Surface-neighbor effects

Because surface curvature depends on radius and different atoms have different sizes, and because the atomic surface tension depends on atomic number, the atomic surface tensions also include surface curvature effects, which has recently been studied as a separate effect.7 Local surface curvature may also correlate with nearest-neighbor proximity and thus may be implicitly included to some extent when semiempirical atomic surface tensions depend on interatomic distances in the solute. 

The existence of multiple peaks for molecular desorption has been attributed to lateral interactions among adsorbed species 62-64). As discussed previously, adsorption onto the surface lattice may occur preferentially in next nearest neighbor sites to form p(2 x 2) structures. Even at low coverages, attractive forces may cause adatoms to occupy next nearest neighbor positions, so that clusters of adsorbate form which have local twofold periodicity 65) with respect to the surface. Such effects are entirely consistent with the perturbations of the surface electronic wave functions due to adsorption 66-68) which show that these binding sites represent the... 

On a Pt(lll) single-crystal surface the effect of the potential on the band position has been evaluated for different coverages [143]. No linear dependence is found for any surface coverage, not even for the singleton frequency. This shows that on Pt(lll) a correction of higher order is necessary and, in this case, the effect is not induced by the presence of neighboring ions alone. 

The removal of an O atom or ion from the MgO surface results in a large relaxation of the lattice. For a neutral Fs center there is an outward displacement of the Mg " ions and an inward movement of the second neighbor O ions by 1-2% with respect to the unrelaxed surface. The effect is much more pronounced for charged vacancies, and changes of 5% and 10% in the Mg-0 distances around the cavity are found for Fs and Fj centers, respectively [39]. In the F or F centers one or two electrons are associated with the defect. The extra electron(s) can either be delocalized over the 3s levels of the Mg " ions around the cavity, with partial reduction of these ions and a change of their charged state from Mg to Mg, or can be localized in the vacancy center. 

The quadratic in (j)s form is preserved with gj - originating now mainly due to the difference in surface-polymer contact energies and g - entirely specified by missing neighbor effect. Both coefficients appearing in the linear form of the surface energy derivative (-dfs/d( ))s=p1+g( )s maybe expressed as [177]... 

In transition metals, for instance, a marked loss of spherical symmetry in the electron density associated with d orbitals appears for atoms located on the surface. The effect is different depending on the face under consideration, because it is related to population differences in the various orbitals. A calculation made by the Hlickel method on very small Ni clusters, in which the neighbors of the central atom are arranged according to the environment of an atom of the (111), (100), (110) surface, and taking into account the s... 

Milner (61) addressed the energetics of polymer brushes. In this case neighboring polymer chains need to avoid one another. This volume exclusion effect provides the driving force for the chains to extend out into the solution. However, the problem is also different from the one chain bonding two particles, above, because one end of the chain is free. Milner also included a correction term for surface tension effects. He concluded that excess energies in the range of 8 to 10 kT were reasonable for many brush conformations. 

Density profiles in the wetting phase (liquid near a strongly attractive surface) and in the drying phase (vapor near a weakly attractive surface) are not affected by the surface transitions. These profiles reflect the competition between the missing neighbor effect and the fluid-wall interaction and may be described in the framework of the theory of the surface critical behavior (see Section 3). In particular, a gradual density adsorption or a density depletion decays exponentially toward the bulk... 

The location of the inflection points of the interfacial-like density profiles of a liquid water is indicated by asterisks in Fig. 30. The thickness L of a drying layer is about 5.2 A at T = 500 K and about 7.8 A at T = 525 K. When a very weak attractive potential with Uq = —0.39 kcal/mol is applied, inflection point can still be detected and L shrinks from 7.8 to 6.6 A at r = 525 K. At T = 500 K, inflection point at the density profile is not seen and liquid density decays exponentially toward the surface. In this case, the drying layer is absent, and the liquid density depletion is determined solely by the missing neighbor effect (see Section 3 for more details). 

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