Sixth-power law

Equation (4.3) gives the inverse sixth power law of Forster,... 

By contrast, those results that involve an inverse sixth-power law are always negative that is, attraction always results from interactions of the following types ... 

In Table 10.1 we saw that all random dipole-dipole interactions follow the inverse sixth-power law except the so-called retarded van der Waals attraction, which varies with the inverse seventh power of the separation. In this section we examine briefly the physical basis of the three different inverse sixth-power laws that describe iritermolecular attractions. Space limitations prevent us from deriving the Debye, Keesom, and London expressions in detail. More complete derivations may be found in many physical chemistry textbooks, such as that by Moelwyn-Hughes (1964). The abbreviated discussion we present should be sufficient, however, to indicate the connection between these attractions and molecular parameters. 

Garner (Ref 14) listed the three stages of thermal decompn as a)surface reaction from which alkali earth atoms result b)subsequent reaction within the crysts and c) finally the spreading of decompn from reaction centers. Experiments by Garner Reeves (Ref 22) showed the thermal decompn of Ca and Sr azides obeyed a third-power law, whereas Ba azide obeyed a sixth-power law. Electrical conductivities of these azides were low and did not change during thermal decompn until the nuclei came into contact... 

Typical potential energy curves for the interaction of two atoms are illustrated in Figure 11.3. There is characteristically a very steeply rising repulsive potential at short interatomic distances as the two atoms approach so closely that there is interpenetration of their electron clouds. This potential approximates to an inverse twelfth-power law. Superimposed upon this is an attractive potential due mainly to the London dispersion forces. This follows an inverse sixth-power law. The total potential energy is given by... 

An empirical rule summarizing the general tendency of the critical coagulation concentration (CCC) of a suspension, an emulsion, or other dispersion, to vary inversely with about the sixth power of the counter-ion charge number of added electrolyte. Also termed the sixth-power law . 

The experiments involved measuring the rates of singlet-singlet EET from the first excited singlet state of DMN to the ketone or dione chromophore. The distance dependence of the EET rates in 82(n) follows an exponential decay, rather than an inverse sixth-power law, thereby confirming that an exchange mechanism and not a... 

Note added in proof. The onc-sixth power law relating dissociation energy and inhomogeneity kinetic energy T2in Eq. (A2.1)hasnow been derived by the present writer (March NH(1991) J Phys B 24 4123). 

CCC is one of the most significant characteristics of cell dispersion. The experimental observations for inorganic colloidal suspension reveal that the variation of CCC as a function of the valence of counterion follows roughly the inverse sixth power law, the classic Schulze-Hardy rule [74,75]. For negatively charged colloids, the CCC ratio of cations of valences 3, 2, and 1 is 3 2 1 , or roughly 1 11 729. Based on the DLVO theory, which considered the electrical repulsive force... 

The eq. (39) and (40) are valid only if the retardation is neglected. If we want to introduce the retardation correction this can be done in the same way as for the flat plates. The integrations are rather tedious though in principle not difficult. The results are given in Fig. 16 which represents the ratio between the London force with retardation and that following the reciprocal sixth power law. As the retardation depends explicitly on the length it is now impossible to express the results as a simple function... 

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