Termination rate constant, molecular weight distribution

Assuming monomer termination as the main termination reaction, L6hr et al. (64) estimated the termination rate constant from the molecular weight distribution of the polymers. No direct evidence for the termination mechanism assumed was given, however. 

The polymerization proceeds without termination or chain transfer to give poly-norbomene with a narrow molecular weight distribution [35], After an induction period, the rate of monomer consumption (rate of polymerization) becomes constant, indicating a zero-order dependence on the monomer concentration. The induction period is caused by part of titanacycle 7 undergoing non-productive, but rapidly reversible, cleavage to norbornene and the titanium methylene complex, Eq. (17 a). 

Table 13.3 presents the expressions for the rate constants applied in this work. The parameters are taken mostly from the work of Xie et al. [6], A distinctive feature of the numerical simulation of the influence of gel effect on the termination in the polymer-phase is described by a relation proposed by Kipparisides et al. [5], This combination of parameters gives realistic results on modeling both the reaction dynamics and the development of the molecular-weight distribution, reproducing closely experimental data (see Figure 13.6). The subscript 1 refers to the monomer phase, 2 to the polymer phase, and 22 to the polymer-phase after the critical conversion Xf. In addition, Table 13.4 presents first-order constants for usual initiators. 

This decrease in termination rate constant, which will be referred to as gel-effect, always causes a significant increase in rate of polymerization and can also shift the molecular weight distribution to higher molecular weights, but the magnitude of the shift depends upon which reactions control molecular weight development. By increase in polymerization rate we mean the increase over the rate which would have been observed had gel-effect been absent. 

The kinetic scheme with constant reaction of the polymer/monomer droplet increases fairly quickly with conversion, and the mobility of the polymer chains rapidly falls below the mobility of the monomer. The reduced diffusion of live polymer chains in the droplet will reduce the rate of termination of polymerization. The associated increase in the number of radicals will cause a rapid increase in the polymerization rate. This phenomenon is well known as the Trommsdorf or gel effect [8,9]. The gel effect causes a growth of the polymer chain length and widening of the molecular weight distribution (Figure 9.5). 

We assume here that the concentrations of monomer and initiator remain sensibly constant during the polymerization, and that any dependence of termination rate constants on macroradical size and concentration or autoacceleration effects can be neglected. Tliis means that the molecular weight distributions to be derived can be expected to apply to low-conversion polymers. Commercial macromolecules, whose polymerizations are often finished at high conversions, may have distributions that differ from those calculated here. Section 6.14.2 discusses the size distributions of such polymers. 

The homopolymers of 10 were branched and exhibited broad GPC molecular weight distributions. Studies of the homopolymers molecular weights from polymerization at different monomer concentrations while (1) holding the [10]/[I] ratio constant, and (2) employing different [10]/[I] ratios confirmed that major differences existed in homopolymerizations of 10 versus vinylferrocene.56 In ethylacetate the rate law was r = k [M]1 [I]0 5. Polymerizations in benzene exhibited low initiator efficiencies. The rate was three halves order in the concentration of 10, similar to that found for 8.53 Polymers incorporating 10 were able to catalyze the selective 1,4-hydrogenation of methyl sorbate, but not terminal or internal olefins.56 This resembled the catalytic behavior of styrene/r 6-(styrene)tricarbonylchromium copolymers in hydrogenation.75... 

The theoretical molecular weight distribution or polydispersity, PD/theo for a weU-controUed polymerization in the absence of significant chain termination and transfer, relates to the concentrations of initiator and deactivator, the rate constants of propagation and deactivation, and the monomer conversion in the following way [ 15]... 

To illustrate more clearly the nature of free radical polymerization, it is instructive to examine the values of the individual rate constants for the propagation and termination steps. A number of these rate constants have been deduced, generally using nonstationary-state measurements such as rotating sector techniques and emulsion polymerization [26]. Recently, the lUPAC Working Party on Modeling of kinetics and processes of polymerization has recommended the analysis of molecular weight distributions of polymers produced in pulsed-laser-initiated polymerization (PLP) to determine values of... 

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