Repulsion factor

It might be thought that this treatment would provide a poor approximation because of the neglect of polarization of each of the two ions in the electric field of the other.36 However, there is reason to think that the neglect of polarization does not introduce great error. First, the effect of multipole polarization as well as of the partial covalent character of the bonds is taken into account in the treatment of the crystals by the evaluation of the Bom exponent n from the observed compressibility and of the repulsion factor from the observed interionic distance. Second, in the gas molecule, in which there is dipole polarization mainly of the anion, its effect in causing increased attraction of the ions may be largely neutralized by the increased repulsion caused... 

When combined with a solute repulsion factor (1-X) eq 30 was found valid in the range of X below 0.2 using membranes whose pore sizes ranged from 45 to 300A (13). Satterfield, Colton and Pitcher on the other hand studied restricted diffusion in heterogeneous solid almina bead catalysts which possessed a pore radius of 16A, by unsteady diffusion and observed a more severe restriction of the solute diffusion in the pore (14). 

Of fundamental importance in this manifold is the idea that steric compression will lead to less bulky cis metallacyclobutanes and, provided that the steric repulsion factors... 

Calculate the expected lattice energy of NaCl again, this time using equation 21.13 and using a Madelung constant of 1.748 and a repulsive factor of 0.321 A. The distance between Na ions and Cl ions is, again, 2.78 A. Compare it to lattice energy of 769 kj/mol. Compare your answer with Example 21.11. 

The interaction of colloidal particles is supposed to contain two components One, the repulsive factor finds its origin in the electrochemical double layer The other Component is the general Lonoon-Van Der Waals attraaion ... 

For example, van den Tempel [35] reports the results shown in Fig. XIV-9 on the effect of electrolyte concentration on flocculation rates of an O/W emulsion. Note that d ln)ldt (equal to k in the simple theory) increases rapidly with ionic strength, presumably due to the decrease in double-layer half-thickness and perhaps also due to some Stem layer adsorption of positive ions. The preexponential factor in Eq. XIV-7, ko = (8kr/3 ), should have the value of about 10 " cm, but at low electrolyte concentration, the values in the figure are smaller by tenfold or a hundredfold. This reduction may be qualitatively ascribed to charged repulsion. 

Hence, the same teclmiques used to calculate are also used for Cg. Note that equation (A1.5.28) has a geometrical factor whose sign depends upon the geometry, and that, unlike tlie case of the two-body dispersion interaction, the triple-dipole dispersion energy has no minus sign in front of the positive coefficient Cg. For example, for an equilateral triangle configuration the triple-dipole dispersion is repulsive and varies... 

Molecular adsorbates usually cover a substrate with a single layer, after which the surface becomes passive with respect to fiirther adsorption. The actual saturation coverage varies from system to system, and is often detenumed by the strength of the repulsive interactions between neighbouring adsorbates. Some molecules will remain intact upon adsorption, while others will adsorb dissociatively. This is often a frinction of the surface temperature and composition. There are also often multiple adsorption states, in which the stronger, more tightly bound states fill first, and the more weakly bound states fill last. The factors that control adsorbate behaviour depend on the complex interactions between adsorbates and the substrate, and between the adsorbates themselves. 

With the aid of (B1.25.4), it is possible to detennine the activation energy of desorption (usually equal to the adsorption energy) and the preexponential factor of desorption [21, 24]. Attractive or repulsive interactions between the adsorbate molecules make the desorption parameters and v dependent on coverage [22]- hr the case of TPRS one obtains infonnation on surface reactions if the latter is rate detennming for the desorption. 

The very low bond dissociation enthalpy of fluorine is an important factor contributing to the greater reactivity of fluorine. (This low energy may be due to repulsion between non-bonding electrons on the two adjacent fluorine atoms.) The higher hydration and lattice enthalpies of the fluoride ion are due to the smaller size of this ion. 

Fhe van der Waals and electrostatic interactions between atoms separated by three bonds (i.c. the 1,4 atoms) are often treated differently from other non-bonded interactions. The interaction between such atoms contributes to the rotational barrier about the central bond, in conjunction with the torsional potential. These 1,4 non-bonded interactions are often scaled down by an empirical factor for example, a factor of 2.0 is suggested for both the electrostatic and van der Waals terms in the 1984 AMBER force field (a scale factor of 1/1.2 is used for the electrostatic terms in the 1995 AMBER force field). There are several reasons why one would wish to scale the 1,4 interactions. The error associated wilh the use of an repulsion term (which is too steep compared with the more correct exponential term) would be most significant for 1,4 atoms. In addition, when two 1,4... 

Figure 5 shows the enhanced concentration of oppositely charged ions near the charged surface, and the depleted concentration of similarly charged ions near the charged surface due to electrostatic attractions and repulsions. Both factors reduce the effective potential, /, as the distance from the surface, X, increases. The distance at which / drops to 1/ (37%) of its value at the Stem plane is called the counterion atmosphere decay distance,... 

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