Surface repulsive potential

Thus, finding correct parameters for our charge/surface repulsion potential (equation... 

The presence of the large repulsive potential barrier between the secondary minimum and contact prevents flocculation. One can thus see why increasing ionic strength of a solution promotes flocculation. The net potential per unit area between two planar surfaces is given approximately by the combination of Eqs. V-31 and VI-22 ... 

The model was also extended11 to single-crystal surfaces of silver. Although the calculated inner-layer capacitances varied in the right way from one face to another, the values were much too low. The problem was suspected to be due to the importance of the d electrons. What is still needed in this model is a better treatment of the solvent phase, valid at higher charge density, and a better way of deriving the repulsive potential of the solvent on the electrons, perhaps by a direct pseudopotential calculation, as done by Price and Halley.98,99... 

Fig. 8. Potential energy surfaces for ligand addition. Case (c) weakly repulsive potential energy surface for approach of the incoming ligand to the high-spin metal fragment.

Just as in gas phase kinetics, reactive molecular beam-surface scattering is providing important molecular level insight into reaction dynamics. There is no surface reaction for which such studies have proven more illuminating than the carbon monoxide oxidation reaction. For example Len, Wharton and co-workers (23) found that the product CO exits a 700K Pt surface with speeds characteristic of temperatures near 3000K. This indicates that the CO formed by the reactive encounter of adsorbed species is hurled off the surface along a quite repulsive potential. 

Sorbie and Murrell have developed a function for triatomic systems based on a many body expansion of PE. It has been applied to repulsive potentials as well and has become an attractive option for fitting ah initio PES. It has sufficient flexibility and extendable to higher polyatomic systems and to two-valued surfaces. The potential for triatomic system is decomposed into one-, two- and three-body terms. The potential is given as... 

The nautre of the He-surface interaction potential determines the major characteristics of the He beam as surface analytical tool. At larger distances the He atom is weakly attracted due to dispersion forces. At a closer approach, the electronic densities of the He atom and of the surface atoms overlap, giving rise to a steep repulsion. The classical turning point for thermal He is a few angstroms in front of the outermost surface layer. This makes the He atom sensitive exclusively to the outermost layer. The low energy of the He atoms and their inert nature ensures that He scattering is a completely nondestructive surface probe. This is particularly important when delicate phases, like physisorbed layers, are investigated. 

Although the surface potential, /, the electrical potential due to the charge on the monolayers, will clearly affect the actual pressure required to thin the lamella to any given dimension, we shall assume, for the purpose of a simple illustration, that 1 Ik, the mean Debye-Huckel thickness of the ionic double layer, will influence the ultimate thickness when the liquid film is under relatively low pressure. Let us also assume that each ionic atmosphere extends only to a distance of 3/k into the liquid when the film is under a relatively low excess pressure from the gas in the bubbles this value corresponds to a repulsion potential of only a few millivolts. Thus, at about 1 atm pressure ... 

Fig. 4.13. Classical turning point in atomic-beam scattering. When the repulsive potential on a He atom at the sample surface equals the kinetic energy of the He atom, as a classical particle, the He atom is turned back.

D. M. Neumark We indeed take the translational energy distribution from CH3O dissociation to be evidence for exit channel interactions on a repulsive potential-energy surface. This is in contrast to photodissociation of the vinoxy radical, for which very little variation of the CH3 + CO translational energy distribution occurs over a 0.5-eV range of excitation energy. 

Thus it seems clear that no direct transitions between essentially repulsive covalent potential surfaces Na + BC and Na + BC are possible. This view is also supported by calculations.68 Under such circumstances an additional ionic potential surface has been postulated,69-70 namely, Na+ + BC, which was supposed to be strongly attractive and to couple with the covalent surfaces. All potentials depend on the molecular distance RM, on the atom-molecule distance Rc during the collision, and on the molecular orientation relative to Rc measured by the angle y. A two-dimensional cut through these surfaces along Rc is shown schematically in Fig. 3 for the... 

The work function contributing factors, namely, the relevant chemical potential p experienced by the particle in the bulk material and the surface dipole potential D. Thus, for positrons and electrons the relevant work functions can be written (Tong, 1972 Hodges and Stott, 1973) as — (j> = p D. The chemical potential contains terms due to the electron and positron interactions with the other electrons and with the ion cores. The surface dipole, which is attractive for positrons and repulsive for electrons, arises mainly from the tailing of the electron distribution into the vacuum for a distance of approximately... 

In more quantitative terms can now be taken in conjunction with the properties of the medium to obtain an expression for the electrostatic repulsive potential energy, V. As an example, Reerink and Overbeek (14) found for two spheres of radius a, with their surfaces separated by a distance h, the expression -... 

Imre, D.G., Kinsey, J.L., Field, R.W., and Katayama, D.H. (1982). Spectroscopic characterization of repulsive potential energy surfaces Fluorescence spectrum of ozone, J. Phys. Chem. 86, 2564-2566. 

A more detailed and realistic treatment is to use the van der Waals surface for the chromophore of interest and use a 1/r12 repulsive potential analogous to Le-onard-Jones treatment. The r12 is based on the point of closest approach and weighted by the surface-surface or volume overlap between chromophores. For the case at hand, such treatment gives results indistinguishable from those of the hard shell repulsion treatment discussed above. 

When the adsorbed molecules are compressed against a solid surface, the nuclear and electronic repulsions, and the increasing electronic kinetic energy, start to overcome the attractive forces, and, therefore, the repulsion forces sharply augment in a very complicated form [43,44], This complication is avoided by proposing approximate repulsion potentials. In this sense, the terms ( )D + ( for the potential energy of interaction of a nonpolar molecule with a surface could be represented by the Lennard-Jones (L-J) (12-6) potential [10,45]... 

---