Size Effects on Half-Wave Potentials

13 Size Effects on Half-Wave Potentials Problem 

For an electrochemically irreversible reduction at a microdisc or microsphere electrode of radius fg, the variation of the voltammetric half-wave potential, 1/2, under steady-state conditions can be shown to vary as 

Explain physically why the peak shifts with the particle radius and estimate a value of a. If the substrate were covered with a monolayer of the silver nanoparticles, explain qualitatively what would be seen. 

The peak shifts with the particle radius such that a greater overpotential is required for transport-limited reduction as the particle shrinks in size. This is because the convergent/divergent regime of mass transport to and from the particle becomes more effective and dominates as the particle shrinks. Accordingly, a greater potential has to be applied to attain the peak current, as faster electrode kinetics are 

To find a value of a, plot a graph of pf vs logjg fNP- A straight line is seen with a slope of 

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