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arxiv: 2501.10578 · v1 · pith:42QF677Jnew · submitted 2025-01-17 · ⚛️ physics.chem-ph · cond-mat.stat-mech

Ionic Associations and Hydration in the Electrical Double Layer of Water-in-Salt Electrolytes

Daniel M. Markiewitz , Zachary A. H. Goodwin , Qianlu Zheng , Michael McEldrew , Rosa M. Espinosa-Marzal , Martin Z. Bazant This is my paper

Pith reviewed 2026-05-23 05:41 UTC · model grok-4.3

classification ⚛️ physics.chem-ph cond-mat.stat-mech
keywords water-in-salt electrolyteselectrical double layerionic associationsCayley tree aggregatesmolecular dynamicselectrochemical impedance spectroscopyLiTFSI
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The pith

A continuum theory for water-in-salt electrolytes predicts asymmetric electrical double layer structure due to voltage-dependent ionic clustering into Cayley tree aggregates.

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

The paper develops a theory that incorporates thermoreversible associations of species into Cayley tree aggregates into a continuum model of the electrical double layer for water-in-salt electrolytes. This leads to predictions of different behaviors at positive and negative electrodes. At negative voltages hydrated lithium ions dominate and cluster aggregation is initially slightly enhanced before disintegrating at higher voltages. At positive voltages clusters are strictly diminished relative to the bulk. The predictions show good qualitative agreement with molecular dynamics simulations and reasonable agreement with electrochemical impedance spectroscopy measurements of differential capacitance.

Core claim

We develop a theory for the electrical double layer of water-in-salt electrolytes that consistently accounts for thermoreversible associations of species into Cayley tree aggregates. The theory predicts an asymmetric structure of the EDL: at negative voltages hydrated Li+ dominate and cluster aggregation is initially slightly enhanced before disintegration at larger voltages, while at positive voltages clusters are strictly diminished compared to the bulk. Atomistic molecular dynamics simulations provide validation with good qualitative agreement, and electrochemical impedance measurements of differential capacitance also show reasonable agreement.

What carries the argument

The consistent incorporation of thermoreversible associations of ions into Cayley tree aggregates within a continuum electrical double layer theory, parameterized from bulk molecular dynamics data.

If this is right

  • At negative voltages, hydrated Li+ ions dominate the interface.
  • Cluster aggregation is initially slightly enhanced at moderate negative voltages before disintegrating at larger magnitudes.
  • At positive voltages, ionic clusters are diminished compared to the bulk electrolyte.
  • The model agrees qualitatively with molecular dynamics simulations of the EDL.
  • Differential capacitance from the theory matches electrochemical impedance spectroscopy data reasonably well.

Where Pith is reading between the lines

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

  • The predicted asymmetry may cause different rates of solid-electrolyte interphase formation at each electrode polarity.
  • The modeling approach could be applied to other concentrated electrolytes to predict interface effects on stability or transport.
  • Device-level tests with controlled voltage polarity could reveal whether the asymmetry affects overall cell performance.
  • Adding interface-specific adjustments to the bulk-derived parameters might improve quantitative matches to experiment.

Load-bearing premise

That thermoreversible associations of species into Cayley tree aggregates can be consistently incorporated into a continuum EDL theory and that bulk MD data suffice to parameterize the interface model without additional interface-specific fitting.

What would settle it

Molecular dynamics simulations or spectroscopic measurements at the interface showing symmetric cluster behavior or no initial enhancement of aggregation at moderate negative voltages would contradict the predicted asymmetry.

Figures

Figures reproduced from arXiv: 2501.10578 by Daniel M. Markiewitz, Martin Z. Bazant, Michael McEldrew, Qianlu Zheng, Rosa M. Espinosa-Marzal, Zachary A. H. Goodwin.

