Polymer molecules, coupling

The growth characteristics of the reaction, however, are those of a polycondensation process, in which polymer molecules couple with other polymer molecules (15). 

The oxidative coupling of 2,6-disubstituted phenols to poly-(arylene oxides) is a polycondensation reaction, in which polymer molecules couple with other polymer molecules as well as with monomer. Unstable quinone ketals formed by coupling of a polymeric aryloxy radical at the para position of the phenolic ring of a second radical are believed to be intermediates or the reaction. The ketals may be converted to polymeric phenols either by a series of intramolecular rearrangements or by disproportionation to aryloxy radicals, leading to a mobile equilibrium between polymer molecules of varying degree of polymerization. Both processes have been shown to occur, with their relative importance determined by the reaction conditions. 

Although reactions of this kind must occur, there are two observations which cannot be explained on this basis. Firstly, the dimer (I) forms a polymer identical with that obtained from 2,6-xylenol since no monomer is present in this case, the above scheme cannot explain polymerization completely. Secondly, when 2,6-xylenol is polymerized, there is a sharp increase in average molecular weight near the end of the reaction this type of behaviour is typical of stepwise reactions in which polymer molecules couple with each other (Section 1.4.5). However, there is no inunediately apparent way by which two polyarylene ether molecules can be coupled. There is experimental evidence (see Reference 8 for an account of this work) that coupling takes place through two processes, namely redistribution and rearrangement with the relative contribution of each depending on reaction conditions. 

In this chapter we examine the elastic behavior of polymers. We shall see that this behavior is quite different from the elasticity displayed by metals and substances composed of small molecules. This is a direct consequence of the chain structure of the polymer molecules. In many polymers elasticity does not occur alone, but coupled with viscous phenomena. The combination of these effects is called viscoelasticity. We shall examine this behavior as well. 

Even though the rate of radical-radical reaction is determined by diffusion, this docs not mean there is no selectivity in the termination step. As with small radicals (Section 2.5), self-reaction may occur by combination or disproportionation. In some cases, there are multiple pathways for combination and disproportionation. Combination involves the coupling of two radicals (Scheme 5.1). The resulting polymer chain has a molecular weight equal to the sum of the molecular weights of the reactant species. If all chains are formed from initiator-derived radicals, then the combination product will have two initiator-derived ends. Disproportionation involves the transfer of a P-hydrogen from one propagating radical to the other. This results in the formation of two polymer molecules. Both chains have one initiator-derived end. One chain has an unsaturated end, the other has a saturated end (Scheme 5.1). 

If chain transfer of the radical center to a previously formed polymer molecule is followed ultimately by termination through coupling with another similarly transferred center, the net result of these two processes is the combination of a pair of previously independent polymer molecules. T. G. Fox (private communication of results as yet unpublished) has suggested this mechanism as one which may give rise to network structures in the polymerization of monovinyl compounds. His preliminary analysis of kinetic data indicates that proliferous polymerization of methyl acrylate may be triggered by networks thus generated. 

Screw rotation. The symmetry element is a screw axis. It can only occur if there is translational symmetry in the direction of the axis. The screw rotation results when a rotation of 360/1V degrees is coupled with a displacement parallel to the axis. The Hermann-Mauguin symbol is NM ( N sub M )-,N expresses the rotational component and the fraction M/N is the displacement component as a fraction of the translation vector. Some screw axes are right or left-handed. Screw axes that can occur in crystals are shown in Fig. 3.4. Single polymer molecules can also have non-crystallographic screw axes, e.g. 103 in polymeric sulfur. 

This type of modification process has been used to form sulfhydryl-reactive dextran polymers by coupling amine spacers with crosslinkers containing an amine reactive end and a thiol-reactive end (Brunswick et al., 1988 Noguchi et al., 1992). The result was a multivalent sulfhydryl-reactive dextran derivative that could couple numerous sulfhydryl-containing molecules per polymer chain. 

Direct quantitative determination of the number of initiator fragments combined with the polymer is feasible only under very exceptional circumstances. Another useful method depends on the determination of the Molecular weight by a suitable method. The number of polymer molecules may then be calculated, and assuming termination by coupling, the number of combined, primary radicals may be considered to be twice the number of molecules, still another method for determining the efficiency depends on the reaction of the chain radicals stoichiometrically with certain inhibitors. 

The PET polymer structure can also be generated from the reaction of ethylene glycol and dimethyl terephthalate, with methyl alcohol as the byproduct. A few producers still use this route. The aromatic rings coupled with short aliphatic chains are responsible for a relatively stiff polymer molecule, as compared with more aliphatic structures such as polyolefin or polyamide. The lack of segment mobility in the polymer chains results in relatively high thermal stability, as will be discussed later. 

It is probable that the 1,2- coupled units are essentially locked in position and can only move as the whole polymer molecule moves. The great complexity of the nmr spectra of polymers containing... 

Note 2 The term halatopolymer is used for a linear polymer formed by the coupling of halato-telechelic polymer molecules, for example, for the linear polymer formed by the coupling of carboxylate end-groups with divalent metal cations [2]. 

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... 

Using the methods described, the values of Cm and Ci in the benzoyl peroxide polymerization of styrene have been found to be 0.00006 and 0.055 respectively [Mayo et al., 1951]. The amount of chain transfer to monomer that occurs is negligible in this polymerization. The chain-transfer constant for benzoyl peroxide is appreciable, and chain transfer with initiator becomes increasingly important as the initiator concentration increases. These effects are shown in Fig. 3-7, where the contributions of the various sources of chain ends are indicated. The topmost plot shows the total number of polymer molecules per 105 styrene monomer units. The difference between successive plots gives the number of polymer molecules terminated by normal coupling termination, transfer to benzoyl peroxide, and transfer to styrene. 

Equation 3-189 gives the probabihty of forming an x-sized polymer molecule by only one of many equally probable pathways. An x-sized polymer molecule can be obtained by couplings of y- and z-sized radicals, z- and y-sized radicals, (y + 1)- and (z — l)-sized radicals, (z — 1)- and (y + l)-sized radicals, (y + 2)- and (z — 2)-sized radicals, (z — 2)- and (y + 2)-sized radicals, (y — 1)- and (z + l)-sized radicals, (z + 1)- and (y — l)-sized radicals, and so on. There are (x — 1) possible pathways of producing an x-sized polymer molecule when x is an even number. Each pathway has the same probability—that given by Eq. 3-189—and the total probability A), for forming an x-sized polymer molecule is given by... 

For a radical polymerization with bimolecular termination, the polymer produced contains 1.30 initiator fragments per polymer molecule. Calculate the relative extents of termination by disproportionation and coupling, assuming that no chain-transfer reactions occur. 

It should be noted that the degree of polymerization in an emulsion polymerization is synonymous with the kinetic chain length. Although termination is by bimolecular coupling, one of the radicals is a primary (or oligomeric) radical, which does not significantly contribute to the size of a dead polymer molecule. The derivation of Eq. 4-7 assumes the absence... 

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... 

While the monomer concentration couples to all equations, the equations for each polymer species are sometimes functions of only species immediately before and after it, so that the equations for each polymer molecule can be solved sequentially. 

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