AC-IMPEDANCE OF THE BIPOLAR MEMBRANE AT LOW AND HIGH-FREQUENCIES

The bipolar membrane or double fixed charge membrane (DFCM) consists o f a central depletion layer of low conductivity surrounded by outer re gions of high conductivity. The Nemst-Plank-Poisson equations for alte rnating currents are solved for each region separately with appropriat e approximations. The two solutions are melded to give the solution fo r the membrane as a whole. The results are presented as the frequency dependence of the relevant capacitance and conductance. At the low and high frequency limits these parameters become independent of frequenc y, with a monotonic dispersion at intermediate frequencies in agreemen t with observation. The dispersion is interpreted in terms of the alte rnating electric field which is confined to the depletion layer at low frequency but is almost uniform through the entire membrane at high f requency. The dispersions are similar to those of a two element Maxwel l-Wagner system, but the elements required for the latter may not be i dentified with the separate regions of the DFCM.