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arxiv: 2402.04039 · v2 · pith:FNQOX6IGnew · submitted 2024-02-06 · ⚛️ physics.chem-ph · cond-mat.stat-mech

Electric Field Induced Associations in the Double Layer of Salt-in-Ionic-Liquid Electrolytes

Daniel M. Markiewitz , Zachary A. H. Goodwin , Michael McEldrew , J. Pedro de Souza , Xuhui Zhang , Rosa M. Espinosa-Marzal , Martin Z. Bazant This is my paper

Pith reviewed 2026-05-24 04:00 UTC · model grok-4.3

classification ⚛️ physics.chem-ph cond-mat.stat-mech
keywords salt-in-ionic-liquid electrolyteselectrical double layerion associationCayley tree aggregatesthermoreversible associationalkali metal cationvoltage-dependent aggregationelectrode screening
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The pith

A theory of salt-in-ionic-liquid electrolytes predicts increased ion aggregation at positive voltages in the electrical double layer.

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 for the electrical double layer of salt-in-ionic-liquid electrolytes that consistently incorporates thermoreversible associations of ions into Cayley tree aggregates. It predicts that IL cations populate the double layer at negative voltages, but alkali metal cations displace them at large negative voltages once associations break. At positive voltages the electrolyte forms large negatively charged aggregates to screen the electrode charge, resulting in a more aggregated state. A reader would care because this reversal of expected field effects influences ion transport and charge storage in battery electrolytes.

Core claim

The theory predicts that the SiIL becomes more aggregated at positive voltages through the formation of large, negatively charged aggregates that screen the electrode charge, while at large negative voltages the alkali metal cations displace the IL cations in the double layer due to their higher charge density after breaking associations.

What carries the argument

Cayley tree aggregates formed by thermoreversible ion associations, incorporated into electrical double layer theory to determine voltage-dependent screening and composition.

If this is right

  • IL cations populate the EDL at negative voltages because they are not strongly bound to anions.
  • At sufficiently large negative voltages, alkali metal cations replace IL cations due to higher charge density.
  • Positive voltages induce formation of large negatively charged aggregates that screen the electrode.
  • The SiIL appears more associated in certain electric fields than expected from conventional intuition.

Where Pith is reading between the lines

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

  • Capacitance or conductivity near the electrode may show non-monotonic dependence on voltage polarity.
  • The model could be used to predict local transference numbers or ion mobility in the double layer.
  • Surface-sensitive experiments could detect changes in aggregate populations by comparing positive and negative electrode polarities.

Load-bearing premise

The electrical double layer theory can incorporate thermoreversible association of ions into Cayley tree aggregates without additional approximations that break at high voltages or concentrations.

What would settle it

Molecular dynamics simulations measuring the size distribution or charge of ion aggregates in the double layer at positive electrode voltages, compared against the bulk, would confirm or refute whether aggregation increases.

Figures

Figures reproduced from arXiv: 2402.04039 by Daniel M. Markiewitz, J. Pedro de Souza, Martin Z. Bazant, Michael McEldrew, Rosa M. Espinosa-Marzal, Xuhui Zhang, Zachary A. H. Goodwin.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic of the modulation of aggregations occurri [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Properties of the EDL of SiILs as a function of applied [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Distributions of properties of SiILs in the EDL as a fu [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Distributions of properties of SiILs in the EDL as a fu [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. a) Screening length of SiIL as a function of mole fract [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
read the original abstract

Ionic liquids (ILs) are an extremely exciting class of electrolytes for energy storage applications because of their unique combination of properties. Upon dissolving alkali metal salts, such as Li or Na based salts, with the same anion as the IL, an intrinsically asymmetric electrolyte can be created for use in batteries, known as a salt-in-ionic liquid (SiIL). These SiILs have been well studied in the bulk, where negative transference numbers of the alkali metal cation have been observed from the formation of small, negatively charged clusters. The properties of these SiILs at electrified interfaces, however, have received little to no attention. Here, we develop a theory for the electrical double layer (EDL) of SiILs where we consistently account for the thermoreversible association of ions into Cayley tree aggregates. The theory predicts that the IL cations first populate the EDL at negative voltages, as they are not strongly bound to the anions. However at large negative voltages which are strong enough to break the alkali metal cation-anion associations, these IL cations are exchanged for the alkali metal cation because of their higher charge density. At positive voltages, we find that the SiIL actually becomes $\textit{more aggregated while screening the electrode charge}$ from the formation of large, negatively charged aggregates. Therefore, in contrast to conventional intuition of associations in the EDL, SiILs appear to become more associated in certain electric fields. We present these theoretical predictions to be verified by molecular dynamics simulations and experimental measurements.

