Charging contributions

In contrast to the point charge model, which needs atom-centered charges from an external source (because of the geometry dependence of the charge distribution they cannot be parameterized and are often pre-calculated by quantum mechanics), the relatively few different bond dipoles are parameterized. An elegant way to calculate charges is by the use of so-called bond increments (Eq. (26)), which are defined as the charge contribution of each atom j bound to atom i. 

The two-center two-electron repulsion integrals ( AV Arr) represents the energy of interaction between the charge distributions at atom Aand at atom B. Classically, they are equal to the sum over all interactions between the multipole moments of the two charge contributions, where the subscripts I and m specify the order and orientation of the multipole. MNDO uses the classical model in calculating these two-center two-electron interactions. 

In the case of ionic adsorbates, the variation in WS50is normally unable to provide a clue to the molecular structure of the solvent since free charge contributions outweigh dipolar effects. In this case UHV experiments are able to give a much better resolved molecular picture of the situation. The interface is synthesized by adsorbing ions first and solvent molecules afterward. The variation of work function thus provides evidence for the effect of the two components separately and it is possible to see the different orientation of water molecules around an adsorbed ion.58,86,87 Examples are provided in Fig. 6. 

Note that when the concentration of added salt is very low, Debye length needs to be modified by including the charge contribution of the dissociating counterions from the polyelectrolytes. Because the equilibrium interaction is used, their theory predicts that the intrinsic viscosity is independent of ion species at constant ionic strength. At very high ionic strength, the intrachain electrostatic interaction is nearly screened out, and the chains behave as neutral polymers. Aside from the tertiary effect, the intrinsic viscosity will indeed be affected by the ionic cloud distortion and thus cannot be accurately predicted by their theory. 

For iron compounds, (yzz)iat and iat are amplified by approximately (1 —yc ) 10 as compared to the point charge contributions 14z and rj obtained from (4.42a) and (4.42b). Nevertheless, the lattice contribution is usually least significant for most iron compounds because it is superseded by a strong EFG from the valence electrons details will be found in Chap. 5. 

The two-center point-charge contribution, is also intuitively appealing. 

Thus, different types of surface charge contribute to the net total particle charge on a colloid, denoted Gp. 

In living systems, chlorine is present as chloride, Cl . In part, chloride is there to balance ont the charges contributed by cations such as sodium and potassium ions. There are mechanisms to get chloride across biological membranes as required to maintain charge neutrality. When such a mechanism goes wrong, it is a problem. 

Thus, the sign of the surface charge contributed by the chemisorbed particles may be determined if one obtains from experiment the sign of Aic (in the case of a doped sample, if the type of conductivity is known) or the sign of Ay> (if the polarization effect can be neglected) i.e., these... 

For the point-charge contributions, the accelerated convergence expression, Eq. (9.21), is used with the substitution, Eq. (9.22). The explicit expression for the point-charge contribution is then (Bertaut 1952)... 

The electrochemical potential p, includes all types of work involved in bringing particles28 (of charges z 0) into material phases. Nothing is left out. The p includes the chemical work p, the charge contribution /, and the dipole contribution %. 

These differences between intrinsic and doped, or impurity, semiconductors complicate the mathematics of the solution of the Poisson-Boltzmann equation, but the picture that emerges remains basically the same A charged cloud, or space charge, and therefore a potential drop, develops inside the semiconductor the space charge contributes to the capacity of the interphase, etc. 

Figure 8-6 Charge contributed by each ion in 1.00 L of solution containing 0.025 0 mol KH2P04 plus 0.030 0 mol KOH. The total positive charge equals the total negative charge.

In the case in which the electroactive species O is adsorbed on the electrode, ixI/2 increases with increasing i (Fig. 4.4D). The Sand equation considers only those molecules of O that have reached the surface by diffusion. As x decreases, the charge contribution to the reduction of Oads consumes an increasingly large fraction of the total current, causing ixI/2 to increase. A typical example of this behavior is the reduction of Alizarin Red S at mercury [7],... 

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