Gurney condition

Gurney found out a condition whereby nonradiative tunneling would occur. If there is to be no radiation, it is clear that the electron must arrive in the same energy state on the other side of the barrier (in a cathodic reaction this would be inside a molecule in solution), perhaps an H3 0 ion, which is then transformed to a hydrogen atom by accepting the tunneled electron. The Gurney condition of radiationless tunnel transition is... 

In solution, the collisional interactions cause a blurring of the vibration-rotational states so that there is a semicontinuum of these states. This fact, together with the absence of a selection rule, causes the fulfillment of the Gurney condition at any energy, whereas the Bohr condition applies only for the situation where the transition moment is nonzero. The smooth relation between current density and overpotential, known as Tafel s law, " (in contrast to the peaked nature of the intensity-energy situation in spectroscopic phenomena) arises, therefore, from a combination of the absence of selection rules in the electrochemical case, and the presence in solution of a semicontinuum of acceptor and emitter states. 

The conditions of the experiment discussed here are different than the restrictions imposed to obtain the Mott-Gurney equation. However, at least qualitatively, Equation 8.38 can describe the space charge-limited current effect. To test this hypothesis, Equation 8.38 was experimentally tested, and it was shown that it is approximately satisfied (see Figures 8.13 and 8.14) [112]. 

To obtain comparable data, the experimental conditions have to be defined precisely. Especially the Gurney constant... 

Gurney s idea was that the tunneUng was possible only when this condition (28) is satisfied. 

However, the chemical model may be employed if the solvent spheres surrounding the dissolved ions can be differentiated from the bulk of the solution, although the stoichiometric conditions are unknown. Such are the models of Frank [Fr 45, Fr 57] and Gurney [Gu 62]. These theories have proved successful for the description of the experimentally measurable properties of solutions in only a few cases nevertheless, they have the merit of having inspired much experimental work. 

The conditions of the charge detonation in metal cylinders, i.e., warheads, are well described by Eq. (5.39). From this equation, it can be seen that the wall velocity during expansion depends on the ratio between the masses of the cylinder and the explosive. The quantity yj2Ef, is called the Gurney constant. 

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