Chain reactions, kinetics

Clustering of crosslinks can be explained by a kinetic chain reaction occurring through the C=C double bonds. Crosslinking by the conventional vulcanization process with sulfur has been shown by NMR to proceed through the allylic hydrogen atoms. 

A kinetic chain reaction usually consists of at least three steps (1) initiation, (2) propagation, and (3) termination. The initiator may be an anion, a cation, a free radical, or a coordination catalyst. Although coordination catalysts are the most important commercially, the ionic initiators will be discussed first in an attempt to simplify the discussion of chain-reaction polymerization. 

It is instructive to sketch this reaction as in Figure 10-1. The chain is fed by initiation reactions that create CHs and terminated by reactions that destroy CHy- to form C2H6. However, the major processes by which the reaction proceeds are the two propagation steps that alternately create and destroy the two chain-propagating radicals CH3 and CHsCOv Thus we have the notion of a chain of reactions, which is a kinetic chain of propagation reaction steps that feed reactants into the chain and spit out stable products. This is a kinetic chain reaction, which is different from the polymerization chain of reactions, which we wiU introduce in the next chapter (although those reactions form both kinetic and polymer chains). 

A ctive free radicals will almost inevitably react in some way with molecular species with which they come in contact. The interaction of radicals in polymerizing systems with either monomer or solvent is well recognized as a transfer step that brings about the formation of inactive polymeric molecules. At the same time, though, new radicals are generated the kinetic chain reaction is usually not seriously impeded although, in some instances, this is not true. 

Living polymerizations are limited to the realm of chain-growth polymerizations, in which a monomer is transformed to a polymer by a reactive species (an initiator, I) via a kinetic chain reaction (Scheme 15.1). An intrinsic limitation of a typical chain-growth process, such as free-radical polymerization, is the occurrence of termination reactions that lead to the formation of dead chains, chains that are incapable of further growth. 

Kinetics of the complex reaction process of auto-oxidation can be described by the mechanism of the so-called kinetic chain reaction. In a kinetic chain reaction, reactive reaction products (radicals) ate first formed in one or more initiation reactions, in the so-called chain start or chain initiation, and these products can then enter so-called propagation reactions. The propagation reactions are characterised by the fact that the radicals ate... 

The so-called secondary antioxidants X convert the hydroperoxides into innocuous non-radical compounds. Thus the chain branching by the start of new kinetic chain reactions is prevented. Therefore these substances are also called hydroperoxide decomposers. The general reaction pattern reads as ... 

Mobility of the reactants and reaction products of the oxidative kinetic chain reaction, of stabilisers and of the polymer molecules themselves affects the kinetics of the radical reactions. Morphology of a polymer material and its physical state, e g. stress, strain and orientation, has an effect on the mobility and therefore on the process of oxidative degradation. Fibres or slit films of polyethylene or pol ropylene are cold-drawn in the production. The orientation of the cold-drawn polymer material produced here has a particularly strong repercussion on oxidation stability. 

In homogeneous kinetics, chain reactions can be grouped into three broad groups ... 

Polyethylene (Section 6 21) A polymer of ethylene Polymer (Section 6 21) Large molecule formed by the repeti tive combination of many smaller molecules (monomers) Polymerase chain reaction (Section 28 16) A laboratory method for making multiple copies of DNA Polymerization (Section 6 21) Process by which a polymer is prepared The principal processes include free radical cationic coordination and condensation polymerization Polypeptide (Section 27 1) A polymer made up of many (more than eight to ten) amino acid residues Polypropylene (Section 6 21) A polymer of propene Polysaccharide (Sections 25 1 and 25 15) A carbohydrate that yields many monosacchande units on hydrolysis Potential energy (Section 2 18) The energy a system has ex elusive of Its kinetic energy... 

The mechanism of these reactions places addition polymerizations in the kinetic category of chain reactions, with either free radicals or ionic groups responsible for propagating the chain reaction. 

The three-step mechanism for free-radical polymerization represented by reactions (6.A)-(6.C) does not tell the whole story. Another type of free-radical reaction, called chain transfer, may also occur. This is unfortunate in the sense that it complicates the neat picture presented until now. On the other hand, this additional reaction can be turned into an asset in actual polymer practice. One of the consequences of chain transfer reactions is a lowering of the kinetic chain length and hence the molecular weight of the polymer without necessarily affecting the rate of polymerization. 