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

1 major / 2 minor

Summary. The manuscript develops a theory for the electrical double layer (EDL) in salt-in-ionic-liquid (SiIL) electrolytes that consistently incorporates thermoreversible association of ions into Cayley-tree aggregates. Key predictions are that IL cations populate the EDL first at moderate negative voltages, alkali-metal cations replace them at large negative voltages due to higher charge density, and at positive voltages the system becomes more aggregated overall via formation of large, negatively charged aggregates that screen electrode charge.

Significance. If the central predictions hold, the work supplies a self-consistent framework for interface behavior in associated asymmetric electrolytes relevant to battery applications. The explicit use of the same bulk association constants in the EDL is a methodological strength that distinguishes it from ad-hoc treatments.

major comments (1)
  1. [Model derivation (likely §2–3)] Model derivation (likely §2–3): the position-dependent chemical potentials for monomers and aggregates are closed using the same thermoreversible association constants as in the bulk. The central claim of increased aggregation at positive voltages is load-bearing on this closure remaining valid under steep potential gradients; the manuscript must demonstrate that no field-dependent shift in binding energies or non-local corrections for large trees are required, or else quantify the regime where the local-density approximation breaks.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'more aggregated while screening the electrode charge' is clear but would benefit from a one-sentence qualifier on the voltage range over which the effect is predicted.
  2. [Discussion/Conclusion] The manuscript states that predictions should be verified by MD and experiment; adding a short paragraph outlining the most direct falsifiable signature (e.g., voltage-dependent cluster-size distribution from simulation) would strengthen the presentation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive evaluation of the work's significance and for the detailed comment on the model. We respond to the major comment below.

read point-by-point responses

  1. Referee: Model derivation (likely §2–3): the position-dependent chemical potentials for monomers and aggregates are closed using the same thermoreversible association constants as in the bulk. The central claim of increased aggregation at positive voltages is load-bearing on this closure remaining valid under steep potential gradients; the manuscript must demonstrate that no field-dependent shift in binding energies or non-local corrections for large trees are required, or else quantify the regime where the local-density approximation breaks.

    Authors: The closure with bulk association constants follows directly from the mean-field treatment in which short-range binding is governed by local monomer densities while the electrostatic potential enters the chemical potentials separately. This is the same approximation used in the bulk theory and is standard in density-functional treatments of associating electrolytes. We agree, however, that the central prediction of increased aggregation at positive voltages would benefit from an explicit statement of the approximation's regime of validity. In the revised manuscript we will add a short paragraph estimating the length scale on which the potential varies relative to aggregate size and binding energy, thereby quantifying where the local-density approximation is expected to remain reasonable. revision: yes

Circularity Check

0 steps flagged

No significant circularity; model extends bulk association to EDL self-consistently

full rationale

The paper develops an explicit theoretical framework for the EDL that incorporates thermoreversible Cayley-tree association via position-dependent chemical potentials and a free-energy functional closed under the same association constants used in bulk. No quoted step reduces a prediction to a fitted parameter on the target EDL data, a self-citation chain, or a renaming of an input. The central claim (increased aggregation at positive voltages) follows from solving the model equations rather than being imposed by definition. External benchmarks (MD, experiment) are invoked for verification, confirming the derivation remains independent of its own outputs.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The model rests on treating ion associations as thermoreversible Cayley tree structures and extending standard EDL theory to include them; association equilibrium constants are likely free parameters.

free parameters (1)
  • association equilibrium constants
    Thermoreversible association into aggregates requires equilibrium constants that are typically fitted to bulk data or chosen to match observations.
axioms (2)
  • domain assumption Ions form thermoreversible Cayley tree aggregates
    Invoked to model clustering in both bulk and EDL; stated in the abstract as the consistent accounting method.
  • domain assumption Standard electrical double layer framework applies with aggregate modifications
    The theory is built by extending existing EDL models to include the aggregates.

