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solvent are too active in transfer, a less active initiator or solvent would be chosen. If the monomer itself is too active in transfer, it sets the upper limit of the molecular weight that can be achieved as long as all other factors are optimized. Case 2 involves a reaction system that yields too high a polymer molecular weight. The simplest method of lowering molecular weight is to add a chain-transfer agent. Equation 3-119 is used to determine the transfer agent and concentration needed to obtain a speci cally desired molecular weight. When used in this manner, transfer agents are called regulators or modi ers. Transfer agents with transfer constants of one or greater are especially useful, since they can be used in low concentrations. Thus, thiols such as 1-dodecanethiol are used in the industrial emulsion copolymerization of styrene and 1,3-butadiene for SBR rubbers. The production of very low-molecular-weight polymers by chain transfer (telomerization) is an industrially useful process. Ethylene polymerized in chloroform yields, after uorination of its end groups, a starting material for uorinated lubricants. Low-molecular-weight acrylic ester polymers have been used as plasticizers. It is also useful to point out that chain-transfer studies yield further corroboration of the concept of functional group reactivity independent of molecular size. Thus one can vary the degree of polymerization for a monomer by using different chain-transfer agents or different concentrations of the same transfer agent. Under these conditions the propagation rate constant kp is found to be independent of X n . Further, the transfer constant ktr for a particular transfer agent is also independent of the size of the propagating radical.
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The previous discussion has ignored the possibility of chain transfer to polymer molecules. Transfer to polymer results in the formation of a radical site on a polymer chain. The polymerization of monomer at this site leads to the production of a branched polymer, for example
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Y CH2 C Mm
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Ignoring chain transfer to polymer does not present a dif culty in obtaining precise values of CI , CM , and CS , since these are determined from data at low conversions. Under these conditions the polymer concentration is low and the extent of transfer to polymer is negligible. Transfer to polymer cannot, however, be neglected for the practical situation where polymerization is carried to complete or high conversion. The effect of chain transfer to polymer plays a very signi cant role in determining the physical properties and the ultimate applications of a polymer [Small, 1975]. As indicated in Chap. 1, branching drastically decreases the crystallinity of a polymer. The transfer constant CP for chain transfer to polymer is not easily obtained [Yamamoto and Sugimoto, 1979]. CP cannot be simply determined by introducing the term CP [P]/[M] into Eq. 3-108. Transfer to polymer does not necessarily lead to a decrease in the overall degree of polymerization. Each act of transfer produces a branched polymer molecule of
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larger size than initially present in addition to prematurely terminating a propagating polymer chain. The evaluation of CP involves the dif cult determination of the number of branches produced in a polymerization relative to the number of monomer molecules polymerized. This can be done by polymerizing a monomer in the presence of a known concentration of polymer of known molecular weight. The product of such an experiment consists of three different types of molecules: Type 1. Unbranched molecules of the initial polymer. Type 2. Unbranched molecules produced by polymerization of the monomer. Type 3. Branched molecules arising from transfer of type 2 radicals to type 1 molecules. The number of new polymer molecules produced in the system yields the number of type 2 molecules. The total number of branches is obtained by performing a mass balance on the system and assuming the size of a branch is the same as a type 2 molecule. This experimental analysis is inherently dif cult and is additionally complicated if chain transfer to initiator, monomer, or some other species is occurring simultaneously. Other methods of determining the polymer transfer constant have also been employed but are usually not without ambiguity. Thus, for example, CP for poly(vinyl acetate) has been determined by degradative hydrolysis [Lindeman, 1967]. This method assumes that transfer occurs at the acetoxy methyl group leading to polymer branches
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