Effective Charges and Ion Softening

We may estimate the ion softening in perturbation theory as in Section 14-B, using the expansion of the wave function to first order in the interatomic matrix elements, Eq. (14-4), which we rewrite 

The terms omitted are of order (77,y /7,-j - Hjj ) -, they are neglected in lowest-order perturbation theory. Thus, if a p state on a chlorine ion in KCl is coupled to an s state on its neighboring potassium ion by a matrix element /7,y (which we will relate to K,p ) and the difference in energy between the two states Hjj - H,-,- = is large compared to the coupling, the probability that an electron in the perturbed state lies on that potassium ion is 

Now we may calculate the effective ionic charge on the potassium in the rock-salt structure. That charge, in units of the electronic charge, is -p 1 minus the contributions from the electrons in p states on the six neighboring 

In die last step the value of was taken from Table 14-2 to obtain a simple universal result. 

The [ states on the six neighbors of a potassium ion in KCl contribute charge to the potassium ion, softening its charge from 1 to about 0.51. The same 50 percent softening is expected in the other alkali halides. 

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Most non-polymeric antistatic finishes are also surfactants that can orient themselves in specific ways at fibre surfaces. The hydrophobic structure parts of the molecule act as lubricants to reduce charge buildup. This is particularly true with cationic antistatic surfactants that align with the hydrophobic group away from the fibre surface, similar to cationic softeners (see Chapter 3, Fig. 3.1). The main antistatic effect from anionic and non-ionic surfactants is increased conductivity from mobile ions and the hydration layer that surrounds the hydrophilic portion of the molecule since the surface orientation for these materials places the hydrated layer at the air interface. 

Practically all unshrinkable treatments tend to make wool rather harsh and after-treatment with softening agents is desirable. These are usually cation-active substances (see Chapter 9), the effective ion of which is deposited on the negatively-charged fibres. When these ions are of such a nature that they will tend to reduce friction, they will lubricate the surface of the fibre and produce a soft handle. A typical example, and probably the fore-runner of all the others, is Sapamine KW ... 

To avoid these undesirable effects, some people install water softeners in their homes. These devices are charged with sodium ions, usually from sodium chloride, that exchange with the calcium and magnesium ions in hard water. Sodium ions do not form scaly deposits as calcium and magnesium do, and they do not react with soap. However, sodium does increase the risk of high blood pressure and must therefore be avoided by those who have high blood pressure or heart problems. 

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