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Modeling the camel-to-bell shape transition of the differential capacitance using mean-field theory and Monte Carlo simulations

  • Guilherme V. Bossa
  • Daniel L. Z. Caetano
  • Sidney J. de Carvalho
  • Klemen Bohinc
  • Sylvio May
Regular Article
  • 35 Downloads

Abstract.

Mean-field electrostatics is used to calculate the differential capacitance of an electric double layer formed at a planar electrode in a symmetric 1:1 electrolyte. Assuming the electrolyte is also ion-size symmetric, we derive analytic expressions for the differential capacitance valid up to fourth order in the surface charge density or surface potential. Our mean-field model accounts exclusively for electrostatic interactions but includes an arbitrary non-ideality in the mixing entropy of the mobile ions. The ensuing criterion for the camel-to-bell shape transition of the differential capacitance is analyzed using commonly used mixing models (one based on a lattice gas and the other based on the Carnahan-Starling equation of state) and compared with Monte Carlo simulations. We observe a reasonable agreement between all our mean-field models and the simulation data for the camel-to-bell shape transition. The absolute value of the differential capacitance for an uncharged (or weakly charged) electrode is, however, not reproduced by our mean-field approaches, not even upon introducing a Stern layer with a thickness equal of the ion radius. We show that, if a Stern layer is introduced, its thickness dependence on the ion size is non-monotonic or, depending on the salt concentration, even inversely proportional.

Graphical abstract

Keywords

Soft Matter: Interfacial Phenomena and Nanostructured Surfaces 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Guilherme V. Bossa
    • 1
    • 2
  • Daniel L. Z. Caetano
    • 2
  • Sidney J. de Carvalho
    • 2
  • Klemen Bohinc
    • 3
  • Sylvio May
    • 1
  1. 1.Department of PhysicsNorth Dakota State UniversityFargoUSA
  2. 2.Department of PhysicsSão Paulo State University (UNESP), Institute of Biosciences, Humanities and Exact SciencesSão José do Rio PretoBrazil
  3. 3.Faculty of Health SciencesUniversity of LjubljanaLjubljanaSlovenia

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