Sodium binding energy

Zhang, J. Ha, T.-K. Knochenmuss, R. Zenobi, R. Theoretical calculation of gas-phase sodium binding energies of common MALDI matrices. J. Phys. Chem. A 2002,106, 6610-6617. 

ESCA was employed to analyze membranes before and after use in the desalination cell. Wide scan ESCA spectra were obtained on the last two membranes listed in Table VII. Table IX lists the binding energies (B.E.) and the atomic fractions (A.F.) for the membranes studied. In addition to the expected carbon, oxygen, sodium, and sulfur peaks, two small peaks were attributed to nitrogen and silicon, which may be due to the contamination in the air (silicon grease). A smaller photo peak was observed at 51.3 eV and remains unasslgned. Overall, there is no significant surface contamination of the membranes. 

Nitrogen Is binding energies have been determined by AT-ray p.e. spectroscopy for [Rh(CO)2(N3)]2, together with some other metal azides. The similarity of their spectra to that of sodium azide suggests that the internal bonding of N3 is little affected by co-ordination i.e. the Rh—N3 bond is essentially ionic. 

We can understand the behaviour of the binding energy curves of monovalent sodium and other polyvalent metals by considering the metallic bond as arising from the immersion of an ionic lattice of empty core pseudopotentials into a free-electron gas as illustrated schematically in Fig. 5.15. We have seen that the pseudopotentials will only perturb the free-electron gas weakly so that, as a first approximation, we may assume that the free-electron gas remains uniformly distributed throughout the metal. Thus, the total binding energy per atom may be written as... 

Fig. 5.14 The binding energy U as a function of the Wigner-Seitz radius fiws for sodium. The bottom of the conduction band, 1 is given by the lower curve to which is added the average kinetic energy per electron (the shaded region). (After Wigner and Seitz (1933).)...

We see that eqn (5.63) mirrors the behaviour found in Fig. 5.14 for sodium by Wigner and Seitz. At metallic densities the bottom of the conduction band is well described by the first contribution in eqn (5.63). As the atoms are brought together, the bonding state becomes more bonding until eventually the repulsive core contribution dominates, and the bottom of the conduction band rises rapidly. From eqn (5.63) the maximum binding energy of this state occurs for... 

Table 6.3 Contributions to the binding energy (in Ry per atom) of sodium, magnesium, and aluminium within the second order real-space representation, eqn (6.73), using Ashcroft empty-core pseudopotentials. L/gf is defined by eqn (6.75). The numbers in brackets correspond to the simple expression, eqn (6.77), for = 0) and to the experimental values of the binding energy and negative cohesive energy respectively.

Sodium-24 (23.990 96 u) decays to magnesium-24 (23.985 04 u). Determine (a) the change in the binding energy per nucleon (b) the change in energy that accompanies the decay. 

Experimental Born-Haber cycle for sodium chloride. The experimental binding energy AH = —8.0 eVis reasonably close to the Madelung energy Em= -8.923446 eV (after one adds to Em a relatively small ad hoc positive rep). 

Recent experiments by Citrin and coworkers (41) have clarified the role of the support in photoemission from small metal clusters. They condensed several monolayers of krypton onto either platinum or sodium metal substrates. By varying the thickness of the krypton from one to ten monolayers, the surface could be converted from metal to semimetal to insulator. The krypton peak position provides a direct measure of the sample vacuum level (32). The krypton layers are thin, less than 10 monolayers, so that the vacuum level is determined by the metal substrate. Onto the krypton layers, sodium clusters were deposited at varying coverages. Shifts in the Kr 4s and Na 2p binding energies were recorded relative to the Fermi level of the grounded substrate. 

The results obtained by Citrin and coworkers are shown in Figure 3. For sodium clusters on a metal support (wigl ML Kr/Pt, filled circles), the Kr 4s binding energy decreases with cluster coverage. This shows that the Fermi levels of the sodium and platinum equilibrate. As the sodium is added, the work function decreases from the value for platinum to the value for a sodium film. Conversely, the Na 2p peak position does not shift with cluster coverage. The rapid electron transfer between the sodium and platinum prevents any accumulation of charge on the cluster in the photoemission final state (41). 

Figure 3. The dependence of the Kr 4s and Na 2p binding energies on the coverage of sodium, the thickness of krypton, and the substrate. (Reproduced with permission from Ref. 41. Copyright 1987 The American Physical Society.)...

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