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

• Published in: The European physical journal. E, Soft matter and biological physics Vol. 41; no. 9; pp. 113 - 9
• Main Authors: Bossa, Guilherme V., Caetano, Daniel L. Z., de Carvalho, Sidney J., Bohinc, Klemen, May, Sylvio
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 27-09-2018; Springer Nature B.V
• Subjects: Biological and Medical Physics; Biophysics; Capacitance; Charge density; Complex Fluids and Microfluidics; Complex Systems; Computer simulation; Condensed matter physics; Dependence; Electric double layer; Electrodes; Electrolytes; Electrostatics; Equations of state; Mean field theory; Monte Carlo simulation; Nanotechnology; Physics; Physics and Astronomy; Polymer Sciences; Regular Article; Soft and Granular Matter; Surface charge; Surfaces and Interfaces; Thickness; Thin Films; Soft Matter: Interfacial Phenomena and Nanostructured Surfaces
• ISSN: 1292-8941; 1292-895X
• DOI: 10.1140/epje/i2018-11723-7

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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