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Reference graph

Works this paper leans on

95 extracted references · 95 canonical work pages

  1. [1]

    This is done for a spectr um of dimensionless electrostatic potential (Φ /eβ ) to allow one to create a sufficiently fine grid, for our purposes here a spacing of 0.001 was used

    First, we solve the our system of equations numerically for ¯φ +, ¯φ − , ¯φ ⊕ ,¯p+− ,¯p− +,Λ over a range of electrostatic potential values. This is done for a spectr um of dimensionless electrostatic potential (Φ /eβ ) to allow one to create a sufficiently fine grid, for our purposes here a spacing of 0.001 was used. Here to simplify further steps, we store...

    work page

  2. [2]

    Using the dimensionless ρe map, we can then numerically solve the Poisson-Boltzmann equation to get a solution for the electrostatic potential profile in t he EDL

    work page

  3. [3]

    The electrostatic potential profile in the EDL along with our interp olation maps al- lows us to predict profiles of the various quantities of interest in the EDL: dimen- sionless charge density, total volume fractions of each species, v olume fraction of free cations, volume fraction free anions, volume fraction aggregates (could additional ex- tract indiv...

    work page

  4. [4]

    From this map, we constructed splines to calculate how the surface charge d ensity depends on 38 the potential at the interface

    In order to obtain our differential capacitance predictions, we fi rst solved for the po- tential at the interface using a wide range of surface charge dens ities for our boundary conditions, for our work here we used a fine grid spacing of 0.0001 C/ m2. From this map, we constructed splines to calculate how the surface charge d ensity depends on 38 the pote...

    work page

  5. [5]

    To obtain the screening length, we next applied a ± 0.0001 V electrostatic potential boundary condition at the surface. From the electrostatic poten tial profile in the EDL, we obtained the screening length by fitting the exponential decay f or the profile, thus extracting the exponential decay constant for a range of mole fr actions of alkali metal salt sho...

    work page

  6. [6]

    The cation exchange voltage and maximum aggregation voltage ut ilized the method in step 1. For these plots, we utilize the values for the case displayed in the main text but individually varied the values of the mole fraction of alkali metal sa lt (xs), regular solution interaction strength ( χ ), and “bare” association constant ( λ 0) extracting the cat...

    work page

  7. [7]

    Watanabe, M

    M. Watanabe, M. L. Thomas, S. Zhang, K. Ueno, T. Yasuda, an d K. Dokko, Chem. Rev. 117, 7190 (2017)

    work page 2017

  8. [8]

    Lewandowski and A

    A. Lewandowski and A. ´Swiderska-Mocek, J. Power Sources 194, 601 (2009)

    work page 2009

  9. [9]

    Balducci, U

    A. Balducci, U. Bardi, S. Caporali, M. Mastragostino, an d F. Soavi, Electrochem. commun. 6, 566 (2004)

    work page 2004

  10. [10]

    Dokko, N

    K. Dokko, N. Tachikawa, K. Yamauchi, M. Tsuchiya, A. Yama zaki, E. Takashima, J.-W. Park, K. Ueno, S. Seki, N. Serizawa, et al. , J. Electrochem. Soc. 160, A1304 (2013)

    work page 2013

  11. [11]

    Xu, Chem

    K. Xu, Chem. Rev. 114, 11503 (2014). 39

    work page 2014

  12. [12]

    L. G. Chagas, S. Jeong, I. Hasa, and S. Passerini, ACS Appl . Mater. Interfaces 11, 22278 (2019)

    work page 2019

  13. [13]

    Q. Zhou, P. D. Boyle, L. Malpezzi, A. Mele, J.-H. Shin, S. P asserini, and W. A. Henderson, Chem. Mater. 23, 4331 (2011)

    work page 2011

  14. [14]

    Monti, E

    D. Monti, E. J´ onsson, M. R. Palacin, and P. Johansson, J. Power Sources 245, 630 (2014)

    work page 2014

  15. [15]

    Armand, F

    M. Armand, F. Endres, D. R. MacFarlane, H. Ohno, and B. Scr osati, Nature materials 8, 621 (2009)

    work page 2009

  16. [16]

