Cage pairing

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. 

Chromic acid oxidation of saturated hydrocarbons starts with hydrogen abstraction to give a caged radical pair.113,114 The collapse of the latter leads to a chromium(IV) ester, which hydrolyzes to the product tertiary alcohol. The postulation of the caged pair was necessary to explain the high degree of retention in oxidation of (+)-3-methylheptane 113... 

The caged pair 16 can lose the second C02 to yield a new pair 18 18 retains the net polarization of 16, which was emission for the CH2, but now acquires in addition a multiplet effect in the sense EjA for the CH2 group. The CH2 in the product phenylethane (19), group 4 in the spectrum, shows superposition of the net emission, E, and a multiplet effect in the predicted sense EjA. (The CH3 of this product is evidendy obscured by the CH3 of the ethyl benzoate.) Ethyl radicals that escape from the cage either react with iodine to give ethyl iodide, groups 3 (CH3) and 5 (CH2), which shows net polarization just opposite... 

When two radicals are in close association as a pair surrounded by a cage of solvent molecules, the two odd electrons will interact with one another just as two electrons do within a molecule. The interaction will yield either a singlet state, if the two electrons have spins paired, or a triplet, if the spins are unpaired. If, for example, the caged pair arose by thermal dissociation of an ordinary ground state molecule, in which all electrons would have been paired, the state would initially be a singlet, S, whereas if the pair arose in a photochemical reaction from dissociation of an excited molecule in a triplet state, it would be initially a triplet, T. 

The initiation step is laser photoexcitation of the molecule to yield a caged geminate pair of atomic iodine radicals. The two competing steps open to the caged pair are 1) separative diffusion to yield atomic iodine radicals and 2) recombination to give molecular iodine. 

Tanko, J. M. Suleman, N. K. Fletcher, B. Viscosity-Dependent Behavior of Geminate Caged-Pairs in Supercritical Fluid Solvent. J. Am. Chem. Soc. 1996, 118, 11958-11959. 

Once one plots the geometry of the transition state with two geometrical coordinates, then in order to locate the transition state one needs to consider two properties of the transition state. One of these, cr, describes the symmetry of the transition state. We choose the symbol a since it is conventionally used in electron transfers (Tafel Law) and in proton transfers (Bronsted Law). Low values of a mean that the transition state is reactant-like, and values of cr approaching unity means that the transition state is product-like. The value of a is of course connected with the Hammond postulate for the symmetry of the transition state. It is helpful now to replace the geometric co-ordinates used hitherto in Figs. 1-4 with bond-order co-ordinates, tj, that measure the degree of nucleophilic participation. These new co-ordinates are defined in (12) and (13), where CP refers to the appropriate caged pair. The relation between bond... 

Besides the destruction of the pair by diffusion, further annihilation of the pair may occur in the cage by reactions with a rate constant kc and decomposition with a rate constant k2. The probability 4>(t) that the caged pair exists at a time t is therefore... 

Braden DA, Parrack EE, Tyler DR. Solvent cage effects. I. Effect of radical mass and size on radical cage pair recombination efficiency. II. Is geminate recombination of polar radicals sensitive to solvent polarity Coord Chem Rev 2001 211 279-94. 

The direct observation of the reactive intermediates by the use of time-resolved picosecond spectroscopy and fast kinetics (Figure 4) enables the course of CT osmylation to be charted in some de. The analysis proceeds from the mechanistic context involving the evolution and metamorphosis of the CT ion pair, as summarized in Scheme 5 (the brackets denote solvent-caged pairs) for the critical initial stq> (equation 24) to form the 1 1 adduct to a benzene donw. 

In such a case the caged pair [A B]c are in thermodynamic equilibrium with A-B, and the last slow step is the diffusion step 3. Such a reaction can be described as a diffusion-controlled reaction even though it contains a far slower chemical step, reaction 1. The rate will now be sensitive to the relative diffusion constant Dab in the given solvent, and the over-all rate should be lower than the rate in the gas phase. There have been a number of attempts to observe this diffusion control. 

When very efficient scavenging is being done, we may neglect reaction 4 and assume that all of the recombination of I2 is coming from initially caged pairs whose probability of geminal recombination is excessively high even when they have separated by a small distance. A crude analysis of this system has been made by Roy, Hamill, and Williams " and a more careful one by Noyes. ... 

The nature of the equilibrium between the dormant system 41 and the pair of radicals 37 and 40 has been probed and exploited by a number of groups. The exact nature of the radical pair, caged pair of radicals, or freely diffusing radicals was probed by a series of crossover experiments.94 This is an important synthetic issue the nitroxide counter-radicals are associated with the same polymeric chain end during the course of the polymerization, or do they diffuse freely to the reaction medium, which affects the ability to insert functional groups at the chain ends. In these experiments, the potential diffusion of the mediating radical from the propagating chain end... 

As mentioned above, the M-M-bonded polymers are of interest as photochemically labile materials (Scheme 20). The quantum yields for the photodegradation of these polymers and model complexes decreased as the chain lengths increased. This effect has been observed in other polymer systems, and several explanations are possible. One invokes the theory that radiationless decay is faster in molecules with more vibrational modes and would thus make the quantum yield for the formation of requisite radical cage pair lower as the chains get longer. ... 

In order to address this issue, a process which involves a much shorter-lived radical pair needed to be examined. Toward this end, Weedon, et al. examined the photo-Fries rearrangement of naphthyl acetate (Scheme 4.4-6) in SCCO2 at 35 and 46 C [56]. Photolysis of 1 leads to caged pair [2/3] reaction in-cage yields the photo-Fries products, 2- or 4-acetylnaphthol (4 and 5). However, cage escape, followed by hydrogen abstraction (isopropanol was present as a hydrogen atom donor) leads to a-naphthol (6). 

A plot of the product ratio (4+5) 6 as a function of pressure is presented in Figure 4.4-5. This plot exhibits a dramatic spike at pressures near the critical pressure which the authors attribute to the onset of solute-solvent clustering disintegration of the caged pair is inhibited because the viscosity at the molecular level is much greater than the bulk viscosity. 

The primary quantum yield for electron formation, determined on a very short time-scale in laser experiments, is a measure of the electrons initially formed on interaction with light (Eq. 9). The primary quantum yield for electron formation has been measured at 355 nm by laser flash photolysis. Quantum yields were 4.6 x 10 to 7.6 X 10 for purified humic substances from several different natural waters and 1.7 x 10 to 4 x 10 for two commercial humic acids (normalized for carbon concentration) [85]. The caged pair generated in Eq. (9) can either collapse back or eject an electron and form the hydrated electron, e q, free in solution (Eq. 10). The steady-state yield, measured with electron scavengers under continuous irradiation, is a measure of the electrons which escape the DOM matrix and are free in solution. The electron thus occurs trapped within the DOM matrix and/or free in solution. 

A description of a bond thermolysis in solution requires at least two elementary steps. This is due to the fact that the immediate product of the bond cleavage step is a pair of radicals which are initially restricted to remain as neighbors by the surrounding solvent molecules. We follow Rabinowitch and Wood and term this reactive species the cage pair intermediate . Scheme 1 depicts a simple chemical model for this kinetic sequence. Subsequent to the... 

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