Radical polymerization chain termination

The theoretical molecular weight distributions for cationic chain polymerizations are the same as those described in Sec. 3-11 for radical chain polymerizations terminating by reactions in which each propagating chain is converted to one dead polymer molecule, that is, not including the formation of a dead polymer molecule by bimolecular coupling of two propagating chains. Equations 2-86 through 2-89, 2-27, 2-96, and 2-97 withp defined by Eq. 3-185... 

The theoretical molecular weight distributions for cationic chain polymerizations (see Problem 8.30) are the same as those described in Chapter 6 for radical chain polymerizations terminating by disproportionation, i.e., where each propagating chain yields one dead polymer molecule. The poly-dispersity index (PDI = DP /DPn) has a limit of 2. Many cationic polymerizations proceed with rapid initiation, which narrows the molecular weight distribution (MDI). In the extreme case where termination and transfer reactions are very slow or nonexistent, this would yield a very narrow MDI with PDI close to one (p. 681). 

The theoretical molecular weight distributions for cationic chain polymerizations (see Problem 8.25) are the same as those described in Chapter 6 for radical chain polymerizations terminating by disproportionation, i.e., where each propagating... 

Radical Polymerization. Radical chain polymerization involves initiation, propagation, and termination. Consider the polymerization of ethylene. Initiation typically involves thermal homolysis of an initiator such as benzoyl peroxide... 

Energies of Activation for Propagation (fp) and Termination (ft) in Free Radical Chain Polymerization... 

Radical chain polymerization is a chain reaction consisting of a sequence of three steps— initiation, propagation, and termination. The initiation step is considered to involve two... 

The kinetic chain length v of a radical chain polymerization is defined as the average number of monomer molecules consumed (polymerized) per each radical, which initiates a polymer chain. This quantity will obviously be given by the ratio of the polymerization rate to the initiation rate or to the termination rate, since the latter two rates are equal. 

Five different types of rate constants are of concern in radical chain polymerization—those for initiation, propagation, termination, chain transfer, and inhibition. The use of polymerization data under steady-state conditions allows the evaluation of only the initiation rate constant kd (or kt for thermal initiation). The ratio kp/k J2 or kp/kl can be obtained from Eq. 3-25, since Rp, Rj, and [M] are measurable. Similarly, the chain-transfer constant k /kp and the inhibition constant kz/kp can be obtained by any one of several methods discussed. However, the evaluation of the individual kp, k ktr, and kz values under steady-state conditions requires the accurate determination of the propagating radical concentration. This would allow the determination of kp from Eq. 3-22 followed by the calculation of kt, kIr, and kz from the ratios kp/ltj2, ktr/kp, and kz/kp. 

One difference in the use of these equations for radical chain polymerizations compared to step polymerizations is the redefinition of p as the probability that a propagating radical will continue to propagate instead of terminating. The value of p is given as the rate of propagation divided by the sum of the rates of all reactions that a propagating radical may undergo... 

Most radical chain polymerizations show a one-half-order dependence of the polymerization rate on the initiation rate Ri (or the initiator concentration [I]). Describe and explain under what reaction conditions [i.e., what type(s) of initiation and/or termination] radical chain polymerizations will show the following dependencies ... 

C olvents have different effects on polymerization processes. In radical polymerizations, their viscosity influences the diffusion-controlled bimolecular reactions of two radicals, such as the recombination of the initiator radicals (efficiency) or the deactivation of the radical chain ends (termination reaction). These phenomena are treated in the first section. In anionic polymerization processes, the different polarities of the solvents cause a more or less strong solvation of the counter ion. Depending on this effect, the carbanion exists in three different forms with very different propagation constants. These effects are treated in the second section. The final section shows that the kinetics of the... 

A case classically associated with radical chain polymerization for which a (pseudo)steady state is assumed for the concentration of active centers this condition is attained when the termination rate equals the initiation rate (the free-radical concentration is kept at a very low value due to the high value of the specific rate constant of the termination step). The propagation rate, is very much faster than the termination rate, so that long chains are produced from the beginning of the polymerization. For linear chains, the polydispersity of the polymer fraction varies between 1.5 and 2. 

Now the ratio A p(M)//c<(M-) = fcp(M)(M-)//c (M-) can be seen to be the ratio of the rate at which monomer is converted into polymer to the rate of termination of radical chains. If termination occurs by recombination, then this ratio is just one-half the average number of monomer units per final polymer chain, which we may represent by n, the mean chain length, or mean degree of polymerization. This permits us to write for the stationary radical concentrations... 

