Termination of macroradicals

The slow rate of copolymerization in acetone was related to the ease of termination of macroradicals by coupling. This coupling was hindered by the coiling of the macroradical chains in benzene, but propagation continued to take place since the monomers were able to pene-... 

For ideal radical polymerization to occur, three prerequisites must be fulfilled for both macro- and primary radicals, a stationary state must exist primary radicals have to be for initiation only and termination of macroradicals only occur by their mutual combination or disproportionation. The rate equation for an ideal polymerization is simple (see Chap. 8, Sect. 1.2) it reflects the simple course of this chain reaction. When the primary radicals are deactivated either mutually or with macroradicals, kinetic complications arise. Deviations from ideality are logically expected to be larger the higher the concentration of initiator and the lower the concentration of monomer. Today termination by primary radicals is an exclusively kinetic problem. Almost nothing has been published on the mechanism of radical liberation from the aggregation of other initiator fragments and from the cage of the... 

The expression for u [eqn. (53)] indicates how important it is to consider primary radical dissociation [the term 1fed/(ki[M])] when correct values of kt pr/fkjkp) are to be obtained, even when termination of macroradicals by secondary phenyl radicals is neglected. In Fig. 6, a graphical representation of eqn. (55) for styrene polymerization with dibenzoylperoxide in benzene is shown. When this dependence is measured for two monomer concentrations, fct pr/(kikp) and kj/kj can be calculated from the slope u. To reduce error,... 

Thus, we must consider those reactions (of termination of macroradical with primary radical (Eq. (9)) which have not necessarily the same reactivity ratio, as the termination of two macroradicals. And this makes it often possible to obtain telechelic oligomers for monomers which give a non-negligible amount of disproportionation reactions in traditional polymerization. 

The expression for u [eqn. (53)] indicates how important it is to consider primary radical dissociation [the term fcd/( i[ ])] when correct values of pr/( i p) obtained, even when termination of macroradicals by... 

The mechanisms for propagation and termination of macroradicals formed by mechanical scission are similar to the radical reactions initiated by other means. The radical mechanism thus can be represented by the following schemes ... 

When monomer and polymer are mutually insoluble, the loss of radical activity may proceed in several ways 1) Burnett and Melville [59] attributed the abnormal behavior of heterogeneous polymerization of vinyl monomer to the enhanced termination of macroradicals by coagulation of colloidal particles containing growing radicals. Thomas and Pellon [60] have found that the rate... 

Meehan et al. [73] reported that the exponent on the initiator concentration was 0.4. The addition of a small amount of a radical scavenger (a retarder) led to an increase of the reaction order from 0.4 up to 0.9. Gerrens et al. [70, 71] discussed this behavior in terms of the degradative chain transfer. As a result of the degradative chain transfer (exponent above 0.5), the expression for the termination of macroradicals (R ) by monomers (allyl acetate [74] and by vinyl chloride [75]) changes from... 

Termination of macroradicals takes place either by bimolecular combination or disproportionation. 

Constrained by the assumption that propagation rates are independent of solution viscosity, termination rate constants have been correlated with media viscosity, cxamulative molar concentration of macroradicals, and molecular size (11,12,13). 

Here, function Qa( ), (a = 1,2) having a meaning of the rate of generating of macroradical with length and a-th type terminal unit, is obtained from the solution of two coupled linear equations... 

Radical polymerizations have three important reaction steps in common chain initiation, chain propagation, and chain termination. For the termination of chain radicals several mechanisms are possible. Since the lifetime of a radical is usually less than 1 s, radicals are continuously generated and terminated. Each propagating radical can add a finite number of monomers between its initiation and termination. If a divinyl monomer is in the monomer mixture, the reaction kinetics changes drastically. In this case, a dead polymer chain may grow again as a macroradical, when its pendant vinyl groups react with radicals, and the size of the macromolecule increases until it extends over the whole available volume. 

If ki and k.i are much larger than kj, the reaction Is controlled by kj. If however, ki and k.i are larger than or comparable to kz, the reaction rate becomes controlled by the translational diffusion determining the probability of collisions which Is typical for specific diffusion control. The latter case Is operative for fast reactions like fluorescence quenching or free-radical chain reactions. The acceleration of free-radical polymerization due to the diffusion-controlled termination by recombination of macroradicals (Trommsdorff effect) can serve as an example. 

Unlike ionic polymerizations, the termination of the growing free radical chains usually occurs by coupling of two macroradicals. Thus, the kinetic chain length (v) is equal to DP/2. The chemical and kinetic equations for bimolecular termination are shown below (Equations 6.17 and 6.18). 

Transfer of the free radical to another molecule serves as one of the termination steps for general polymer growth. Thus, transfer of a hydrogen atom at one end of the chain to a free radical end of another chain is a chain transfer process we dealt with in Section 6.2 under termination via disproportionation. When abstraction occurs intramolecularly or intermolecularly by a hydrogen atom some distance away from the chain end, branching results. Each chain transfer process causes the termination of one macroradical and produces another macroradical. The new radical sites serve as branch points for chain extension or branching. As noted above, such chain transfer can occur within the same chain as shown below. 

The termination of the reaction can take place in two ways recombination (3) of two macroradicals Mn and Mp forming a macrochain Mll+p or disproportionation (4) yielding a double bond Mn = and a C-H bond at the chain terminus MpH. 

