Straight chain reactions

The closed sequence radical reaction introduces a multiplicative kinetic factor with respect to the initiation so that there is a certain analogy with homogeneous and heterogeneous catalysis, which is also characterized by the existence of closed sequences. However, a big difference exists between chain reactions and so-called catalytic reactions. In fact, in catalytic reactions, the total number of active centres is fixed, whereas that of chain reactions is determined by the competition between the initiation and termination reactions. The rate of a chain reaction is therefore a function of both the kinetic characteristics of the initiation, propagation and termination reactions. 

In what follows, the principal characteristics of straight chain reactions will be discussed for the case of the pyrolysis of neopentane, which will then allow the kinetic rules fi i Y, which are useful for the generation of reaction mechanisms to be discussed. 

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The reaction between hydrogen and bromine illustrates many of the general features of straight chain reactions. This reaction system has been studied by many investigators, and the body of accumulated experimental data represents as nearly a consistent and complete collection of data as is available for any reaction in the literature. 

If virtually all the initiatory radicals react with RH, while the peroxyl radicals produced in reaction (2i) react primarily with the inhibitor, oxidation proceeds as a straight chain reaction (in the RH 02 InH I system, reactions (i), (1), (7), and (8) occur). In this case... 

The duration of the inhibition period of a chain-breaking inhibitor of autoxidation is proportional to its efficiency. Indeed, with an increasing rate of chain termination, the rates of hydroperoxide formation and, hence, chain initiation decrease, which results in the lengthening of the induction period (this problem will be considered in a more detailed manner later). It should be noted that when initiated oxidation occurs as a straight chain reaction, the induction period depends on the concentration of the inhibitor, its inhibitory capacity, and the rate of initiation, but does not depend on the inhibitor efficiency. 

As shown above (see earlier) for straight chain reactions, the inhibitor is consumed at a constant rate v-Jf Similarly, during the inhibited autoxidation of RH, the inhibitor is initially consumed at a constant rate vi0/f, but then the rate of inhibitor consumption drastically increases [57,58], which leads to a rapid accumulation of hydroperoxide and the enhancement of initiation (see Figure 14.1). 

However, since the QSSA has been used to elucidate most reaction mechanisms and to determine most rate coefficients of elementary processes, a fundamental answer to the question of the validity of the approximation seems desirable. The true mathematical significance of QSSA was elucidated for the first time by Bowen et al. [163] (see also refs. 164 and 165 for history and other references) by means of the theory of singular perturbations, but only in the case of very simple reaction mechanisms. The singular perturbation theory has been applied by Come to reaction mechanisms of any complexity with isothermal CFSTR [118] and batch or plug flow reactors [148, 149]. The main conclusions arrived at for a free radical straight chain reaction (with only quadratic terminations) carried out in an isothermal reactor can be summarized as follows. 

The classical example of a complex straight-chain reaction for which the results of the steady-state approximation agree with experimental measurements is the hydrogen-bromine reaction H2 T Br2 2HBr [5]. The inferred mechanism is... 

From equation (44) we see that the reactant concentration decreases monotonically with time from its initial value C (0), while that of the product increases monotonically. The concentration of the chain carrier exhibits a more complicated behavior, according to equation (45). If — 0 initially, then there is a linear increase of with time at early times by initiation. If /Cj > (a — l)kpCj (0) (which applies, for example, to straight-chain reactions), then dc /dt decreases continually with time, and after a sufficient amount of reactant depletion and carrier buildup, begins to decrease and eventually decays exponentially through termination with a time constant /c that is, Cq However, there are other ranges of parameters in... 

Straight chain reactions include three main categories of elementary reactions ... 

If only a single new active nucleus is formed besides the reaction product in the interaction between the active nucleus and a valence-saturated molecule, a straight-chain reaction will take place. If, however, two or more active nuclei are generated in the reaction of the active nucleus, a branched-chain reaction is induced resulting in the formation of multiple chains. 

Consequently, the rate of disappearance of methane is equal to what it would be in the case of a straight-chain reaction, namely 2ri(oi/at), multiplied by an exponential function of I times the net branching factor. 

In the case of unsaturated starting materials with an electron configuration which is the reverse of that of olefins, the above-mentioned effects are also reversed. Thus, acrylates form straight chain reaction products preferentially at high temperatures and low pressures. For details see the individual chapters. 

The modeling of straight chain reactions aims to determine the influence of the different variables on the average length of the chains and the reaction rate. This type of modeling was developed by Semenov. 

There is no generic way to calculate of the mean length of a chain and therefore no general relation is applicable for ary sort of straight chain reaction, whichever stmcture this has. To calculate the mean length, we will study two specific cases that will allow us to develop the Sochet s method, which is a very generic application. 

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