Radical chain polymerization, as noted above, is a chain reaction consisting of a sequence of three steps—initiation, propagation, and termination. The initiation step is considered to involve two reactions. The first is the production of free radicals. There are many ways to accomplish this, but the most common method involves the use of a thermolabile compound, called an initiator (or catalyst), which decomposes to yield free radicals. The usual case is the homolytic dissociation of an initiator I to yield a pair of radicals R-... 

Problem 6.18 For a radical chain polymerization with bimolecular termination, the polymer produced contains on the average 1.60 initiator fragments per polymer molecule. Calculate the relative extents of termination by disproportionation and by coupb ng, assuming that no chain transfer reactions occur. Derive first a general relation for this calculation. 

The second step of initiation [Eq. (8.83)], being slower than the first [Eq. (8.82)], is rate-determining for initiation (unlike in the case of free-radical chain polymerization) and so though the amide ion produced upon chain transfer to ammonia can initiate polymerization it is but only at a rate controlled by the rate constant, ki, for initiation. Therefore, this chain transfer reaction may be considered as a true kinetic-chain termination step and the application of steady-state condition gives Eq. (8.90). 

Free-Radical Chain Polymerization. In contrast to the typically slow stepwise polymerizations, chain reaction polymerizations are usually rapid with the initiated species rapidly propagating until termination. A kinetic chain reaction usually consists of at least three steps, namely, initiation, propagation, and termination. The initiator may be an anion, cation, free radical, or coordination catalyst. 

Radical chain polymerization, as noted above, is a chain reaction which involves mainly three steps - initiation, propagation, and termination, taking place in sequence. The overall scheme of the polymerization of a vinyl or related monomer M, initiated by the decomposition of a free-radical initiator I, may be schematically represented as follows (Ghosh, 1990) ... 

A radical chain polymerization is started when the initiator begins to decompose according to Eq. (6.3) and the concentration of radicals in the system, [M ], increases from zero. The rate of termination or disappearance of radicals, being proportional to [M ]- [cf. Eqs. (6.17)-(6.19)], is thus zero in the beginning and increases with time, till at some stage it equals the rate of radical generation. The concentration of radicals in the system then becomes essentially constant (or steady ), as radicals are formed and destroyed at equal rates. This condition, described as steady-state assumption or steady-state approximation , can thus be described by the following two equations ... 

Table 6.4 Some Values of Propagation Rate Constant, kp, and Termination Rate Constant, kt, and Activation Energies in Radical Chain Polymerization...

It is often observed that the measured molecular, weight of a polymer product made by free-radical chain polymerization is lower than the molecular weights predicted from Eq. (6.102) for termination by either coupling [Eq. (6.103)] or disproportionation [Eq. (6.104)]. Such an effect, when the mode of termination is known to be disproportionation, can be due to a growing polymer chain terminating prematurely by transfer of its radical center to other species, present in the reaction mixture. These are referred to as chain transfer reactions and may be generally written as... 

As we have seen in previous sections, the radical chain polymerization involves several possible modes of chain termination — disproportionation, coupling, and various chain transfer reactions. These contribute to the complexity of molecular... 

Figure 6.19 Schematic representation of the grafting-from technique for the preparation of terminally attached polymer monolayers by radical chain polymerization. (After Pmcker and Riihe, 1998.)...

Though resembling free-radical chain polymerization in terms of initiation, propagation, transfer, and termination steps, ionic polymerizations have signif-... 

Reactivity ratios rj are defined by r, = ka/kij, the ratio of homopropagation, ka, to cross-propagation, rate coefficients, where fcy refers to the addition of monomer j to a free-radical chain-end terminating in species i. Under ideal polymerization conditions the mole fraction of monomer units i contained in the copolymer Fj is given by eq (4.6-14), which holds for both the terminal and the implicit penultimate unit models (see Section 4.6.4.3) [45]. 

Radical polymerization is initiated by trace amounts of a radical initiator. Styrene can readily undergo radical chain polymerization in the presence of a radical impurity. BHT is a radical scavenger. It reacts with radicals to produce sterically hindered, resonance stabilized radicals that are not reactive enough to continue the chain. Therefore addition of BHT prevents the polymerization of styrene due to radical impurities by terminating the chains. 

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