Electrical response of an electrolytic cell submitted to a small direct current electric field when the electrodes are ohmic

We theoretically investigate the influence of the ohmic character of the electrodes on the direct current (dc) response and on the ionic relaxation time of an electrolytic cell, in the shape of a slab. The analysis is performed by assuming that the fundamental equations of the problem can be linearized. This implies that, for monovalent ions, the applied difference of potential is smaller than 25 mV. We show that the finite ohmic conductivity of the electrodes is responsible for a reduction of the relaxation time. An explicit expression for the relaxation time, valid when the Debye length is very small with respect to the thickness of the sample is deduced. The analysis of the dc current allows us to determine the contribution of the electrodes to the effective electrical resistance. We show also that the equivalent circuit relevant to the present problem cannot be used to evaluate the relaxation time of the cell. (c) 2007 American Institute of Physics.