# 1.7: Diffusion Limited Corrosion

$$\newcommand{\vecs}{\overset { \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$

So far all reactions have been assumed to proceed (if they are thermodynamically possible) at the rate predicted by the Tafel analysis. In reality, reactions are often limited by other factors and don’t achieve this maximum rate. One such factor is the availability of oxygen in solution.

In aqueous solutions that contain dissolved oxygen, an important cathodic reaction is the oxygen reduction reaction:

O2 + 4 H+ + 4 e- → 2 H2O

The reaction takes place at the surface of the metal and so oxygen must be present at that site. If the reaction occurs quickly enough, the concentration of oxygen at the surface cannot be maintained at the same level as that in the bulk of the solution. In this case the rate of oxygen diffusion may become a limiting factor. With less oxygen available, the cathodic reaction slows down and so must the anodic reaction to conserve electrons (electrons can only be used up at the same rate as they are released as charge must always be conserved).

Fick’s first law* can be used to find the maximum rate of oxygen diffusion. Since each oxygen molecule consumes 4 electrons, according to the reaction above, this maximum rate of diffusion corresponds to a maximum current density that the oxygen reduction reaction can sustain and, hence, a maximum corrosion rate for the anode (since electrons must be used at the cathode at the same rate as they are released at the anode).

Since the corrosion current is limited, the cathodic arm of the Tafel plot is flattened:

Oxygen reduction is not the only process that deviates from the Tafel analysis. The hydrogen evolution reaction can be limited by the rate at which molecules desorb from the cathode surface. This is usually the rate-determining factor for hydrogen evolution on iron, copper, platinum and other metals. Relatively few metals behave as predicted by the Tafel analysis, examples being cadmium, mercury and lead.