Termination macroradicals

In the course of the depolymerization primary and tertiary terminal macroradicals are formed. A difference in the reactivity these radicals is explained by assuming that the /3-scission depends on the rotational energy barrier the terminal C-C- bond in the primary and tertiary terminal radicals (52). 

Several authors have studied the effects of degree of ionization on reactivity ratios of t Cgacrylic acid/acrylamide system - a weak acid with a non-ionizing monomer. From this work, it has been well established that the reactivity of an acrylate terminated macroradical with acrylate monomer decreases as the degree of ionization increases. For example, Ponratnam and Kapur showed that the reactivity ratio fell from 0.92 at a pH of 2 to only 0.33 at pH 6. This was explained in terms of electrostatic... 

The indices i and j indicate the individual chain lengths of the terminating macroradicals. There has been considerable confusion in the past on whether to incorporate the factor 2 from the rate law expression into the termination rate coefficient. The factor 2 is necessary if the rate law describes the rate of the loss of macroradicals however, it is unnecessary if only termination events are considered. Nevertheless, the lUPAC ruling on this is clear termination rate coefficients are to be reported without the incorporated factor 2. All termination rate coefficients given in this article are in accordance with the lUPAC guideline. 

Fig 5 Greneral step function for the termination rate coefficient as a fimction of the chain length of terminating macroradicals. For details see text. 

Macroscopic kt values are thus made up of a weighted sum of all possible termination events between macroradicals of different chain lengths, each being characterized by a different rate coefficient. These microscopic termination coefficients are usually depicted as kY, where i and j represent the chain lengths of the terminating macroradicals involved. The relation between the average kt, denoted as termination rate coefficients follows simply from equalizing the macroscopic and microscopic rates of the loss of radicals, and was first put forward by Allen and Patrick [138] ... 

For the termination between B-terminated macroradicals the expressions obtained are exactly the same as Eqs. (97) and (98). For the reaction between A- and B-terminated macroradicals we find ... 

The terminal macroradicals considered above in turn react with the macromolecules with the process assisted by energy distributed along the chains. By the above scheme, the number of scissions greatly exceeds the number of macroradicals formed by direct mechanical action. Experimental results are reported in Volume 2, Chapter VI. 

Termination is probably the most complex step in the free radieal process, owing to the fact that fe, depends on monomer conversion, pressure, temperature, system viscosity, and the chain length of the terminating macroradicals [31, 32]. The complexity of termination is manifested in the widely spread values found in the literature for any given system [33, 34] ... 

The ratios /cactc/ ad and kucrc/kjjA were estimated, respectively, as 6 and 0. This means a growing chain terminated by a MA- unit adds a CTC much more readily than adding free VA. In contrast, the VA- terminated macroradical does not add the CTC. 

Important contributions in this field have been made by Levin [205]. Chaigneau and Le Moan [206], Tsuchiya and Sumi [207], and many others. Lattimer [208] found two oligomer series in the mass spectra of PO, that of 1-alkenes and that of a, ai-alkadienes. Vinyl groups are formed from secondary (or tertiary) macroradicals j6-scission. a, >-Alkadenes are cleaved from second (or tertiary) vinyl terminated macroradicals. Vinyl groups content increases with increasing pyrolysis temperatures. 

Similar work by the same researchers concluded that the end initiation reactions from a terminal TTD and a TVD lead to the formation of a primary terminal macroradical and a tertiary terminal macroradical respectively, and also that the concentration ratio scarcely depends on the initiation reactions 615213. ... 

Decreasing with chain transfer to monomer or transfer agents. (This process is not as limited by diffusion as macro-radical-macroradical termination reactions.)... 

The chain termination rate varies inversely with the viscosity of the polymerization medium because of the Trommsdorff Effect (i.e., the reduction of the macroradical mobility with increasing reaction viscosity). This effect significantly influences reaction rate[ ,2, 10]. 

It can be seen from equation (2) that when y 0 the model falls into the classical expression for the rate of conversion of free radical polymerization. Equation (la) shows that this will be the case whenever all macroradicals have the same high mobility (i.e., as n tends to infinity) or when both entangled and non-entangled radicals have the same termination rate constant (i.e. a is equal to unity). 

As the polymerization reaction proceeds, scosity of the system increases, retarding the translational and/ or segmental diffusion of propagating polymer radicals. Bimolecular termination reactions subsequently become diffusion controlled. A reduction in termination results in an increase in free radical population, thus providing more sites for monomer incorporation. The gel effect is assumed not to affect the propagation rate constant since a macroradical can continue to react with the smaller, more mobile monomer molecule. Thus, an increase in the overall rate of polymerization and average degree of polymerization results. 

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). 

