 Debye–Hückel approximation

The Debye–Hückel approximation linearizes mobile-ion Boltzmann densities about a neutral bulk electrolyte. It is valid for ionic potential energies small compared with $k_{B}T$. The inverse Debye–Hückel screening length satisfies ${\kappa }_D^2={\sum }_i{n}_i{z}_i^2{e}^2/(\epsilon k_{B}T)$. The quadratic screened charging free energy includes both electric field energy and the linearized ionic-response term $\epsilon {\kappa }_D^2{\varphi }^2/2$.