Theoretical description of quantum yields

To gain a theoretical insight into the factors that govern the activity of a metal-oxide photocatalyst, a very simple mechanism of the initial steps of a surface photochemical process is considered. It corresponds to the general mechanism of photoexcitation of the solid specimen (reactions 5.114-5.117) (see Figs. 5.12 and 5.23). 

Application of the steady-state condition to the concentration of snrface-active centres (eq. 5.118) and carriers (eqs. 5.119 and 5.120) gives a reaction rate that can be represented by reaction 5.121 for the snrface reaction involving the snbstrate. 

The latter implies that under the above conditions the qnantnm yield depends on k, the concentration of surface-active centres [S], and the snrface concentration of charge carriers, ns (A is the fraction of light absorbed, i.e. absorptance, and p is the photon flow). It is therefore possible to query those factors that govern the snrface concentration of charge carriers, and the activity of the photocatalyst through the quantum yield (f . For this, the functionality of the surface charge-carrier concentration and the parameters that affect it need to be examined. 

The surface concentration of free charge carriers can be determined from the solution to the continuity equation, eq. 5.124, under the steady-state approximation and with suitable boundary conditions, such as Js= s % (Emeline et al., 2003), 

Surface recombination processes are similar to those in the bulk. However, surface defects such as corners, edges, terraces, dislocations and new near-surface structures) can lead to a greater rate of carrier recombination on the surface compared with the bulk, causing a decrease of the concentration n(x) of carriers in the near-surface space in the solid. The decrease in n(x) leads to diffusion of carriers / from the bulk to the surface, as given by eq. 5.125. 

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