{"id":"97cf2ed8-ae4d-4207-8da9-7ce8639caea4","arxiv_id":"2607.09292","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A cellular kinetic rate-equation method for aqueous corrosion recovers Nernst–Planck and Butler–Volmer behaviour, reduces to phase-field or cellular automata in limits, and is demonstrated on simple 1D/2D tests.","lead":"The paper introduces a Kinetic Cellular Model that treats corrosion via rate equations on cells, recovering Nernst–Planck, Butler–Volmer, phase-field, and cellular-automata limits. It is an early-stage computational framework aimed at bridging atomistic detail and continuum corrosion scales.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.5","headline":"Mg dissolution demo collapses under the local-equilibrium premise that underpins the multi-scale claim.","rationale":"The reader correctly isolates the local-equilibrium/rate-form assumption as the weakest link and notes the sub-fs instability of the Mg demo. That is not a peripheral numerical detail; it is the only place the paper attempts a genuine corrosion process (dissolution + charge separation + phase change). Because the multi-scale claim is justified precisely by the ability to treat such coupled processes under the cell-equilibrium premise, the failure of that demo to remain stable on any chemically relevant timescale is load-bearing. The analytic diffusion and Gouy–Chapman tests remain valid, so the method is still defensible for the restricted class of problems in which the premise holds; hence the verdict stays CONDITIONAL rather than REJECT. No stronger independent concern (e.g., formal inconsistency of the continuum limits) appears. The concrete integrator test would settle whether the premise can be rescued by better numerics or whether a deeper rate-separation treatment is required before the method can be regarded as ready for multi-process corrosion.","tokens_in":15901,"tokens_out":606,"duration_ms":7693,"concrete_test":"Re-run the §III.D Mg dissolution setup with an implicit (or Crank–Nicolson) integrator and a time step at least 10^3–10^4 times larger (∼0.1–1 fs), keeping the same free-energy parameters and φ threshold. If the interface dipole and Mg++ profile cannot be advanced stably for at least several picoseconds without artificial damping or ad-hoc rate separation, the local-equilibrium premise fails for the process the method is intended to capture.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim is that generalised rate equations (Eqs. 1–2) with cell electrochemical potentials extend accessible scales while recovering Nernst–Planck/Butler–Volmer and permitting local rearrangements. That claim rests on the premise (§II) that each cell is nearly in internal equilibrium so transfer is fully fixed by µ_α,i and a single ν_α, with rearrangements either instantaneous or PF-like. In the only corrosion-relevant demonstration (Mg dissolution, §III.D), the spontaneous reaction Mg ⇌ Mg++ + 2e- is triggered by a phase-field threshold φ < 0.95, free-energy interpolation (Eqs. 29–42) is used, and an explicit Euler step of 10^{-4} fs is required; the run becomes unstable after 0.7 fs. The authors themselves note that charge build-up may stall further dissolution and that product formation is deferred. Thus the regime in which rearrangement and inter-cell transfer rates become comparable—the regime the paper admits degrades accuracy—is precisely the regime needed for the multi-scale corrosion claim, yet no stable multi-process trajectory is shown.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","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.","tokens_in":16270,"tokens_out":951,"duration_ms":9012,"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":[{"comment":"§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.","section":null},{"comment":"§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.","section":null}],"minor_comments":[{"comment":"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.","section":null},{"comment":"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.","section":null},{"comment":"§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.","section":null},{"comment":"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.","section":null},{"comment":"References: the similarity to Watanabe & Fujita (2022) is noted; a short paragraph contrasting algorithmic choices would help readers place the contribution.","section":null}],"recommendation":"major_revision","confidential_remarks":"The paper is methodologically honest about its early stage and the instability of the Mg demo. I recommend major revision rather than reject because the continuum limits and analytic benchmarks are solid; the authors already flag the integrator and product-formation gaps. Scope is appropriate for a materials-modelling journal provided the numerical robustness of the multi-process case is demonstrated or clearly deferred with a concrete roadmap."