Evidence of the ambipolar diffusion in the impedance spectroscopy of an electrolytic cell

We argue that the impedance spectroscopy of an electrolytic cell in the low-frequency range can give information on the ambipolar diffusion. Our analysis is based on a theoretical investigation of the real part of the electrical impedance of an electrolytic cell. When the mobility of the positive ions differs from that of the negative ions, a second plateau of the resistance of the cell, in series representation, is expected close to the dc limit of the applied voltage. The effective diffusion coefficient, related to the measured resistance of the cell, in the dc limit, coincides with the ambipolar diffusion coefficient. The associated relaxation time corresponds to the ambipolar diffusion, and it is proportional to the square of the thickness of the sample. In the high-frequency range, the relaxation time coincides with the Debye relaxation time, connected to the free diffusion coefficient, and it is independent of the thickness of the sample. Finally, we propose a method to calculate the diffusion coefficients of the individual ions from the impedance spectrum and we discuss the implications of ambipolar diffusion in impedance measurements and interpretation of experimental quantities.