Chain cycle

Improved sensitivity and scope can be achieved by coupling two (or more) enzymatic reactions hi a chain, cycling, or catalytic mechanism (9). For example, a considerable enhancement of the sensitivity of enzyme electrodes can be achieved by enzymatic recycling of the analyte in two-enzyme systems. Such an amplification... 

A sequence of elementary steps of radical reaction leading to the regeneration of the original radical is called the chain cycle, whereas the particular reaction steps are the events of chain propagation. 

Most systems of interest in combustion include numerous chain steps. Thus it is important to introduce the concept of a chain length, which is defined as the average number of product molecules formed in a chain cycle or the product reaction rate divided by the system initiation rate [1]. For the previous... 

In sum, we have one class of elements that we can employ to create straight or branched chains, cycles, and so forth, and a second class that permits us to bring the process to a conclusion by tying up all the loose ends. We shall begin to see how this works out shortly in the case of creating carbon-carbon chemical bonds. 

Figure 10-1 Sketch of the chain reaction for acetaldehyde decomposition. The chain cycles between CHs and CH3CO" radicals in the propagation steps and is fed by acetaldehyde and terminated by methyl recombination.

The experimental proof of the existence of H04°, necessary for the verification of this reaction pathway proposed by Hoigne, is missing. These radicals are not found in the radical chain cycles of the model from Tomiyasu et al. (1985). However, the result of both models is the same ... 

The term catenation is used to describe the tendency for covalent bond formation between atoms of a given element to form chains, cycles, layers, or 3D frameworks. Catenation is common in carbon compounds, but it only occurs to a limited extent in silicon chemistry. The reason can be deduced from the data listed in Table 14.4.1. 

Using Nff in mixture with H2 eases this problem because the oxidation of H2 is a chain branching process which can provide chain carriers to the reduction of NO by NHft The chain cycle by which this happens consists of reaction 4 followed by reactions 8 and 9. 

In analyzing all such reactions it is sometimes convenient to discuss the mean lifetime of an intermediate passing through a reaction step, which may be defined as the reciprocal of the rate constant (or its product with some concentration). Thus in the above scheme the mean time of Cl in step 1 is n = [ i X (H2)] and for II in step 2, t2 = [A2 X (Cyi h The mean time of chain cycle is then Tc = ri + t2. If Td is the mean lifetime for the destruction of intermediates, then the above criteria imply that Td Tc in order for the induction period to be small. ... 

We see that the rate of production of products is determined by two quantities, the first a quasi-thermodynamic quantity, the equilibrium concentration of free radicals, and the second a kinetic quantity, namely, the rate at which each radical can go through a chain cycle. When the cycle is made up of two steps of disproportionate speed as in the present case, it is the slower step (in this case Br + H2) which is of importance in determining the over-all rate. It is this feature which explains in this case the specific inhibition by HBr even though the over-all reaction is essentially not reversible. The slow step in a chain will in general (though not always) be endothermic. This implies that its reverse is exothermic and hence of lower activation energy, and so faster. We can thus always expect inhibition by products in chain reactions except in those cases in which the fast steps are of unusual speed. 

The H2 + Br2 reaction provides a classic example of a much more general type of chain reaction, the two-center chain. In the case of H2 + Br2, the two centers are the H and Br atoms, both of which are required to complete the chain cycle and both of which may be involved in chain termination. A more general type of two-center chain system is the one exemplified by the over-all reaction. ... 

We sec that there are two alternate chain cycles in the above mechanism, one which proceeds via the primary butyl radical and ethyl radicals (reactions 3 and 6) and whose principal products would be presented by... 

The other chain is produced by the decomposition of the sec-butyl radicals (reaction 6 ) to give methyl radicals + propylene. The chain cycle consists of reactions 6 and 8 and would be represented by the over-all stoichiometry... 

