Imaging force

Wliether the potentials are derived from quantum mechanical calculations or classical image forces, it is quite generally found that there is a stronger barrier to the adsorption of cations at the surface than anions, in agreement with that generally. ... 

NakatsujI H, Nakal H and Fukunishi Y 1991 Dipped adcluster model for chemisorptions and catalytic reactions on a metal surface Image force correction and applications to Pd-02 adclusters J. Chem. Phys. 95 640-7 NakatsujI H and Nakal H 1992 Dipped adcluster model study for the end-on chemisorption of O2 on an Ag surface Can. J. Chem. 70 404-8... 

Figure 44.20 represents a typical process-roll configuration. The arrows indicate the force vectors generated by the wire, belt, or product wrap around these rolls. The left roll has a force vector at 45° down to the left the right roll has a mirror image force vector and the bottom roll has a vertical vector. 

Carnie and Chan and Blum and Henderson have calculated the capacitance for an idealized model of an electrified interface using the mean spherical approximation (MSA). The interface is considered to consist of a solution of charged hard spheres in a solvent of hard spheres with embedded point dipoles, while the electrode is considered to be a uniformly charged hard wall whose dielectric constant is equal to that of the electrolyte (so that image forces need not be considered). 

As previously noted the work function O is the work required to bring an electron from the Fermi level of the metal to a point outside the metal where the image forces are negligible, i.e., typically 1 to 0.1 pm outside the metal surface.9,10,16 22 The Volta potential at this point is defined so that the energy required to bring an electron from that point to an "infinite" distance from the metal surface is e. ... 

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 inner electrical potential 0 may consist of two components. Firstly, the phase may possess some excess electrical charge supplied from outside. This charge produces an outer electrical potential 0. This is defined as the limit of the ratio w/q for <7—>0, where w is the work expended for the infinitely slow transfer of charge q from an infinite distance to a point in the vacuum adjacent to the surface of the given phase and just outside the range of image forces. A particle transferred from this point further on in the... 

In addition to the nonelectrostatic adsorptive force, there is an image force between a dipole and a metal, which will be present whenever charged or dipolar particles in a medium of one dielectric constant are near a region of another dielectric constant. If the metal is treated as an ideal conductor, the image-force contribution to the energy of a dipole in the electrolyte is proportional to p2j z3, where z is the distance of the dipole from the plane boundary of the metal (considered ideal, with no surface structure), and to 1 + cos2 0. This ideal term is, of course, the same for all metals. If... 

The interface is, from a general point of view, an inhomogeneous dielectric medium. The effects of a dielectric permittivity, which need not be local and which varies in space, on the distribution of charged particles (ions of the electrolyte), were analyzed and discussed briefly by Vorotyntsev.78 Simple models for the system include, in addition to the image-force interaction, a potential representing interaction of ions with the metal electrons. 

For neutral dipolar molecules, the value of B depends on the dipole moment itself, and the value of y is 3/2 or, in the presence of image forces, 5/2. The former of these has been verified experimentally for the adsorption of such molecules as 2-chloropyridine on mercury. 

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 ... 

If image force effects are taken into account (Marcus version ),... 

Similar derivations apply for the electrochemical case when taking the image force effect into account. More precisely, in the expression of the potential at the surface of the A sphere, the contribution of the electrical image of A (which bears an opposite charge and which center is located at a distance d, from the center of A) has to be taken into account. 

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