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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...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2021
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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. |
format | Online Article Text |
id | pubmed-7918844 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
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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