That is, the z-dependent chemical potential for dilute ions is determined by the energetics of the charge interacting with the screened electrode. Note that the difference between Poisson-Boltzmann and Gouy-Chapman theory (dashed and solid black lines in Fig. ) reveal that the linear approximation utilized to get from Eq. 15 to Eq. 16 is not valid for the parameters of this system (e.g., applied potential and electrolyte concentration). The agreement between Ψ GC and φ thus reveals that the effective strength of ion-potential interactions are small compared to k B T . Apparently, the polarization of interfacial water molecules, and their excluded volume, lead to a much lower effective potential for the electrolyte species. It is also worth mentioning that in order to generate this Poisson potential profile it is necessary to input a value of ϵ int ≈ 5. We comment further on the subtleties of capturing water's dielectric properties later in this subsection.