Thomas-Fermi layer

Figure 4.1 Model of the electrochemical double layer on a metal electrode. TF Thomas-Fermi layer, iH layer of specific adsorption (inner Helmholtz layer), H Helmholtz layer (outer Helmholtz layer), and GC Gouy-Chapman layer.

The calculations were subsequently extended to moderate surface charges and electrolyte concentrations.8 The compact-layer capacitance, in this approach, clearly depends on the nature of the solvent, the nature of the metal electrode, and the interaction between solvent and metal. The work8,109 describing the electrodesolvent system with the use of nonlocal dielectric functions e(x, x ) is reviewed and discussed by Vorotyntsev, Kornyshev, and coworkers.6,77 With several assumptions for e(x,x ), related to the Thomas-Fermi model, an explicit expression6 for the compact-layer capacitance could be derived ... 

As early as 1928, Rice [29] attempted to estimate the contribution of the metal to the interfacial capacity within the framework of the Thomas-Fermi theory. However, he obtained a positive contribution of the metal to the capacity, which was practically the same for all metals. Only some 50 years later, Komyshev and coworkers [30] showed that Thomas-Fermi-like models are unsuitable for double-layer theory because they do not give a realistic description of the work functions and the surface potentials of metals. 

One of the earliest treatments of a metal surface was based upon a jellium model (Bardeen, 19.36). If the electron gas terminated abruptly at the surface of the jellium there would be no net potential to contain the electrons in the metal. Therefore the electron gas extends beyond the metal, giving a dipole layer, as illustrated in Fig. 17-5. Bardeen attempted the self-consistent calculation of the resulting potential. It should be mentioned that the Fermi-Thomas approximation is not adequate for this task and was not used by Bardeen it is not difficult to see that it would predict the Fermi energy to be at the vacuum level, corresponding to a vanishing work function. 

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