Cage effect

Radical generated according to reactions (26) and (27) cannot be mutually independent immediately after their formation. According to Noyes [111], the surrounding molecules form a kind of cage hindering their separation. 

The occurrence of molecule X during radical formation according to reaction (27) is a strongly complicating factor. The primary cage is affected by intervention of the fragment X which can separate the radical pair and thus reduce the probability of their mutual reaction. 

The last step is the further separation of the two radicals to a distance approaching the average radical spacing in the system. The probability of mutual reaction is small for a pair that has passed the third stage. Radicals that have escaped immediate contact (the primary cage) can react with the monomer or with their twin or with the radical product of the reaction of the twin with the monomer. While the primary cage R ---R can be physically 

The difference between the latter state and 2 R is a matter of convention based on the probability of radical reactions [l 12a]. 

The process of mutual radical separation in the pair should be diffusion--controlled. Therefore the rate of radical liberation from the cage depends on the viscosity of the medium. Actually, some correlation between the two quantities has been observed but it is not simple. 

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Figure A3.6.12. Photolytic cage effect of iodme in snpercritical ethane. Points represent measured photodissociation quantum yields [37] and the solid curve is the result of a numerical simnlation [111].

The traditional difhision model pemiits estimation of the magnitude of the cage effect in solntion according to [37]... 

The simple difhision model of the cage effect again can be improved by taking effects of the local solvent structure, i.e. hydrodynamic repulsion, into account in the same way as discussed above for bimolecular reactions. The consequence is that the potential of mean force tends to favour escape at larger distances > 1,5R) more than it enliances caging at small distances, leading to larger overall photodissociation quantum yields [H6, 117]. 

Figure A3.6.13. Density dependence of die photolytic cage effect of iodine in compressed liquid n-pentane (circles), n-hexane (triangles), and n-heptane (squares) [38], The solid curves represent calculations using the diffusion model [37], the dotted and dashed curves are from static caging models using Camahan-Starling packing fractions and calculated radial distribution fiinctions, respectively [38],...

Otto B, Schroeder J and Tree J 1984 Photolytic cage effect and atom recombination of iodine in compressed gases and liquids experiments and simple models J. Chem. Phys. 81 202... 

Wang W, Nelson K A, Xiao L and Coker D F 1994 Molecular dynamics simulation studies of solvent cage effects on photodissociation in condensed phases J. Chem. Phys. 101 9663-71... 

Bunker D L and Davidson B S 1972 Photolytic cage effect. Monte Carlo experiments J. Am. Chem. Soc. 94 1843... 

Murrell J N, Stace A J and Dammel R 1978 Computer simulation of the cage effect in the photodissociation of iodine J. Chem. Soc. Faraday Trans. II 74 1532... 

Northrup S H and Hynes J T 1979 Short range caging effects for reactions in solution. I. Reaction rate constants and short range caging picture J. Chem. Phys. 71 871-83... 

With heteroaromatic substrates it is possible to prepare, for example, thiazolyipyridines. It is noteworthy that basic solvents (e.g., heterocyclic nitrogen compounds) increase the yield of substitution by a cage effect (see Tables III-37 and III-38) (208). 

Let us estimate a typical value for A. Choosing ta = rt = 5 A, p. = 2 x 10 g,T = 300 K, we find A 4 x 10 M s". This is for the gas phase. In solution the situation is somewhat different because of the solvent cage effect described in Section 4.1. During each bimolecular encounter within a solvent cage, several collisions may occur. This results in a predicted A value for liquid solutions somewhat larger than that for gases. ... 

Even without a cage effect, the entropy effect will be somewhat more favorable for ortho reaction when hydrogen bonding to an azine-nitrogen atom generates the necessary nucleophile. The possibility of proton transfers between the solvent molecules (MeOH) near the reaction site and the more distant MeO is expected to produce a favorable increase (relative to other solvents) in the entropy of activation, which can reinforce the effect of a favorable point of... 

The inhibitive efficiency of boric acid polyesters differs greatly. The highest efficiency is exhibited by polyesters of boric acid, aromatic diols and triols. This derives from the fact that in this case the radicals are accepted not only by boron, but also by the aromatic nucleus. Among the aromatic polyesters, most efficient is ester of boric acid and pyrocatechin due to the Frank-Rabinovich cage effect. The efficiency of inhibi-... 

However, when MAIs are thermolyzed in solution, the role of the cage effect has to be taken into account. The thermolytically formed macroradicals can, due to their size, diffuse only slowly apart from each other. Therefore, the number of combination events will be much higher for MAIs than for low-molecular weight AIBN derivatives. As was shown by Smith [16], the tendency toward radical combination depends significantly on the rigidity and the bulkiness of the chain. Species such as cyclohexyl or diphenylmethyl incorporated into the MAI s main chain lead to the almost quantitative combination of the radicals formed upon thermolysis. In addition, combination chain transfer reactions may... 

Recombination reactions between two different macroradicals are readily observable in the condensed state where molecular mobility is restricted and the concentration of radicals is high. Its role in flow-induced degradation is probably negligible at the polymer concentration normally used in these experiments (< 100 ppm), the rate of radical formation is extremely small and the radicals are immediately separated by the velocity gradient at the very moment of their formation. Thus there is no cage effect, which otherwise could enhance the recombination efficiency. 

The value of initiator association and the rate constant may be evaluated. Viscosity is not expected to have a significant cage effect as in free radical systems, but the extent of association may be dependent on viscosity, or other properties of the fluid media. 

The efficiency of the intitiator is a measure of the extent to which the number of radicals formed reflects the number of polymer chains formed. Typical initiator efficiencies for vinyl polymerisations lie between 0.6 and 1.0. Clearly the efficiency cannot exceed 1.0 but it may fall below this figure for a number of reasons, the most important being the tendency of the newly generated free radicals to recombine before they have time to move apart. This phenomenon is called the cage effect . 

G. W. Hoffman T. J. Chuang, and K. B. Eisenthal, Picosecond smdies of the cage effect and collision induced predissociation of iodine in liquids. Chem. Phys. Lett. 25(2), 201-205 (1974). 

Matheson s widely accepted explanation in terms of the cage effect appears to be based on an unrealistic interpretation of the rates of the processes involved. 

Figure 3. Calculated efficiencies. (1) From the cage effect model and no primary radical termination (Case I) (2) From the assumption of an overall efficiency and no primary radical termination (Case II) (3) From the assumption of an overall efficiency and primary radical termination (Case III) ( l) Calculated from equation (A) with fo - 0.663.

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