Electric-double-layer potential distribution in multiple-layer immiscible electrolytes: effect of finite ion sizes

In a recent study [S. Das and S. Hardt, Phys. Rev. E 84, 022502 (2011).], we provided analytical results for the electric-double-layer (EDL) electrostatic potential distribution in a system of immiscible electrolyte layers confined between plates with gap dimensions comparable to the EDL thickness. We demonstrated that the intrinsic jumps in the ion-solvent interactions across the interface of the immiscible electrolytes lead to nontrivial electrostatic potential distributions that may completely defy or substantially augment the effect of the boundary wall potential. In this Brief Report, I extend this calculation to obtain analytical and numerical results for the case with finite ion sizes (or a finite ionic steric effect). It is found that the finite steric effect substantially enhances the contributions of jump in the ion-solvent interactions in the overall electrostatic potential distribution. More importantly, I demonstrate that such jumps in the ion-solvent interactions, owing to the immiscibility of the electrolytes, ensure that even for very weak wall zeta potentials, the steric effect can significantly affect the electrostatic potential distribution.