Hard cage

FIGURE 19.1 Cosine type angle dependence of the potential energy of the molecule or radical orientation in the model of anisotropic hard cage of the polymer matrix. 

Hardy effect.248-249 The internal return part of the ionization equilibrium is particularly hard to detect since it is almost completely independent of the concentration of anything in the bulk of the solution outside of the solvent cage. The extent of internal return will depend on the reactivity of the cage walls and their resistance to the escape of either ion. Unless internal return has been eliminated by the use of an extremely reactive cage wall, the measured rate is not that of the ionization but the lesser rate of ion pair dissociation. In the case of the acetolysis of a, a-dimethylallyl chloride (XXXIX), internal return is detectable by virtue of the fact that the chloride ion can return to either of two allylic carbon atoms.248... 

The simplest model for an atomic assembly is to consider the atoms as hard spheres with a radius a. Computer simulations have been used to describe the physical behaviour of such assemblies as the number density is changed. At low number densities the assembly is a fluid and the hard spheres diffuse in a gaseous fashion. There are three degrees of freedom corresponding to kBT(2 for each orthogonal translational direction. At intermediate densities the motion of an individual sphere becomes more complex. Some of the time it will move inside a transient cage of... 

Let us assume a many-electron atom enclosed within an infinitely hard spherical cavity of radius R and develop the method and calculations so that we may recover the free-atom case when . This procedure also allows to look at the evolution of its ground state energy as the cage volume shrinks as has been done elsewhere [25,53]. The TFDW energy-density functional for an atom enclosed within a spherical cavity of radius R is written as... 

The effect of pressure on the ground-state electronic and structural properties of atoms and molecules have been widely studied through quantum confinement models [53,69,70] whereby an atom (molecule) is enclosed within, e.g., a spherical cage of radius R with infinitely hard walls. In this class of models, the ground-state energy evolution as a function of confinement radius renders the pressure exerted by the electronic density on the wall as —dEldV. For atoms confined within hard walls, as in this case, pressure may also be obtained through the Virial theorem [69] ... 

With so many uncertainties, it is hardly surprising that the difficulties inherent in a successful application of the diffusion equation (or molecular pair analysis) to recombination probability experiments are very considerable. Chemically induced dynamic polarisation (Sect. 4) is a fairly new technique which may assist in the study of recombination of radicals following their diffusive separation from the solvent cage. 

Monchick [36, 273] has used the diffusion equation and radiation boundary conditions [eqns. (122) and (127)] to discuss photodissociative recombination probabilities. His results are similar to those of Collins and Kimball [4] and Noyes [269]. However, Monchick extended the analysis to probe the effect of a time delay in the dissociation of the encounter pair. It was hoped that such an effect would mimic the caging of an encounter pair. Since the cage oscillations have periods < 1 ps, and the diffusion equation is hardly adequate over such times (see Chap. 11, Sect. 2), this is a doubtful improvement. Nor does using the telegraphers equation (Chap. 11, Sect. 3.3) help significantly as it is only valid for times longer than a few picoseconds. 

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