    Matsumoto, J

    K. Matsumoto, J. Hwang, S. Kaushik, C.-Y. Chen, and R. Ha giwara, Energy & Environmental Science 12, 3247 (2019)

    work page 2019

  17. [17]

    T. C. Mendes, F. Zhou, A. J. Barlow, M. Forsyth, P. C. Howl ett, and D. R. MacFarlane, Sustainable Energy & Fuels 2, 763 (2018)

    work page 2018

  18. [18]

    J. Zhao, G. Gorbatovski, O. Oll, T. Thomberg, and E. Lust , Electrochimica Acta 319, 82 (2019)

    work page 2019

  19. [19]

    Yamamoto and T

    T. Yamamoto and T. Nohira, The Chemical Record 23, e202300169 (2023)

    work page 2023

  20. [20]

    Q. Guo, P. Fan, Y. Zhang, L. Guan, H. Wang, A. Croft, and G. Z. Chen, RSC Sustainability (2024)

    work page 2024

  21. [21]

    Basile, M

    A. Basile, M. Hilder, F. Makhlooghiazad, C. Pozo-Gonza lo, D. R. MacFarlane, P. C. Howlett, and M. Forsyth, Advanced Energy Materials 8, 1703491 (2018)

    work page 2018

  22. [22]

    D. R. MacFarlane, N. Tachikawa, M. Forsyth, J. M. Pringl e, P. C. Howlett, G. D. Elliott, J. H. Davis, M. Watanabe, P. Simon, and C. A. Angell, Energy En viron. Sci. 7, 232 (2014)

    work page 2014

  23. [23]

    D. R. MacFarlane, M. Forsyth, P. C. Howlett, M. Kar, S. Pa sserini, J. M. Pringle, H. Ohno, M. Watanabe, F. Yan, W. Zheng, et al. , Nature Reviews Materials 1, 1 (2016)

    work page 2016

  24. [24]

    Welton, Chem

    T. Welton, Chem. Rev. 99, 2071–2084 (1999)

    work page 2071

  25. [25]

    Weing¨ artner, Angew

    H. Weing¨ artner, Angew. Chem. Int. Ed. 47, 654 (2008)

    work page 2008

  26. [26]

    J. P. Hallett and T. Welton, Chem. Rev. 111, 3508–3576 (2011)

    work page 2011

  27. [27]

    M. V. Fedorov and A. A. Kornyshev, Chem. Rev. 114, 2978 (2014)

    work page 2014

  28. [28]

    McEldrew, Z

    M. McEldrew, Z. A. H. Goodwin, N. Molinari, B. Kozinsky, A. A. Kornyshev, and M. Z. Bazant, J. Phys. Chem. B 125, 13752 (2021)

    work page 2021

  29. [29]

    B. Qiao, G. M. Leverick, W. Zhao, A. H. Flood, J. A. Johnso n, and Y. Shao-Horn, J. Am. Chem. Soc. 140, 10932 (2018)

    work page 2018

  30. [30]

    Gouverneur, J

    M. Gouverneur, J. Kopp, L. van W¨ ullen, and M. Sch¨ onhoff, Phys. Chem. Chem. Phys. 17, 40 30680 (2015)

    work page 2015

  31. [31]

    Gouverneur, F

    M. Gouverneur, F. Schmidt, and M. Sch¨ onhoff, Phys. Chem. Chem. Phys. 20, 7470 (2018)

    work page 2018

  32. [32]

    Brinkk¨ otter, A

    M. Brinkk¨ otter, A. Mariani, S. Jeong, S. Passerini, an d M. Sch¨ onhoff, Adv. Energy Sustain- ability Res. 2, 2000078 (2021)

    work page 2021

  33. [33]

    Ackermann and M

    F. Ackermann and M. Sch¨ onhoff, J. Phys. Chem. C 125, 266 (2021)

    work page 2021

  34. [34]

    Molinari, J

    N. Molinari, J. P. Mailoa, N. Craig, J. Christensen, and B. Kozinsky, J. Power Sources 428, 27 (2019)

    work page 2019

  35. [35]

    Molinari, J

    N. Molinari, J. P. Mailoa, and B. Kozinsky, J. Phys. Chem . Lett. 10, 2313 (2019)

    work page 2019

  36. [36]

