Length Dependent Kinetic Analyses

Model-Independent Chain-Length Dependent Kinetic Analysis 

Let us first consider the rate of termination in a single-pulse PLP experiment. If it is assumed that the radical generation due to the laser pulse is instantaneous and if no other means of initiation are present, it follows that  

Moreover, the loss of radicals of course results in the formation of dead polymeric material. Here a crucial assumption is made and only termination by combination will be considered. Disproportionation reactions as well as chain tranfer reactions are ignored. Consequently, every termination event results in the formation of one dead polymer chain, hence  

Rewriting of equation 3.22 and subsequent substitution of equation 3.24 then results in  

The average termination rate coefficient is now completely expressed as a function of the rate of polymer formation and is a time-dependent variable. Information on this rate can be obtained from the MWD of the resulting polymer. Considering a volume V, the rate of polymer formation can be expressed as  

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As for deaminase, the kinetic analysis suggests a partial mixed-type inhibition mechanism. Both the Ki value of the inhibitor and the breakdown rate of the enzyme-substrate-inhibitor complex are dependent on the chain length of the PolyP, thus suggesting that the breakdown rate of the enzyme-substrate-inhibitor complex is regulated by the binding of Polyphosphate to a specific inhibitory site (Yoshino and Murakami, 1988). More complicated interactions were observed between PolyP and two oxidases, i.e. spermidine oxidase of soybeen seedling and bovine serum amine oxidase. PolyP competitively inhibits the activities of both enzymes, but may serve as an regulator because the amino oxydases are also active with the polyamine-PolyP complexes (Di Paolo et al., 1995). 

The kinetic analysis is shown in Fig. 17 and leads to detail concerning the concentration of the active species, insight into the superposition of the A1 isotherm and its dependence on the chain length of the starting Ti-alkyl group, and determination of a reaction order equal to one for the monomer dependence. 

Based on an analysis of kinetic data on small radical additions and the first few propagation steps in free-radical polymerization, backed up by theoretical investigations of the propagation rate coefficient, we proposed the empirical formula given by Eq. 8 for the description of the chain-length dependence of the propagation rate coeffi-... 

This kinetic analysis, however, has two disadvantages (i) the obtained kinetic parameters kp and kt are determined as combined fit parameters and their accuracy is dependent upon the determination of either [i ]o or kp from (mostly) independent experiments and (ii) a constant value of kt is used instead of a chain-length dependent one. The first disadvantage is inherent to non-stationary experiments and is difficult to overcome. Conversion is inextricable linked to radical concentrations and propagation rate coefficients. The latter disadvantage, however, can be overcome in several ways and is discussed below. 

The second kinetic analysis that can be used to study the chain-length dependence of termination reactions, discussed in section 3.3, is based on a careful analysis of a quantitatively determined number MWD. Equations 4.2 and 4.3 summarize this kinetic tool. 

Summarizing the above, it can be concluded that single-pulse pulsed-laser polymerization techniques are amongst the most powerful techniques that are nowadays available to study the chain-length dependence of termination reactions. When using a dedicated kinetic analysis, as presented in this thesis, model-independent data for the chain-length dependence of kt can be obtained. These data allow for better predictions for the MWD of the final polymer product and so of the final product properties. 

It is useful to start the kinetic analysis with an idealized case, which avoids complications that arise due to unequal stoichiometry, chain length-dependent reactivity, monofunctional impurities, cyclization, and reversible polymerization. The model addressed here is a linear AB step polymerization. 

This chapter has discussed the analysis of reactors for step-growth polymerization assuming the equal reactivity hypothesis to be valid. Polymerization involves an infinite set of elementary reactions under the assumption of this hypothesis, the polymerization can be equivalently represented by the reaction of functional groups. The analysis of a batch (or tubular) reactor shows that the polymer formed in the reactor cannot have a polydispersity index (PDI) greater than 2. However, the PDI can be increased beyond this value if the polymer is recycled or if an HCSTR is used for polymerization. A comparison of the kinetic model with experimental data shows that the deviation between the two exists because of (1) several side reactions that must be accounted for, (2) chain-length-dependent reactivity, (3) unequal reactivity of various functional groups, or (4) comphca-tions caused by mass transfer effects. 

Such a model makes it possible to calculate a change of fibers distribution along the length in the boundary layer. At present, practically the sole approach to the analysis of destruction when the fiber filler flows in the basic mass, outside the boundary layer, is an experimental determination of destruction kinetics for a given pair — fiber filler and polymer. Such dependencies can be obtained with the help of, say, rotary viscosimeters [47],... 

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