Termination in free-radical polymerization

They are discrete transforms and can therefore operate directly on the separate equations for each species, reducing them to one expression. Nonlinear terms arising from condensation polymerization can be handled and, with some difficulty, so can realistic terminations in free radical polymerization. They are a special case of the generating functions and can be used readily to calculate directly the moments of the distribution, and thus, average molecular weights and dispersion index, etc. Abraham (2) provided a short table of Z-transforms and showed their use with stepwise addition. 

It is believed that most macroradicals terminate in free-radical polymerizations predominantly or entirely by combination. Experimental measurements of polymer systems are scanty, however. It can be expected that disproportionation will be... 

The formation of polymers with terminal LM during chain termination in free-radical polymerization is based on the ability of anthracene and some of its derivatives to participate in homolytical reactions It was established that anthracene-containing compounds interact with macroradicals which are generated in free-radical... 

Problem 6.28 The bimolecular chain termination in free-radical polymerization is a diffusion-controlled reaction that can be treated as a three-stage process (North and Reid, 1963 Odian, 1991), described below. 

Reaction (O 23.105) describes a termination reaction with an impurity X present. Impurity termination in free-radical polymerization can also take place, but in free-radical chain... 

Chain-Length Dependent Bimolecular Termination in Free-Radical Polymerization Theory, Validation and Experimental Application of Novel Model-Independent Methods... 

Chain-Length Dependent Bimolecular Termination in Free-Radical Polymerization... 

Chain-length dependent bimolecular termination in free-radical polymerization ... 

Zhu S, Tian Y, Hamielec AE, Eaton DR. Radical trapping and termination in free-radical polymerization of methyl methacrylate. Macromolecules 1990 23 1144-1150. 

Buback M, Muller E, Russell GT. SP-PLP-EPR smdy of chain-length-dependent termination in free-radical polymerization of n-dodecyl methacrylate, cyclohexyl methacrylate, and benzyl methacrylate evidence of composite behavior. J Phys Chem A 2006 110 3222-3230. 

II / 418 ACTIVATION ENERGIES OF PROPAGATION AND TERMINATION IN FREE RADICAL POLYMERIZATION TABLE 3. cont d... 

Such a mechanism is open to serious objections both on theoretical and experimental grounds. Cationic polymerizations usually are conducted in media of low dielectric constant in which the indicated separation of charge, and its subsequent increase as monomer adds to the chain, would require a considerable energy. Moreover, termination of chains growing in this manner would be a second-order process involving two independent centers such as occurs in free radical polymerizations. Experimental evidence indicates a termination process of lower order (see below). Finally, it appears doubtful that a halide catalyst is effective without a co-catalyst such as water, alcohol, or acetic acid. This is quite definitely true for isobutylene, and it may hold also for other monomers as well. 

Although this mechanism is an oversimplification, it does give the basic idea. Chain termination is more complicated than in free radical polymerization. Coupling and disproportionation are not possible since two negative ions cannot easily come together. Termination may result from a proton transfer from a solvent or weak acid, such as water, sometimes present in just trace amounts. 

What is the termination mechanism in free radical polymerization is the average DP = v ... 

Fig. 57. Chain transfer in free radical polymerization with a side group of the-dead polymer. Note After termination of the radical one side chain and a free linear chain are obtained.

Once least squares values of the /3 s were obtained, it was desirable to extract from them as much information as possible about the original parameters. To do so, we make one further statement concerning the relations between the rate constants for mutual termination of polymeric radicals of different size. It has been shown (2) that termination rates in free radical polymerizations are determined by diffusion rates rather than chemical factors. The relative displacement of two radicals undergoing Brownian motion with diffusion coefficients D and D" also follows the laws of Brownian diffusion with diffusivity D = D -J- D" (11). It... 