Figure 1
Figure 1. Figure 1: Schematic of the modulation of aggregation occurring in the EDL of WiSE near [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Cluster distribution of bulk 15m water-in-LiTFSI. Here we use [PITH_FULL_IMAGE:figures/full_fig_p017_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Distributions of properties of 15m WiSEs in the EDL as a function from the [PITH_FULL_IMAGE:figures/full_fig_p019_3.png] view at source ↗
Figure 3
Figure 3. Figure 3: b), a sharp peak in ϕ¯ 001 is observed in the middle of the condensed layer at 3λD. A little outside of the condense layer, ϕ¯ 001 peaks again at 8λD to around a fourth of its first peak’s amplitude. Following this, ϕ¯ 001 decays and fluctuates around its bulk value. In [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗
Figure 3
Figure 3. Figure 3: f), the theory predicts that the volume fraction of hydrated cations increases when [PITH_FULL_IMAGE:figures/full_fig_p021_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Distributions of properties of 15m WiSEs in the EDL as a function from the [PITH_FULL_IMAGE:figures/full_fig_p025_4.png] view at source ↗
Figure 4
Figure 4. Figure 4: g), ¯p0+ is observed to have a strikingly similar behavior to the simulation prediction with negligible decay in much of the EDL before rapidly decaying close to the interface. Overall, the theory appears to adequately agree with the qualitative trends presented in the MD predictions for the association probabilities in the EDL. Finally, let us consider how ionic associations are impacted by the EDL throug… view at source ↗
Figure 5
Figure 5. Figure 5: Aggregation length scale and cluster distributions through the EDL in WiSEs. a) [PITH_FULL_IMAGE:figures/full_fig_p030_5.png] view at source ↗
Figure 5
Figure 5. Figure 5: a). In Fig. 5.c), the cluster distribution is [PITH_FULL_IMAGE:figures/full_fig_p031_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: EDL predictions of WiSEs. a) Theory prediction for the differential capacitance [PITH_FULL_IMAGE:figures/full_fig_p035_6.png] view at source ↗
read the original abstract

Water-in-Salt-Electrolytes (WiSEs) are an exciting class of concentrated electrolytes finding applications in energy storage devices because of their expanded electrochemical stability window, good conductivity and cation transference number, and fire-extinguishing properties. These distinct properties are thought to originate from the presence of an anion-dominated ionic network and interpenetrating water channels for cation transport, which indicates that associations in WiSEs are crucial to understanding their properties. Currently, associations have mainly been investigated in the bulk, while little attention has been given to the electrolyte structure near electrified interfaces. Here, we develop a theory for the electrical double layer (EDL) of WiSEs, where we consistently account for the thermoreversible associations of species into Cayley tree aggregates. The theory predicts an asymmetric structure of the EDL. At negative voltages, hydrated Li$^+$ dominate and cluster aggregation is initially slightly enhanced before disintegration at larger voltages. At positive voltages when compared to the bulk, clusters are strictly diminished. Performing atomistic molecular dynamics (MD) simulations of the EDL of WiSE provides EDL data for validation and bulk data for parameterization of our theory. Validating the predictions of our theory against MD showed good qualitative agreement. Furthermore, we performed electrochemical impendence measurements to determine the differential capacitance of the studied LiTFSI WiSE and also found reasonable agreement with our theory. Overall, the developed approach can be used to investigate ionic aggregation and solvation effects in the EDL, which amongst other properties, can be used to understand the pre-cursers for solid-electrolyte interphase formation.

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 paper develops a continuum EDL theory for water-in-salt electrolytes that grafts thermoreversible Cayley-tree ionic association equilibria (parameterized from bulk MD) onto a modified Poisson-Boltzmann framework. It predicts an asymmetric EDL structure in which, at negative voltages, hydrated Li+ dominate and clustering is initially slightly enhanced before disintegrating at larger voltages, while at positive voltages clusters are strictly diminished relative to bulk. The theory is validated against MD simulations of the EDL (showing good qualitative agreement) and against EIS measurements of differential capacitance (reasonable agreement).

Significance. If the result holds, the work supplies a practical route to incorporate association effects into continuum models of concentrated-electrolyte interfaces, which is relevant for understanding voltage-dependent solvation and aggregation that precede SEI formation in WiSE-based devices. The explicit asymmetry prediction and the linkage to both simulation and capacitance data give the framework immediate utility for electrolyte screening, even if quantitative error metrics are not yet supplied.

