Potential-Current Relation under Transport Control

Potential-Current Relation under Transport Control 

We have considered above the Butler-Volmer equation for the relationship between current density and potential under the situation when transport of ions in solution makes little or no difference to the rate of an electrode reaction. In order to considered the situation in which transport does control the flow we shall adopt a correspondingly simple counterassumption electron transfer at the interface no longer has control of the electrode reaction. 

The overpotential caused by electron transfer is assumed to be limitingly low. Under these conditions, the relationship between potential and current density is given by considering it to consist of the shift in the equilibrium potential due to a change in the concentration of reactants in solution away from that at equilibrium to that caused by the holdup in transport control. 

The fact that the situation is not quite like this in reality is not very important at the moment in order for us to get a basic relationship. Further on in the chapter we shall state, without deduction, the full relationship which takes into account both transport control and activation control. 

Thinking now of the simplification to which we have just referred, we 

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Potential-Current Relation under Transport Control... 

We also require that the theory explain the observed dependence of current on potential under various circumstances. In Chapter 1, we saw that current is often limited wholly or partially by the rate at which the electroreactants are transported to the electrode surface. This kind of limitation does not concern a theory of interfacial kinetics. More to the point is the case of low current and efficient stirring, in which mass transport is not a factor determining the current. Instead, it is controlled by interfacial dynamics. Early studies of such systems showed that the current is often related exponentially to the overpotential 7], That is. 

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