---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '20483'
abstract:
- lang: eng
  text: A parallel plate capacitor containing an electrolytic solution is the simplest
    model of a supercapacitor or electric double-layer capacitor. Using both analytical
    and numerical techniques, we solve the Poisson-Nernst-Planck equations for such
    a system, describing the mean-field charging dynamics of the capacitor, when a
    constant potential difference is abruptly applied to its plates. Working at constant
    total number of ions, we focus on the physical processes involved in the relaxation
    and, whenever possible, give its functional shape and exact time constants. We
    first review and study the case of a symmetric binary electrolyte, where we assume
    the two ionic species to have the same charges and diffusivities. We then relax
    these assumptions and present results for a generic strong (i.e fully dissociated)
    binary electrolyte. At low electrolyte concentration, the relaxation is simple
    to understand, as the dynamics of positive and negative ions appear decoupled.
    At higher electrolyte concentration, we distinguish several regimes. In the linear
    regime (low voltages), relaxation is multiexponential, it starts by the buildup
    of the equilibrium charge profile and continues with neutral mass diffusion, and
    the relevant timescales feature both the average and the Nernst-Hartley diffusion
    coefficients. In the purely nonlinear regime (intermediate voltages), the initial
    relaxation is slowed down exponentially due to increased capacitance, while bulk
    effects become more and more evident. In the fully nonlinear regime (high voltages),
    the dynamics of charge and mass are completely entangled and, asymptotically,
    the relaxation is linear in time. We finally discuss nonideal behavior in real
    capacitors and provide conditions for which mean-field is expected to hold.
acknowledgement: This work has received funding from the European Union's Horizon
  2020 and Horizon Europe research and innovation programs under the Marie Skłodowska-Curie
  Grants No. 674979-NANOTRANS (I.P., P.B.W., B.R., and E.T.), No. 101034413 (I.P.),
  and No. 101119598-FLUXIONIC (M.D., B.R., and E.T.), as well as from the European
  Research Council under Grant No. 863473 (B.R.). B.R. acknowledges financial support
  from the French Agence Nationale de la Recherche (ANR) under Grant No. ANR-21-CE29-0021-02
  (DIADEM). I.P. thanks Anđela Šarić for further support at ISTA.
article_number: '035417'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Ivan
  full_name: Palaia, Ivan
  id: 9c805cd2-4b75-11ec-a374-db6dd0ed57fa
  last_name: Palaia
  orcid: ' 0000-0002-8843-9485 '
- first_name: Adelchi J.
  full_name: Asta, Adelchi J.
  last_name: Asta
- first_name: Megh
  full_name: Dutta, Megh
  last_name: Dutta
- first_name: Patrick B.
  full_name: Warren, Patrick B.
  last_name: Warren
- first_name: Benjamin
  full_name: Rotenberg, Benjamin
  last_name: Rotenberg
- first_name: Emmanuel
  full_name: Trizac, Emmanuel
  last_name: Trizac
citation:
  ama: 'Palaia I, Asta AJ, Dutta M, Warren PB, Rotenberg B, Trizac E. Poisson-Nernst-Planck
    charging dynamics of an electric double-layer capacitor: Symmetric and asymmetric
    binary electrolytes. <i>Physical Review E</i>. 2025;112(3). doi:<a href="https://doi.org/10.1103/p4dg-snqf">10.1103/p4dg-snqf</a>'
  apa: 'Palaia, I., Asta, A. J., Dutta, M., Warren, P. B., Rotenberg, B., &#38; Trizac,
    E. (2025). Poisson-Nernst-Planck charging dynamics of an electric double-layer
    capacitor: Symmetric and asymmetric binary electrolytes. <i>Physical Review E</i>.
    American Physical Society. <a href="https://doi.org/10.1103/p4dg-snqf">https://doi.org/10.1103/p4dg-snqf</a>'
  chicago: 'Palaia, Ivan, Adelchi J. Asta, Megh Dutta, Patrick B. Warren, Benjamin
    Rotenberg, and Emmanuel Trizac. “Poisson-Nernst-Planck Charging Dynamics of an
    Electric Double-Layer Capacitor: Symmetric and Asymmetric Binary Electrolytes.”
    <i>Physical Review E</i>. American Physical Society, 2025. <a href="https://doi.org/10.1103/p4dg-snqf">https://doi.org/10.1103/p4dg-snqf</a>.'
  ieee: 'I. Palaia, A. J. Asta, M. Dutta, P. B. Warren, B. Rotenberg, and E. Trizac,
    “Poisson-Nernst-Planck charging dynamics of an electric double-layer capacitor:
    Symmetric and asymmetric binary electrolytes,” <i>Physical Review E</i>, vol.
    112, no. 3. American Physical Society, 2025.'
  ista: 'Palaia I, Asta AJ, Dutta M, Warren PB, Rotenberg B, Trizac E. 2025. Poisson-Nernst-Planck
    charging dynamics of an electric double-layer capacitor: Symmetric and asymmetric
    binary electrolytes. Physical Review E. 112(3), 035417.'
  mla: 'Palaia, Ivan, et al. “Poisson-Nernst-Planck Charging Dynamics of an Electric
    Double-Layer Capacitor: Symmetric and Asymmetric Binary Electrolytes.” <i>Physical
    Review E</i>, vol. 112, no. 3, 035417, American Physical Society, 2025, doi:<a
    href="https://doi.org/10.1103/p4dg-snqf">10.1103/p4dg-snqf</a>.'
  short: I. Palaia, A.J. Asta, M. Dutta, P.B. Warren, B. Rotenberg, E. Trizac, Physical
    Review E 112 (2025).
corr_author: '1'
date_created: 2025-10-16T13:15:16Z
date_published: 2025-09-29T00:00:00Z
date_updated: 2025-12-01T13:06:51Z
day: '29'
ddc:
- '530'
department:
- _id: AnSa
doi: 10.1103/p4dg-snqf
ec_funded: 1
external_id:
  arxiv:
  - '2303.07859'
  isi:
  - '001586173200001'
file:
- access_level: open_access
  checksum: 658a9b1ce6b2edcf138b54c55a566f0e
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  creator: dernst
  date_created: 2025-10-23T09:15:56Z
  date_updated: 2025-10-23T09:15:56Z
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  file_size: 1211712
  relation: main_file
  success: 1
file_date_updated: 2025-10-23T09:15:56Z
has_accepted_license: '1'
intvolume: '       112'
isi: 1
issue: '3'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
publication: Physical Review E
publication_identifier:
  eissn:
  - 2470-0053
  issn:
  - 2470-0045
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Poisson-Nernst-Planck charging dynamics of an electric double-layer capacitor:
  Symmetric and asymmetric binary electrolytes'
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 112
year: '2025'
...