The termination reaction

The termination process in ftee-radical polymerization is caused, as is shown earlier, by one of three types of reactions (1) a second-order radical-radical reaction, (2) a second-order radical-molecule reaction, and (3) a first-order loss of radical activity. 

It was suggested that a basic rule of thumb can be applied to determine which termination reaction predominates in a typical homopolymerization. Thus, polymerizations of 1,1-disubstituted olefins are likely to terminate by disproportionation because of steric effects. Polymerization of other vinyl monomers, however, favor terminations by combination unless they contain particularly labile atoms for transferring. Higher activation energies are usually required for termination reactions by disproportionation. This means that terminations by combination should predominate at lower temperatures. 

The ease with which chain transferring takes place depends upon the bond strength between the labile atoms that are abstracted and the rest of the molecule to which they are attached. For instance, chain transferring in methyl methacrylate polymerization to the solvent occurs in the following order  

Examples of molecules that have particularly labile atoms and that contribute readily to chain transferring are mercaptans and halogen compounds, like chloroform, carbon tetrachloride, etc. 

A polymer that was prematurely terminated in its growth by chain transferring may be a telomer. In most cases of telomer formation, the newly formed radical and the monomer radical are active enough to initiate new chain growth. Thus, the life of the kinetic chain is maintained. 

The first reaction can be either one of combination or of disproportionation. In a combination reaction, two unpaired spin electrons, each on the terminal end of a different polymer-radical, unite to form a covalent bond and a large polymer molecule. In disproportionation, on the other hand, two polymer-radicals react and one abstracts an atom from other one. This results in formation of two inactive polymer molecules. The two differ from each other in that one has a terminal saturated structure and the other one has a terminal double bond. Usually, the atom that is transferred is hydrogen. 

For a polymer radical that simply grows by adding monomeric units and still possesses an active center after the growth, the number of monomeric units (r) added to a radical center during the time interval t, according to Tobita [112], ccMiforms to the following Poisson distribution  

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Polypropylene polymerized with triethyl aluminum and titanium trichloride has been found to contain various kinds of chain ends. Both terminal vinylidene unsaturation and aluminum-bound chain ends have been identified. Propose two termination reactions which can account for these observations. Do the termination reactions allow any discrimination between the monometallic and bimetallic propagation mechanisms ... 

Methyl ethyl ketone, a significant coproduct, seems likely to arise in large part from the termination reactions of j -butylperoxy radicals by the Russell mechanism (eq. 15, where R = CH and R = CH2CH2). Since alcohols oxidize rapidly vs paraffins, the j -butyl alcohol produced (eq. 15) is rapidly oxidized to methyl ethyl ketone. Some of the j -butyl alcohol probably arises from hydrogen abstraction by j -butoxy radicals, but the high efficiency to ethanol indicates this is a minor source. 

Bulk Polymerization. This is the method of choice for the manufacture of poly(methyl methacrylate) sheets, rods, and tubes, and molding and extmsion compounds. In methyl methacrylate bulk polymerization, an auto acceleration is observed beginning at 20—50% conversion. At this point, there is also a corresponding increase in the molecular weight of the polymer formed. This acceleration, which continues up to high conversion, is known as the Trommsdorff effect, and is attributed to the increase in viscosity of the mixture to such an extent that the diffusion rate, and therefore the termination reaction of the growing radicals, is reduced. This reduced termination rate ultimately results in a polymerization rate that is limited only by the diffusion rate of the monomer. Detailed kinetic data on the bulk polymerization of methyl methacrylate can be found in Reference 42. 

The auto-acceleration effect appears most marked with polymers that are insoluble in their monomers. In these circumstances the radical end becomes entrapped in the polymer and termination reactions become very difficult. It has been suggested that, in thermodynamic terms, methyl methacrylate is a relatively poor solvent for poly(methyl methacrylate) because it causes radicals to coil while in solution. The termination reaction is then determined by the rate at which the radical ends come to the surface of the coil and hence become available for mutual termination. 

The termination reaction is the removal of the carrier from the system ... 

It is assumed that for each initiation there are many propagation cycles before termination. The main reaction is therefore given by the addition of the propagation steps alone, which gives the correct stoichiometric equation. A small amount of ethane, C2Hg, is expected due to the termination reaction. 

The increase in the temperature reduces the viscosity of the polymerization medium which increases the termination reactions. This is attributed to an increase in chain transfer reactions higher than that of propagation reactions [16,51]. Consequently, the weight-average molecular weight of the formed polymer decreases. 

Depending on the termination reaction of the vinyl monomer, termination by disproportionation or termination by combination occurs. As a result, AB or ABA block copolymers might be obtained. 

A chain transfer reaction between the monomer and the growing polymer produces an unsaturated polymer. This occurs when the concentration of the monomer is high compared to the catalyst. Using ethylene as the monomer, the termination reaction has this representation ... 

The third mode of termination which occurs in some carbonium ion polymerizations involves rearrangement of the active carbonium ion into an inactive one which cannot continue the propagation. These reactions can be avoided to a great extent by working at sufficiently low temperatures, and on the whole, they only contribute significantly to the termination reaction in a few systems. 

The nature of the termination reaction in MMA polymerization has been investigated by a number of groups using a wide range of techniques (Tabic 5.5), There is general agreement that there is substantial disproportionation. However, there is considerable discrepancy in the precise values of k tk. In some cases the difference has been attributed to variations in the way molecular weight data are interpreted or to the failure to allow for other modes of termination under the polymerization conditions (chain transfer, primary radical termination).154 In other eases the reasons for the discrepancies are less clear. MALDI-TOF mass... 

