Charged colloidal particles, diffusion coefficients

Let us consider the electrode kinetics associated with charge transfer from an n-type semiconductor particle to an electrode. As indicated by Albery et al. [164], the crucial difference between the electrochemistry of a colloidal particle and an ordinary electrochemically active solution phase species is the number of electrons transferred from the particle to the electrode may be large and will depend upon the potential of the electrode. Fig. 9.5 shows the model for an encounter of a particle with an electrode used by Albery and co-workers. kD is the mass-transfer coefficient for the transport of the particles to the electrode surface. In the simplest case, wherein it is assumed that the lifetime of the transferable electrons (majority carriers of thermal or photonic origin) is greater than the time taken by a particle to traverse the ORDE diffusion layer, this is given by... 

At the point of zero charge, there is no repulsive electrical force on the particles and so the full adhesion between the grains is developed. If this adhesion is strong, then each Brownian collision between singlet particles will produce a doublet. This was the case considered by Smoluchowski in 1917 and extended by Fuchs in 1934. The theory was based on the idea that colloidal particles behave like molecules which can react to form abimolecular compound. Thus the rate of appearance of doublets dAf /df is proportional to the square of singlet concentration N per unit volume by the law of mass action, and is limited by the Brownian diffusion coefficient to give... 

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