. 3.75 fs^{-1} for electrons, 0.1 fs^{-1} for Mg/Mg++) to control hop rates; not derived from first principles in the paper.
  • χ_Mg and χ_Mg++ interstitial/vacancy energy scales
    Estimated as 1 eV each to stiffen bulk solid free energies; chosen for a minimal dissolution model.
  • Phase-field width parameter w
    Set to 0.01 to control how rapidly φ switches with effective Mg occupancy; ad hoc smoothing scale.
  • Relative free-energy offsets (electron 4.5 eV, Mg transfer 6.88 eV, Mg++ -2.12 eV, etc.)
    Assembled from literature numbers plus modeling choices (half water band gap, sequence of vacuum ionization/solvation steps); absolute scale is conventional zero in metal, but several intermediate choices are free modeling decisions.
  • Dielectric constants by region (metal/film/solution)
    Assigned region-wise (e.g. 100/10/80 or uniform 80) rather than computed; strongly affect potential profiles.
  • Mesh spacing a and explicit Euler time step
    a = 1 Å and Δt down to 10^{-4} fs chosen for numerical stability; practical free numerical parameters that limit accessible times.
assumptions (6)
  • domain assumption Each cell is nearly in internal equilibrium so transfer rates depend only on cell electrochemical potentials and attempt frequencies.
    Stated as the fundamental physical assumption in §II; accuracy fails when internal rearrangement and inter-cell transfer rates are comparable.
  • domain assumption Hop rate R_{α,i→j} = ν_α exp[-(μ_{α,j}-μ_{α,i})/(2 k_B T)] yields correct equilibrium and recovers Butler–Volmer-like kinetics.
    Eq. 2; standard detailed-balance form, not derived from microscopic dynamics in this paper.
  • ad hoc to paper Configurational entropy of mixing is carried by the hopping dynamics, not by an extra term in μ (except possibly internal cell terms).
    Explicit modeling choice in §II.1 so that free-energy expressions omit usual ideal-solution entropy.
  • ad hoc to paper Multi-phase cells are represented by a concentration-dependent phase parameter φ with linear free-energy interpolation and optional surface terms set to zero.
    Eqs. 21–42; surface Δμ terms neglected so dissolution is driven only by bulk free-energy differences.
  • domain assumption Fast reactions (e.g. e- + H+ → ½ H2) may be treated as instantaneous stoichiometric updates.
    §II.2; used in the hydrogen-evolution illustration.
  • domain assumption Poisson electrostatics with piecewise dielectric and uniform charge density per cell is adequate.
    Eqs. 3–4; standard continuum electrostatics on the cellular mesh.
invented entities (1)
  • Kinetic Cellular Model (KCM) as a unified computational framework
    purpose: Organize particle transfer, local reactions, multi-phase free energies, and electrostatics on a common cellular rate-equation footing for corrosion.
    The paper’s primary contribution is this organizing method rather than a new physical particle or force; independent evidence is the reduction to known continuum limits and agreement on simple analytics, not external experimental confirmation of a new entity.

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Pith. "Pith review of Kinetic Cellular Model of Corrosion." pith.science (2026). https://pith.science/paper/Z6AOHMDW

@misc{pith2026260709292,
  author       = {Pith},
  title        = {Pith review of: Kinetic Cellular Model of Corrosion},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Z6AOHMDW}},
  note         = {Machine review of arXiv:2607.09292}
}
read the original abstract

Aqueous corrosion of metals involves multiple interconnected processes. Thus, computer simulation of corrosion as a whole needs to be able to describe the individual processes and how they influence each other. Atomistic simulations are designed to obtain detailed information for small regions of space over short times. Thus there are limits to the understanding that can be obtained by atomistic simulations alone. Here is presented a method that uses generalised rate equations to extend the length and time scales that can be accessed. It is shown to reduce to either the phase field or cellular automata methods in certain limits. The generalised kinetic equations can reproduce the behaviour described by both the Nernst-Planck and Butler-Volmer equations, which are frequently used to describe corrosion. In addition, the method can describe local rearrangements of atoms such as chemical reactions. Example results are shown for illustrative 1D and 2D problems, with good agreement being found with other methods.

Figures

Figures reproduced from arXiv: 2607.09292 by the authors.

Figure 1
Figure 1. FIG. 1. This figure shows the diffusion profiles at three different times. Both the solutions from the KCM [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The variation of potential with position in a solution of NaCl in water between two charged elec [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The initial and final distributions of the electrons and protons with the associated potentials. The [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. This is a representation of the Mg [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. The simulation produces the expected dissolution of Mg into solution as Mg [PITH_FULL_IMAGE:figures/full_fig_p020_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The diffusion profiles for a 2D system that starts with a very narrow distribution in the center of the [PITH_FULL_IMAGE:figures/full_fig_p023_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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