Jellium

Figure 2. Sketch of an uncharged metal surface (simulated by the jellium model) covered by a macroscopic solvent layer, showing the components of the electric potential drop. 8%M is the surface potential of the metal modified by the solvent layer %s + 6%s is the surface potential of the solvent modified by the contact with the metal %s is the unmodified surface potential of the solvent layer at the external surface.

Schmidder and Henderson282 have studied several solvents and metals, using the jellium model for the metal and the MSA for the solution. Deviations of the Parsons-Zobel plot from linearity in the experimental results72,286-288 at the highest concentration have been attributed to the onset of ion-specific adsorption. However, data at other electrode charges... 

According to Vitanov et a/.,61,151 C,- varies in the order Ag(100) < Ag(lll), i.e., in the reverse order with respect to that of Valette and Hamelin.24 63 67 150 383-390 The order of electrolytically grown planes clashes with the results of quantum-chemical calculations,436 439 as well as with the results of the jellium/hard sphere model for the metal/electro-lyte interface.428 429 435 A comparison of C, values for quasi-perfect Ag planes with the data of real Ag planes shows that for quasi-perfect Ag planes, the values of Cf 0 are remarkably higher than those for real Ag planes. A definite difference between real and quasi-perfect Ag electrodes may be the higher number of defects expected for a real Ag crystal. 15 32 i25 401407 10-416-422 since the defects seem to be the sites of stronger adsorption, one would expect that quasi-perfect surfaces would have a smaller surface activity toward H20 molecules and so lower Cf"0 values. The influence of the surface defects on H20 adsorption at Ag from a gas phase has been demonstrated by Klaua and Madey.445... 

The C, values for Sb faces are noticeably lower than those for Bi. Just as for Bi, the closest-packed faces show the lowest values of C, [except Bi(lll) and Sb(lll)].28,152,153 This result is in good agreement with the theory428,429 based on the jellium model for the metal and the simple hard sphere model for the electrolyte solution. The adsorption of organic compounds at Sb and Bi single-crystal face electrodes28,152,726 shows that the surface activity of Bi(lll) and Sb(lll) is lower than for the other planes. Thus the anomalous position of Sb(lll) as well as Bi(lll) is probably caused by a more pronounced influence of the capacitance of the metal phase compared with other Sb and Bi faces28... 

Figure 5.7. Schematic representation of the definitions of work function O, chemical potential of electrons i, electrochemical potential of electrons or Fermi level p = EF, surface potential %, Galvani (or inner) potential

The hypothetical metal jellium consists of an ordered array of positively charged metal ions surrounded by a structureless sea of electrons that behaves as a free electron gas (Fig. 6.13). 

Figure 6.13. The electron distribution in the model metal jellium gives rise to an electric double layer at the surface, which forms the origin of the surface contribution to the work function. The electron wave function reaches...

Figure 6.26. Density functional calculations show the change in the density of states induced by adsorption of Cl, Si and Li on jellium. Lithium charges positively and chlorine negatively. [From N.D. Lang and A.R. Williams,...

Figure 6.27. Charge density contours for the adsorption of Cl, Si, and Li on jellium. (a) Total charge and (b) induced charge solid lines indicate an increase in electron density, dashed...

When an atom with a filled level at energy approaches a metal surface it will first of all chemisorb due to the interaction with the sp electrons of the metal. Consider for example an oxygen atom. The 2p level contains four electrons when the atom is isolated, but as it approaches the metal the 2p levels broaden and shift down in energy through the interaction with the sp band of the metal. Fig. 6.28(a) and (b) show this for adsorption on jellium, the ideal free-electron metal. 

In this contribution we will deal with electron-electron correlation in solids and how to learn about these by means of inelastic X-ray scattering both in the regime of small and large momentum transfer. We will compare the predictions of simple models (free electron gas, jellium model) and more sophisticated ones (calculations using the self-energy influenced spectral weight function) to experimental results. In a last step, lattice effects will be included in the theoretical treatment. 

A simple metal like lithium or aluminum should best reveal the properties of the jellium model. To be sure, all long range order influence has been switched off, we measured S(q, co) of liquid A1 (T = 1000K). Figure 6 shows the result of a measurement for q = 1.5 a.u. together with theoretical calculations. 

Figure 11 shows the influence of correlation and lattice effects on the shape of n (k) for the case of lithium. The short dashed line shows (k) according to the jellium model with no electron-electron interaction included. Inclusion of correlation effects can be described using a model-w(k) ... 

The picture of the compact double layer is further complicated by the fact that the assumption that the electrons in the metal are present in a constant concentration which discontinuously decreases to zero at the interface in the direction towards the solution is too gross a simplification. Indeed, Kornyshev, Schmickler, and Vorotyntsev have pointed out that it is necessary to assume that the electron distribution in the metal and its surroundings can be represented by what is called a jellium the positive metal ions represent a fixed layer of positive charges, while the electron plasma spills over the interface into the compact layer, giving rise to a surface dipole. This surface dipole, together with the dipoles of the solvent molecules, produces the total capacity value of the compact double layer. 

Schmickler, W., A jellium-dipole model for the double layer, J. Electroanal. Chem., 150, 19 (1983). 

Data taken in another mass range also showed the inertness of AlJ7. While it was not produced by reaction of larger clusters, of which there are few, it was, however, found to be unreactive over a wide oxygen concentration range. In general, our results support the electron droplet Jellium model, although some anomalies (for... 

With respect to the thermodynamic stability of metal clusters, there is a plethora of results which support the spherical Jellium model for the alkalis as well as for other metals, like copper. This appears to be the case for cluster reactivity, at least for etching reactions, where electronic structure dominates reactivity and minor anomalies are attributable to geometric influence. These cases, however, illustrate a situation where significant addition or diminution of valence electron density occurs via loss or gain of metal atoms. A small molecule, like carbon monoxide,... 

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