A mean-field theory on the differential capacitance of asymmetric ionic liquid electrolytes

The size of ions significantly influences the electric double layer structure of room temperature ionic liquid (IL) electrolytes and their differential capacitance (C-d). In this study, we extended the mean-field theory (MFT) developed independently by Kornyshev (2007 J. Phys. Chem. B 111 5545-57) and Kilic, Bazant, and Ajdari (2007 Phys. Rev. E 75 021502) (the KKBA MFT) to take into account the asymmetric 1:1 IL electrolytes by introducing an additional parameter xi for the anion/cation volume ratio, besides the ionic compressibility gamma in the KKBA MFT. The MFT of asymmetric ions becomes KKBA MFT upon xi = 1, and further reduces to Gouy-Chapman theory in the gamma -> 0 limit. The result of the extended MFT demonstrates that the asymmetric ILs give rise to an asymmetric C-d, with the higher peak in C-d occurring at positive polarization for the smaller anionic size. At high potential, C-d decays asymptotically toward KKBA MFT characterized by gamma for the negative polarization, and characterized by xi gamma for the positive polarization, with inverse-square-root behavior. At low potential, around the potential of zero charge, the asymmetric ions cause a higher C-d, which exceeds that of Gouy-Chapman theory.