Under current treatment of statistical method a set of the states of the Markovian stochastic process describing the ensemble of macromolecules with labeled units can be not only discrete but also continuous. So, for instance, when the description of the products of living anionic copolymerization is performed within the framework of a terminal model the role of the label characterizing the state of a monomeric unit is played by the moment when this unit forms in the course of a macroradical growth [25]. 

The reactivity of a macroradical is controlled only by the type of its terminal monomeric unit. 

Thus, the problem on the growth of a block copolymer chain in the course of the interphase radical copolymerization may be formulated in terms of a stochastic process with two regular states corresponding to two types of terminal units (i.e. active centers) of a macroradical. The fact of independent formation of its blocks means in terms of a stochastic process the independence of times ta of the uninterrupted residence in every a-th stay of any realization of this process. Stochastic processes possessing such a property have been scrutinized in the Renewal Theory [75]. On the basis of the main ideas of this theory, the set of kinetic equations describing the interphase copolymerization have been derived [74],... 

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... 

The propagation of a a-th type block of a macroradical may be interrupted either because of the addition of monomer or owing to the loss of an active center caused by the chain termination reaction. The probabilities of these events within the interval dxa = dl/0a are equal to Vap(l)dxa and Tadra = ktaR adra, respectively. Hereafter, kla is the constant of the chain termination reaction while R a stands for the concentration of a-th type active centers in the surface layer of the a-th phase. Function wa(r ), having the sense of the probability for a a-th type terminal block of a macroradical to attain length rj, reads as... 

Having hypothetically assumed that rates Vn( ) and V21 ( ) of an active center transition through the interface do not depend on length of the growing terminal block of a macroradical, one will find the distribution of blocks for length (Eq. 75) to be exponential. In this unreal case, the solution of Eqs. 73 and 74 will formally reduce to the solutions of the traditional equations of radical copolymerization [76] for the concentrations Ra(l) of radicals with... 

Interestingly enough, quantity Ha (Eq. 84) has a rather transparent probabilistic meaning. In fact, the growth of the terminal a-th type block of a macroradical may be over either by the transition of an active center into another phase, or by its vanishing due to the chain termination reaction. The probabilities of these events, coinciding with the probabilities that a block chosen at random will be either internal or external, are equal to Ha and 1 -Ha, respectively. 

Quinones are formed by the reaction of the peroxyl radical with phenoxyls (see Chapter 15). They are known as inhibitors of free radical polymerization of monomers where they retard the reaction terminating chains by the reaction with macroradicals [9]. Quinones do not react with peroxyl radicals and react with alkyl radicals by a few orders magnitude [5-7] more slowly than dioxygen does. It was a surprising phenomena that quinones appeared to... 

Acceptors of alkyl radicals are known to be very weak inhibitors of liquid-phase hydrocarbon oxidation because they compete with dioxygen, which reacts very rapidly with alkyl radicals. The situation dramatically changes in polymers where an alkyl radical acceptor effectively terminates the chains [3,49], The study of the inhibiting action of p-benzoquinone [50], nitroxyl radicals [51-53], and nitro compounds [54] in oxidizing PP showed that these alkyl radical acceptors effectively retard the oxidation of the solid polymer at concentrations ( 10-3 mol L 1) at which they have no retarding effect on liquid hydrocarbon oxidation. It was proved from experiments on initiated PP oxidation at different p02 that these inhibitors terminate chains by the reaction with alkyl macroradicals. The general scheme of such inhibitors action on chain oxidation includes the following steps ... 

Nitroxyl radicals, p-benzoquinone, and dinitrotoluene terminate chains only by the reaction with alkyl macroradicals. They form the following series according to their activity nitroxyl radical > quinone > nitro compound. 

Relative Rate Constants of Inhibitors Terminating the Chains by Reactions with Alkyl and Peroxyl Macroradicals... 

The phenomena of nitroxyl radicals regeneration has been discovered in the study of the retarding effect of 2,2,6,6-tetramethyl-4-benzoyloxypiperidine-A-oxyl on PP initiated oxidation [51]. It has been shown that the limiting step of chain termination by the nitroxyl radical is the reaction with the alkyl macroradical of PP. The resulting compound AmOP is fairly reactive with respect to the peroxyl radical and nitroxyl radical is regenerated in this reaction. Thus, the cycle includes the following two reactions (mechanism I) [60-64] ... 

This calculation shows that the discussed reaction is very exothermic. The activation energy of this reaction calculated by the IPM method (see Chapter 6) is equal to 8.7 kJ mol 1 and rate constant is k = 7.3 x 106 L mol-1 s-1 at T= 400 K. This rate constant is close to that of the acceptance of the alkyl macroradical by the nitroxyl radical. Hence, this reaction is rapid enough to be the efficient step in cyclic chain termination in polymer. 

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. 

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