Interactions dependence

It is thus seen that the dipole-induced dipole propagation gives an exponential rather than an inverse x cube dependence of U x) with x. As with the dispersion potential, the interaction depends on the polarizability, but unlike the dispersion case, it is only the polarizability of the adsorbed species that is involved. The application of Eq. VI-43 to physical adsoiption is considered in Section XVII-7D. For the moment, the treatment illustrates how a long-range interaction can arise as a propagation of short-range interactions. 

The second contribution to the energy arises from the electrostatic repulsion between pairs III electrons. This interaction depends on the electron-electron distance and, as we have seen, is calculated from infegrals such as ... 

System models assume the independent probabilities of basic event failures. Violators oithis assumed independence are called Systems Interactions, Dependencies, Common Modes, or Common Cause Failure (CCF) which is used here. CCF may cause deterministic, possibly delayed, failures of equipment, an increase in the random failure probability of affected equipment. The CCF may immediately affect redundant equipment with devastating effect because no lime is available for mitigation. If the effect of CCF is a delayed increase in the random failure probability and known, time is available for mitigation. 

As the system passes from the active to the passive state the initial interaction depends on the composition of the aqueous phaseAn initial chemisorbed state on Fe, Cr and Ni has been postulated in which the adsorbed oxygen is abstracted from the water molecules. This has features in common with the metal/gaseous oxygen interaction mentioned previously. With increase in anodic potential a distinct phase oxide or other film substance emerges at thicknesses of 1-4 nm. Increase in the anodic potential may lead to the sequence... 

The London interaction is universal in the sense that it applies to all molecules regardless of their chemical identity. Similarly, the dipole-dipole interaction depends only on the polarity of the molecule, regardless of its chemical identity. However, there is another very strong interaction between molecules that is specific to molecules with certain types of atoms. 

The hybrid orbital has cylindrical symmetry, and accordingly the introduction of d character and f character in the axial bond itself does not lead to an interaction dependent on the relative azimuthal orientation of the two groups. 

The third step is solvation of the ions by solvent molecules. Water molecules cluster around each ion, oriented to give attractive ion-dipole interactions. This step releases energy. Although each individual ion-dipole interaction is weak, each ion forms from four to eight such interactions, depending on the size of the ion and the concentration and temperature of the solution. Taken together, the vast number of ion-dipole interactions results in a substantial release of energy. 

While the rate of change of dipolar interaction depends on t its magnitude depends only on the internuclear distance and is independent of t,. Thus the dipole-dipole relaxation depends on the molecular correlation time T the internuclear distance r, and the gyromagnetic ratios of the two nuclei, y and js -... 

Deuterium NMR has recently been used to study molecular motion of organic adsorbates on alumina (1.) and in framework aluminosilicates (2). The advantage of NMR is that the quadrupole interaction dominates the spectrum. This intramolecular interaction depends on the average ordering and dynamics of the individual molecules. In the present work we describe NMR measurements of deuterated benzene in (Na)X and (Cs,Na)X zeolite. 

The dipole interaction depends on the distance between the ions (6.4). Therefore, the transition probability increases with increasing concentration of magnetic ions. Studies of the concentration dependence of the relaxation can be conveniently performed on samples of amorphous frozen solutions with a uniform distribution... 

Each interaction involves numerous chemical processes. The dominance of a specific interaction depends on the type of waste, the characteristics of the brine and rock in the reservoir, and environmental conditions. Table 20.14 describes some of the more common processes that may result in incompatibility. 

Effect of off-diagonal dynamic disorder (off-DDD). The interaction of the electron with the fluctuations of the polarization and local vibrations near the other center leads to new terms VeP - V P, Vev - Vev and VeAp - VAPd, VA - VAd in the perturbation operators V°d and Vfd [see Eqs. (14)]. A part of these interactions corresponding to the equilibrium values of the polarization P0l and Po/ results in the renormalization of the electron interactions with ions A and B, due to their partial screening by the dielectric medium. However, at arbitrary values of the polarization P, there is another part of these interactions which is due to the fluctuating electric fields. This part of the interaction depends on the nuclear coordinates and may exceed the renormalized interactions of the electron with the donor and the acceptor. The interaction of the electron with these fluctuations plays an important role in processes involving solvated, trapped, and weakly bound electrons. 

When the metal complexes constitute the peripheral units (Fig. lb) and/or belong to the branches (Fig. 1 c) of a dendrimer, a number of equivalent metal-based centers are present since dendrimers are usually highly symmetric species by their own nature. The metal-based centers may or may not interact, depending on distance and nature of the connector units. Multielectron redox processes can therefore be observed, whose specific patterns are related to the degree of interaction among the various units. 

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