    Chen and M

    F. Chen and M. Forsyth, Phys. Chem. Chem. Phys. 18, 19336 (2016)

    work page 2016

  37. [37]

    Kubisiak, P

    P. Kubisiak, P. Wr` obel, and A. Eilmes, J. Phys. Chem. B 124, 413 (2020)

    work page 2020

  38. [38]

    T. C. Lourenco, L. G. Dias, and J. L. Da Silva, ACS Appl. En ergy Mater. (2021)

    work page 2021

  39. [39]

    Molinari and B

    N. Molinari and B. Kozinsky, J. Phys. Chem. B 124, 2676 (2020)

    work page 2020

  40. [40]

    J. B. Haskins, W. R. Bennett, J. J. Wu, D. M. Herna´ andez, O. Borodin, J. D. Monk, J. Charles W. Bauschlicher, and J. W. Lawson, J. Phys. Chem. B 118, 11295 (2014)

    work page 2014

  41. [41]

    Ren and T

    X. Ren and T. Yan, The Journal of Physical Chemistry B (20 23)

    work page

  42. [42]

    Z. A. H. Goodwin, M. McEldrew, B. Kozinsky, and M. Z. Baza nt, PRX Energy 2, 013007 (2023)

    work page 2023

  43. [43]

    McEldrew, Z

    M. McEldrew, Z. A. Goodwin, S. Bi, M. Z. Bazant, and A. A. K ornyshev, J. Chem. Phys. 152, 234506 (2020)

    work page 2020

  44. [44]

    McEldrew, Z

    M. McEldrew, Z. A. H. Goodwin, H. Zhao, M. Z. Bazant, and A . A. Kornyshev, J. Phys. Chem B 125, 2677–2689 (2021)

    work page 2021

  45. [45]

    McEldrew, Z

    M. McEldrew, Z. A. Goodwin, S. Bi, A. Kornyshev, and M. Z. Bazant, J. Electrochem. Soc. 168, 050514 (2021)

    work page 2021

  46. [46]

    Reber, R

    D. Reber, R. Grissa, M. Becker, R.-S. K¨ uhnel, and C. Bat taglia, Advanced Energy Materials 11, 2002913 (2021)

    work page 2021

  47. [47]

    J. B. Haskins, J. J. Wu, and J. W. Lawson, J. Phys. Chem. C 120, 11993 (2016)

    work page 2016

  48. [48]

    Z. A. Goodwin, M. McEldrew, J. P. de Souza, M. Z. Bazant, a nd A. A. Kornyshev, J. Chem. Phys. 157, 094106 (2022)

    work page 2022

  49. [49]

    Z. A. Goodwin and A. A. Kornyshev, Electrochim. Acta 434, 141163 (2022)

    work page 2022

  50. [50]

    Z. A. Goodwin, G. Feng, and A. A. Kornyshev, Electrochim . Acta 225, 190 (2017)

    work page 2017

  51. [51]

    M. Chen, Z. A. H. Goodwin, G. Feng, and A. A. Kornyshev, 41 J. Electroanal. Chem. 819, 347 (2018)

    work page 2018

  52. [52]

    Z. A. H. Goodwin and A. A. Kornyshev, Electrochem. Commu n. 82, 129 (2017)

    work page 2017

  53. [53]

    Zhang, T

    Y. Zhang, T. Ye, M. Chen, Z. A. Goodwin, G. Feng, J. Huang, and A. A. Kornyshev, Energy Environ. Mater. 3, 414–420 (2020)

    work page 2020

  54. [54]

    G. Feng, M. Chen, S. Bi, Z. A. Goodwin, E. B. Postnikov, N. Brilliantov, M. Urbakh, and A. A. Kornyshev, Phys. Rev. X 9, 021024 (2019)

    work page 2019

  55. [55]

    Jones, F

    P. Jones, F. Coupette, A. H¨ artel, et al. , The Journal of Chemical Physics 154 (2021)

    work page 2021

  56. [56]

    Gongadze, U

    E. Gongadze, U. van Rienen, V. Kralj-Igliˇ c, and A. Igli ˇ c, Computer methods in biomechanics and biomedical engineering 16, 463 (2013)

    work page 2013

  57. [57]

    W. H. Stockmayer, The Journal of chemical physics 11, 45 (1943)

    work page 1943

  58. [58]

