“…The self-energy due to image charge repulsion appears in the Boltzmann factor and is responsible for the depletion layer in the ion distribution near the surface, as shown in Figure 5. Note, however, in the original WOS theory as well as in subsequent treatments, 14,26,27,37,38 the image charge term was added to the Boltzmann factor ad hoc based on physical intuition, whereas in our theory, its appearance is the result of systematic derivation. Therefore, our theory not only recovers the WOS theory (upon making additional approximations, e.g., by using the constant bulk screening length for the image force potential) but also provides the means for systematically improving the WOS theory.…”