dorsal/arxiv
View SchemaSteric effects in the dynamics of electrolytes at large applied voltages: II. Modified Poisson-Nernst-Planck equations
| Authors | Mustafa Sabri Kilic, Martin Z. Bazant, Armand Ajdari |
|---|---|
| Categories | |
| ArXiv ID | physics/0611232 |
| URL | https://arxiv.org/abs/physics/0611232 |
Abstract
In situations involving large potentials or surface charges, the Poisson Boltzman(PB) equation has shortcomings because it neglects ion-ion interactions and steric effects. This has been widely recognized by the electrochemistry community, leading to the development of various alternative models resulting in different sets "modified PB equations", which have had at least qualitative success in predicting equilibrium ion distributions. On the other hand, the literature is scarce in terms of descriptions of concentration dynamics in these regimes. Here, adapting strategies developed to modify the PB equation, we propose a simple modification of the widely used Poisson-Nernst-Planck (PNP) equations for ionic transport, which at least qualitatively accounts for steric effects. We analyze numerical solutions of these MPNP equations on the model problem of the charging of a simple electrolyte cell, and compare the outcome to that of the standard PNP equations. Finally, we repeat the asymptotic analysis of Bazant, Thornton, and Ajdari(2004} for this new system of equations to further document the interest and limits of validity of the simpler equivalent electrical circuit models introduced in Part I for such problems.
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"abstract": "In situations involving large potentials or surface charges, the Poisson\nBoltzman(PB) equation has shortcomings because it neglects ion-ion interactions\nand steric effects. This has been widely recognized by the electrochemistry\ncommunity, leading to the development of various alternative models resulting\nin different sets \"modified PB equations\", which have had at least qualitative\nsuccess in predicting equilibrium ion distributions. On the other hand, the\nliterature is scarce in terms of descriptions of concentration dynamics in\nthese regimes. Here, adapting strategies developed to modify the PB equation,\nwe propose a simple modification of the widely used Poisson-Nernst-Planck (PNP)\nequations for ionic transport, which at least qualitatively accounts for steric\neffects. We analyze numerical solutions of these MPNP equations on the model\nproblem of the charging of a simple electrolyte cell, and compare the outcome\nto that of the standard PNP equations. Finally, we repeat the asymptotic\nanalysis of Bazant, Thornton, and Ajdari(2004} for this new system of equations\nto further document the interest and limits of validity of the simpler\nequivalent electrical circuit models introduced in Part I for such problems.",
"arxiv_id": "physics/0611232",
"authors": [
"Mustafa Sabri Kilic",
"Martin Z. Bazant",
"Armand Ajdari"
],
"categories": [
"physics.chem-ph"
],
"title": "Steric effects in the dynamics of electrolytes at large applied voltages: II. Modified Poisson-Nernst-Planck equations",
"url": "https://arxiv.org/abs/physics/0611232"
},
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