Electrostatic image forces

AHa for the Adsorption of Alkali Metals. If an alkali metal atom is located at an infinite distance from a metal surface at zero potential, then the heat of adsorption comprises the work done in (1) transferring an electron from the atom to the metal, and (2) bringing the positive ion to its equiUbrium distance from the metal surface (127). In the first step, the energy change is (e0 — el), where is the work function of the metal and I is the ionization potential of the alkali metal atom. In the second, the force of attraction on the positive ion at a distance d from the metal surface, i.e., the electrostatic image force, is e /4d hence, the heat Uberated is e /4do, where do is the equilibrium distance of the adsorbed ion from the metal surface. This distance is often assumed to be equal to the ionic radius, which is 1.83 A. for the Na ion. The initial heat of adsorption, therefore, is... 

The summation in Equation 4.1 is carried out over aU components. UsnaUy an equimolecular dividing surface with respect to the solvent is introduced for which the adsorption of the solvent is set zero by definition [4,5]. Then the snmmation is carried ont over aU other components. Note that F, is an excess surface concentration with respect to the bulk F is positive for surfactants, which decreases o in accordance with Equation 4.1. On the contrary, F is negative for aqneous solutions of electrolytes, whose ions are repelled from the surface by the electrostatic image forces [5] consequently, the addition of electrolytes increases the surface tension of water [6]. For surfactant concentrations above the critical micellization concentration (CMC) = constant and, consequently, a = constant (see Equation 4.1). 

The concept of just outside must be defined more closely. When the test charge is moved from the point of reference toward the surface, work is performed due to the (primary) electrostatic field being discussed. However, very close to the surface, image forces start to act on the test charge they give rise to an additional... 

It follows from Eq. (9.2) that the work function has a chemical and an electrostatic component. Its overall value can be measured, whereas an exact determination of its individual components is not possible. The chemical component depends on the interaction between the charge and the surrounding medium moreover, it includes the work performed in overcoming the image forces. 

The dielectric displacement must be calculated from electrostatics for a reactant in front of a metal surface the image force has to be considered. For the simple case of a spherical ion in front of a metal electrode experiencing the full image interaction, a straightforward calculation gives ... 

Two additional electrostatic forces, the space charge effect and the image force, are also present. As shown by Shapiro et al. [54], their effect can, however, be neglected when q and the dust concentration are sufficiently small. 

A rapid survey of some of the more recent publications seems to point to DNA indeed being a very broad-gap semiconductor or insulator for lengths exceeding a few hundred base pairs. This conclusion was reached in references [74] and [75] on the basis of electrostatic imaging, in reference [77] using conducting atomic force microscopy on A-DNA, in [78] using 300-nm DNA strands both of poly(GG) and of A-DNA, and in [52] for A-DNA supported on mica. 

The outer potential ip is an electrostatic potential at the closest distance ( lx 10 3mm) to the surface that a charged particle can approach without being affected by any image force from the condensed phase. 

The upper sign corresponds to a water-dielectric , and the lower one to a water-conductor type of interface. Equation (7) shows that a charge located next to a conductor will be attracted by its own image, and dielectrics in aqueous solutions will repel it. For a review of statistical-mechanical models of the double layer near a single interface we refer to [7], and here we would like only to illustrate how the image forces will alter the ion concentration and the electrostatic potential distribution next to a single wall. At a low electrolyte concentration the self-image forces will mostly dominate, and the ion-surface interaction will only be affected by the polarization due... 

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