A tremendous number of various fragments are used in structure-property studies atoms, bonds, topological torsions , chains, cycles, atom- and bond-centered fragments, maximum common substructures, line notation (WLN and SMILES) fragments, atom pairs and topological multiplets, substituents and molecular frameworks, basic subgraphs, etc. Their detailed description is given below. 

Completion of the chain cycle posed a difficult problem, since it was clear from kinetic considerations [39] that reaction (5) would only compete with reaction (6), viz. 

In contrast to the alkene theory the predominant mode of oxidation of the alkyl radicals is by oxygen addition and the alkylperoxy radical so formed then undergoes homogeneous intramolecular rearrangement (reaction (14)). Decomposition of the rearranged radical (reaction (16)) usually leads to a hydroxyl radical and stable products which include O-heterocycles, carbonyl compounds and alcohols with rearranged carbon skeletons relative to the fuel and alkenes. The chain-cycle is then completed by unselective attack on the fuel by the hydroxyl radical (reaction (12)). 

The major product from the oxidation of n-heptane [83, 84] is the conjugate 0-heterocycle 2-methyl-5-ethyltetrahydrofuran. The predominant chain cycle therefore involves initial attack at a secondary C—H, followed by addition of oxygen, 1 6-hydrogen transfer from another secondary C—H and decomposition of the 7-hydroperoxyalkyl radical by simple cyclization and loss of OH, e.g. 

The principal difference between the results at 295 and 340 °C is that, at the higher temperature, formaldehyde is formed in relatively greater yield than the other aldehydes. During the induction period, which was shorter than at the lower temperature, the same products were formed. The initial chain cycle at both temperatures was therefore envisaged by Cullis and Warwicker [26] as being precisely analogous to those already suggested for the lower aliphatic alcohols. 

Considerable sensitivity to contaminants was evident this leads to induction periods. The proposed mechanism involves the chain cycle (7)-(10) with some or all of the termination steps (11)-(14), viz. 

The products of the reaction are unimportant and undetectable in our system because Reaction 10 occurs infrequently. An upper limit to Reaction lO s importance is made by considering the following information. The ratio 3/ 4 is about 75, discussed below, but even at [NH3] / [O3] 0 Ij [02]/[03]o — 1.0, which indicates that Reaction 4 leads ultimately to the bulk of O3 decomposition. The chain lengths must be large—Le., 500 also four O3 molecules are consumed in each chain cycle. Therefore any product from Reaction 10 has a final concentration < 5 X 10 [O3]o, which would be undetectable. Nevertheless we can speculate about Reaction 10. For example, the isomeric HNOH form of NH2O possibly is involved and reacts with itself to produce N2 + 2H2O via the intermediate... 

When a few torr of NO is present, an inhibiting effect can be observed, while at NO pressures above 15 torr catalysis occurs Inhibition of the thermal decomposition of p-methyl- and p-chlorobenzaldehyde by NO has also been reported One of the features distinguishing the decomposition of benzaldehyde from that of other substances dealt with so far is that the inhibition curve is independent of the initial aldehyde concentration. Thus, it follows that one of the chain carriers decomposes within the chain cycle. 

Elements of algebraic topology, chains, cycles, and homology groups. The techniques of algebraic topology are applicable for the description and concise characterization of molecular shapes. Homology theory is usually... 

The hierarchical character of reaction systems does not end with decomposition of reactions into steps. At the next level, many reactions taken together make up pathways. In bioprocesses, such pathways form long chains, cycles, and branching structures that accomplish biologically identifiable functions. In other processes, a pathway is used to describe the sequence of transformations that are needed to obtain the desired product from the available raw materials. One might even envision, at the next level, pathways combined to describe entire chemical plants or families of processing technologies. 

Series of linked elementary reactions that propagate in chain cycles -> A reaction intermediate is produced in an initiation step. 

T. S. Zwier, The Infrared spectroscopy of hydrogen-bonded clusters chains, cycles, cubes, and three-dimensional networks, In Advances in Molecular Vibrations and Collision Dynamics, edited by J. M. Bowman (JAI, Greenwich, 1998), pp. 249-280. 

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