These results explain the findings of Blackley and Haynes who also showed that the molecular weight of the polymer formed in the presence of ethyl benzene was lower than that in its absence. Calculation from their experimental data shows that their n varied from 0.005 to 0.039 radicals per particle, well into Case 1. Thus, their explanation on the basis of the Trommsdorff "gel" effect cannot be correct since this requires the mutual termination of two macroradicals in a particle, which obtains only under Case 3 kinetics. Similar experiments on the effect of the diluents on "insitu" (unseeded) and seeded emulsion polymerization indicates that n decreases due to desorption of free radicals from the particles (27). 

Equation (13.10) indicates that the total concentration of macroradicals depends on the ratio of initiation to termination rates, but not on the propagation rate. In numerous studies only the initiator decomposition is considered as rate limiting for the formation of first radicals, and therefore we may write ... 

In recent years, considerable work has been devoted to polymerization reactions of vinyl monomers at higher conversions which permit useful quantitative interpretation of the results. A useful review of studies of the gel effect, chain transfer reactions, and new theoretical postulates and studies at elevated conversions has been presented by Gladyshev and Rafikov (24). This accumulated work has demonstrated the effects of conditions at elevated conversions not only on the termination rate constant, but on initiator efficiency, propagation rate constants, and therefore, the concentration of macroradicals. A rigorous quantitative theory, however, has not yet been developed. 

It is seen that free radical micromolecular or macromolecular initiators have been successfully employed for the synthesis of di-, tri- or multiblock copolymers. However, once again, the structure of these block copolymers depends upon the termination step of the polymerization, and especially on the recombination or disproportionation of macroradicals produced. Besides, such a method also generates homopolymers. Separation and purification of these different structures are usually very difficult or even impossible. Moreover, the copolymers obtained usually exhibit a broad polydispersity, a defect inherent in the classical radical process. 

The counter radical method has been studied with various monomers more or less successfully. However, the synthesis of only few block or grafted copolymers is effectively described. This is a strong indication that a true control of the polymerization is still not achieved with all monomers although progress is constant. Nevertheless, it is clear that the possibility of reversibly controlling the termination step offers a tool of choice for the synthesis of well-defined and pure block copolymers and many studies are still necessary to understand properly the precise mechanism of macroradical end capping in order to control the reversible character and possible secondary reactions. 

North confirmed the controlling effect of diffusion in the bimolecular termination of two macroradicals [4], It is useful to remember that diffusion is manifested by several overall effects, each of which can be considered independently the main of these are... 

Thus f, (m) is the (unnormalized) length distribution of inactive chains formed by disproportionation, particularly in systems where disproportionation represents an exclusive or predominating termination mechanism. f2(m) corresponds to the (unnormalized) length distribution of macroradicals. 

By means of the latter relations, kinetic schemes can be completely solved, mean degrees of polymerization can be derived, as well as the polydispersity coefficients of polymers terminated by disproportionation (= Sf +1 V p) and of macroradicals or inactive macroradicals after transfer (= S + 1 /S l). For the number, weight, and z average, k = 0, 1, and 2, respectively. 

This equation is too complicated to be confronted with experimental results. It can be greatly simplified when reaction (46) is neglected. The assumption about the small importance of macroradical termination by phenyl radicals appears acceptable. First of all, the concentration of phenyl radicals is much smaller than that of benzoyloxyl radicals, kt pr should not substantially differ from kt pr, and finally the reactive phenyl radical should be immediately consumed by initiation. Equation (51) then assumes the form... 

Termination of free radical polymerization is a reaction between two macroradicals R + Rm —> diamagnetic product(s)... 

In many free-radical polymerizations, the molecular weight of the polymer produced is lower than that predicted from Eq. (6-64). This is because the growth of macroradicals in these systems was terminated by transfer of an atom to the macroradical from some other species in the reaction mixture. The donor species itself becomes a radical in the process, and the kinetic chain is not terminated if this new radical can add monomer. Although the rate of monomer consumption may not be altered by this change of radical site, the initial macroradical will have ceased to grow and its size is less than it would have been in the absence of the atom transfer process. These reactions are called chain transfer processes. They can be classified as varieties of propagation reactions (Section 6.3.2). 

The ideal free-radical kinetics without chain transfer culminate in Eiqs. (6-64) and (6-65) in which termination of the growth of polymeric radicals is accounted for only by mutual reaction of two such radicals. Chain transfer can also end the physical growth of macroradicals, and the polymerization model will now be amended to include the latter process. This can be easily done by changing Eq. (6-62) to include transfer reactions in the rate of polymer production, <7[polymer]/[Pg.209]

Atom transfer to form a stable radical which does not reinitiate polymerization, as in the reaction of poly(vinyl acetate) radical and diphenylamine to yield a diphenyl nitrogen radical which will not add vinyl acetate but may terminate a macroradical. 

We first consider the polymerization where each kinetic chain yields one polymer molecule. This is the case for termination of the growth of macroradicals by disproportionation and/or chain transfer (A,c = 0). The situation is completely analogous to that for linear, reversible step-growth polymerization described in Section 5.4.3. If we randomly select an initiator residue at the end of a macromolecule, the probability that the monomer residue which was captured by this primary radical has added another monomer is S and the probability that this end is attached to a macromolecule which contains at least i monomers is S . The probability that this macromolecule contains exactly i monomers equals the product of 5 and the probability of a termination or transfer step. The latter probability must be equal to (I — S) since it is certain that the last monomer under consideration will undergo one of these three reactions. That is, the probability that a randomly selected molecule contains t monomer units is 5 (l — S). Since such probabilities are equal to the corresponding mole fraction of this size molecule, jc,, we have the expression... 

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