The application of the transform of Kramers-Kronig for computing the polarization resistance

摘要

Some general considerations on the use of the Kramers-Kronig transform for computing the real andimaginary parts of the electrode impedance Z(ω) are given and the relationship between R{sub}pand Z{sub}r(0) is established by considering a simple electric network. Experimental applicationsconcern the behaviour of iron in 5 wt% HCl solutions, containing a specific inhibitor for thisenvironment with concentration values ranging from 0.1 to 3.0 g/kg, at temperatures of 65, 75, 80and 90℃. Electrode impedance determinations were performed over the [0.08, 2× l0{sup}4] Hzfrequency interval under current control. The values of R{sub}s were usually determined byprocessing experimental data belonging to the [0.08, 2×l0{sup}4 Hz frequency interval. The valuesof R{sub}p, based on the use of the first Kramers-Kronig relation between Z{sub}r (ω) and Z{sub}i(ω), were computed using the D01GAF subroutine of the NAG library. The accuracy of thisprocedure was verified by comparing the experimental and computed values of Z{sub}r (ω).Comparison of the two sets of values of Z{sub}r (ω) confirmed that the use of the Kramers-Kronigtransform was pertinent to analyse experimental data because the reproduction of all examinedexperimental data was rather faithful over the [0.08, 2× 10{sup}4 Hz frequency interval. At last, thefirst Kramers-Kronig relation provide a valid mathematical tool to compute the correct magnitudeorder of R{sub}p as a function of inhibitor concentration.