Jump-Between-Wells method

So far we only considered transport of particles by diffusion. As mentioned in 1 the continuous description was not strictly necessary, because diffusion can be described as jumps between cells and therefore incorporated in the multivariate master equation. Now consider particles that move freely and should therefore be described by their velocity v as well as by their position r. The cells A are six-dimensional cells in the one-particle phase space. As long as no reaction occurs v is constant but r changes continuously. As a result the probability distribution varies in a way which cannot be described as a succession of jumps but only in terms of a differential operator. Hence the continuous description is indispensable, but the method of compounding moments can again be used. 

In the studies of induced transport it is customary to differentiate between two mechanisms - mobile carriers and channels[14]. The theory of mobile carriers was advanced comparatively recently[13,14], but is already well-established. But the task that remains is to measure the rate of the different stages of transport for different carriers. The most promising results seem likely to come from different variants of the relaxation methods - the temperature jump and potential jump methods[15]. 

Before proceeding to such types of analysis and computations in the sections that follow, we begin with a statement of the full problem with as much of the physics represented as possible. Our approach is to work with macroscopic models of the interface separating the fluid phases. This approach represents the interface by a sharp dynamic surface embedded in three-dimensional space, across which flow and concentration variables can jump in a manner specified by physical boundary conditions. The alternative microscopic approach seeks to describe the three-dimensional thin transition layer between the two phases using statistical or continuum mechanical methods. The reader is referred to Chapters 15-18 of the text by Edwards, Brenner and Wasan as well as the many references therein. 

The difference between the regular flow methods (2) and the solvent-jump method is manifested in experimental procedures and in the evaluation of the data as well. 

The depassivated area during one cycle, Aa, can hardly be assessed. Some authors assume in first instance that it is equal to the apparent area of the sliding track. However, it is well known that the contact takes place only on a fraction of that area. An evaluation of the depassivated area from currents resulting from an electrochemical depassivation achieved by a potential jump was proposed (Garcia et al., 2001). This method also allowed them to evaluate the oxide thickness formed in between two successive depassivation events. They obtained oxide layer thicknesses in the range of a few nanometers. 

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