Nernst Diffusion Layer

Nernst Diffusion Layer

Nernst Diffusion Layer

One of the most simple and useful ways of understanding the time dependent effects of current flow through an electrode is the concept of the diffusion layer introduced by Nernst in 1904. When an

electrode is polarized, the surface concentration of the species that is either being oxidized or reduced falls to zero. Additional material will then diffuse to the electrode surface towards this region of lower concentration. If the electrolysis experiment is carried out in an agitated solution, i.e. the solution is in motion with respect to the electrode or vice versa, then the resulting concentration-distance profile at the electrode surface can be represented as shown here.

In this diagram the electrode is represented by the blue bar on the left hand side of the picture. The x-axis is a scalar axis and represents distance away from the electrode. The point of origin (x = 0) represents the surface of the electrode. The y-axis represents concentration. The maximum concentration is represented by CO which is its concentration in the bulk solution.

If we look closely at the diagram we notice two regions of concentration. Because the solution is well mixed, in the bulk region the concentration is constant with respect to distance. This is represented by the horizontal line where C = CO (this is known as the convective region). There is then a region where the concentration drops, falling to zero at the electrode surface. The Nernst diffusion layer associated with this drop has thickness ?. The exact thickness of the Nernst diffusion layer depends upon the nature of the solution into which it extends. For stirred aqueous solutions the thickness of the diffusion layer can be between 0.01 and 0.001 mm. An important assumption of this model is that when material reaches the surface of the electrode it is instantaneously oxidized or reduced thereby maintaining a zero

concentration at the electrode surface. In practice, this is easy to achieve by selecting a suitable polarizing voltage. In summary, what the Nernst diffusion layer theory tells us is: *

There is a stationary thin layer of solution in contact with the electrode surface which has a thickness equal to ?. *

Nernst Diffusion Layer

Within this layer, diffusion alone controls the ionic transfer to the electrode. This occurs down a concentration gradient. *

Outside this layer, diffusion is negligible and the concentration of the considered species is maintained at a value of CO by convective transfer.

If we look at the concentration gradient in the diffusion layer, we note that it is both linear and constant. We can represent the concentration gradient mathematically as:

Because the concentration of chemical species considered at the electrode surface is zero, this equation can be simplified to give:

By considering the flux J to the electrode surface, we can define the limiting current iL for the stirred solution as:

When the chemical species being reacted at a surface participates in the conducting current through migration a generic form of the layer has to be used. When only one cation is involved in plating, for example, the limiting current at the cathode could be written as follows for the specific plating of nickel ions in Watts solution rich in conducting ions:

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