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arxiv: 2603.07203 · v2 · submitted 2026-03-07 · ❄️ cond-mat.soft

Reversible Ionic Aggregation Kinetics in Concentrated Electrolytes

Zachary A. H. Goodwin This is my paper

Pith reviewed 2026-05-15 14:48 UTC · model grok-4.3

classification ❄️ cond-mat.soft
keywords reversible ionic aggregationconcentrated electrolytesSmoluchowski aggregation equationassociation kineticsmolecular dynamicsopen occupied sitesnon-equilibrium dynamics
0
0 comments X p. Extension

The pith

A macroscopic rate equation for open and occupied association sites solves the reversible Smoluchowski aggregation equation and tracks ionic cluster changes after step changes in concentrated electrolytes.

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

The paper develops a formalism for reversible ionic aggregation kinetics by deriving a macroscopic rate equation that governs the fractions of open and occupied association sites. This equation is shown to be a solution of the reversible Smoluchowski aggregation equation, allowing predictions of how ionic associations evolve following sudden changes in conditions such as concentration or temperature. Tests against atomistic molecular dynamics simulations of a salt-in-ionic liquid yield good qualitative agreement, though quantitative differences emerge that point to the presence of multiple time scales. A sympathetic reader would care because the approach supplies a tractable way to model non-equilibrium dynamics in electrolytes without requiring full microscopic resolution at every step.

Core claim

The derived macroscopic rate equation of open/occupied association sites is a solution of the reversible Smoluchowski aggregation equation and predicts how ionic associations change subject to a step-change in conditions, with good qualitative agreement to atomistic MD simulations but quantitative differences highlighting multiple time scales.

What carries the argument

Macroscopic rate equation tracking the fractions of open and occupied association sites, which solves the reversible Smoluchowski aggregation equation for ionic clusters.

If this is right

  • The formalism can be applied to investigate non-Newtonian flow behaviour in concentrated electrolytes.
  • It provides a route to model double-layer charging dynamics under changing conditions.
  • It describes the slow relaxation of electrolyte structure in confined geometries.
  • It enables study of non-equilibrium behaviour without full atomistic simulation at each instant.

Where Pith is reading between the lines

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

  • The same rate-equation structure may apply directly to related systems such as thermoreversible polymers and patchy particles.
  • The observed quantitative gaps indicate that future refinements could incorporate at least two distinct relaxation times to improve accuracy for specific electrolyte compositions.
  • The model offers a practical starting point for simulating electrolyte response in devices where sudden perturbations occur, such as during rapid charging or shear flow.

Load-bearing premise

The assumption that a single macroscopic rate equation for association sites captures the essential reversible aggregation kinetics without additional microscopic details or separate fitted time scales.

What would settle it

Time-resolved measurement of the fraction of occupied association sites after an abrupt change in ion concentration or temperature that deviates from the functional form predicted by the single rate equation beyond the reported quantitative mismatch.

Figures

Figures reproduced from arXiv: 2603.07203 by Zachary A. H. Goodwin.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic of non-equilibrium kinetics of ionic aggregation in the studied salt-in-ionic liquid (SIIL). The alkali metal [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: correspond to the charge rescaling case (see Molec￾ular Dynamics Section for further description). In the SI, we show results for the temperature rescaling non￾equilibrium conditions. The same conclusions are drawn from those, but where smaller changes in coordination numbers are observed. Figure 2a) shows the simulations at 300 K. Initially, even though the charges of all atoms are essentially 0, we find … view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Gelation criteria in NaTFSI [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Cluster distributions [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
read the original abstract

Here we develop a formalism for reversible ionic aggregation kinetics in an example concentrated electrolyte, building on previous equilibrium work of McEldrew and co-workers, and thermoreversible polymers and patchy particle systems. This is achieved through solving a macroscopic rate equation of open/occupied association sites, shown to be a solution of the reversible Smoluchowski aggregation equation, which predicts how ionic associations in electrolytes change subject to a step-change in conditions. We test the derived equations against atomistic molecular dynamics simulations of a salt-in-ionic liquid, where good qualitative agreement is obtained, but quantitative differences are found. This highlights the multiple time scales that exist in concentrated electrolytes, with a fast timescale preceding a longer timescale. We hope this formalism opens new avenues in understanding the dynamics and non-equilibrium behaviour in electrolytes. For example, the formalism can be developed further to investigate the non-Newtonian behaviour of concentrated electrolytes, double layer charging, and the slow dynamics of these electrolytes in confinement.

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 / 3 minor

Summary. The paper develops a formalism for reversible ionic aggregation kinetics in concentrated electrolytes by deriving a macroscopic rate equation tracking open and occupied association sites. This equation is presented as a solution to the reversible Smoluchowski aggregation equation and is used to predict the response of ionic associations to step changes in conditions. The model is tested against atomistic MD simulations of a salt-in-ionic liquid, yielding qualitative agreement but quantitative differences that highlight multiple timescales in the system.

