Barrier height, tunneling, determination separation

The significant variation of the barrier height observed for immersed junctions reflects the experimental difficulties associated with determining the tunneling constant, k. Two key issues are contamination of the junction and uncertainty as to the structural and electronic character of the tip [104], Recent data clearly reveal a dependence of the apparent barrier height on tip-substrate separation [7,92-94,104]. Specifically, the effective barrier is observed to diminish for resistance values below <10 Q as shown in Fig. 

From the above discussion, it is clear that various kinetic criteria (reaction orders, Tafel slopes, and log/-AGads plots on different electrode materials, where appropriate) can be used to determine the reaction mechanism and the coverage conditions. For reactions involving protons, the separation factors (H-T or H-D) can also be used as another criterion, since the barrier heights vary characteristically with mechanism because of the relatively large zero point energy difference between the isotopes and their different quantum mechanical tunneling properties. This is evaluated in Refs. 50 and 51, and may be used to confirm other evidence. 

The various energy levels of the system exhibit a tunnel splitting and the energy eigenfunctions split into two separate manifolds with even and odd symmetry. The height of the barrier determines the energy difference between the lowest even and odd symmetry. This so-called tunnel splitting can be expressed as a tunnel frequency Uf... 

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