A new generalized membrane polarization frequency-domain impedance formula

Abstract

A frequency-domain membrane polarization impedance formula was suggested previously by Marshall and Madden for a sequence of ion selective and non-selective regions of equal cross-sections. We generalized the formula for the case of non-equal cross-sections and small Debye lengths (common case). This formula is a simplification of a general analysis of the impedance, given by Buchheim and Irmer, which is tedious for computations and does not give physical insight into the process. The obtained results are physically consistent for the effect of the different cross-sections on the limiting resistance at high frequencies. It is, also, consistent in behaviour with the chargeability formula given by Titov. The impedance model considering regions of non-equal cross-sections may be useful for modeling complex impedance of partially and fully water-saturated rocks. Our study also gives, in detail, the essential equations not given in Buchheim and Irmer derivation, while the lengthy intermediation steps are omitted. Some typing errors in the equations of the previous derivation are rectified. Our approach and formula for the impedance is more rigourous than the formula given by Bücker and Hördt.