Weak adsorption limit

The weak adsorption limit (X/b 1) has been studied less extensively. The only... 

In the weak-adsorption limit < 1 and < 1, the adsorbate local density of states poo consists only of a continuous part and behaves as a Lorentx function ... 

The line width of the resonance-broadened adsorbate level is proportional to the square of the overlap energy and varies inversely as the bandwidth of the surface valence electron levels. The general form of the LDOS in the weak-adsorption limit... 

Figure 2.42. Bond-order overlap population density between adatom and endatom, one-dimensional chain (schematic), a weak adsorption limit b surface molecule limit.

It is of interest to discuss the poles (the values E for which Goo becomes infinite) in two limits, the ideal weak adsorption limit and the quasi-surface molecule limit. The solutions for both limits are sketched in Fig.(2.48). The explicit expressions for A and r are given in the caption of Fig.(2.48). In the weak adsorption limit, the width of undisturbed surface LDOS Pw E T = a) is larger than or + — oro ... 

Figure 2.48. Ideal weak adsorption limit (a) and quasi surface molecule limit (b) solutions (schematic).

Ek]uations (2.245) which we derived within the weak adsorption limit are useful to illustrate more explicitly the consequences of image potential charges for the chemical bond strength. 

The importance of q.(2.320) is that it indicates that local electrostatic terms play a role in the adsorption energies of adsorbates. An example will be given in the next section. In the weak adsorption limit, q.(2.245) for the chemisorptive bond energy has to be replaced by Eq.(2.321) if surface dipole layer effects and electrostatic consequences of differences in particle size have to be discussed. 

In the weak adsorption limit p -C 1 (Fig. 3.29a), there is a small broadening of the electron density at the atoms. The broadening 2Fe equals... 

In the weak adsorption limit, the interaction energy is proportional to the metal local electronic density of states at the Fermi level [p E)f] -... 

A schematic illustration that summarizes the essential electronic structure features that determine chemisorption was proposed by Hoffmann l and is reproduced here in Fig. 3.35. In the weak adsorption limit interactions (1) and (2) represent the attractive HOMO-LUMO interactions described in Section 3.3. Interaction (3) between the doubly occupied... 

In the weak adsorption limit, we provide an exact analytical solution for polyelectrolyte-sphere adsorption by replacing the Debye-Huckel potential by the Hulthen potential. Other geometries require different approaches. As a generic concept, we propose application of the WKB method of quanmm mechanics, which we adopted to electrostatic polyelectrolyte adsorption problems. We have demonstrate that this description provides valuable analytical solutions and resolves a long-standing puzzle about the scaling properties of critical polyelectrolyte adsorption in curved geometries. 

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