A mean-field theory on the differential capacitance of asymmetric ionic liquid electrolytes. II. Accounts of ionic interactions.

A size-asymmetric mean-field theory with ionic interactions is developed for the electric double layer of room temperature ionic liquid (IL) electrolytes, based on the previous work on non-interacting ions (Y. Han et al., J. Phys.: Condens. Matter, 2014, 26, 284103). By solving the modified Poisson-Boltzmann equation with some simplified assumptions following a recent work (Z. A. H. Goodwin et al., Electrochim. Acta, 2017, 225, 190-197), an analytical expression of differential capacitance can be derived, with a scaled electrode potential due to the ionic interactions. Compared with non-interacting ions, the main effect of ionic interactions is the insufficient screening of the electrode potential, and this depresses the differential capacitance compared with the non-interactive case.