Gurney potential

GURjj, the so-called Gurney potential (Gurney, 1953), which... 

Removal of the inconsistency in the manner Ninham, Bostrom and co-workers have described in a series of papers goes part of the way to a resolution, but only at the level of the primitive model. More is involved once the molecular nature of the solvent is taken into account. Ionic polarisability is combined at the same level with electrostatics to determine local induced water structure around ions. That is a key determinant of hydration, and of so-called ion specific Gurney potentials of interactions between ions due to the overlap of these solute-induced solvent profiles so too for ionic adsorption at interfaces. The notions involved here embrace quantitatively the conventional ideas of cosmotropic, chaotropic, hard and soft ions. Some insights into this matter can be obtained via the alternative approach of computer simulation techniques of Jungwirth etal. But the insights are hamstrung so far by a pragmatic restriction that limits... 

In a recent upsurge of studies on electron transfer kinetics, importance was placed on the outer shell solvent continuum, and the solvent was replaced by an effective model potential or a continuum medium with an effective dielectric constant. Studies in which the electronic and molecular structure of the solvent molecules are explicitly considered are still very rare. No further modem quantum mechanical studies were made to advance the original molecular and quantum mechanical approach of Gurney on electron and proton (ion) transfer reactions at an electrode. 

There is no doubt that this field, like few others, owes very much to its founder, Ronald Gurney, because of the fast start he gave it by applying quantum mechanics to interfacial electron transfers shortly after the publication of Schrodinger s wave equation (1926). The early seminal contributions (to which must be added that of J. A. V. Butler in the same period)22 founded quantum electrochemistry and led to its broader development by Gcrischer (1960), in particular the idea of the absolute scale of potentials and the equation... 

In the Gurney-Mott mechanism, the trapped electron exerts a coulombic attraction for the interstitial silver ion. This attraction would be limited to a short distance by the high dielectric constant of the silver bromide. Slifkin (1) estimated that the electrostatic potential of a unit point charge in silver bromide falls to within the thermal noise level at a distance of "some 15 interatomic spacings." The maximum charge on the sulfide nucleus would be 1 e. The charge on a positive kink or jog site after capture of an electron would not exceed e/2. An AgJ would have to diffuse to within the attraction range before coulombic forces could become a factor. 

If the difference in energy level between a free ion and one bound to the surface of the metal is Y, and the difference in level between a free ion and a hydrated one is W, then the difference in energy level between the hydrated ion, and the ion at the surface of the metal is W—Y. The energy level of the ions in solution depends, however, on the concentration of these ions this produces the well-known effect of concentration on electromotive force. Gurney gives9 the strength of the double layer, i.e. the difference in electrostatic potential set up between metal a and electrolyte s, as... 

This controversy was reviewed by Langmuir in the paper cited above, and Gurney s account in Chapter XVI of his book is illuminating. It is clear, however, that there is no real difficulty the contact potential between the dry metals is often the principal term in the sum of phase boundary potentials which make up the e.m.f. of the cell. 

Readers of Gurney s paper in 1931 have sometimes considered, from the frequent appearance of the thermionic work function in this paper, that the values of over-potential should, on the theory that the block lies at (9), depend on g. This does not appear to be justified although electrons have to be extracted from the metal, they do also in a reversible electrode, and in either case the x 8 cancel out, as described at the end of 4, through a second contact potential elsewhere in the circuit. A glance at the figures for overpotential on p. 324 shows no correlation with x> from Table XVI. 1 Z. phyrikal. Chem., 113, 213 (1924). 

Figure 9. Illustration of how change in Fermi energy (Ep) acts on the energy barrier. E = potential energy C = Nuclear configuration p1 = density of filled metallic states in metal electrode. (A). Gurney s model8 with initial (I) and final (F) states at the same potential. (B). Non-Franck-Condon transfer in equilibrium. (C). Non-Franck-Condon transfer out of equilibrium.

Since electrochemical surface reactions involve electron transfer to or from the surface, a quantum mechanical approach becomes necessary to account for electron tunneling in such processes. Quantum mechanical treatments of electron transfer and adsorption have been reviewed recently (67-77). The Gurney treatment (68, 72, 73) assumes the transfer of an electron at the Fermi level of the metal to an H3O at its ground state at the outer Helmholtz plane. The electrode potential changes the minimum vibrational energy of the bond necessary to induce tunneling. Levich (67) has... 

Figure 1. Potential energy profile diagrams for a charge transfer process as in ion discharge with coupled atom transfer (based on representations by Gurney and Butler L In (b), curve / represents the H /H20 proton interaction potential and m that for discharged H with the metal M. R is the repulsive interaction of H with H2O and A the resultant interaction curve for H with M.

In the original treatment of Gurney/ the current was expressed as the integral of the product of electrolyte and electron energy distribution functions but with the electronic one written as a Boltzmann factor, exp( A /fcT). The symmetry factor was introduced intuitively in terms of the shift of intersection point of energy profiles in relation to change of electrode potential, i.e., of the Fermi-level energy (cf. Butler ). 

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