major comments (2)
  1. [Theory parameterization and validation sections] The association constants are obtained solely from bulk MD and then used both to construct the EDL model and to validate its predictions against the same class of simulation. This circularity is load-bearing for the central claim of transferable Cayley-tree equilibria; any position- or field-dependent shift in the underlying free energies would change the reported cluster profiles and the predicted asymmetry (see the skeptic note on transferability).
  2. [EDL structure predictions] The model assumes that the association equilibria remain position-independent even though local ion density, water coordination, and electric-field strength vary sharply within a few angstroms of the electrode. No auxiliary calculation or sensitivity test is presented to quantify how violations of this assumption would alter the negative-bias enhancement versus positive-bias depletion behavior that constitutes the main result.
minor comments (2)
  1. [Abstract] The abstract states 'good qualitative agreement' and 'reasonable agreement' with MD and EIS but supplies no quantitative metrics, R² values, or error bars, nor any discussion of how post-hoc choices in the MD force-field parameterization propagate into the EDL predictions.
  2. [Abstract] Typographical errors: 'impendence' (should be 'impedance') and 'pre-cursers' (should be 'precursors').

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful comments on our manuscript. We address each major comment below and agree that further clarification on the model's assumptions is needed.

read point-by-point responses

  1. Referee: [Theory parameterization and validation sections] The association constants are obtained solely from bulk MD and then used both to construct the EDL model and to validate its predictions against the same class of simulation. This circularity is load-bearing for the central claim of transferable Cayley-tree equilibria; any position- or field-dependent shift in the underlying free energies would change the reported cluster profiles and the predicted asymmetry (see the skeptic note on transferability).

    Authors: The association constants are derived from bulk MD simulations that are independent of the EDL simulations. The EDL MD simulations serve as validation data and were not used to fit any parameters. This structure avoids direct circularity. The agreement with EDL MD supports the applicability of the bulk-derived model to the interface. We recognize that the transferability assumption regarding position- or field-dependent free energies is central and not explicitly tested beyond the overall validation. We will add text in the revised manuscript to discuss this assumption more explicitly and its implications for the asymmetry prediction. revision: partial

  2. Referee: [EDL structure predictions] The model assumes that the association equilibria remain position-independent even though local ion density, water coordination, and electric-field strength vary sharply within a few angstroms of the electrode. No auxiliary calculation or sensitivity test is presented to quantify how violations of this assumption would alter the negative-bias enhancement versus positive-bias depletion behavior that constitutes the main result.

    Authors: The continuum model is formulated under the assumption of position-independent association equilibria to maintain computational tractability and consistency with the bulk parameterization. We agree that this is a significant approximation given the sharp variations near the electrode. No sensitivity test is provided in the current work. In the revised version, we will incorporate a discussion of this limitation and include a simple sensitivity analysis, for instance by perturbing the association constants as a function of position or field strength to assess robustness of the asymmetric behavior. revision: yes

Circularity Check

0 steps flagged

No significant circularity; model derivation and validation remain independent

full rationale

The paper constructs a continuum EDL model by incorporating thermoreversible Cayley-tree associations into a modified Poisson-Boltzmann framework. Association parameters are obtained from bulk MD and the resulting predictions are compared to separate EDL MD profiles plus experimental EIS capacitance data. No equation reduces to its own input by construction, no fitted quantity is relabeled as a prediction, and no load-bearing step relies on a self-citation chain or imported uniqueness theorem. The transferability assumption is an explicit modeling choice whose validity is tested against held-out EDL data rather than enforced by the fitting procedure itself.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The model rests on a domain-specific aggregation assumption and on parameters extracted from bulk MD; no machine-checked proofs or independent experimental constants are supplied.

free parameters (1)
  • association constants / energies
    Used to set the thermoreversible equilibrium; extracted from bulk MD simulations for parameterization of the EDL theory.
axioms (1)
  • domain assumption Ionic associations form thermoreversible Cayley tree aggregates
    Invoked to account for clustering consistently in both bulk and EDL; stated in the abstract as the core modeling choice.
invented entities (1)
  • Cayley tree aggregates at the interface no independent evidence
    purpose: To represent ionic clustering in the EDL
    New application of the aggregate model to the electrified interface; no independent falsifiable evidence supplied beyond the MD comparison.

pith-pipeline@v0.9.0 · 5860 in / 1349 out tokens · 25627 ms · 2026-05-23T05:41:17.228906+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Theory of Cation Solvation in the Helmholtz Layer of Li-ion Battery Electrolytes

    cond-mat.stat-mech 2025-03 unverdicted novelty 6.0

    A theory of Li+ solvation in the Helmholtz layer, parameterized from bulk MD, finds binding probabilities remain equal to bulk values, supporting bulk solvation as a proxy for SEI studies.

Reference graph

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