Ambipolar diffusion in the low frequency impedance response of electrolytic cells

The electrical response of an electrolytic cell to an external ac excitation is analysed by solving the equations of the Poisson-Nernst-Planck (PNP) continuum model for two ions (ambipolar) and one mobile ion diffusive systems. The theoretical predictions of the ambipolar system, formed by positive ions of mobility μ p and negative ions of mobility μ m, are investigated in the limit in which one of the mobilities goes to zero. The analysis reveals that these predictions correspond to the ones arising from the one mobile ion diffusive system only in the frequency range ω ≫ ω D μ m/μ p, in which ω D is the Debye's frequency. For very low frequencies, it shows that the physical system formed by two mobile ions, one of which has a very low mobility, is clearly distinct from the physical system in which just one of the ions is mobile. We argue that apparent deviations of the experimental spectra from the predictions of the PNP model in the low frequency region, usually interpreted as an interfacial property, may be connected with the difference in the diffusion coefficients of cations and anions.