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Debye-Hückel Free Energy of an Electric Double Layer with Discrete Charges Located at a Dielectric Interface

Poisson–Boltzmann theory provides an established framework to calculate properties and free energies of an electric double layer, especially for simple geometries and interfaces that carry continuous charge densities. At sufficiently small length scales, however, the discreteness of the surface char...

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Detalles Bibliográficos
Autores principales: Bossa, Guilherme Volpe, May, Sylvio
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7918844/
https://www.ncbi.nlm.nih.gov/pubmed/33672797
http://dx.doi.org/10.3390/membranes11020129
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author Bossa, Guilherme Volpe
May, Sylvio
author_facet Bossa, Guilherme Volpe
May, Sylvio
author_sort Bossa, Guilherme Volpe
collection PubMed
description Poisson–Boltzmann theory provides an established framework to calculate properties and free energies of an electric double layer, especially for simple geometries and interfaces that carry continuous charge densities. At sufficiently small length scales, however, the discreteness of the surface charges cannot be neglected. We consider a planar dielectric interface that separates a salt-containing aqueous phase from a medium of low dielectric constant and carries discrete surface charges of fixed density. Within the linear Debye-Hückel limit of Poisson–Boltzmann theory, we calculate the surface potential inside a Wigner–Seitz cell that is produced by all surface charges outside the cell using a Fourier-Bessel series and a Hankel transformation. From the surface potential, we obtain the Debye-Hückel free energy of the electric double layer, which we compare with the corresponding expression in the continuum limit. Differences arise for sufficiently small charge densities, where we show that the dominating interaction is dipolar, arising from the dipoles formed by the surface charges and associated counterions. This interaction propagates through the medium of a low dielectric constant and alters the continuum power of two dependence of the free energy on the surface charge density to a power of 2.5 law.
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spelling pubmed-79188442021-03-02 Debye-Hückel Free Energy of an Electric Double Layer with Discrete Charges Located at a Dielectric Interface Bossa, Guilherme Volpe May, Sylvio Membranes (Basel) Article Poisson–Boltzmann theory provides an established framework to calculate properties and free energies of an electric double layer, especially for simple geometries and interfaces that carry continuous charge densities. At sufficiently small length scales, however, the discreteness of the surface charges cannot be neglected. We consider a planar dielectric interface that separates a salt-containing aqueous phase from a medium of low dielectric constant and carries discrete surface charges of fixed density. Within the linear Debye-Hückel limit of Poisson–Boltzmann theory, we calculate the surface potential inside a Wigner–Seitz cell that is produced by all surface charges outside the cell using a Fourier-Bessel series and a Hankel transformation. From the surface potential, we obtain the Debye-Hückel free energy of the electric double layer, which we compare with the corresponding expression in the continuum limit. Differences arise for sufficiently small charge densities, where we show that the dominating interaction is dipolar, arising from the dipoles formed by the surface charges and associated counterions. This interaction propagates through the medium of a low dielectric constant and alters the continuum power of two dependence of the free energy on the surface charge density to a power of 2.5 law. MDPI 2021-02-14 /pmc/articles/PMC7918844/ /pubmed/33672797 http://dx.doi.org/10.3390/membranes11020129 Text en © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Bossa, Guilherme Volpe
May, Sylvio
Debye-Hückel Free Energy of an Electric Double Layer with Discrete Charges Located at a Dielectric Interface
title Debye-Hückel Free Energy of an Electric Double Layer with Discrete Charges Located at a Dielectric Interface
title_full Debye-Hückel Free Energy of an Electric Double Layer with Discrete Charges Located at a Dielectric Interface
title_fullStr Debye-Hückel Free Energy of an Electric Double Layer with Discrete Charges Located at a Dielectric Interface
title_full_unstemmed Debye-Hückel Free Energy of an Electric Double Layer with Discrete Charges Located at a Dielectric Interface
title_short Debye-Hückel Free Energy of an Electric Double Layer with Discrete Charges Located at a Dielectric Interface
title_sort debye-hückel free energy of an electric double layer with discrete charges located at a dielectric interface
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7918844/
https://www.ncbi.nlm.nih.gov/pubmed/33672797
http://dx.doi.org/10.3390/membranes11020129
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