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

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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.

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Authors and Affiliations

  1. Department of Physics, North Dakota State University, 58108-6050, Fargo, ND, USA

    Guilherme V. Bossa & Sylvio May

  2. Department of Physics, São Paulo State University (UNESP), Institute of Biosciences, Humanities and Exact Sciences, 15054-000, São José do Rio Preto, SP, Brazil

    Guilherme V. Bossa, Daniel L. Z. Caetano & Sidney J. de Carvalho

  3. Faculty of Health Sciences, University of Ljubljana, Poljanska 26a, 1000, Ljubljana, Slovenia

    Klemen Bohinc

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  1. Guilherme V. Bossa
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  2. Daniel L. Z. Caetano
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  4. Klemen Bohinc
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Correspondence to Sylvio May.

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Bossa, G.V., Caetano, D.L.Z., de Carvalho, S.J. et al. Modeling the camel-to-bell shape transition of the differential capacitance using mean-field theory and Monte Carlo simulations. Eur. Phys. J. E 41, 113 (2018). https://doi.org/10.1140/epje/i2018-11723-7

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