Redox-initiated polymerization rate equation

Usually, the rate equation of redox initiated polymerization is shown as follows ... 

In eq. 8, the rate of polymerization is shown as being half order in initiator (T). This is only true for initiators that decompose to two radicals both of which begin chains. The form of this term depends on the particular initiator and the initiation mechanism. The equation takes a slightly different form in the case of thermal initiation (S), redox initiation, diradical initiation, etc. Side reactions also cause a departure from ideal behavior. 

The kinetic chain length is thus inversely dependent on the radical concentration [Eq. (6.123)] or the polymerization rate [Eq. (6.124)]. This is of great practical significance as it shows that any attempt to increase the rate of polymerization by increasing the radical concentration will be only at the expense of producing smaller size polymer molecules. Equations (6.123) and (6.124) are applicable for all cases of bimolecular termination irrespective of the exact mechanism (combination or disproportionation) and also irrespective of the nature of the initiation process. Thus, for any monomer the Idnetic chain length will be Independent of whether the polymerization is initiated by thermal, redox, or photochemical means, or of the initiator used, if the [M ] or Rp is the same. 

In free-radical polymerization carried out in aqueous medium, the decomposition of peroxide or persulfate is greatly accelerated by the presence of a reducing system. This method of free-radical initiation is referred to as redox initiation. The initiation resulting from the thermal decomposition of oiganic compounds discussed above is appropriate only for polymerizations carried out at room temperature or higher. The enhanced rate of free-radical formation in redox reactions permits polymerization at relatively lower temperatures. Typical redox reactions for emulsion polymerization are shown in Equations 1.5-11. 

For any specific type of initiation (i.e., radical, cationic, or anionic) the monomer reactivity ratios and therefore the copolymer composition equation are independent of many reaction parameters. Since termination and initiation rate constants are not involved, the copolymer composition is independent of differences in the rates of initiation and termination or of the absence or presence of inhibitors or chain-transfer agents. Under a wide range of conditions the copolymer composition is independent of the degree of polymerization. The only limitation on this generalization is that the copolymer be a high polymer. Further, the particular initiation system used in a radical copolymerization has no effect on copolymer composition. The same copolymer composition is obtained irrespective of whether initiation occurs by the thermal homolysis of initiators such as AIBN or peroxides, redox, photolysis, or radiolysis. Solvent effects on copolymer composition are found in some radical copolymerizations (Sec. 6-3a). Ionic copolymerizations usually show significant effects of solvent as well as counterion on copolymer composition (Sec. 6-4). 

Equation (6.25) for rate of polymerization is general in that the reaction for the production of radicals [e.g., Eq. (6.3)] is not specified and the reaction rate is simply shown as jRj. A variety of initiator systems can be used and radicals can be produced from them by a variety of thermal, photochemical, and redox methods [3-5]. 

A variety of other means, besides thermal decomposition of initiator, can be used to produce radicals for chain initiation, such as redox reactions, ultraviolet irradiation, high-energy irradiation, and thermal activation of monomers. The expression for Ri wUl be different in each case and inserting it into the same equation (6.23) will yield the corresponding expression for the rate of polymerization. 

The hydrogen peroxide itself undergoes S, reduction to hydroxyl ion and hydroxyl radical, the latter being able to initiate a polymerization reaction, as schematically indicated in the second part of the equation. Certain redox systems require a comparatively low activation energy, and if such a system is employed in an emulsion polymerization, the reaction can proceed at a temperature of, for instance, 0°C with a satisfactory rate. 

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