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When the cathodic reagent at the corroding surface is in short supply, the mass transport of this reagent could become rate controlling. A frequent case of this type of control occurs when the cathodic processes depend on the reduction of dissolved oxygen. Because the rate of the cathodic reaction is proportional to the surface concentration of the reagent, the reaction rate will be limited by a drop in the surface concentration. For a sufficiently fast charge transfer (small activation overvoltage), the surface concentration will fall to zero and the corrosion process will be totally controlled by mass transport. For purely diffusion controlled mass transport, the flux of a species O to a surface from the bulk is described with Fick's first law: (reference)
Where: JO is the flux of species O (mol s-1 cm-2), DO the diffusion coefficient of species O (cm2 s-1) and dCO/dx the concentration gradient of species O across the interface (mol cm-4)
The diffusion coefficient of an ionic species at infinite dilution can be estimated with the help of Nernst-Einstein relating DO with the conductivity of the species (lO):
Where: zO is the valency of species O , R the gas constant, i.e. 8.314 J mol-1 K-1, T the absolute temperature (K), and F the Faraday's constant, i.e. 96485 C mol(e-)-1
The region near the metallic surface where the concentration gradient occurs is also called Nernst diffusion layer (d). Since the concentration gradient is greatest when the surface concentration of species O is completely depleted at the surface, i.e. CO = 0, it follows that the cathodic current is limited in that condition, as expressed by the following equation.
For intermediate cases, hconc can be evaluated using an expression derived from the Nernst equation.
where 2.303·R·T/F = 0.059 V when T = 298.16 K
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