IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v582y2021ics0378437121005252.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437121005252
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2021.126252?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sajid, Mohammad & Raza, Zahid, 2017. "Energy-aware stochastic scheduler for batch of precedence-constrained jobs on heterogeneous computing system," Energy, Elsevier, vol. 125(C), pages 258-274.
    2. Capasso, Clemente & Lauria, Davide & Veneri, Ottorino, 2018. "Experimental evaluation of model-based control strategies of sodium-nickel chloride battery plus supercapacitor hybrid storage systems for urban electric vehicles," Applied Energy, Elsevier, vol. 228(C), pages 2478-2489.
    3. Jorge Leon-Quiroga & Brittany Newell & Mahesh Krishnamurthy & Andres Gonzalez-Mancera & Jose Garcia-Bravo, 2020. "Energy Efficiency Comparison of Hydraulic Accumulators and Ultracapacitors," Energies, MDPI, vol. 13(7), pages 1-23, April.
    4. Xu, Ying & Ren, Li & Zhang, Zhongping & Tang, Yuejin & Shi, Jing & Xu, Chen & Li, Jingdong & Pu, Dongsheng & Wang, Zhuang & Liu, Huajun & Chen, Lei, 2018. "Analysis of the loss and thermal characteristics of a SMES (Superconducting Magnetic Energy Storage) magnet with three practical operating conditions," Energy, Elsevier, vol. 143(C), pages 372-384.
    5. Hernández-Balaguera, Enrique, 2023. "Fractional model of the chemical inductor," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    6. Francisco G. Montoya & Raul Baños & Alfredo Alcayde & Maria G. Montoya & Francisco Manzano-Agugliaro, 2018. "Power Quality: Scientific Collaboration Networks and Research Trends," Energies, MDPI, vol. 11(8), pages 1-16, August.
    7. Jakubowska-Ciszek, A. & Walczak, J., 2018. "Analysis of the transient state in a parallel circuit of the class RLβCα," Applied Mathematics and Computation, Elsevier, vol. 319(C), pages 287-300.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:582:y:2021:i:c:s0378437121005252. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.