Diffusion current, charged molecule

Here the first term is the usual diffusive current, with Dc being the usual cooperative diffusion constant of the polymer molecule. The second term is a convective current due to the presence of induced electric field arising from all charged species in the system, p is the electrophoretic mobility of the polymer molecule derived in the preceding section. From the Poisson equation, we obtain... 

Difficulties arise when turning to homogeneous reactions. Neither substrates nor catalysts sit still but diffuse freely in solution, making it impossible with current microscopy techniques to follow their fate for more than few milliseconds. Moreover, fast diffusion of the molecules significantly reduces the fluorescence intensity that can be detected in one pixel of a charge-coupled... 

As the field of electrochemical kinetics may be relatively unfamiliar to some readers, it is important to realize that the rate of an electrochemical process is the current. In transient techniques such as cyclic and pulse voltammetry, the current typically consists of a nonfaradaic component derived from capacitive charging of the ionic medium near the electrode and a faradaic component that corresponds to electron transfer between the electrode and the reactant. In a steady-state technique such as rotating-disk voltammetry the current is purely faradaic. The faradaic current is often limited by the rate of diffusion of the reactant to the electrode, but it is also possible that electron transfer between the electrode and the molecules at the surface is the slow step. In this latter case one can define the rate constant as ... 

In the case in which the electroactive species O is adsorbed on the electrode, ixI/2 increases with increasing i (Fig. 4.4D). The Sand equation considers only those molecules of O that have reached the surface by diffusion. As x decreases, the charge contribution to the reduction of Oads consumes an increasingly large fraction of the total current, causing ixI/2 to increase. A typical example of this behavior is the reduction of Alizarin Red S at mercury [7],... 

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