Decay chains intermediate species

Because in nature the ground state of a stable nuclide is often attained by decay chains involving intermediate species decaying at different rates, it is worth evaluating the implications of the relative magnitudes of the various decay constants on the isotopic composition of the element. 

Chain reactions are a t3q)e of overall reactions, which require two or more steps to accomplish. They are also known as consecutive reactions or sequential reactions. Examples of chain reactions include nuclear hydrogen burning, nuclear decay chains, ozone production, and ozone decomposition. Some steps of a chain reaction may be rapid and some may be slow. The slowest step is the ratedetermining step. During a chain reaction, some intermediate and unstable species may be produced and consumed continuously. 

The above condition of equal activity of all radioactive nuclides in a decay chain (except for branch decays) is known as secular equilibrium. More detailed solutions for the concentration evolution of intermediate species can be found in Box 2-6. 

If a system initially contains only but no other daughters of in the decay chain, in the first hundred thousand years, the decay of would mostly produce the intermediates °Th, and Ra, and the final stable product ° Pb. Figure 2-10 shows the activity evolution of selected species with time. 

Other conditions being equal, the intermediate species with longer half-lives in a decay series have more opportunities to be fractionated from their parents. Hence, in the decay series of two nuclides °Th and Ra have a greater chance to be fractionated. In the decay series, Pa (half-life 32.8 has the greatest chance to be fractionated. In the Th decay series, all the intermediate species have short half-lives (the longest half-life of Intermediates is 5.75 3T for Ra (A, = 0.1205 3 ) and the disturbance of this decay system does not have much utility. That is, the U-series (including U and U series) disequilibrium is much more often applied. Some examples of disturbed decay chain (i.e., fractionation of the intermediate species) are given below ... 

Reactions 2-145, 2-146, 2-148, 2-151, 2-152, and 2-153 are called the PP IB chain (6 steps). Reactions 2-149 and 2-152 are p-decays, but the former is through electron capture, and the latter is through the emission of a positron. Because PP III chain accounts for only about 0.1% of the three PP chains, only PP I and PP II chains (i.e., from Reaction 2-145 to Reaction 2-150) are considered below. The first step (Reaction 2-145) in the PP chains is the slowest step and controls the overall rate of the reaction. The intermediate species have low concentrations. 

The advances in the molecular design of new polymeric materials with targeted properties require advanced molecular characterization of the polymers. ESR techniques are among the methods under continuous development in the quest for more comprehensive physical and chemical information that could correlate microscopic properties with materials performance. ESR spectroscopy has been used in various areas of polymer science, with different goals, such as to study mechanisms of chemical reactions in polymerization and radiation effects, to identify intermediate species, to observe decay and conversion of different species, or to investigate relaxation phenomena of polymer chains by observing temperature-dependent ESR spectra of radical species trapped in solid and liquid polymers. 

In the M. trichosporium OB3b system, a third intermediate, T, with kmax at 325 nm (e = 6000 M-1cm 1) was observed in the presence of the substrate nitrobenzene (70). This species was assigned as the product, 4-nitrophenol, bound to the dinuclear iron site, and its absorption was attributed primarily to the 4-nitrophenol moiety. No analogous intermediate was found with the M. capsulatus (Bath) system in the presence of nitrobenzene. For both systems, addition of methane accelerated the rate of disappearance of the optical spectrum of Q (k > 0.065 s-1) without appreciatively affecting its formation rate constant (51, 70). In the absence of substrate, Q decayed slowly (k 0.065 s-1). This decay may be accompanied by oxidation of a protein side chain. 

The mechanistic proposal for the chain reaction of 02 " with the DTT anion represented by reactions (84)-(89) (Lai et al. 1997) deviates slightly from the original proposal (Zhang et al. 1991). The essential aspect, however, remains the addition of 02 to the thiolate thereby forming a three-electron-bonded intermediate [reaction (84) for other three-bonded intermediates see Chap. 7.4] and its subsequent decay into an oxidizing species [reaction (85)]. It has been calculated that the rate constant of the rate-determining step, reaction (84), is 35 dm3 mol1 s. This reaction is even slower than the H-abstraction reaction of the H02 radical discussed above. 

During the ferroxidation reaction, a blue color with an absorption maximum of 650 run appears. This persists in oxygen-limited conditions and decays as iron oxidation proceeds. " In frog H-chain ferritin, resonance Raman studies indicate a similar absorption is associated with an Fe(III)-tyrosinate. Harrison and Treffty have considered these and other studies and attribute the transient color to formation of a /x-l,2-peroxodiferric intermediate, which decays to a more stable /x-oxodiferric species as occurs in methane monooxygenase, ribonucleotide reductase, and model compounds. Protein radicals distinct from reactive oxygen species have been observed that have been attributed to damage caused by Fenton chemistry. ... 

Figure 14 shows the concentrations of all species in a log—log-representation as functions of time for the parameters given above. As qualitatively expected, the decay of Y leads to an intermediate stationary state of the radical concentrations. This state is entered at the time to = l/6ky, and for ky = 3 x 10 3 s this is at to = 56 s. It breaks down at the much larger time t 1.2 x 107 s = 3300 h. This may seem surprising, because the natural lifetime of Y is only 1 /ky = 330 s. The explanation is that the unstable persistent species is present in this form only for a small fraction of time and stays essentially incorporated in the dormant chains where it does not decay. This time fraction is approximately equal to [Y]/[I]o = 0.1% for the region where [Y] is constant (Figure 14). 

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