Combination versus Disproportionation

Plots of the type shown in Fig. 12 (F versus n) were first given by Katz et al Their treatment, however, suffers from a number of limitations. These are (i) the numerical labor involved in generating the moment expansion, (ii) the imperfect resolution involved in generating the cumulative distribution [Eq. (64)] rather than the full distribution, and (iii) the neglect of exit, transfer, and bimolecular combination by disproportionation. Point (ii) may be illustrated as follows. Consider a combination-dominated system in two limits the fuUy compartmentalized case of n = O.S, when one has Sbc oc exp(—at ), and the bulk case, where n = oc. when one has Sbc°ctexp(—ar l. where a is a parameter proportional to Oc. Figure IS... 

Figure 3.23 Termination rate eoeffieient versus chain length for the Smoluchowski model including Poisson broadening (no chain transfer to monomer) variation of the amount of combination over disproportionation. The line represents the input value of the simulation.

In the kinetic analysis, the fact that termination and chain transfer are second and first order processes with respect to the radical concentration, respectively, can then be exploited. The scaling of the number MWD now has to be done such that the radical concentration versus time that is derived from this distribution, is in agreement with the amount of material that is found to originate from chain transfer to monomer. Hence, the degree of freedom in the scaling of the number MWD is limited by a second kinetic condition. It should be noted, however, that knowledge of the ratio of termination by combination over disproportionation is needed for that. 

Il is particularly informative to compute P as a function of H for combination-dominated and disproportionation-dominated stems (note incidentally that 0.5 is the lower limit of n in such a system). It will be seen that when S 2, the compartmentalized system is indeed a minibulk system, with compartmentalization effects becoming more pronounced as n becomes smaller. The P versus n results shown in Figs. 5 and 6 were obtained by fixing p and systematically varying either (Fig. 12) or (Fig. I3I. The values of P were obtained from tbe MWD expressions given in Sections I1.D.I (valid for n < 0.7) and II D,2 (valid for any ii). 

When we added NHPI in combination with EBHP reasonable selectivities were obtained up to 12 % conversion (Table 3). Although yields and selectivities obtained in this case were not so high as in the case of cumene and cyclohexyl-benzene, the same trend can be discerned. At low conversions selectivities are always much higher tiien at higher conversions where - due to the number of terminations which have taken place - the amount of byproducts due to disproportionation of alkylperoxy radicals is substantial. NHPI is able to substantially change the ratio of selectivity versus conversion. In Figure 3, the selectivity is plotted as a function of conversion. 

Gibian, M. J. and Corley, R.C., Organic radical-radical reactions disproportionation versus combination, Chem. Rev., 73,441 64, 1973. 

The molecular weight of a polymer prepared by radical-chain polymerization depends on the relative rate of propagation versus the rates of steps that stop the growth of the polymer chain. One of the processes that stops chain growth is termination, which can occur either by combination of two radical centers or by disproportionation, to give one polymer with a saturated end group and another with a vinyl end group ... 

Rp (Equation 3.10) and DP are both dependent on k /kt, with DP also a function of mode of termination (disproportionation versus combination) and chain transfer. Transfer can occur to monomer, solvent or any other species in the system. In some cases, chain transfer agents are added deliberately to Umit and control polymer DP . These agents are... 

One can alternatively estimate the concentration of antibody by assuming bivalence and extrapolating the binding curve (r/c versus r) to the abscissa to estimate the total concentration of combining sites. This extrapolation requires the assumption that no disproportionate amount of low affinity antibody is present. 

The relative importance of termination by disproportionation versus combination expressed by S [ Eq. (8)] is difficult to measure. The value depends largely on the structure of the monomer S is in the range of 0.5-0.8 for a-methylvinyl monomers such as the methacrylates and 0.05-0.2 for styrene and acrylates [3]. A weak temperature dependency has been proposed, but is difficult to verify within the scatter of the data [19]. 

In these model studies, evaluation of fetd/fetc is simplified because reactions that compete with disproportionation or combination are more readily detected and allowed for. However, by their very nature, model studies carmot exactly simulate all aspects of the polymerization process. Consequendy, a number of factors must be borne in mind when using model studies to investigate the termination process. These stem from differences inherent in polymerization versus simple organic reaaions and include the following ... 

GPC-derived weight average molecular weights are often less prone to error than number average molecular weights. When termination is wholly by disproportionation or chain transfer and chains are long (> 10 units), classical kinetics predicts Vn = Vw/2 (Section 3.04.4.4.1). It follows that Co- can be obtained from the slope of a plot of 2/Xw versus [T]o/[M]o. The errors introduced even when the dominant process for radical-radical termination is combination (e.g., S polymerization) are small as long as Xn is small in relation to X o ... 

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