The termination reaction was chosen in part because it brings the proposed scheme... 

This reaction corresponds to the basic process during the initiation of cationic polymerizations by RX/MtXn and when reversed is the termination reaction. It will be handled more in detail in part 4.2. When X = H, the reaction enthalpy of the previous equation is equal to the hydride ion affinity (HIA) which is shown for various relevant... 

We should point out that one of the postulates on which the kinetic equations were derived is that the rate constant of the termination reaction between entangled radicals, k, is... 

The free-radical concentrations will be small—and the quasi-steady state hypothesis will be justified— whenever the initiation reaction is slow compared with the termination reaction, kj /f[CH3CHO]. 

At high copper(ri) concentrations the rate of reduction of peroxydisulphate becomes independent of copper(n) concentration and is unaffected by the presence of oxygen. This can be explained by the occurrence of the termination reaction... 

In the presence of sufficient arsenic(III) reaction (45) is so rapid that the termination reactions (72) and (70) can be left out of consideration. The decrease of the peroxydisulphate current, /, should be proportional to the rate of reaction (50), viz. 

It should be mentioned that there is no decrease in the peroxydisulphate current in the presence of both iron(ril) and arsenic(III). Presumably, the iron(II)-peroxydisulphate reaction is too slow to compete with the reduction of peroxydisulphate at the DME at the given concentration. However, iron(III) reduces the kinetic current in the presence of copper(II) and arsenic(ril). This can be accounted for by the termination reactions... 

A superficially related dependence of on the medium has been observed by Norrish and Smith working with methyl methacrylate, and by Burnett and Melville with vinyl acetate. Rates in poor solvents are high, and determination of by the rotating sector method reveals what appears to be a decrease in kt in the poor solvents. This apparent decrease in kt accounts for the increased rate of polymerization. Actually, precipitation of the polymer seems to be responsible for the effect. The growing radicals become imbedded in precipitated droplets, presumably of very small size. The termination reaction is suppressed owing to isolation of the chain radical in one droplet from that in another. This gel effect is fairly common in systems yield-... 

If the chains are long, the composition of the copolymer and the arrangement oi units along the chain are determined almost entirely by the relative rates of the various chain propagation reactions. On the other hand, the rate of polymerization depends not only on the rates of these propagation steps but also on the rates of the termination reactions. Copolymer composition has received far more attention than has the rate of copolymerization. The present section will be confined to consideration of the composition of copolymers formed by a free radical mechanism. 

Esterbauer et cil. (1992) have studied the in vitro effects of copper on LDL oxidation and have shown that there are three distinct stages in this process. In the first part of the reaction, the rate of oxidation is low and this period is often referred to as the lag phase the lag phase is apparently dependent on the endogenous antioxidant content of the LDL, the lipid hydroperoxide content of the LDL particle and the fatty acid composition. In the second or propagation phase of the reaction, the rate of oxidation is much faster and independent of the initial antioxidant status of the LDL molecule. Ultimately, the termination reactions predominate and suppress the peroxidation process. The extensive studies of Esterbauer et al. have demonstrated the relative importance of the endogenous antioxidants within the LDL molecule in protecting it from oxidative modification. 

Here, we see that the rate of the reaction depends on the square root of the concentration of the initiator and linearly on the concentration of the monomer. The steady state approximation fails when the concentration of the monomer is so low that the initiation reaction cannot occur at the same rate as the termination reaction. Under these conditions, the termination reaction dominates the observed kinetics. 

This relation expresses the fact that under steady-state conditions, the rate of the initiation reaction is equal to the rate of the termination reaction, and the steady-state bromine atom concentration is equal to that which would arise from the equilibrium Br2 2Br that is,... 

If equations 4.2.25 and 4.2.26 are substituted for equations 4.2.11 and 4.2.15, respectively, in the mechanism described above, the effect is to replace kx by k [M] and k5 by /c 5[M] everywhere that they appear. Since these quantities appear as a ratio in the final rate expression, the third body concentration will drop out and kjks) becomes identical with k /k 5 The necessity for the use of the third body concentration thus is not obvious in kinetic studies of the thermal reaction. However, from studies of photochemical reaction between hydrogen and bromine, there is strong evidence that the termination reaction is termolecular. This fact and... 

A reaction rate expression that is proportional to the square root of the reactant concentration results when the dominant termination step is reaction (4c), that is, the termination reaction occurs between two of the radicals that are involved in the unimolecular propagation step. The generalized Rice-Herzfeld mechanism contained in equations 4.2.41 to 4.2.46 may be employed to derive an overall rate expression for this case. 

During the chain oxidation of hydrocarbons, sulfides and disulfides terminate chains by reacting with peroxyl radicals [40,42,44], which, as opposed to phenols, are weak inhibitors (see Table 17.6). The mechanism and stoichiometry of the termination reaction by sulfides remain yet unclear. Since sulfenic acid is an efficient scavenger of free radicals, the oxidation of tetralin in the presence of dialkylsulfoxide occurs only if the initiation rate v > vimin is proportional to the concentration of sulfoxide [5], so that the rate of oxidation is... 

Such a behavior is expected in cationic polymerization where, because carbocations are not reacting among themselves, only one propagating species is involved in the termination reaction. 

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