---
res:
  bibo_abstract:
  - 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.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Ivan
      foaf_name: Palaia, Ivan
      foaf_surname: Palaia
      foaf_workInfoHomepage: http://www.librecat.org/personId=9c805cd2-4b75-11ec-a374-db6dd0ed57fa
    orcid: ' 0000-0002-8843-9485 '
  - foaf_Person:
      foaf_givenName: Adelchi J.
      foaf_name: Asta, Adelchi J.
      foaf_surname: Asta
  - foaf_Person:
      foaf_givenName: Megh
      foaf_name: Dutta, Megh
      foaf_surname: Dutta
  - foaf_Person:
      foaf_givenName: Patrick B.
      foaf_name: Warren, Patrick B.
      foaf_surname: Warren
  - foaf_Person:
      foaf_givenName: Benjamin
      foaf_name: Rotenberg, Benjamin
      foaf_surname: Rotenberg
  - foaf_Person:
      foaf_givenName: Emmanuel
      foaf_name: Trizac, Emmanuel
      foaf_surname: Trizac
  bibo_doi: 10.1103/p4dg-snqf
  bibo_issue: '3'
  bibo_volume: 112
  dct_date: 2025^xs_gYear
  dct_identifier:
  - UT:001586173200001
  dct_isPartOf:
  - http://id.crossref.org/issn/2470-0045
  - http://id.crossref.org/issn/2470-0053
  dct_language: eng
  dct_publisher: American Physical Society@
  dct_title: 'Poisson-Nernst-Planck charging dynamics of an electric double-layer
    capacitor: Symmetric and asymmetric binary electrolytes@'
...