Rate of termination reaction

The rate of termination reaction is slower than that observed in the homogenous bulk or solution polymerization since the limited number of free radicals exists in the polymerization loci having a reasonably small volume (i.e., monomer swollen forming latex particle). Higher degree of polymerizations can be achieved in an emulsion system relative to the homogenous polymerization due to the existence of this limitation. 

When a free-radical polymerization is started, the number of radicals in the system will- increase from zero as the initiator begins to decompose according to Eq. (6.2). The rate of termination reaction will also increase from zero in the beginning because the rates of these reactions are proportional to the square of the total concentration of radicals in the system [Eqs. (6.16)—(6.18)]. Eventually the rate of radical generation will be balanced by the rate at which radicals undergo mutual annihilation, and the concentration of radicals in the system will reach a steady value. It can be shown that in typical polymerizations this steady state is reached very early in the reaction. The assumption that the rate of initiation equals the rate of termination is called the steady-state assumption. It is equivalent to the following two statements ... 

The major termination process in most oxidations involves interactions of R02- with like (self-reaction) or unlike R02- to form stable products through the intermediacy of R04R. Other possible interactions such as RO- and R02- or 2RO- are not observed ordinarily because the high reactivity of RO- keeps the concentration of RO- too low to permit a significant contribution to the total rate of termination. Reactions of R02- and R- are important only at low oxygen pressures and were extensively investigated by Bateman and his coworkers [6]. 

Rates of termination reactions are generally assumed to be strongly influenced by diffusion most of the rate coefficients are in the kt 10 -10 mol dm s range. This diffusion-limited behavior is also shown by the conversion and solvent dependence of kt. During polymerization in bulk the viscosity of the liquid gradually increases with the conversion, which results in decreasing diffusivity and decreasing Jq. In solution polymerization Jq decreases with the solvent viscosity. 

This is a quasi-equilibrium, which is valid when the rates of termination reactions (e.g., and k terms in Eq. (Pll.20.2)) are negligibly small compared with those of addition and fragmentation ikadd and kfr terms inEq. (Pll.20.2)). 

Since the effects of heavy metals increase the amount of free radicals in the lipid phase, not only do the rates of initiation and propagation reactions increase, but also the rate of termination reaction increases. Heavy metals therefore also change the composition of the reaction products. At high concentrations of free radicals, the termination reaction may dominate and metals then act as the inhibitors of autoxidation. Autoxidation reaction can also be inhibited by metals when they are present at higher concentrations. It is assumed that the reason is the oxidation and reduction of free hydrocarbon radicals to anions and cations by ions of Fe and Cu and the formation of complexes of free radicals. Other complexes are also formed with Co. All these reactions interrupt the radical chain autoxidation reaction. Reactions with Fe ions are given as examples. 

Antioxidants (see Section 11.2.2) are substances that can react with free radicals of the autoxidation chain, especially with peroxyl radicals (Figure 3.66). The reaction creates hydroperoxides or other non-radical Hpid products. The antioxidant is transformed to the form of a free radical, which, however, is fairly stable, so it is unable to continue in the autoxidation reaction. The role of the antioxidant thus lies in shortening the autoxidation chain and increasing the rate of termination reactions. During the reaction the antioxidant is consumed. When aU of the antioxidant has been consumed, the autoxidation reaction proceeds as if no antioxidant was present. Antioxidants therefore cannot completely stop the autoxidation reaction they just slow this reaction down, ideally to the initial reaction rate. 

The average chain length may be expressed more generally in terms of a quantity the average number of dead chains produced per termination reaction, which equals the ratio of the rate of dead chain formation to the rate of termination reactions. Since each disproportionation reaction produces two dead chains and each combination one,... 

The branching of the chains, by increasing considerably the number of active centres, prevents the establishment of a steady state, because the rate of termination reactions is too low to compensate for the increase in the number of active centres. 

ESR studies on the propagating radicals of macromonomer ESR spectroscopy is the most useful tool for the study on the nature of propagating radicals. Under the usual polymerization conditions, the stationary concentration of propagating radicals is too low to observe the ESR signals with a conventional ESR instrument. However, there is a possibility of the ESR observation of the radicals when the rate of termination reaction is lowered. 

Polar monomers such as 2-vinylpyridine and methyl methacrylate are normally polymerized in polar solvents such as tetrahydrofuran and at low temperature (-78 °C). In addition, additives such as LiCl are often added to help lower the rates of termination reactions to levels insignificant in the time frame of the reaction. Block copolymers made with nonpolar and polar monomers start with the nonpolar monomer because of its greater reactivity. These active centers are then typically capped with 1,1-diphenylethylene to lower then-reactivity before the addition of the polar monomer. This helps eliminate side reactions resulting from addition of the active center to electrophilic sites in the polar monomers. The two polar polymers, polystyrene-2-vinylpyridine (PS-P2VP) and polystyrene-poly methyl methacrylate (PS-PMMA) have been extensively studied in thin films. 

The result of the steady-state condition is that the overall rate of initiation must equal the total rate of termination. The application of the steady-state approximation and the resulting equality of the initiation and termination rates permits formulation of a rate law for the reaction mechanism above. The overall stoichiometry of a free-radical chain reaction is independent of the initiating and termination steps because the reactants are consumed and products formed almost entirely in the propagation steps. 

