F-pairs

An individual radical from the RP may encounter a radical from a different RP to fomi what are known as random RPs or F pairs. F pairs which happen to be in the singlet state have a high probability of recombining, so the remaining F pairs will be in the triplet state. Consequently, the initial condition for F pairs is the triplet state in nearly all cases. 

Figure Bl.16.7. Kaptein s niles for net and multiplet RPM of CIDNP. The variables are defined as follows p = -t for RP fonned from triplet preeursor or F pairs and - for RP fonned from singlet preeursor. e = -t for reeombination (or disproportionation)/eage produets and - for seavenge/eseape produets. + if nuelei ...

Consider now an encounter (F) radical pair formed from two free radicals. Since there are three components to the triplet state, T+i, To and T j, and only one singlet component, S, the encounter of two free radicals having uncorrelated spins leads to a statistical distribution of T and S radical pairs. However, some of the S radical pairs will react without undergoing T-S mixing, and this has the effect of increasing the relative number of T radical pairs. Consequently the F-pairs will give the sam e type of polarization as the T-pairs, but the degree of polarization will be less. 

What became known as the tetrad effect was first observed in the late 1960s during lanthanide separation experiments [25]. Fig. 1.3 shows a plot of log K, where is the distribution ratio between the aqueous and organic phases in a liquid-liquid extraction system. There are four humps separated by three minima, first at the f /f pair, secondly at the f point, and thirdly at the pair. 

Typical binding energy -Ebmd °f pairing fluctuation is of the same order as inverse life-time rf oc 1/ T — Tc, whereas for quasiparticles... 

Bf is the proportionality constant for the f pair of concentration and spectral factors. 

Let us now analyze, following Rogulis and Kotomin [102], the experimental non-stationary tunnelling luminescence kinetics observed after a sudden temperature change for V, F pairs in KBr, Ag° and in KCl-Ag as well as for an electron thermal release from Ag° (Ag° and Ag2+ in NaCl-Ag). 

Ionic bonding is the result of the mutual attraction of ions of opposite charge. The energy of the bond, f/pair, between a pair of oppositely charged ions depends on the charges on the ions and their separation,... 

When one metal ion is used as a donor for sensitizing the emission of a second accepting metal ion, the characteristic lifetimes r of their excited states, which are related to their deactivation rates by r = k l, are affected by the metal-to-metal communication process. This situation can be simply modeled for the special case of an isolated d-f pair, in which the d-block chromophore (M) sensitizes the neighboring lanthanide ion (Ln) thanks to an energy transfer process described by the rate constant k 1 ". In absence of energy transfer, excited states of the two isolated chromophores decay with their intrinsic deactivation rates kxl and kLn, respectively, which provides eqs. (32) and (33) yielding eqs. (34) and (35) after integration ... 

This situation is encountered for a large number of d-f pairs, because the intrinsic deactivation rates of the d-block donor kM are often considerably larger than the deactivation of the Ln-centered 4f excited states. For instance, it occurs for the Ru Yb... 

There is the relationship between the new ((D), and old (F), pair distributions matrices ... 

Table 6 lists the polarization effects of the initial compounds, normal addition products and trichlorobutene observed in the photolysis of allyltriorganogermanes in the presence of CCl3Br. The analysis of the detected 1II CIDNP shows that, similarly to the reaction of allyltriethylstannane described above, the polarization is formed in the diffusion F-pair... 

Based upon the current theories of CIDEP and CIDNP, we propose that in many photochemical systems the primary photochemical reaction of the excited triplet state contributes to magnetic polarization via the triplet mechanism. The secondary reaction of the polarized primary radicals may transfer their initial polarization to the "secondary radicals" provided that the radical reactions can compete with the radical spin-lattice relaxation process (59,97). On the other hand, secondary reactions of the primary radical pair or the uncorrelated F pair contribute to polarization by the radical-pair mechanism. A general scheme showing the possible and simultaneous operations of both the... 

Unlike constrained RPs, those in homogeneous solution present a unique situation in that radicals that escape from their geminate cage to bulk solution have the possibility of encountering other radicals that have shared the same fate. Such an encounter leads to the formation of a new RP. Such an RP is formed through free diffusion and is referred to as a freely diffusing RP or f-pair. Until recently, only a single publication... 

For the geminate field, a MFE of about 4% is developed immediately and is unchanged throughout the rest of the reaction period. For the field applied only after the geminate phase is complete, the f-pair MFE is observed to slowly build from nothing to about 4% over the next 60 (ts. Thus, it is clear that MFEs from g-pairs are distinct in terms of timescale. There are some other important differences between g-and f-pairs that are confirmed in these experiments. 

Regardless of the of the spin multiplicity with which a g-pair is bom, f-parrs will always show MFEs of the same sense as a triplet-born g-pair. F-pairs are formed by randomly encountering RPs. If RPs encounter in a singlet state, then they will immediately react and be removed. However, radicals encountering in a triplet state are initially unreactive and do not lead to product formation. However, these unreactive encounters may be turned into reactive ones through the now familiar spin-state evolution of the RP. If, for example, a... 

FIGURE 8.9 Magnetic field pulse schemes used in the measurement of g-pair lifetime and the separation of g- and f-pair RP kinetics. 

FIGURE 8.10 Time dependence of the g- and f-pair MFEs for the photoexcitation of benzophenone in cyclohexanol solution. 

For molecular precursors that produce an unsymmetrical RP, the pair members are predefined in a g-pair. However, f-pairs produced in such a reaction may be composed of any combination of the two types of radical. Figure 8.11 shows the different combinations possible. This means that the MARY dependence of f-pair MFEs must depend on the members that compose the f-pair. As the MARY curve can reveal something about the nature of its members based on the B1/2 value and the size of the LFE, the MARY curve can be used to probe the nature of the f-parr throughout the reaction period. This has recently been demonstrated for the first time for the photolysis of 2-hydroxy-4 -(2-hydro-xyethoxy)-2-methylpropiophenone in cyclohexanol. The RP has large HFCs... 

FIGURE 8.11 Formation and reaction of f-pairs generated from a nonsymmetric g-pair. 

The observation of MFEs in f-pairs is important as this is how most ordinary chemical reactions take place. Most recombination reactions of organic free radicals do not occur through photochemically generated RPs with initially pure spin states, but instead through the random encounter of radicals in solution (think of the classic termination reaction in free radical chain reactions). 

F-pair-pair of radicals met in the solvent bulk as a result of random wandering (an encounter)... 

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