Mode of termination

The number-average degree of polymerization X , defined as the average number of monomer molecules contained in a polymer molecule, is related to the kinetic chain length. If the propagating radicals terminate by coupling (Eq. 3-16a), a dead polymer molecule is composed of two kinetic chain lengths and 

For termination by disproportionation (Eq. 3-16b) the kinetic chain length is synonymous with the number-average degree of polymerization 

The number-average molecular weight of a polymer is given by 

The mode of termination is experimentally determined from the observation of the number of initiator fragments per polymer molecule. This requires the analysis of the molecular 

The general relationship between the degree of polymerization and the kinetic chain length is 

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Tlie formation of initiator radicals is not the only process that determines the concentration of free radicals in a polymerization system. Polymer propagation itself does not change the radical concentration it merely changes one radical to another. Termination steps also occur, however, and these remove radicals from the system. We shall discuss combination and disproportionation reactions as modes of termination. 

The degree of polymerization values in the two combining radicals can have any value, and the molecular weight of the product molecule will be considerably higher on the average than the radicals so terminated. The polymeric product molecule contains two initiator fragments per molecule by this mode of termination. 

This mode of termination produces a negligible effect on the molecular weight of the reacting species, but it does produce a terminal unsaturation in one of the dead polymer molecules. Each polymer molecule contains one initiator fragment when termination occurs by disproportionation. 

A kinetic analysis of the two modes of termination is quite straightforward, since each mode of termination involves a bimolecular reaction between two radicals. Accordingly, we write the following ... 

As with the rate of polymerization, we see from Eq. (6.37) that the kinetic chain length depends on the monomer and initiator concentrations and on the constants for the three different kinds of kinetic processes that constitute the mechanism. When the initial monomer and initiator concentrations are used, Eq. (6.37) describes the initial polymer formed. The initial degree of polymerization is a measurable quantity, so Eq. (6.37) provides a second functional relationship, different from Eq. (6.26), between experimentally available quantities-n, [M], and [1]-and theoretically important parameters—kp, k, and k. Note that the mode of termination which establishes the connection between u and hj, and the value of f are both accessible through end group characterization. Thus we have a second equation with three unknowns one more and the evaluation of the individual kinetic constants from experimental results will be feasible. 

Only one additional stipulation needs to be made before adapting the results that follow from Eq. (5.24) to addition polymers. The mode of termination must be specified to occur by disproportionation to use the results of Sec. 5.4 in this chapter, since termination by combination obviously changes the particle size distribution. We shall return to the case of termination by combination presently. 

This contrasts with a limiting ratio of 2 for the case of termination by disproportionation. Since and can be measured, this difference is potentially a method for determining the mode of termination in a polymer system. In most instances, however, termination occurs by some proportion of both modes. Although general expressions exist for the various averages and their ratio when both modes of termination are operative, molecular weight data are generally not sufficiently precise to allow the proportions of termination modes to be determined in this way. 

The third mode of termination which occurs in some carbonium ion polymerizations involves rearrangement of the active carbonium ion into an inactive one which cannot continue the propagation. These reactions can be avoided to a great extent by working at sufficiently low temperatures, and on the whole, they only contribute significantly to the termination reaction in a few systems. 

Since the mode of termination clearly plays an important part in determining the polymer end groups and the molecular weight distribution, a knowledge of the disproportionatiomeombination ratio (ki(t/kK) is vital to the understanding of structure-property relationships. Unsaturated linkages at the ends of polymer... 

The nature of the termination reaction in MMA polymerization has been investigated by a number of groups using a wide range of techniques (Tabic 5.5), There is general agreement that there is substantial disproportionation. However, there is considerable discrepancy in the precise values of k tk. In some cases the difference has been attributed to variations in the way molecular weight data are interpreted or to the failure to allow for other modes of termination under the polymerization conditions (chain transfer, primary radical termination).154 In other eases the reasons for the discrepancies are less clear. MALDI-TOF mass... 

Therefore, the classical polymerization model Is applicable only to those conversion trajectories that yield polydispersitles betwen 1.5 and 2 regardless of the mode of termination. Although this Is an expected result, It has not been Implemented, the high conversion polymerization models reported to date are based on the classical equations for which the constraint given by equation 24 Is applicable. The result has been piecewise continuous models, (1-6)... 

The distribution of molecular mass is complicated in case of the radical polymerisation, since there are various types of termination. Let us consider the simplest mode of termination, i.e., termination by... 

Another mode of termination by monomer, which has been suggested for the polymerization of N-vinylcarbazole, is formation of a quaternary ammonium ion from the growing cation and the monomer [25] which is essentially the same as reaction (XIa). 

For termination of the long chain, these free radicals can combine in different ways to form polythene. One mode of termination of chain is shown as under ... 

The mode of termination varies with monomer and reaction conditions. While styrene macroradicals typically terminate by coupling, methyl methacrylate macroradicals terminate by coupling at temperatures below 60°C, but by disproportionation at higher temperatures. 

Termination can also occur by a combination of coupling and disproportionation. The two different modes of termination can be represented in general terms by... 

