Short-range repulsion potential

The vibrational motion of atoms in diatomic molecules and, by extension, in crystals cannot be fully assimilated to harmonic oscillators, because the potential well is asymmetric with respect to Xq. This asymmetry is due to the fact that the short-range repulsive potential increases exponentially with the decrease of interionic distances, while coulombic terms vary with 1/Z (see, for instance, figures 1.13 and 3.2). To simulate adequately the asymmetry of the potential well, empirical asymmetry terms such as the Morse potential are introduced ... 

The contributions from the short-range repulsive potential and the long-range attractive potential are shown explicitly in Fig. 12.6. Also shown are the full Stockmayer potential for three different orientations of the dipole moments. The curve listed as no dipole is for orientation angles ft = Gj = rjr — n/2. In this case the x term in Eq. 12.9 is zero. The potential has a minimum at r, - = 21/6a,y, with an attractive well depth of e,y. The curve listed as attractive dipole has orientation angles ft = 6j = 0. Thus x = 2, and this orientation has the maximum (attractive) contribution from the dipole-dipole term. The well depth in this case is almost a factor of 6 deeper due to the dipole interaction. The repulsive... 

Luther, E.P. et al.. Development of short-range repulsive potentials in aqueous, silicon nitride slurries, J. Am. Ceram. Soc., 77, 1047, 1994. 

The description of both water-metal and ion-metal interactions by a short-range repulsive potential without significant adsorption energy, augmented by the image charge model of electrostatics, leads to contact adsorption of Br and L and to no adsorption in the case of Li+ and F . CL is a borderline case. 

Under certain conditions, the basal surface of mica is known to develop a short-range repulsive potential called the hydration (or solvation, in general)... 

Equation 117 is often approximated by a short-range repulsion potential that is mathematically expressed with the space S function (Staverman, 1962 Yamakawa, 1971 Freed, 1972)... 

As an examph of application of this procedure, the main terms in the e expansion of the index u are calculated using the simplest model of the short-range repulsion potential... 

There is a further refinement of the shell model that is occasionally used, known as the breathing shell model (Schroder 1966). He re the shell is given a finite variable radius on which the short-range repulsive potential acts. In addition a harmonic restoring force is included about the equilibrium radius. The coupling of forces via variable radii creates a many body force that allows for the change in ionic environments between different materials. 

One such approximation is to express the short-range repulsive potential energy as inversely proportional to a high power of r. 

The short-range repulsive potentials Erep can be represented as a polynomial or a spline in SK files. They are determined as the difference of total energy resulting from a DFT calculation and a DFTB calculation with only the electronic part... 

B. Use the higher velocity data shown in Figure 2.4 and Eq. (4.24) to draw conclusions about the i -dependence of the short-range repulsive potential. What can you conclude from the low-velocity end of the plot ... 

Because of its major significance, deposition at quasi-continuous surfaces has been investigated extensively in terms of the RSA model. Most results concern hard spherical particle deposition at planar interfaces of infinite extension [1, 5, 44-48]. However, there exist also results for polydisperse spherical particles [52] and for anisotropic hard particles of a convex shape like squares [53], rectangles (cylinders), spherocylinders (disk rectangles) and ellipses (spheroids) [2]. Results are also available for particles interacting via the short-range repulsive potential stemming from the electric double layers [5, 13, 43, 44, 48]. 

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