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On the Gouy–Chapman–Stern model of the electrical double-layer structure with a generalized Boltzmann factor

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  • Allagui, Anis
  • Benaoum, Hachemi
  • Olendski, Oleg

Abstract

The classical treatment of the electrical double-layer (EDL) structure at a planar metal/electrolyte junction via the Gouy–Chapman–Stern (GCS) approach is based on the Poisson equation relating the electrostatic potential to the net mean charge density. The ions concentration in the diffuse layer are assumed to follow the Boltzmann distribution law, i.e. ∝exp(−ψ̃) where ψ̃ is the dimensionless electrostatic potential. However, even in stationary equilibrium in which variables are averaged over a large number of elementary stochastic events, deviations from the mean-value are expected. In this study we evaluate the behavior of the EDL by assuming some small perturbations superposed on top of its Boltzmann distribution of ion concentrations using the Tsallis nonextensive statistics framework. With this we assume the ion concentrations to be proportional to [1−(1−q)ψ̃]1/(1−q)=expq(−ψ̃) with q being a real parameter that characterizes the system’s statistics. We derive analytical expression and provide computational results for the overall differential capacitance of the EDL structure, which, depending on the values of the parameter q can show both the traditional inverse bell-shaped curves for aqueous solutions and bell curves observed with ionic liquids.

Suggested Citation

  • Allagui, Anis & Benaoum, Hachemi & Olendski, Oleg, 2021. "On the Gouy–Chapman–Stern model of the electrical double-layer structure with a generalized Boltzmann factor," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    • Handle: RePEc:eee:phsmap:v:582:y:2021:i:c:s0378437121005252
    DOI: 10.1016/j.physa.2021.126252
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    References listed on IDEAS

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    1. Garcı́a-Morales, V & Cervera, J & Pellicer, J, 2004. "Coupling theory for counterion distributions based in Tsallis statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 339(3), pages 482-490.
    2. Fouda, M.E. & Elwakil, A.S. & Radwan, A.G. & Allagui, A., 2016. "Power and energy analysis of fractional-order electrical energy storage devices," Energy, Elsevier, vol. 111(C), pages 785-792.
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