Propagation conversion dependence

A variety of behaviors are observed for the polymerization rate versus conversion depending on the relative rates of initiation, propagation, and termination, which are in turn dependent on the monomer and reaction conditions (Fig. 4-2). Irrespective of the particular behavior observed, three intervals (I, II, III) can be discerned in all emulsion polymerizations based on the particle number N (the concentration of polymer particles in units of number of... 

The intense heat dissipated by viscous flow near the walls of a tubular reactor leads to an increase in local temperature and acceleration of the chemical reaction, which also promotes an increase in temperature the local situation then propagates to the axis of the tubular reactor. This effect, which was discovered theoretically, may occur in practice in the flow of a highly viscous liquid with relatively weak dependence of viscosity on degree of conversion. However, it is questionable whether this approach could be applied to the flow of ethylene in a tubular reactor as was proposed in the original publication.199 In turbulent flow of a monomer, the near-wall zone is not physically distinct in a hydrodynamic sense, while for a laminar flow the growth of viscosity leads to a directly opposite tendency - a slowing-down of the flow near the walls. In addition, the nature of the viscosity-versus-conversion dependence rj(P) also influences the results of theoretical calculations. For example, although this factor was included in the calculations in Ref.,200 it did not affect the flow patterns because of the rather weak q(P) dependence for the system that was analyzed. 

The same authors used photoDSC to obtain time- or conversion-dependent ratios of the termination and propagation rate coefficients 2kt/kp for the polymerization of VA. The starting point of this approach is the classical equation derived from formal kinetics ... 

The evolution of molecular weight with conversion depends primarily on the rates of initiation and/or termination relative to propagation, and on the effect of monomer concentration on transfer. Transfer reduces molecular weight. Kinetically, transfer can be divided into reactions which are either first or zero order in monomer. First-order react ions occur when monomer is involved in the rate-limiting step of the transfer process, even though... 

From the conversion dependence of the insolubilization process, it was concluded that both inter- and intramolecular propagation reactions occur during the polymerization of the epoxy ring. Blends of epoxidized polyisoprene and difunctional vinyl ether or aciylate monomers were shown to undergo a fast and extensive cross-linking polymerization, with formation of interpenetrating polymer networks. 

The local strain approximation is used to cailculate the conversion dependence of Fj and Fp as shown in Fig. 4. Monomer units are subjected to a force f(X) due to lattice strain and initiation and propagation produce identical local lattice distortions. The crystal, is assumed to relax to its new average strain after the reaction barrier has been crossed locally. Then ... 

As shown in Figure 6.6, a catalytic cycle for the copolymerization of ethylene and MA involving catalytic intermediates of the types 6.35 and 6.39 may be proposed. Conversion of 6.35 to 6.41 is simply an insertion reaction and that of 6.41 to 6.42 are multiple insertions of ethylene and MA, i.e., propagation steps. The relative numbers of ethylene and MA that take part in the propagation steps depend on the reactivity ratio, i.e., ratio of the rate constants for insertions of the two monomers. 

The relative importance of these mechanisms, and the value of the overall kt, depends on the molecular weight and dispersity of the propagating species, the medium and the degree of conversion. The value of k, is not a constant ... 

We shall use Rp to represent the rate of polymerization as well as the rate of propagation, therefore. According to Eq. (12), the rate of polymerization should vary as the square root of the initiator concentration. If/ is independent of the monomer concentration, which will almost certainly be true if / is near unity, the conversion of monomer to polymer will be of the first order in the monomer concentration. On the other hand, if / should be substantially less than unity, it may then depend on the concentration of monomer in the extreme case of a very low efficiency, / might be expected to vary directly as [M whereupon the chain radical concentration becomes proportional to Mand the polymerization should be three-halves order in monomer. 

The susceptibility of the polymerization of a given monomer to autoacceleration seems to depend primarily on the size of the polymer molecules produced. The high propagation and low termination constants for methyl acrylate as compared to those for other common monomers lead to an unusually large average degree of polymerization (>10 ), and this fact alone seems to account for the incidence of the decrease in A f at very low conversions in this case. 

Mechanisms depending on carbanionic propagating centers for these polymerizations are indicated by various pieces of evidence (1) the nature of the catalysts which are effective, (2) the intense colors that often develop during polymerization, (3) the prompt cessation of sodium-catalyzed polymerization upon the introduction of carbon dioxide and the failure of -butylcatechol to cause inhibition, (4) the conversion of triphenylmethane to triphenylmethylsodium in the zone of polymerization of isoprene under the influence of metallic sodium, (5) the structures of the diene polymers obtained (see Chap. VI), which differ. both from the radical and the cationic polymers, and (6)... 

This reaction undergoes conversion in one sequence of consecutive elementary reaction steps and so only one propagating front is formed in a spatially distributed system [68]. Depending on the initial ratio of reactants, iodine as colored and iodide as uncolored product, or both, are formed [145]. 

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