Reactivity ratios for the copolymerization of AN with 7 in methanol at 60 °C, proved to be equal to rx AN= 3,6 0,2 and r%n = 0 0,06, i.e., AN is a much more active component in this binary system. The low reactivity of the vinyl double bond in 7 is explained by the specific effect of the sulfonyl group on its polarity26. In addition to that, the radical formed from 7 does not seem to be stabilized by the sulfonyl group and readily takes part in the chain transfer reaction and chain termination. As a result of this, the rate of copolymerization reaction and the molecular mass of the copolymers decrease with increasing content of 7 in the initial mixture. 

It remains a common misconception that radical-radical termination is suppressed in processes such as NMP or ATRP. Another issue, in many people s minds, is whether processes that involve an irreversible termination step, even as a minor side reaction, should be called living. Living radical polymerization appears to be an oxymoron and the heading to this section a contradiction in terms (Section 9.1.1). In any processes that involve propagating radicals, there will be a finite rate of termination commensurate with the concentration of propagating radicals and the reaction conditions. The processes that fall under the heading of living or controlled radical polymerization (e.g. NMP, ATRP, RAFT) provide no exceptions. 

The strongly acceleratory character of the exponential law cannot be maintained indefinitely during any real reaction. Sooner or later the consumption of reactant must result in a diminution in reaction rate. (This behaviour is analogous to the change from power law to Avrami—Erofe ev equation obedience as a consequence of overlap of compact nuclei.) To incorporate due allowance for this effect, the nucleation law may be expanded to include an initiation term (kKN0), a branching term (k N) and a termination term [ftT(a)], in which the designation is intended to emphasize that the rate of termination is a function of a, viz. 

In the above reactions, I signifies an initiator molecule, Rq the chain-initiating species, M a monomer molecule, R, a radical of chain length n, Pn a polymer molecule of chain length n, and f the initiator efficiency. The usual approximations for long chains and radical quasi-steady state (rate of initiation equals rate of termination) (2-6) are applied. Also applied is the assumption that the initiation step is much faster than initiator decomposition. ,1) With these assumptions, the monomer mass balance for a batch reactor is given by the following differential equation. 

Two steady state conditions apply one to the total radical concentration and the other to the concentrations of the separate radicals Ml- and M2-. The latter has already appeared in Eq. (2), which states that the rates of the two interconversion processes must be equal (very nearly). It follows from Eq. (2) that the ratio of the radical population, Mi - ]/ [Mpropagation reaction rate constants. The steady-state condition as applied to the total radical concentration requires that the combined rate of termination shall be equal to the combined rate of initiation, i.e., that... 

The diffusion constant of a primary radical must be of the order of 10 cm.2 sec.- the radius r is about 5X10 cm., and as we have seen 1 10 " per second. Hence ]ag l0 radicals per cc. But the radicals are being generated at a rate of 10 cc. sec. hence the average lifetime of a radical from generation to capture by a polymer particle will be only 10 sec. " The rate of termination by reaction between two radicals in the aqueous phase at the calculated equilibrium concentration, 10 radicals per cc., will be given by... 

The termination constants kt found previously (see Table XVII, p. 158) are of the order of 3 X10 1. mole sec. Conversion to the specific reaction rate constant expressed in units of cc. molecule" sec. yields A f=5X10". At the radical concentration calculated above, 10 per cc., the rate of termination should therefore be only 10 radicals cc. sec., which is many orders of magnitude less than the rate of generation of radicals. Hence termination in the aqueous phase is utterly negligible, and it may be assumed with confidence that virtually every primary radical enters a polymer particle (or micelle). Moreover the average lifetime of a chain radical in the aqueous phase (i.e., 10 sec.) is too short for an appreciable expectation of addition of a dissolved monomer molecule by the primary radical prior to its entrance into a polymer particle. 

This is the simplest of the models where violation of the Flory principle is permitted. The assumption behind this model stipulates that the reactivity of a polymer radical is predetermined by the type of bothjts ultimate and penultimate units [23]. Here, the pairs of terminal units MaM act, along with monomers M, as kinetically independent elements, so that there are m3 constants of the rate of elementary reactions of chain propagation ka ]r The stochastic process of conventional movement along macromolecules formed at fixed x will be Markovian, provided that monomeric units are differentiated by the type of preceding unit. In this case the number of transient states Sa of the extended Markov chain is m2 in accordance with the number of pairs of monomeric units. No special problems presents writing down the elements of the matrix of the transitions Q of such a chain [ 1,10,34,39] and deriving by means of the mathematical apparatus of the Markov chains the expressions for the instantaneous statistical characteristics of copolymers. By way of illustration this matrix will be presented for the case of binary copolymerization ... 

Finally, we have studied the reaction of amino-terminated polyoxyethylenes with the poly(vinylbenzyl chloride) latex (18). The rate of this reaction was found to be independent of the length of the chain carrying the terminal amine. Attachment of these chains stabilized the latex against coagulation, in analogy with the "steric stabilization" produced by adsorbed polymer chains (19 ). ... 

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. 

---