Charge density inhomogeneity

The coordinate dependence of n,. s resulting from the charge-density inhomogeneity of one-carrier SCL current flow is assumed here to be negligible. 

However, the direct gaps are not substantially improved. As seen from Table XVI, the Improved description of charge density Inhomogeneity and that of electron screening both appear to play equally important roles. 

Since the positive background is in the form of ions, it is not really a continuous density profile depending only on the coordinate perpendicular to the interface. The electron density, though always smoother than the positive charge density, is likewise more complicated than a one-dimensional profile. However, it is rare to see calculations for the electron density which take into account inhomogeneities in the parallel directions, except when adsorbed atoms are being considered. 

The interfacial layer is the inhomogeneous space region intermediate between two bulk phases in contact, and where properties are notably different from, but related to, the properties of the bulk phases (see Figure 6.1). Some of these properties are composition, molecular density, orientation or conformation, charge density, pressure tensor, and electron density [2], The interfacial properties change in the direction normal to the surface (see Figure 6.1). Complex profiles of interfacial properties take place in the case of multicomponent systems with coexisting bulk phases where attractive/repulsive molecular interactions involve adsorption or depletion of one or several components. 

In essence, dispersion forces arise from the correlation between dynamic charge density fluctuations in two different systems or in distant parts of one system. The difficulty [228] in describing vdW forces in the static LDA or gradient approaches is therefore not surprising since in a highly inhomogeneous system (exemplified by, but not limited to, a pair of separated subsystems) these correlations may be quite different from those in the uniform or near-uniform electron gas upon which the LDA and the various gradient approximations are bas. ... 

Rose and Benjamin [194, 187] studied the adsorption of Na+ and CF on the Pt(lOO) surface and concluded that the structure of the solvation complex around Na and Cl is very similar to the structure in the bulk . In this study, the same model for the water-metal interactions was used as in the preceding study of Li+ and F hydration [189]. The ion-surface interactions, however, were described by a modified image charge potential which was smoothly truncated. The authors discussed in some detail the anisotropy of the hydration complex that is induced by the density inhomogeneities at the interface. In a study of Fe + and Fe + hydration [197],... 

The metal surface probably acquires an electrochemical inhomogeneity, i.e. energy discontinuity [38], on contact with condensed moisture inhibited by Tet. The initial acts of Tet adsorption take place on active centers with maximum positive charge density. These centers are concentrated on anodic areas of the Fe surface, where Fe(II) ions are generated. Subsequently, two processes take place simultaneously on the sample surface ... 

Comparison of (20) and (21) shows that at large separations, the force T decays as jd, irrespective of the charge density created on the particle surface by the PE brush. In the case of a sparse PE brush with fairly uniform distribution of counterions within the layer of thickness = A, the crossover to logarithmic force decay occurs smoothly at d = A. By contrast, in the case of the osmotic brush with strongly inhomogenous distribution of counterions (most of them trapped inside the brush), the repulsive force T sharply increases at d = H(°o), i.e., when the coronas of colloidal PE brushes approach close contact. 

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