Langmuir adsorption processes and ion transport under bias potential in capacitive deionisation cells

The electric response of a capacitive deionisation cell submitted to a periodic external electric field is investigated. The case in which the applied potential has a nonzero average value on one period (polarised cell) is considered. The theoretical analysis of the experimental data, relevant to nearly symmetric electrodes, is done in the framework of the Poisson-Nernst-Planck model. The current densities on the electrodes are described by kinetic equations related to the adsorption phenomenon in the presence of a bias potential. We propose a new form for the Langmuir isotherm in which the effective adsorption coefficients depend on the bias potential according to the Boltzmann statistics. This kinetic equation extends the Butler-Volmer equation for non-blocking electrodes also to the blocking ones. The equation proposed here is such that for dc external voltage the total current across the electrodes vanishes.