Dipole fields

Differentiating once with respect to electric field, with respect to dipole field. 

Calculates dipole-field interaction and the corresponding energy spent on I polarizing the solvent. 

Conversely, an atom in Fig. 6.23 with an affinity level that initially is empty becomes partly occupied upon adsorption. Hence, charge is transferred from the metal to the atom. This sets up a dipole that increases the surface contribution to the work function. This is the case for adsorbed halides, which will be negatively charged at the surface. We will later see that such dipole fields can explain promotion and inhibition effects caused by various adsorbates in catalysis. 

Figure 8.29. Schematic effect of, for example, potassium deposited on a surface. The potassium sets up a dipole field which may interact with that of adsorbed species and molecules in transition states, resulting in lower or increased activation barriers. With...

The dependence on the electrical field can be approximated either analytically, e.g., with a dipole field interaction, or by simulations including an external field. In either case, the electric field would give rise to a correction term, AG (G), to be added to Equation (3.3). As will also be discussed later, this correction will in most cases be small. 

A substantial number of electrons are elastically scattered, and this gives rise to a strong elastic peak in the spectrum. When an electron of low energy (2-5 eY) approaches a surface, it can be scattered inelastically by two basic mechanisms, and the data obtained are dependent upon the experimental geometry - specifically the angles of the incident and the (analysed) scattered beams with respect to the surface (0 and 02 in Figure 5.47). Within a certain distance of the surface the incident electron can interact with the dipole field associated a particular surface vibration, e.g. either the vibrations of the surface atoms of the substrate itself, or one or other... 

The method of Thole was developed with the help of the induced dipole formulation, when all dipoles interact through the dipole field tensor. The modification introduced by Thole consisted in changing the dipole field tensor ... 

This simple derivation omits the angular dependence of the field which varies as the cosine of the angle between the dipole axis (the moment vector) and the distance expressed as a vector, r. Therefore, the field is a maximum along the axis of the dipole. Equation 3.18 makes the point that the dipole field decreases rapidly with distance. The units here are electrostatic (CGS) for simplicity. 

For polarizable charge distributions, additional classical-type interactions arise from the induced dipole, quadrupole, and higher moments on each monomer, which are proportional to the fields created by the asymmetric charge distribution on the other monomer. The proportionality constants for each multipole field are the monomer polarizabilities aa and ah (a111 for dipole fields, a(Q) for quadrupole fields, etc.). The leading two induction interactions are ... 

Figure 5. Model spectra of a naked neutron star. The emitted spectrum with electron-phonon damping accounted for and Tsurf = 106 K. Left panel uniform surface temperature right panel meridional temperature variation. The dashed line is the blackbody at Tsurf and the dash-dotted line the blackbody which best-fits the calculated spectrum in the 0.1-2 keV range. The two models shown in each panel are computed for a dipole field Bp = 5 x 1013 G (upper solid curve) and Bp = 3 x 1013 G (lower solid curve). The spectra are at the star surface and no red-shift correction has been applied. From Turolla, Zane and Drake (2004).

Furthermore, as mentioned above the screening of the dipole field by the conduction electrons can be represented by an image dipole inside the metal. This complex of the chemisorbed molecule and its image has a vibration frequency different from that of the free molecule. The electrodynamic interaction between a dipole and its image has been discussed in many works. The theoretical problem is that the calculated frequency shift is extremely sensitive to the position of the image plane (Fig. 3a). One can with reasonable parameter values obtain a downward frequency shift of the order of 5-50 cm S but the latest work indicates that the shift due to this interaction is rather small. 

All this work on the dipole-dipole interaction has been made for modes oriented normal to the surface or for the normal component of n and they predict an upward frequency shift for increasing coverage. Hayden et al. suggested that a downward shift could occur for modes oriented parallel to the surface and this idea has also been used to assign modes of H/W(100). However, it should be clear that the interaction must be much weaker for modes parallel to the surface, as the dipole field in accordance with the infrared selection rule mentioned in section 2 is screened by the metal surface. At least, in a theoretical model this has to be taken into account. 

When in motion, the diffnse electrical donble-layer aronnd the particle is no longer symmetrical and this canses a rednction in the speed of the particle compared with that of an imaginary charged particle with no donble-layer. This rednction in speed is cansed by both the electric dipole field set np which acts in opposition to the applied field (the relaxation effect) and an increased viscons drag dne to the motion of the ions in the donble-layer which drag liqnid with them (the electrophoretic retardation effect). The resnlting combination of electrostatic and hydrodynamic forces leads to rather complicated eqnations which, nntil recently, conld only be solved approximately. In 1978, White and O Brien developed a clever method of nnmerical solntion and obtained detailed cnrves over the fnll range of Ka valnes (0 °°)... 

Fig. 2.20 (a) Schematic diagram showing the field distribution above a protruding surface atom. This distribution is the superposition of a uniform applied field and a dipole field. 

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