Terminal double bond, TDB

The classes approach is applicable to multidimensional problems where the range of the second and higher dimensions is restricted to a small range. In the examples of this approach we will discuss presently, these second dimensions are the numbers of terminal double bonds (TDBs) on a chain in the case of poly(vinyl acetate) (PVAc) and the numbers of radical sites on a chain in the case of low-density polyethylene (LDPE). The idea simply is to solve the problem rigorously in the first dimension, chain length, for separate classes with a fixed value for the second dimension. Thus, a 2D problem is reduced to a set of ID problems, where the size of the set is determined by the number of values of the second variable - the number of classes - for which the solution is desired. Obviously, this is only feasible when the number of classes is limited, since the equations have to be implemented separately for each class. A different classes approach is followed by Pladis and Kippar-issides [8], who combined it with a method of moments. 

Notation m, n chain length i, j number of terminal double bonds (TDB) per chain k, 1 number of branches per chain. 

CLD/Number of Terminal Double Bonds (TDB) Distribution for Poly(vinyl acetate) -More than one TDB per Chain... 

The problem of incorporation of chains with a terminal double bond (TDB) exists in polymerizations discussed above, such as radical polymerization of vinyl acetate and olefin polymerization with a constrained-geometry metallocene catalyst (CGC). Tobita [15] has developed an MC algorithm for this problem for the PVAc case. It is assumed that TDBs are created by transfer to monomer only, while recombination is absent, which results in a maximum of one TDB per chain. We largely follow Tobita s explanation, but differ in that we will assume that disproportionation is the termination mechanism, while transfer to solvent and to polymer are not yet being accounted for. Later we will address the real PVAc problem, which in fact has two branching mechanisms TDB propagation and transfer to polymer. 

Tip 8 Terminal double bond polymerization. Transfer to monomer and termination by disproportionation lead to dead polymer molecules with a TDB. This TDB may react with a polymer radical, thus forming a radical center somewhere along the chain of the combined molecules. This radical center, on propagation with monomer, will evenmally form a trifunctionally branched chain. 

Since we will not address branching here, the set has to be reduced to 2D, by summation over the branching index fe. The second dimension, the number of TDBs per chain, is concerned with the manner in which they are created. One of two possible mechanisms is transfer to monomer, producing a monoradical with a TDB according to the reaction equation shown in Table 9.4. Subsequent propagation of this monoradical leads to a chain with a TDB. The second mechanism is disproportionation, directly leading to chain with a TDB. Now, chains with more than one terminal double bond can be created in two ways insertion of chains with a TDB created by disproportionation termination, or by termination by recombination. If... 

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