2015/07/16 by A. C. Maggs, R. Podgornik, Maggs, A. C. +1 · 1 citation
Physics and Astronomy · #Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Soft Condensed Matter (cond-mat.soft) #cond-mat.soft #physics.chem-ph
paper · pdf · doi:10.48550/arxiv.1507.04533
9 pages, 6 figures
arxiv created 2015/07/16 · arxiv updated 2015/07/17
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.