    M. S. Wertheim, Journal of statistical physics 35, 19 (1984)

    work page 1984

  59. [59]

    M. S. Wertheim, Journal of statistical physics 35, 35 (1984)

    work page 1984

  60. [60]

    Wertheim, Journal of statistical physics 42, 459 (1986)

    M. Wertheim, Journal of statistical physics 42, 459 (1986)

    work page 1986

  61. [61]

    Wertheim, Journal of statistical physics 42, 477 (1986)

    M. Wertheim, Journal of statistical physics 42, 477 (1986)

    work page 1986

  62. [62]

    Lar ´ ıa, H

    D. Lar ´ ıa, H. R. Corti, and R. Fern´ andez-Prini, Journa l of the Chemical Society, Faraday Transactions 86, 1051 (1990)

    work page 1990

  63. [63]

    Blum and O

    L. Blum and O. Bernard, Journal of statistical physics 79, 569 (1995)

    work page 1995

  64. [64]

    Simonin, O

    J.-P. Simonin, O. Bernard, and L. Blum, The Journal of Ph ysical Chemistry B 103, 699 (1999)

    work page 1999

  65. [65]

    Sciortino, E

    F. Sciortino, E. Bianchi, J. F. Douglas, and P. Tartagli a, The Journal of chemical physics 126 (2007)

    work page 2007

  66. [66]

    Guldbrand, B

    L. Guldbrand, B. J¨ onsson, H. Wennerstr¨ om, and P. Lins e, The Journal of chemical physics 80, 2221 (1984)

    work page 1984

  67. [67]

    Kjellander and S

    R. Kjellander and S. Marˇ celja, Chemical physics lette rs 127, 402 (1986)

    work page 1986

  68. [68]

    Grochowski and J

    P. Grochowski and J. Trylska, Biopolymers: Original Re search on Biomolecules 89, 93 (2008)

    work page 2008

  69. [69]

    R. R. Netz, The European Physical Journal E 5, 557 (2001)

    work page 2001

  70. [70]

    M. Z. Bazant, M. S. Kilic, B. D. Storey, and A. Ajdari, Adv ances in colloid and interface science 152, 48 (2009)

    work page 2009

  71. [71]

    M. Z. Bazant, B. D. Storey, and A. A. Kornyshev, Phys. Rev . Lett. 106, 046102 (2011)

    work page 2011

  72. [72]

    J. P. de Souza, Z. A. Goodwin, M. McEldrew, A. A. Kornyshe v, and M. Z. Bazant, Phys. Rev. Lett. 125, 116001 (2020). 42

    work page 2020

  73. [73]

    J. P. de Souza, A. A. Kornyshev, and M. Z. Bazant, The Jour nal of Chemical Physics 156 (2022)

    work page 2022

  74. [74]

    Y. Avni, R. M. Adar, and D. Andelman, Physical Review E 101, 010601 (2020)

    work page 2020

  75. [75]

    R. M. Adar, S. A. Safran, H. Diamant, and D. Andelman, Phy sical Review E 100, 042615 (2019)

    work page 2019

  76. [76]

    A. Levy, M. McEldrew, and M. Z. Bazant, Physical Review M aterials 3, 055606 (2019)

    work page 2019

  77. [77]

    Z. Yu, N. P. Balsara, O. Borodin, A. A. Gewirth, N. T. Hahn , E. J. Maginn, K. A. Persson, V. Srinivasan, M. F. Toney, K. Xu, K. R. Zavadil, L. A. Curtiss , and L. Cheng, ACS Energy Lett. 7, 461 (2022)

    work page 2022

  78. [78]

    A. A. Kornyshev, J. Phys. Chem. B 111, 5545 (2007)

    work page 2007

  79. [79]

    Ahmadiparidari, S

    A. Ahmadiparidari, S. Fuladi, L. Majidi, S. Plunkett, E . Sarnello, H. Gholivand, Z. Hemmat, S. Rastegar, S. N. Misal, N. Jimenez, et al. , Journal of Power Sources 491, 229506 (2021)

    work page 2021

  80. [80]

    Robin, N

    P. Robin, N. Kavokine, and L. Bocquet, Science 373, 687 (2021)

    work page 2021

Showing first 80 references.