General theory of asymmetric steric interactions in electrostatic double layers

We study the mean-field Poisson-Boltzmann equation in the context of dense ionic liquids where steric effects become important. We generalise lattice gas theory by introducing a Flory-Huggins entropy for ions of differing volumes and then compare the effective free energy density to other existing l...

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Bibliographic Details
Published in:Soft matter 2016-01, Vol.12 (4), p.1219-1229
Main Authors: Maggs, A. C, Podgornik, R
Format: Article
Language:English
Subjects:
Approximation
Entropy
Free energy
Lattices
Mathematical analysis
Mathematical models
Physics
Steric effects
Thermodynamics
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Summary:We study the mean-field Poisson-Boltzmann equation in the context of dense ionic liquids where steric effects become important. We generalise lattice gas theory by introducing a Flory-Huggins entropy for ions of differing volumes and then compare the effective free energy density to other existing lattice gas approximations, not based on the Flory-Huggins Ansatz. Within the methodology presented we also invoke more realistic equations of state, such as the Carnahan-Starling approximation, that are not based on the lattice gas approximation and lead to thermodynamic functions and properties that differ strongly from the lattice gas case. We solve the Carnahan-Starling model in the high density limit, and demonstrate a slow, power-law convergence at high potentials. We elucidate how equivalent convex free energy functions can be constructed that describe steric effects in a manner which is more convenient for numerical minimisation. We study the mean-field Poisson-Boltzmann equation in the context of dense ionic liquids where steric effects become important.
ISSN:1744-683X
1744-6848
DOI:10.1039/c5sm01757b