Chain transfer reactions to monomer and/or solvent also occur and lower the kinetic chain length without affecting the rate of polymerization ... 

The overall effect, aside from the change in the polymer composition, is a decrease in the rate of monomer reaction, the kinetic chain length, and the polymer molecular weight (83). 

An important descriptor of a chain reaction is the kinetic chain length, ie, the number of cycles of the propagation steps (eqs. 2 and 3) for each new radical introduced into the system. The chain length for a hydroperoxide reaction is given by equation (10) where HPE = efficiency to hydroperoxide, %, and 2/ = number of effective radicals generated per mol of hydroperoxide decomposed. For 100% radical generation efficiency, / = 1. For 90% efficiency to hydroperoxide, the minimum chain length (/ = 1) is 14. 

N. Semenov, Chemical Kinetics and Chain Reactions, Oxford University Press, London, 1935, p. 68. 

Autooxidation. Liquid-phase oxidation of hydrocarbons, alcohols, and aldehydes by oxygen produces chemiluminescence in quantum yields of 10 to 10 ° ein/mol (128—130). Although the efficiency is low, the chemiluminescent reaction is important because it provides an easy tool for study of the kinetics and properties of autooxidation reactions including industrially important processes (128,131). The light is derived from combination of peroxyl radicals (132), which are primarily responsible for the propagation and termination of the autooxidation chain reaction. The chemiluminescent termination step for secondary peroxy radicals is as follows ... 

The main reason that the decreases as the polymerization temperature increases is the increase in the initiation and termination reactions, which leads to a decrease in the kinetic chain length (Fig. 17). At low temperature, the main termination mechanism is polystyryl radical coupling, but as the temperature increases, radical disproportionation becomes increasingly important. Termination by coupling results in higher PS than any of the other termination modes. 

For example, at 60°C, = 2300 and = 2.9 x 10. An estimate of kinetic chain lifetime, ie, the time from initiation to termination by reaction with... 

Termination. The conversion of peroxy and alkyl radicals to nonradical species terminates the propagation reactions, thus decreasing the kinetic chain length. Termination reactions (eqs. 7 and 8) are significant when the oxygen concentration is very low, as in polymers with thick cross-sections where the oxidation rate is controlled by the diffusion of oxygen, or in a closed extmder. The combination of alkyl radicals (eq. 7) leads to cross-linking, which causes an undesirable increase in melt viscosity. 

Radical Scavengers Hydrogen-donating antioxidants (AH), such as hindered phenols and secondary aromatic amines, inhibit oxidation by competing with the organic substrate (RH) for peroxy radicals. This shortens the kinetic chain length of the propagation reactions. 

In many gaseous state reactions of technological importance, short-lived intermediate molecules which are formed by die decomposition of reacting species play a significant role in die reaction kinetics. Thus reactions involving die mediane molecule, CH4, show die presence of a well-defined dissociation product, CH3, die mediyl radical, which has a finite lifetime as a separate entity and which plays an important part in a sequence or chain of chemical reactions. 

Certain kinetic aspects of free-radical reactions are unique in comparison with the kinetic characteristics of other reaction types that have been considered to this point. The underlying difference is that many free-radical reactions are chain reactions that is, the reaction mechanism consists of a cycle of repetitive steps which form many product molecules for each initiation event. The hypothetical mechanism below illustrates a chain reaction. 

The overall rate of a chain process is determined by the rates of initiation, propagation, and termination reactions. Analysis of the kinetics of chain reactions normally depends on application of the steady-state approximation (see Section 4.2) to the radical intermediates. Such intermediates are highly reactive, and their concentrations are low and nearly constant throughout the course of the reaction ... 

Radical substitution reactions by iodine are not practical because the abstraction of hydrogen from hydrocarbons by iodine is endothermic, even for stable radicals. The enthalpy of the overall reaction is also slightly endothermic. Thus, because of both the kinetic problem excluding a chain reaction and an unfavorable equilibrium constant for substitution, iodination cannot proceed by a radical-chain mechanism. 

The kinetics of reaction of free radical chain reactions are complicated compared to the second-order kinetics of epoxy and urethane adhesives. Many of these complications offer practical advantages to the process of using acrylic adhesives. 

---