= Debye–Hückel approximation
{c}
{title2=$(\nabla^2-\kappa_D^2)\phi=-\rho_{\rm fixed}/\varepsilon$}
The Debye–Hückel approximation linearizes mobile-ion Boltzmann densities about a neutral bulk electrolyte. It is valid for ionic potential energies small compared with $k_BT$. The inverse <Debye–Hückel screening length> satisfies $\kappa_D^2=\sum_i n_i z_i^2e^2/(\varepsilon k_BT)$. The quadratic screened charging free energy includes both <electric field> energy and the linearized ionic-response term $\varepsilon\kappa_D^2\phi^2/2$.
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