Under conditions where bimolecular termination between propagating radicals becomes difficult because of the increased viscosity or heterogeneity, primary termination may become important or even the only mode of termination. The latter leads to Rp being second-order in [M] and zero-order in [I],... 

Whether the formation of poly(p-xylylene) should be included in this chapter is not clear. Decisive data are not available to indicate the classification of this polymerization as a step or chain reaction. The formation of high polymer occurs instantaneously when p-xyly-lene contacts the cool surface, precluding the evaluation of polymer molecular weight versus conversion. Also, the mode of termination for this reaction is unknown. 

Using 14C-labeled AIBN as an initiator, a sample of styrene is polymerized to an number-average degree of polymerization of 1.52 x 104. The AIBN has an activity of 9.81 x 107 counts min-1 mol 1 in a scintillation counter. If 3.22 g of the polystyrene has an activity of 203 counts min-1, what is the mode of termination ... 

The value of h during intervals II and III is of critical importance in determining Rp and has been the subject of much theoretical and experimental work. Three cases can be distinguished—cases 1, 2, and 3. The major differences between the three cases are the occurence of radical diffusion out of the polymer particles (desorption), the particle size, modes of termination, and the rates of initiation and termination relative to each other and to the other reaction parameters. The quantitative interplay of these factors leading to case 1, 2, or 3 behavior has been discussed [Gao and Penlidis, 2002 Gilbert, 1995 Nomura, 1982 ... 

Termination by combination differs from the other modes of termination in that the kinetic chain is usually terminated, since the concentration of the initiator-coinitiator complex decreases. 

Water, alcohols, acids, anhydrides, and esters have varying chain-transfer properties [Mathie-son, 1963]. The presence of any of these transfer agents in sufficient concentrations results in Reaction 5-28 becoming the dominant mode of termination. Termination by these compounds involves transfer of HO, RO, or RCOO anion to the propagating carbocation. Aromatics, ethers, and alkyl halides are relatively weak chain-transfer agents. Transfer to aromatics occurs by alkylation of the aromatic ring. 

The overall kinetics vary considerably depending largely on the mode of termination in a particular system. Consider the case of termination exclusively by combination of the propagating center with the counterion (Eq. 5-21). The kinetic scheme of initiation, propagation, and termination consists of Eqs. 5-3, 5-4, 5-16, and 5-21, respectively. The derivation of the... 

The expressions (Eqs. 5-34 and 5-42) for Rp in cationic polymerization point out one very significant difference between cationic and radical polymerizations. Radical polymerizations show a -order dependence of Rp on while cationic polymerizations show a first-order depenence of Rp on R,. The difference is a consequence of their different modes of termination. Termination is second-order in the propagating species in radical polymerization but only first-order in cationic polymerization. The one exception to this generalization is certain cationic polymerizations initiated by ionizing radiation (Secs. 5-2a-6, 3-4d). Initiation consists of the formation of radical-cations from monomer followed by dimerization to dicarbo-cations (Eq. 5-11). An alternate proposal is reaction of the radical-cation with monomer to form a monocarbocation species (Eq. 5-12). In either case, the carbocation centers propagate by successive additions of monomer with radical propagation not favored at low temperatures in superpure and dry sytems. 

Termination occurs by transfer of a positive fragment, usually a proton, from the solvent or some transfer agent (often deliberately added), although other modes of termination are also known. Many anionic polymerizations are living polymerizations when the reaction components are appropriately chosen. 

However, in the majority of cases, the substrates with substituted double bonds give complex mixtures of products, due to competition of both modes of termination, exo- and //[Pg.421]

Fouassier and Chesneau [219] is not consistent with the experimental observations. From the values of the rate constants of triplet decay presented in Table 8, and taking into account that k3/k2 = 0.23 (as determined by Kasche and Lindqvist), we calculate the quantum yield of D + under the polymerization conditions. For Eosin (3 x 10 5 M) and MDEA (0.1 M) the yield of semioxidized Eosin radical is 4 x 10 3 M in the presence or in the absence of 2 x 10 3 M PDO. From the values for the quantum yield of photopolymerization and the molecular weight in the absence of PDO we calculate a quantum yield of initiation between 0.086 and 0.17, the actual value depending on the mode of termination. Therefore, we conclude that formation of a-amino radicals according to Scheme 10 represents only a minor contribution to the quantum yield of initiation observed in the presence of PDO. 

The most probable mode of termination of long-chain polymers may result from a wrong addition of an activated monomer, e. g. 

Which mode of termination occurs can be determined by measuring the number of initiator fragments per polymer molecule. If there are two initiator fragments in each molecule, termination must have occurred by combination. One initiator fragment per molecule indicates disproportionation. Apparently, ethenylbenzene polymerizations terminate by combination, but with methyl 2-methylpropenoate, both reactions take place, disproportionation being favored. 

The most important mode of termination of a radical polymerization is the bimolecular interaction of its reactive centers. Radicals rapidly recombine or disproportionate, and these reactions anihilate the growing ends. On the other hand, neither recombination nor disproportionation takes place in an ionic polymerization, and hence a collision between two ionically growing centers usually does not lead to termination. 

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