ON THE APPLICATION OF THE KRAMERS-KRONIG RELATIONS TO EVALUATE THE CONSISTENCY OF ELECTROCHEMICAL IMPEDANCE DATA

The use of the Kramers-Kronig (KK) relations to evaluate the consistency of impedance data has been limited by the fact that the experimental frequency domain is necessarily finite. Current algorithms do not distinguish between the residual errors caused by a frequency domain that is too narrow and discrepancies caused by a system which does not satisfy the constraints of the KK equations. A new technique is presented which circumvents the limitation of applying the KK relations to impedance data which truncate in the capacitive region. The proposed algorithm calculates impedance values below the lowest experimental frequency which "force" the data set to satisfy the KK equations. Internally consistent data sets yield low-frequency impedance values which are continuous at the lowest measured experimental frequency. A discontinuity between the calculated low-frequency values and the experimental data indicates inconsistency which cannot be attributed to the finite experimental frequency domain.