The influence of excluded volume and excess ion polarizability on the capacitance of the electric double layer

Geraint Minton, Leo Lue

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We apply a modified Poisson-Boltzmann theory which permits ions of different sizes and excess polarizabilities to the study of these properties' effects on the differential capacitance of the electric double layer. For a planar electrode, we find an analytical expression for the differential capacitance, which is examined in the limits of low and high applied potential. In the low potential limit, a reduction of the solution relative permittivity caused by the ion polarizability causes the differential capacitance to decrease above a certain concentration, relative to the Gouy-Chapman-Stern theory. A similar effect is observed for the excluded volume, but only if the ions are of different sizes. In the high potential limit, the differential capacitance decreases inversely with the square root of the applied voltage. In a mixed electrolyte, asymmetries in both ion size and excess polarizability alter the surface adsorption of species: at high potentials, smaller ions displace larger ions and less polarizable ions displace more polarizable ions. The extent of the displacement agrees favorably with experimental data. A further consequence of this displacement is the appearance of a second peak in the differential capacitance, which is enhanced by excess ion polarizability.
LanguageEnglish
Pages2477-2491
Number of pages15
JournalMolecular Physics
Volume114
Issue number16-17
Early online date12 Apr 2016
DOIs
Publication statusPublished - 2016

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Electric Capacitance
Capacitance
capacitance
Ions
ions
Heavy ions
Electrolytes
Permittivity
Adsorption
Electrodes

Keywords

  • capacitance
  • excess ion polarizability
  • excluded volume
  • electric double layer
  • electrolyte

Cite this

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title = "The influence of excluded volume and excess ion polarizability on the capacitance of the electric double layer",
abstract = "We apply a modified Poisson-Boltzmann theory which permits ions of different sizes and excess polarizabilities to the study of these properties' effects on the differential capacitance of the electric double layer. For a planar electrode, we find an analytical expression for the differential capacitance, which is examined in the limits of low and high applied potential. In the low potential limit, a reduction of the solution relative permittivity caused by the ion polarizability causes the differential capacitance to decrease above a certain concentration, relative to the Gouy-Chapman-Stern theory. A similar effect is observed for the excluded volume, but only if the ions are of different sizes. In the high potential limit, the differential capacitance decreases inversely with the square root of the applied voltage. In a mixed electrolyte, asymmetries in both ion size and excess polarizability alter the surface adsorption of species: at high potentials, smaller ions displace larger ions and less polarizable ions displace more polarizable ions. The extent of the displacement agrees favorably with experimental data. A further consequence of this displacement is the appearance of a second peak in the differential capacitance, which is enhanced by excess ion polarizability.",
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author = "Geraint Minton and Leo Lue",
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The influence of excluded volume and excess ion polarizability on the capacitance of the electric double layer. / Minton, Geraint; Lue, Leo.

In: Molecular Physics, Vol. 114, No. 16-17, 2016, p. 2477-2491.

Research output: Contribution to journalArticle

TY - JOUR

T1 - The influence of excluded volume and excess ion polarizability on the capacitance of the electric double layer

AU - Minton, Geraint

AU - Lue, Leo

PY - 2016

Y1 - 2016

N2 - We apply a modified Poisson-Boltzmann theory which permits ions of different sizes and excess polarizabilities to the study of these properties' effects on the differential capacitance of the electric double layer. For a planar electrode, we find an analytical expression for the differential capacitance, which is examined in the limits of low and high applied potential. In the low potential limit, a reduction of the solution relative permittivity caused by the ion polarizability causes the differential capacitance to decrease above a certain concentration, relative to the Gouy-Chapman-Stern theory. A similar effect is observed for the excluded volume, but only if the ions are of different sizes. In the high potential limit, the differential capacitance decreases inversely with the square root of the applied voltage. In a mixed electrolyte, asymmetries in both ion size and excess polarizability alter the surface adsorption of species: at high potentials, smaller ions displace larger ions and less polarizable ions displace more polarizable ions. The extent of the displacement agrees favorably with experimental data. A further consequence of this displacement is the appearance of a second peak in the differential capacitance, which is enhanced by excess ion polarizability.

AB - We apply a modified Poisson-Boltzmann theory which permits ions of different sizes and excess polarizabilities to the study of these properties' effects on the differential capacitance of the electric double layer. For a planar electrode, we find an analytical expression for the differential capacitance, which is examined in the limits of low and high applied potential. In the low potential limit, a reduction of the solution relative permittivity caused by the ion polarizability causes the differential capacitance to decrease above a certain concentration, relative to the Gouy-Chapman-Stern theory. A similar effect is observed for the excluded volume, but only if the ions are of different sizes. In the high potential limit, the differential capacitance decreases inversely with the square root of the applied voltage. In a mixed electrolyte, asymmetries in both ion size and excess polarizability alter the surface adsorption of species: at high potentials, smaller ions displace larger ions and less polarizable ions displace more polarizable ions. The extent of the displacement agrees favorably with experimental data. A further consequence of this displacement is the appearance of a second peak in the differential capacitance, which is enhanced by excess ion polarizability.

KW - capacitance

KW - excess ion polarizability

KW - excluded volume

KW - electric double layer

KW - electrolyte

U2 - 10.1080/00268976.2016.1169327

DO - 10.1080/00268976.2016.1169327

M3 - Article

VL - 114

SP - 2477

EP - 2491

JO - Molecular Physics

T2 - Molecular Physics

JF - Molecular Physics

SN - 0026-8976

IS - 16-17

ER -