Differential capacitance of uniformly charged hard-sphere ions in planar electric double layers

Abstract

The theoretical model, which is based both on the modified fundamental-measure theory for the hard-sphere contribution and on the mean-spherical approximation for the cross correlation between the hard-sphere contribution and Coulomb interaction, has been developed to study the differential capacitance of uniformly charged hard-sphere ions. The charge distribution of ions, electronic valence, bulk concentration and ion size are affected on the differential capacitance and the camel-to-bell shape transition. The charge distribution of ions enhances the differential capacitance and tends to delay the camel-to-bell shape transition. The low bulk concentration predicts higher differential capacitance. The transition from a camel-shaped to bell-shaped curve occurs when the bulk concentration rises to an appropriate value. The camel-to-bell shape transition occurs at a large ion size with increasing the bulk concentration. The high electrical valence tends to delay the transition and raise the transition concentration. The increase of electronic valence shifts the maximum to the low surface charge density. The decrease of , after passing through the maximum , results from the packing effect due to the formation of counterion layers.