Solution of the Debye-Hückel Equations for a Polarized Electrode

Abstract

The Debye‐Hückel equations are solved for the case of a polarized electrode, yielding, for the mean ionic concentration at a distance x from a plane cathode immersed into an aqueous solution of a uni‐univalent electrolyte of concentration aN₀ molecules/cm³, $$n_1{\mathrm{=aN}}_0\hspace{0.17em}{\mathrm{cotanh}}^2\text{Kx/2,}$$ 1/K being the Debye length. The mean local charge density and the mean local potential are calculated, and it is shown that the latter quantity is merely the thermodynamical potential resulting from the increased activity of the cations near the electrode, the system behaving as a concentration cell.