Estimation of Some Parameters in the Point Defect Model (PDM) for the Passivity of Metals

In this paper, we justify that the potential drop at the barrier layer/solution (bl/s) interface of the barrier layer of the passive film on a metal, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>φ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>/</mml:mo> <mml:mi>s</mml:mi> </mml:mrow> </mml:msub> <mml:mo>,</mml:mo> </mml:math> is a linear function of the applied voltage V and pH in the case of sufficiently thin barrier layer. Furthermore, we show that a relationship exists between parameters α (the dependence of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>φ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>/</mml:mo> <mml:mi>s</mml:mi> </mml:mrow> </mml:msub> </mml:math> on V ) and β (the dependence of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>φ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>/</mml:mo> <mml:mi>s</mml:mi> </mml:mrow> </mml:msub> </mml:math> on pH), that is, those parameters are not independent, in the general case. It is also shown that some dependence of parameters α and β on temperature can exist. However, this dependence in the practical region (0 °C–100 °C) is weak and, in many cases, it is possible to neglect the dependence of parameters α and β on temperature. Finally, we show that it is possible to estimate, theoretically, the parameter β (and accordingly parameter α ) by using models for specific systems. For the system considered in the current report (carbon steel in concrete pore water), the estimated value of parameter β is confirmed experimentally. These findings are discussed in terms of the electronic and point defect structures of the barrier layer.