Diffusion controlled reaction, transient effects

Fig. 7.42. A potentiostatic transient. The current (A-B) ascends almost vertically after being switched on, because all of it goes to charge the double layer. In B-C, the current is increasingly used in the form of electrons crossing the double layer. After C the current should decline slowly as diffusion control sets in. In reality, at solid polycrystalline electrodes, in reactions involving adsorbed intermediates, there is often some further variation of /, owing to, e.g., surface crystalline rearrangements and the effect of impurities from the solution.

Polymers are not homogeneous in a microscopic scale and a number of perturbed states for a dye molecule are expected. As a matter of fact, non-exponential decay of luminescence in polymer systems is a common phenomenon. For some reaction processes (e.g, excimer and exciplex formation), one tries to fit the decay curve to sums of two or three exponential terms, since this kind of functional form is predicted by kinetic models. Here one has to worry about the uniqueness of the fit and the reliability of the parameters. Other processes can not be analyzed in this way. Examples include transient effects in diffusion-controlled processes, energy transfer in rigid matrices, and processes which occur in a distribution of different environments, each with its own characteristic rate. This third example is quite common when solvent relaxation about polar excited states occurs on the same time scale as emission from those states. Careful measurement of time-resolved fluorescence spectra is an approach to this problem. These problems and many others are treated in detail in recent books (9,11), including various aspects of data analysis. 

If the partial pressure on both sides is not maintained constant, the differences in P02 level out (we switch off the gas flows in Fig. 7.2). We designate this as chemical depolarization. Its transient behaviom permits calculation of chemical diflhision coefficients or effective rate constemts of the surface reaction. Similarly and k can be obtained from the transient of the chemical polarization (i.e. one-sided steplike change in the partial pressure of o g gen starting from the homogeneous initial situation). Figure 7.11 shows the stoichiometry profiles for a diffusion-controlled chemical polarization. These profiles are obtainable via Yi dc/dx. and c(x,t) by solution of the second Fick s law with the initial condition c(x,0) = Ci and the boundary conditions c(0,t) = C2 and c(L,t) = ci = c(x,0) (see e.g. [431]). 

Most reactions on surfaces are complicated by variations in mass transfer and adsorption equilibrium [70], It is precisely these complexities, however, that afford an additional means of control in electrochemical or photoelectrochemical transformations. Not only does the surface assemble a nonstatistical distribution of reagents compared with the solution composition, but it also generally influences both the rates and course of chemical reactions [71-73]. These effects are particularly evident with photoactivated surfaces the intrinsic lifetimes of both excited states and photogenerated transients and the rates of bimolecular diffusion are particularly sensitive to the special environment afforded by a solid surface. Consequently, the understanding of surface effects is very important for applications that depend on chemical selectivity in photoelectrochemical transformation. 

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