Non-Linear First-Harmonic Impedance in Ion-Exchange Membrane Systems under Potentiostatic Control in the Limiting Current Regime

The harmonic response of ion-exchange membrane systems under potentiostatic control in the limiting current regime is studied. The transport of an electroneutral binary electrolyte through a cation-exchange membrane and the two diffusion boundary layers adjacent to the membrane is described by means of a Nernst-Planck analysis. The full system is perturbed with a sine voltage of a single frequency superimposed on a direct voltage, and it is obtained the decomposition in a Fourier series of the resulting electric current using the network simulation method. The effect of the different parameters characterizing the perturbing voltage (amplitude, frequency and dc component) on the second harmonic of the resulting current, and their influence on the first-harmonic impedance in a highly biased ion-exchange membrane system, are analyzed and discussed. The behavior of the resistance associated to the first harmonic impedance at the limit of zero frequency has been particularly analyzed and an analytical expression to roughly estimate its dependence on the voltage amplitude has been derived. Auxiliary methods for linearity assessment such as Kramers-Kronig transforms, Lissajous plots and waveforms are also discussed.