Differential capacitance of the electric double layer: The interplay between ion finite size and dielectric decrement

Yasuya Nakayama, David Andelman

Research output: Contribution to journalArticle

50 Citations (Scopus)

Abstract

We study the electric double layer by combining the effects of ion finite size and dielectric decrement. At high surface potential, both mechanisms can cause saturation of the counter-ion concentration near a charged surface. The modified Grahame equation and differential capacitance are derived analytically for a general expression of a permittivity ε(n) that depends on the local ion concentration, n, and under the assumption that the co-ions are fully depleted from the surface. The concentration at counter-ion saturation is found for any ε(n), and a criterion predicting which of the two mechanisms (steric vs. dielectric decrement) is the dominant one is obtained. At low salinity, the differential capacitance as function of surface potential has two peaks (so-called camel-shape). Each of these two peaks is connected to a saturation of counter-ion concentration caused either by dielectric decrement or by their finite size. Because these effects depend mainly on the counter-ion concentration at the surface proximity, for opposite surface-potential polarity either the cations or anions play the role of counter-ions, resulting in an asymmetric camel-shape. At high salinity, we obtain and analyze the crossover in the differential capacitance from a double-peak shape to a uni-modal one. Finally, several nonlinear models of the permittivity decrement are considered, and we predict that the concentration at dielectrophoretic saturation shifts to higher concentration than those obtained by the linear decrement model.

Original languageEnglish
Article number044706
JournalJournal of Chemical Physics
Volume142
Issue number4
DOIs
Publication statusPublished - Jan 28 2015

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Radiation counters
Capacitance
capacitance
Ions
ion concentration
counters
saturation
ions
salinity
Permittivity
permittivity
Surface potential
Anions
Cations
proximity
polarity
crossovers
anions
cations
causes

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

Cite this

Differential capacitance of the electric double layer : The interplay between ion finite size and dielectric decrement. / Nakayama, Yasuya; Andelman, David.

In: Journal of Chemical Physics, Vol. 142, No. 4, 044706, 28.01.2015.

Research output: Contribution to journalArticle

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