Nanoparticles compared to microelectrodes

The particular behavior of a single miaoelectrode or an ensemble of millions of microelectrodes is discussed in Section 14.3. Since a nanoparticle is the ultimate case of an ultramicroelectrode, it is appropriate to discuss some of the properties of nanoparticles employing the equations developed for microelectrodes, in order to calculate the increased rate of diffusion towards an isolated nanoparticle and the corresponding decrease in solution resistance. 

For a single nanoparticle, assumed to be spherical, the limiting current is given by 

The solution resistance (cf Eq. (3.8) and Section 14.3) for the same nanopartide is given by 

To be exact, one should point out that the above calculation is only approximate. Thus, microelectrodes are usually made as fiat discs of the desired metal, embedded in an insulator and polished to be flush with the surface. Nanopartides, on the other hand, are usually prepared separately and attached to the surface, so their interface with the electrolyte may be in the form of a hemisphere. In any case neither are really spherical. However, the calculation above is given to show orders of magnitude of the 

This looks like an ideal situation for conducting electrochemical measurements at current densities far below the limiting current density, with an insignificant error caused by mass-transport limitation or by the potential drop across the solution resistance but there is a problem. The surface area of a nanosphere of 5 nm radius is about 3 X 10 cm. Hence at 0.1 A cm , the total current is only 3 x 10 A This is measurable, but not useful for any device. In order to build a power source (e.g. a battery or a fuel cell) one would have to pack huge numbers of nanopartides per xmit geometrical surface area. On the other hand, when the nanopartides are packed dose together, mass transport by diffusion is reduced to the value found for planar electrodes, since the diffusion fields of all the particles completely overlap each other. The same applies to the solution resistance, which increases to values characteristic of planar electrodes. 

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