Propagation distance interface

Figure 18. (A) Propagation distance for a Cu-vacuum interface as a function of...

A discussion of the charge transfer reaction on the polymer-modified electrode should consider not only the interaction of the mediator with the electrode and a solution species (as with chemically modified electrodes), but also the transport processes across the film. Let us assume that a solution species S reacts with the mediator Red/Ox couple as depicted in Fig. 5.32. Besides the simple charge transfer reaction with the mediator at the interface film/solution, we have also to include diffusion of species S in the polymer film (the diffusion coefficient DSp, which is usually much lower than in solution), and also charge propagation via immobilized redox centres in the film. This can formally be described by a diffusion coefficient Dp which is dependent on the concentration of the redox sites and their mutual distance (cf. Eq. (2.6.33). 

If the rate is controlled by diffusive mass transfer (Figure 1-1 lb) and if other conditions are kept constant, then (i) the growth (or dissolution) distance is proportional to the square root of time, referred to as the parabolic growth law (an application of the famous square root law for diffusion), (ii) the concentration in the melt is not uniform, (iii) the concentration profile propagates into the melt according to square root of time, and (iv) the interface concentration is near saturation. For the rate to be controlled by diffusion in the fluid, it cannot be stirred. 

In order to propagate the electromagnetic wave along the interface, or to reflect it totally to the optically denser medium, there must be a zero net flux of energy across the interface. However, there is a finite decaying electric field across the interface that extends some distance z into the rarer medium. The amplitude of this evanescent... 

Attenuated total reflection FTIR is a well-established technique for obtaining absorbance spectra of opaque samples. The mode of interaction is unique because the probing radiation is propagated in a high index-of-refraction internal reflection element (IRE). The radiation interacts with the material of interest, which is in close contact with the IRE, forming an interface across which a nonpropagating evanescent field penetrates the surface of the material of interest to a depth in the order of one wavelength of the radiation. The electric field at the interface penetrates the rarer medium in the form of an evanescent field whose amplitude decays exponentially with distance into the rarer medium. 

---