Some considerations on the polarization resistance method

A new mathematical approach aimed at giving light on the polarization resistance method is developed and its basic ideas are discussed to establish a suitable criterion to be used to compute the left bound Δ E 1 and the right bound Δ E 2 of the Δ E interval where the linear approximation works properly with reference to a prefixed degree of accuracy. Examination of the results relating to the theoretical cases, characterized by the Tafel slope values (40, 120) and (80, 100) mV, stresses that the width L( ε) of the interval, where the linear approximation can be considered valid for a given value of ε, depends on B a and B c, their values determining the position of the inflection point Δ E i of i(Δ E) where G(Δ E)=∣( αe αΔ E + βe − βΔ E )/( α+ β)−1∣ exhibits a maximum. The maximum per cent value of the relative error μ, that is less than 10, for ε values ranging from 1 to 15 indicates that it is reasonable to replace i′(0) with the incremental ratio computed at Δ E 1 or Δ E 2. Furthermore, the Newton method was always successful in determining the values of Δ E 1 and Δ E 2. Applications to experimental polarization data refer to the behaviour of iron in 1 N H 2SO 4 solutions containing KCl at various concentrations. All the experimental polarization curves of the current transient type were best-fitted with a polynomial of the fourth degree over the [−50, 50] mV interval to determine the analytical expression of G(Δ E). The good agreement of the values of R p, R pa and R pc, which are computed at Δ E 2 and Δ E 1 respectively for the case ε=10, underlines the validity of the present approach in providing accurate information on the resistance to corrosion of iron.