Chain and Oscillating Reactions

The kinetics of certain kinds of reactions are interesting enough that they deserve special attention. In this section, we will consider two interesting kinds of reaction kinetics. 

Consider a gas-phase reaction in which one or two reactant species are converted into species that are very reactive themselves. For example, a molecule of bromine can be broken into two individual bromine atoms, each with an unpaired electron  

In turn, each of these bromine atoms, which are free radicals, can react with another species, say a hydrogen molecule  

A new free radical, in this case a hydrogen atom with an unpaired electron, is generated. This reactive free radical can now react with an unreacted bromine molecule to make a product molecule and another free radical  

The newly generated bromine atom, a free radical, can react with another hydrogen molecule as shown in reaction b, after which the new hydrogen atom can react with another bromine molecule as given in reaction c, and so forth. Such a reaction cycle can continue undiminished until one reactant is virtually depleted, or until two free radicals combine to make a molecule that is relatively unreactive, like each of these  

---

Are these phenomena unique, or are they typical of biological systems From a mathematical perspective, enzyme systems fall into a class of nonlinear organization, and a chain of enzyme reactions with negative feedback easily can demonstrate oscillatory behavior [520]. Glass has noted that in general, any nonlinear system with multiple negative feedback may demonstrate oscillations that lead to chaotic behavior [595]. 

III A) 1967 Degn, H. Evidence of a Branched Chain Reaction in the Oscillating Reaction of Hydrogen Peroxide, Iodine and Iodate, Acta Chem. Scand. vol. 21, 1057-1066... 

Degn, H., Evidence of a branched chain reaction in the oscillating reaction hydrogen peroxide, iodine and iodate, Acta Cham. Scand.. 21, 1057-1066, 1967. 

In this volume we also considered the self-organizing systems consisting of the oscillating reactions, of which the Belousov-Zhabotinsky reaction is a well-known example. Attempt was made to demonstrate a generality of the problem on the identification of critical phenomena in branching-chain reactions and in the nonlinear reaction systems as a whole. 

The experimental observation of Turing patterns is the result of a long chain of improvements in practical methods to design both new chemical oscillating reactions and open spatial reactors. 

The reaction of benzene cations with polymer chains was indicated by an increase in the electrical conductivity of the solution relative to that of neat 02-saturated benzene (see Figure 1.14). The increase in conductivity was more pronounced the longer the polymer chain length - an effect that was attributed to the fact that the charges diffuse over the entire length of the chains and encounter chain ends within one period of the oscillating electric field. Consequently, the measured intrachain conductivity was seen to be frequency-dependent with a tendency to increase with increasing microwave frequency [104]. 

There is less information available in the scientific literature on the influence of forced oscillations in the control variables in polymerization reactions. A decade ago two independent theoretical studies appeared which considered the effect of periodic operation on a free radically initiated chain reaction in a well mixed isothermal reactor. Ray (11) examined a reaction mechanism with and without chain transfer to monomer. 

The inlet monomer concentration was varied sinusoidally to determine the effect of these changes on Dp, the time-averaged polydispersity, when compared with the steady-state case. For the unsteady state CSTR, the pseudo steady-state assumption for active centres was used to simplify computations. In both of the mechanisms considered, D increases with respect to the steady-state value (for constant conversion and number average chain length y ) as the frequency of the oscillation in the monomer feed concentration is decreased. The maximum deviation in D thus occurs as lo 0. However, it was predicted that the value of D could only be increased by 10-325S with respect to the steady state depending on reaction mechanism and the amplitude of the oscillating feed. Laurence and Vasudevan (12) considered a reaction with combination termination and no chain transfer. 

---