Ion adsorption and external electric field effects on isotropic liquids using a Fermi-like distribution

A Fermi-like distribution for charged particles is used to investigate adsorption and external electric field effects in a typical confined sample of an isotropic liquid. In the absence of adsorption, expressions for the reduced potential across the sample and for the specific differential capacitance of the double layer are established as a function of the applied dc voltage. In the presence of adsorption, without external field, the fundamental equations of the electrostatic model are analytically solved in the limit of small potential. Simple expressions for the reduced and chemical potential as well as for the specific differential capacitance of the double layer are established. The behavior of these quantities are analyzed as a function of the adsorption energy, the total density of ions in the bulk, and the potential drop between the electrode surface and the bulk.