title: General theory of asymmetric steric interactions in electrostatic double layers.
abstract: 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.
authors.affiliation: Laboratoire PCT, Gulliver CNRS-ESPCI UMR 7083, 10 rue Vauquelin, 75231 Paris Cedex 05, France.
authors.forename: A C
authors.initials: AC
authors.lastname: Maggs
authors.affiliation: Department of Theoretical Physics, J. Stefan Institute and Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia.
authors.forename: R
authors.initials: R
authors.lastname: Podgornik