Solution reactions cage pair

The cage effect described above is also referred to as the Franck-Rabinowitch effect (5). It has one other major influence on reaction rates that is particularly noteworthy. In many photochemical reactions there is often an initiatioh step in which the absorption of a photon leads to homolytic cleavage of a reactant molecule with concomitant production of two free radicals. In gas phase systems these radicals are readily able to diffuse away from one another. In liquid solutions, however, the pair of radicals formed initially are caged in by surrounding solvent molecules and often will recombine before they can diffuse away from one another. This phenomenon is referred to as primary recombination, as opposed to secondary recombination, which occurs when free radicals combine after having previously been separated from one another. The net effect of primary recombination processes is to reduce the photochemical yield of radicals formed in the initiation step for the reaction. 

The observed rate constant is kobs = kkn(k + vD)-1. For the fast reactions with k vD the rate constant is kobs = kI). In the case of a slow reaction with k vD the rate constant is k0bs = kx KAb, where KAB = k y vn is the equilibrium constant of formation of cage pairs A and B in the solvent or solid polymer matrix. The equilibrium constant KAB should not depend on the molecular mobility. According to this scheme, the rate constant of a slow bimolecular reaction kobs = kKAB(kobs kD) should be the same in a hydrocarbon solution and the nonpolar polymer matrix. However, it was found experimentally that several slow free radical reactions occur more slowly in the polymer matrix than in the solvent. A few examples are given in Table 19.1. 

Fig. 10. Solute-solvent cage charge-transfer complex model for an electron-transfer reaction between a redox reactant pair donor D and acceptor A...

The decomposition of an initiator seldom produces a quantitative yield of initiating radicals. Most thermal and photochemical initiators generate radicals in pairs. The self-reaction of these radicals is often the major pathway for the direct conversion of primary radicals to non-radical products in solution, bulk or suspension polymerization. This cage reaction is substantial even in bulk polymerization at low conversion when the medium is essentially monomer. The importance of the process depends on the rate of diffusion of these species away from one another. 

Collisions in the gas phase, whether they result in a reaction or not, are timed somewhat uniformly. In solutions, however, solute pairs undergo multiple collisions within a solvent cage. Once two solute species are in one cage, they are likely to remain neighbors for some time, during which they experience repeated collisions. 

The very low yield of radicals by the reaction of ozone with cumene was found to be the result of the intensive ozone reaction with the benzene ring of cumene with molozonide formation. The values of the parameter e in other reactions are typical of the cage effect of radical pairs in solutions. The rate constants of ozone reactions with various compounds are presented in Table 3.7 and Table 3.8. 

Figure 3.2 An enthalpy profile for a unimolecular reaction in solution, involving the formation of a radical pair inside a solvent cage. Adapted from [61],...

At high pressures, a non-covalent ionic complex can be regarded as a microsolvated ion. It represents the simplest model for ions generated in a dynamic environment, such as in a solvent cage in solution. The main difference is that the behavior of a microsolvated ion is not perturbed by those environmental factors (solvation, ion pairing, etc.) which normally affect the fate of intimate ion-dipole pairs in solution. Hence, a detailed study of the dynamics and the reactivity of microsolvated ions may provide valuable information on the intrinsic factors governing the reaction and how these factors may be influenced by the solvent cage in solution.4 493... 

If the photo-Fries reaction would occur via a concerted mechanism, the absence of solvent should be of minor importance for the formation of rearranged products. However, conclusive evidence supporting the radical pair mechanism arises from the experiments carried out with phenyl acetate (10) in the vapor phase. The major product in the irradiations of 10 is phenol (13), which accounts for 65% of the photoproducts. Under these conditions, less than 1% of ortho -hydroxyace-tophenone (11) appears to be formed [19,20]. Conversely, when a high cage effect is expected, as in rigid matrixes (i.e., polyethylene), the result is completely different, and phenol is practically absent from the reaction mixtures [29]. In the intermediate situation (liquid solution), both rearranged products and phenol are formed in variable amounts depending on solvent properties. These observations... 

It is convenient to label the relative slowness of encounter pair reaction as due to an activated process and to remark that the chemical reaction (proton, electron or energy transfer, bond fission or formation) can be activation-limited. This is an unsatisfactory nomenclature for several reasons. Diffusion of molecules in solution not only involves a random walk, but oscillations of the molecules in solvent cages. Between each solvent cage in which the molecule oscillates, a transformation from one state to another occurs by passage over an activation barrier. Indeed, diffusion is activated (see Sect. 6.9), with a typical activation energy 8—12 kJ mol-1. By contrast, the chemical reaction of a pair of radicals is often not activated (Pilling [35]), or rather the entropy of activation... 

It is generally much easier to study unimolecular than bimolecular processes. It should be noted in this connection that some reactions that are bimolecular in solution are unimolecular in crystals. For example, the coupling or disproportionation of two radicals generated in a crystal cage from a single precursor molecule is a first-order reaction of a radical pair, not a second-order reaction of independent radicals. 

If an electron acceptor is available in homogeneous solution, photochemical reaction can be observed. For example, when 2 is excited (X > 350 nm) in anhydrous dimethylsulfoxide (DMSO), methylation occurs, ultimately giving rise to 9,9-dimethyl-fluorene in >80% yield. By analogy with Tolbert s mechanism for photomethylation in DMSO (4), such a process may be initiated by electron transfer to DMSO to form a caged radical-radical anion pair from which subsequent C-S cleavage occurs (eqn 4). 

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