Gurney’s model

Figure 15. Distribution of density of states as a function of energy (Gurney s model).86 Eq and Eq are the neutralization energy of H+ - H2O and Cl- - H2O, in its ground level, respectively.

Bockris and his colleagues essentially followed Gurney s model for the hydrogen evolution reaction, but they included the interaction between the electrode and hydrogen. They usually used y = 1 at > 0 and neglected the distribution at < as... 

Nisbet, R.M. and W.S.C. Gurney. 1982. Modeling Fluctuating Populations. John Wiley Sons, Chichester, U.K., pp. 1-3. 

Gurney s Quantum Mechanical Model of Proton Transfer... 

Unfortunately, at that time Gurney s work did not influence the development of electrochemistry to the fullest extent. This is due, on the one hand, to the imperfection of his model, and on the other, to some erroneous concepts. These errors actually do not follow from the physical principles involved but they naturally cast a shadow of doubt over the entire theory. Here we mean such conclusions like a direct effect of the electron work function on the rate of electrode reaction or a disregard of the hydrogen adsorption energy. 

This dilemma led us to investigate the feasibility of a nonlinear extrapolation for the evaluation of E°. For the sake of brevity, we will not reproduce here the detailed mathematical derivations of Gronwall, LaMer, and Sandved s extended terms of the Debye-Hlickel theory. One can find these derivations in their original paper (4) or in Hamed and Owens classic monograph. For a description of the basic assumptions and the physical model of the interionic attraction theory one should consult Hamed and Owens monograph as well as the work of Gurney (8,9). 

Carlson, R. W., Pearson, D. G., Boyd, F. R., Shirey, S. B., Irvine, G., Menzies, A. H. Gurney, J. J. 1999. Regional age variation of the southern African mantle significance for models of lithospheric mantle formation. In Gurney, J. J., Gurney, J. L., Pascoe, M. D. Richardson, S. H. (eds) Proceedings of the 7 th International Kimberlite Conference, Cape Town. Red Roof Design, Cape Town, 99-108. 

In the present author s view, the Gaussian distribution function based on the solvent fluctuation model, which is developed for a simple redox couple, is used too often even when the basic assumption is not valid. For example, this type of distribution function is often drawn for the hydrogen evolution reaction where the oxidized state is H+ and reduced state is H2.105 Certainly the nature of the solvation is completely different between H+ and H2. Moreover, when one considers the kinetics of the hydrogen evolution reaction, one should consider not the energy level of H+/H2 but that of H+/H(a) as Gurney did. 

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