Branching by Chain Transfer

The direction of each chain s growth is indicated by an arrow, which also marks the point at which transfer terminates its growth. Instances in which branching by transfer may assume importance were cited in Chapter VI. 

The structure shown above bears an obvious resemblance to that of the A—R—B/ i-type condensation polymers shown in Fig. 64, 

The degree of branching by transfer with polymer obviously will increase with the conversion since the relative incidence of branching must depend on the ratio of polymer to monomer in the system. To examine the matter from the point of view of reaction rates, let 6 represent the fraction of monomer molecules which have polymerized out of a total of iVo in the system, and let v represent the total number of branches. (At variance with the definition used elsewhere. No is the total number of units polymerized and unpolymerized as well.) The rates of generation of branches and of polymerization can then be written 

The equivalent function of the degree of conversion is encountered in the cross-linking of diene polymers discussed below. It is plotted in Fig. 73 in relation to the latter problem. For present purposes it is necessary merely to replace the ordinate in Fig. 73 with p/Cp. Regardless of the absolute magnitude of the branching transfer constant, the relative amount of branching must increase rapidly with conversion. 

A molecule whose first primary chain was formed early in the polymerization will, on the average, acquire more branches than a molecule originated later even among those originating in the same time inter- 

---

Nonlinear structures may arise in vinyl polymerizations through chain transfer with monomer or with previously formed polymer molecules, but such processes usually occur to an extent which is scarcely significant. A more common source of nonlinearity in the polymerization of a 1,3-diene is the incorporation in a growing chain of one of the units of a previously formed polymer molecule. The importance of both branching by chain transfer and cross-linking by addition of a polymer unit increases with the degree of conversion of monomer to polymer. 

Branching occurs in some. free-radical polymerization of monomers like ethylene, vinyl chloride, and vinyl acetate in which the propagating polymer radical is very reactive and can lead to branching by chain transfer to the backbone chain of another polymer molecule or onto its own chain (see Chapter 6). 

As in the case of intramolecular hydrogen abstraction, branching by chain transfer is not a problem when alkenes are polymerized under Ziegler-Natta conditions because free radicals are not intermediates in coordination polymerization. 

End Groups and Branching. Both saturated and unsaturated end groups can be formed during polymerization by chain transfer to monomer or polymer and by disproportionation. Some of the possible chain end groups are... 

Glass-Transition Temperature. The T of PVP is sensitive to residual moisture (75) and unreacted monomer. It is even sensitive to how the polymer was prepared, suggesting that MWD, branching, and cross-linking may play a part (76). Polymers presumably with the same molecular weight prepared by bulk polymerization exhibit lower T s compared to samples prepared by aqueous solution polymerization, lending credence to an example, in this case, of branching caused by chain-transfer to monomer. 

The main topic of interest is the properties of molecules of finite size, having no large rings, and in general having trifunctional branch-points. These are typically produced by chain-transfer with polymer in free-radical polymerizations, though they can of course be made in other ways. Molecules with branch-points of higher functionality are also of interest, especially star-shaped molecules with several arms, as these are both easy to synthesize and relatively easy to discuss theoretically. 

The compartmentalization of radicals may produce another important effect when large-sized branched polymer molecules are formed by chain transfer to polymer plus combination termination. As clarified in Sect. 4.1, when the n value is small, the frequency of bimolecular termination reactions between large polymer radicals drops significantly compared to models that do not account for compartmentalization of radicals. From this fact, it is easy to see that the size of branched polymer molecule is smaller than that calculated without considering compartmentalization effects [281]. 

Molecular weight distributions in commercial polymers are characterized by ratios of about 3 for substances like polystyrene in which transfer to polymer does not appear to be important. Where long branches can be formed by chain transfer to polymer, the molecular weight distribution will be even broader and M /M ratios of 50 and more are observed in some polyethylenes made by free-radical syntheses. 

Note that the molecular weight distributions of high-conversion polymers made under conditions where the growth of macromolecules is limited primarily by chain transfer will be random, as described in Section 6.14.1 for low-conversion ca.ses. Then M /M will be 2. An exception to this rule occurs when the chain transfer reactions which determine the polymer molecular weight are to monomer and can result in branching [as in reactions (6-79) or (6-84)]. Tlie molecular weight distributions of the branched polymers that are produced will be broader than the random one, and bimodal distributions may also be observed. 

Ionic routes such as formation of the polymer anion by reaction with a strong base or the direct reaction of a polyamide with sodium are less likely to be used in reactive processing than is free-radical initiation. The process of self-graft polymerization by chain transfer to polymer, when it occurs in a single monomer/polymer system during polymerization, is an example of chain branching that is discussed in the next section. 

The kinetic scheme of this process was studied in greater detail by German researchers102 the formation of long-chain branches (chain transfer on the polymer) and short-chain branches (intramolecular chain transfer) was taken into account. 

In the Soviet study110, the following elementary stages were taken into account in the kinetic scheme of vinyl acetate polymerization chain transfer to the monomer, solvent, and polymer, and chain termination caused by the disproportionation of radicals. It was assumed that long-chain branches could be formed by chain transfer both to the acetate group hydrogen atoms and to the main chain hydrogen. 

PREPARATION OF HIGHLY BRANCHED GRAFT COPOLYMERS BY CHAIN TRANSFER REACTION... 

Taking the reaction mechanism mentioned above into consider-ration, we derived the relationship between the chain transfer constant, extent of monomer conversion, and the number of branches in the graft copolymerization by chain transfer mechanism (6). 

Pressure exerts a marked effect on the polymerization reaction rate constant and can be used to control the reaction rate and molecular weight in addition to the more usual variables of initiator concentration and temperature. Since the number of short branches and the molecular weight are determined by chain transfer reactions which are more influenced by temperature and less by pressure than the polymerization reaction, it follows that the molecular weight decreases and the degree of short branching increases with increasing temperature (and vice versa with pressure). 

---