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General theory of asymmetric steric interactions in electrostatic double layers

We study the Poisson-Boltzmann equation in the context of dense charged fluids where steric effects become important. We generalise the lattice gas theory by introducing a Flory-Huggins entropy for ions of differing volumes and then compare the effective free energy density to other approximations, valid for more realistic equations of state, such as the Carnahan-Starling approximation and find strong differences in the shapes of the free energy functions. 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.