Surface potential

Surface potential

The relation between surface charge and surface potential can be expressed by the Grahame equation, derived from the Gouy-Chapman theory by assuming the electroneutrality condition, which states that the total charge of the double layer must be equal to the negative of the surface charge. Using the one-dimensional Poisson equation and assuming that, at an infinitely great distance, the potential gradient is equal to 0, the Grahame equation is obtained: $${\displaystyle \sigma ={\sqrt {8c_{0}\varepsilon \varepsilon _{0}k_{\mathrm {B} }N_{A}T}}\sinh \left({\frac {ze\psi _{0}}{2k_{\mathrm {B} }T}}\right)}$$ where ${\displaystyle c_{0}}$ is the bulk concentration of the electrolyte, ${\displaystyle N_{A}}$Avogadro's constant, and T the absolute temperature.