A Poisson–Boltzmann description for the double-layer capacitance of an electrolytic cell

A Poisson–Boltzmann approach is used to determine the double-layer integral and differential capacitances in a finite-length situation for an electrolytic cell. By means of simple analytical calculations, it is shown how these quantities exhibit the bell-like and the camel-like shapes as a function of the applied voltage, when the thickness of the sample or the surface charge is varied. The problem is formulated in such a way that an applied voltage dependent Debyeʼs screening length arises as a fundamental length governing the electrical behavior of the system.