Independent Chain-Length Dependent Kinetic Analysis

Model-Independent Chain-Length Dependent Kinetic Analysis 

The efforts described above to include chain-length dependent termination rate coefficients in the TR-SP-PLP kinetics still suffer from the assumption of a kinetic model prior to data analyses. However, by looking from a somewhat different perspective at the kinetics presented above, this disadvantage can be eliminated in a very simple fashion. In addition, as will be demonstrated below, estimations of [i ]o are no longer needed to obtain kt values but rather, an estimate for [i ]o results from the kinetic trace that has been measured. 

The kinetic analysis starts (instead of ends) by considering the rate of polymerization versus time of an experimental TR-SP-PLP trace. Provided that kp is known, the radical concentration versus time can be simply determined according to  

As the monomer concentration versus time is monitored on-line by MR spectroscopy, its derivative is of course known as well. A fair estimate for the concentration of radicals at time t = 0 can be obtained simply by extrapolation of the calculated profile to time / = 0. This provides a very simple alternative for the methods mentioned above to determine [i ]o. Similar to calculating the radical concentration versus time, the termination rate coefficient can be determined, by rewriting the termination rate equation to  

It should be stressed that equation 3.8 is not completely assumption free. First of all, the propagation rate coefficient has been assumed to be independent of chain length. 

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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. 

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. 

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