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The one thing worth knowing is that Sezer and Horsfield give a coherent cellular rate-equation construction (Eqs. 1–2 plus electrochemical potentials and Poisson) that recovers Nernst–Planck under small potential differences, Butler–Volmer-like rates, and the conserved phase-field / cellular-automata limits they claim. That packaging is the real contribution; it is not brand-new physics, and they themselves flag the similarity to Watanabe–Fujita, but it is a usable methods frame for people who want free-energy models and reactions living on the same mesh as transport.\n\nWhat they do well is the simple tests. Diffusion matches the error-function solution essentially perfectly (Fig. 1). The linearized Gouy–Chapman potential is close (Fig. 2), with the residual differences they explain (finite electrode response, no linearization). The free-energy interpolation for Mg (Eqs. 27–42) is internally consistent with the chemical potentials they derive, and the parameters are assembled from tabulated energies plus a band-gap estimate rather than fitted to force a dissolution curve. 2D diffusion also tracks the analytic Gaussian until the finite box matters. Citations are appropriate and the math is standard where it needs to be.\n\nThe soft spots are real but proportionate. The local-equilibrium premise (cells nearly equilibrated internally so transfer is fixed by µ and a single ν) is stated up front, and they admit accuracy degrades when rearrangement and inter-cell rates are comparable. That is exactly the regime the only corrosion-relevant demo enters: Mg dissolution uses a phase threshold, needs 10^{-4} fs explicit Euler steps, and dies after 0.7 fs with charge build-up. Product formation and mechanics are deferred. So the multi-scale corrosion claim remains a prospectus, not a demonstrated tool. Free parameters (attempt frequencies, χ, w, dielectric regions, mesh) are numerous, as expected at this stage. Code and data are not shipped.\n\nThis is for methods people in computational corrosion and continuum electrochemistry who want a clean host for free-energy models. It deserves a serious referee; the core reductions and analytic matches are solid enough that the instability and missing multi-process demos can be handled in revision rather than desk rejection. I would engage with the formulation and cite the reductions if I were building something similar; I would not yet treat it as a ready multi-scale corrosion engine.","headline":"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.","tokens_in":16846,"tokens_out":590,"would_cite":true,"duration_ms":7194,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"A cell-based kinetic model of corrosion bridges atomistic detail and continuum length and time scales.","keywords":["corrosion modelling","kinetic cellular model","Nernst–Planck","Butler–Volmer","phase field","cellular automata","electrochemical potential","multi-scale simulation"],"falsifier":"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.","tokens_in":16756,"feed_emoji":"⚙️","tokens_out":602,"duration_ms":6739,"temperature":0.7,"pith_summary":"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.","feed_headline":"Cell kinetic equations unify corrosion across scales","feed_subtitle":"One rate framework recovers continuum electrochemistry and phase-field limits while keeping local reactions","key_machinery":"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.","core_discovery":"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.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Kinetic cells bridge atomistic and continuum corrosion","One cellular rate model spans corrosion scales","Generalised rates unify corrosion from atoms to continuum","Cellular kinetics recover electrochemistry and phase fields","Rate equations on cells extend corrosion modelling scales"],"cache_read_input_tokens":128,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Kinetic cells bridge atomistic and continuum corrosion","One cellular rate model spans corrosion scales","Generalised rates unify corrosion from atoms to continuum","Cellular kinetics recover electrochemistry and phase fields","Rate equations on cells extend corrosion modelling scales"]},"model":"grok-4.5","effort":"low","cost_usd":0.003506,"raw_usage":{"total_tokens":1105,"prompt_tokens":685,"num_sources_used":0,"completion_tokens":50,"cost_in_usd_ticks":35060000,"prompt_tokens_details":{"text_tokens":685,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":370,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":685,"tokens_out":50,"duration_ms":3736,"temperature":1.0,"reasoning_tokens":370,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-13T04:05:41.790635+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"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.","supporting_citations":[],"review_version":1}