Solution of the Debye-Hückel Equations for a Polarized Electrode

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, n1=aN0 cotanh2Kx/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.