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The Poisson-Boltzmann (PB) equation provides a mean-field theory of electrolyte solutions at interfaces and in confinement, describing how ions reorganize close to charged surfaces to form the so-called electrical double layer (EDL), with…

Soft Condensed Matter · Physics 2024-09-10 Cecilia Herrero , Laurent Joly

Electrical double layers (EDLs) arise when an electrolyte is in contact with a charged surface, and are encountered in several application areas including batteries, supercapacitors, electrocatalytic reactors, and colloids. In the modeling…

Soft Condensed Matter · Physics 2023-08-24 Aniruddha Seal , Utkarsh Tiwari , Ankur Gupta , Ananth Govind Rajan

The equilibrium electric double layer (EDL) that surrounds the colloidal particles is determinant for the response of a suspension under a variety of static or alternating external fields. An ideal salt-free suspension is composed by the…

Soft Condensed Matter · Physics 2017-09-13 R. Roa , F. Carrique , E. Ruiz-Reina

We present a continuation of our theoretical research into the influence of co-solvent polarizability on a differential capacitance of the electric double layer [EPL 111, 28002 (2015)]. We formulate a modified Poisson-Boltzmann theory,…

Soft Condensed Matter · Physics 2016-05-11 Yu. A. Budkov , A. L. Kolesnikov , M. G. Kiselev

The electric double layer structure in an electrolyte close to a solid substrate near the three-phase contact line is approximated by considering the linearized Poisson-Boltzmann equation in a wedge geometry. The mathematical approach…

Soft Condensed Matter · Physics 2012-09-03 Aaron Dörr , Steffen Hardt

Metal-oxide surfaces act as both Br{\o}nsted acids and bases, which allows the exchange of protons with the electrolyte solution and generates either positive or negative proton charges depending on the environmental pH. These interfacial…

Chemical Physics · Physics 2024-08-13 Lisanne Knijff , Mei Jia , Chao Zhang

The electric double layer (EDL) has a pivotal role in screening charges on surfaces as in supercapacitor electrodes or colloidal and polymer solutions. Its structure is determined by correlations between the finite-sized ionic charge…

Soft Condensed Matter · Physics 2023-11-21 Peter Cats , Andreas Härtel

The electrical double layer (EDL) is fundamental to the operation of devices for electrochemical energy storage and conversion. Existing models of EDL in solid electrolytes focus predominantly on the space charge layer and lack a complete…

Materials Science · Physics 2025-08-12 Zeeshan Ahmad

We derive a formally simple approximate analytical solution to the Poisson-Boltzmann equation for the spherical system via a geometric mapping. Its regime of applicability in the parameter space of the spherical radius and the surface…

Soft Condensed Matter · Physics 2012-02-01 Zhenwei Yao , Mark J. Bowick , Xu Ma

Electric double layer (EDL) formation underlies the functioning of supercapacitors and several other electrochemical technologies. Here, we study how the EDL formation near two flat blocking electrodes separated by $2L$ is affected by…

Chemical Physics · Physics 2025-09-23 David Fertig , Mathijs Janssen

In electrochemical systems, the structure of electrical double layers (EDLs) near electrode surfaces is crucial for energy conversion and storage functions. While the electrodes in real-world systems are usually heterogeneous, to date the…

The electrical double layer (EDL) at aqueous solution-metal oxide interfaces critically affects many fundamental processes in electrochemistry, geology and biology, yet understanding its microscopic structure is challenging for both theory…

The electric double layer (EDL) formed around charged nanostructures at the liquid-solid interface determines their electrochemical activity and influences their electrical and optical polarizability. We experimentally demonstrate that…

Soft Condensed Matter · Physics 2020-04-29 Kevin Namink , Xuanhui Meng , Marc T. M. Koper , Philipp Kukura , Sanli Faez

A nonlinear phase-field model is developed to simulate corrosion damage. The motion of the electrode$-$ electrolyte interface follows the usual kinetic rate theory for chemical reactions based on the Butler-Volmer equation. The model links…

Chemical Physics · Physics 2024-08-28 M. Makuch , S. Kovacevic , M. R. Wenman , E. Martínez-Pañeda

Charged surfaces in contact with liquids containing ions are accompanied in equilibrium by an electric double layer consisting of a layer of electric charge on the surface that is screened by a diffuse ion cloud in the bulk fluid. This…

Soft Condensed Matter · Physics 2018-09-21 Jeffrey C. Everts , Miha Ravnik

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…

Applied Physics · Physics 2022-01-11 Anis Allagui , Hachemi Benaoum , Oleg Olendski

The electric double layer (EDL) that forms at the interface between metals and ionic solutions is at the heart of various energy technologies. Recent experimental data have challenged our traditional understanding of the EDL charging…

Statistical Mechanics · Physics 2026-03-05 Nils Bruch , Michael Eikerling , Tobias Binninger

The description of a conducting medium in thermal equilibrium, such as an electrolyte solution or a plasma, involves nonlinear electrostatics, a subject rarely discussed in the standard electricity and magnetism textbooks. We consider in…

Chemical Physics · Physics 2018-08-01 C. G. Gray , P. J. Stiles

Electric double layers (EDL) with counterions only, say electrons with the elementary charge $-e$, in thermal equilibrium at the inverse temperature $\beta$ are considered. In particular, we study the effect of the surface charge modulation…

Statistical Mechanics · Physics 2022-07-26 Ladislav Šamaj

Understanding the electrical double layer (EDL), i.e, the distribution of electrolyte at an electrified interface, in concentrated electrolytes is important for various technologies, such as supercapacitors, batteries and electrocatalysis.…

Soft Condensed Matter · Physics 2026-05-01 Zachary A. H. Goodwin
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