Another synthetic approach based on pyridium salt photochemistry involves the use of alkoxy radicals which are formed in both direct and sensitized decomposition of pyridinium ions in free radical polymerization [78]. Obviously, polytetrahydrofuran (PTHF), terminated by JV-alkoxy pyridinium ions, can act as macrophotoinitiator for the polymerization of monomers such as methyl methacrylate (MMA) that readily polymerize by a free-radical mechanism. PTHF macrophotoinitiators were prepared by termination of living polymerization of THF by the corresponding IV-oxides, The well-defined macrophotoinitiators with exact functionalities, confirmed by H-NMR, UV-visible and g.p.e. analysis, were obtained. Upon irradiation of macroinitiators at suitable wavelengths, polymeric alkoxy radicals are produced. The overall process is shown for the pyridinium macrophotoinitiator in the following Scheme 21. 

As in free radical polymerization, there are initiation and propagation steps. Various initiators, such as organometallic compounds, alkali metals, Grignard reagents, or metal amides, like sodium amide, shown in Figure 3-31, can be used. Propagation proceeds in the usual manner, but there is no termination... 

As in so many things in this field, if you want to work through the arguments yourself, you cannot do better than go to Flory— see Principles of Polymer Chemistry, Chapter EX. Stockmayer s equation illustrates the point we wish to make with dazzling simplicity as f the number of branches, increases, the polydispersity decreases. Thus for values of/equal to 4, 5 and 10, the polydispersity values are 1.25, 1.20 and 1.10, respectively. Note also that for / = 2, where two independent chains are combined to form one linear molecule (Figure 5-28), the polydispersity is predicted to be 1.5. Incidentally, an analogous situation occurs in free radical polymerization when chain termination is exclusively by combination. 

The bimolecular termination reaction in free-radical polymerization is a typical example of a diffusion controlled reaction, and is chain-length-depen-dent [282-288]. When pseudobulk kinetics appUes, the MWD formed can be approximated by that resulting from bulk polymerization, and it can be solved numerically [289-291]. As in the other extreme case where no polymer particle contains more than one radical, the so-caUed zero-one system, the bimolecular termination reactions occur immediately after the entrance of second radical, so unique features of chain-length-dependence cannot be found. Assuming that the average time interval between radical entries is the same for all particles and that the weight contribution from ohgomeric chains formed... 

Nonlinear polymer formation in emulsion polymerization is a challenging topic. Reaction mechanisms that form long-chain branching in free-radical polymerizations include chain transfer to the polymer and terminal double bond polymerization. Polymerization reactions that involve multifunctional monomers such as vinyl/divinyl copolymerization reactions are discussed separately in Sect. 4.2.2. For simplicity, in this section we assume that both the radicals and the polymer molecules that formed are distributed homogeneously inside the polymer particle. 

The number-average degree of polymerization can be obtained from the rates of propagation (eqn 10.65) and chain breaking (sum of eqns 10.66 and 10.67) as in free-radical polymerization with termination by chain transfer to a transfer agent (see eqn 10.42) ... 

The distribution is as in free-radical polymerization with termination by disproportionation or terminating chain transfer (eqn 10.45 in Section 10.3.4) and, with increase of the progression factor as conversion increases, in step-growth polymerization of bifimctional monomers (eqn 10.19 in Section 10.2.3). According to eqn 10.81, the progression factor is... 

In free-radical polymerization with termination by coupling, there are three possible termination steps reaction of end groups -MA with -MA, of -MA with —Mb, and of -MB with — MB. Each eliminates two reactive end groups. Leaving the possibility open that all steps contribute significantly, the termination rntc is... 

If ftp is determined, ftt can be estimated from the readily observable relation between ftp/ftt outlined in Section 6.10. Techniques for measuring ft, directly are summarized in specialized reports [1 Ij. Note, however, that termination rates in free-radical polymerizations are always diffusion controlled (see Section 6.13.1) and the apparent value of ft, will depend on the conditions under which it has been measured. 

The absence of termination during a living polymerization leads to a very narrow molecular-weight distribution with polydispersities as low as 1.06. By comparison, polydispersities above 2 and as high as 20 are typical in free radical polymerization. 

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