Significance. If the central derivation is shown to hold under the relevant approximations, the work supplies a useful reduced-order model for non-equilibrium ionic aggregation, extending equilibrium theories to dynamics. The parameter-free character of the derivation and the direct, falsifiable predictions for step-change responses are strengths. The qualitative match to MD supports potential applications to double-layer charging and non-Newtonian flow, though the quantitative discrepancies indicate the model captures only part of the multi-scale physics.

major comments (2)
  1. [Theory/derivation section (around the rate-equation introduction)] The claim that the macroscopic rate equation is a solution of the reversible Smoluchowski aggregation equation is central but lacks explicit derivation steps showing the required closure (e.g., size-independent kernel or neglect of higher-order correlations). In concentrated electrolytes, long-range Coulomb forces and chain/network aggregates likely violate standard closures, as implied by the reported quantitative mismatch with MD; this needs to be demonstrated or the claim qualified as approximate.
  2. [Results and MD comparison] The MD comparison (results section) reports good qualitative agreement but unresolved quantitative differences in relaxation timescales. This directly tests the model's predictive power; without addressing why a single ODE fails to capture the observed multi-timescale behavior (e.g., via additional terms or explicit justification of the closure), the validation remains incomplete for the claimed regime.
minor comments (3)
  1. [Abstract] The abstract states 'good qualitative agreement' without specifying the comparison metric or the magnitude of deviations; adding this would improve clarity.
  2. [Figures] Figure captions for the step-change predictions should explicitly list the initial and final conditions (concentration, temperature) and the observable plotted.
  3. [References] Citations to the Smoluchowski framework and McEldrew equilibrium work should include the precise references used for the reversible kernel.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for providing constructive feedback. We address each of the major comments point by point below, and have made revisions to the manuscript where necessary to strengthen the presentation of the derivation and the discussion of the model's limitations.

read point-by-point responses

  1. Referee: [Theory/derivation section (around the rate-equation introduction)] The claim that the macroscopic rate equation is a solution of the reversible Smoluchowski aggregation equation is central but lacks explicit derivation steps showing the required closure (e.g., size-independent kernel or neglect of higher-order correlations). In concentrated electrolytes, long-range Coulomb forces and chain/network aggregates likely violate standard closures, as implied by the reported quantitative mismatch with MD; this needs to be demonstrated or the claim qualified as approximate.

    Authors: We appreciate the referee pointing out the need for more explicit steps in the derivation. In the revised manuscript, we have added a new appendix that provides a detailed derivation from the reversible Smoluchowski equation to the macroscopic rate equation, explicitly stating the closure approximations, including the use of a size-independent kernel and mean-field neglect of higher-order correlations. We agree that in concentrated electrolytes, long-range Coulomb forces and the possibility of chain or network aggregates can violate these standard closures, which likely contributes to the quantitative differences with MD. We have therefore qualified the claim in the main text as an approximate solution under the mean-field assumption, valid for capturing the primary aggregation kinetics. revision: yes

  2. Referee: [Results and MD comparison] The MD comparison (results section) reports good qualitative agreement but unresolved quantitative differences in relaxation timescales. This directly tests the model's predictive power; without addressing why a single ODE fails to capture the observed multi-timescale behavior (e.g., via additional terms or explicit justification of the closure), the validation remains incomplete for the claimed regime.

    Authors: We concur that the single ODE does not fully capture the multi-timescale relaxation seen in the MD simulations. The model is intended to describe the slower, reversible aggregation process, while the faster timescales arise from local ion dynamics and solvent effects not included in this reduced description. In the revised results section, we have added explicit discussion justifying the closure and explaining the origin of the timescale separation. We also outline how the formalism could be extended with additional terms or coupled equations to account for multiple modes, thereby improving the validation for the claimed regime of concentrated electrolytes. revision: yes

Circularity Check

0 steps flagged

Derivation chain is self-contained with no circular reductions

full rationale

The paper derives the macroscopic rate equation for open/occupied association sites and states that it is shown to be a solution of the reversible Smoluchowski aggregation equation, building on prior equilibrium work of McEldrew et al. and thermoreversible polymer frameworks. Validation occurs against independent atomistic MD simulations of a salt-in-ionic liquid, yielding qualitative agreement with noted quantitative differences attributed to multiple timescales. No load-bearing step reduces by construction to parameters fitted from the same validation data, no self-citation chain supplies an unverified uniqueness theorem, and no ansatz is smuggled via citation. The derivation remains independent of the target simulation results, satisfying the criteria for a non-circular finding.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that a macroscopic rate equation for association sites solves the reversible Smoluchowski equation and that this reduced description suffices for the observed kinetics; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption The macroscopic rate equation of open/occupied association sites is a solution of the reversible Smoluchowski aggregation equation
    Explicitly stated as the basis for deriving the kinetic predictions
  • domain assumption Qualitative features of ionic aggregation kinetics can be captured by tracking only the fraction of associated sites without resolving full microscopic configurations
    Implicit in the comparison to MD simulations and the claim of multiple time scales

pith-pipeline@v0.9.0 · 5456 in / 1364 out tokens · 31345 ms · 2026-05-15T14:48:40.120451+00:00 · methodology

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Reference graph

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