ISSN:
0025-116X
Keywords:
Chemistry
;
Polymer and Materials Science
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
,
Physics
Notes:
In order to assess the general consequences of an eventual chain length dependence of the bimolecular termination rate constant kt in free radical polymerization, an iterative procedure for solving the kinetic scheme was developed for this case. The iteration process is based on the equation for the propagation probability of a radical chain of length x, αx, which constitutes a cyclic definition of the α-values, \documentclass{article}\pagestyle{empty}\begin{document}$$ \alpha _x = \left[{{1} + {\nu _{\rm o} ^{ - 2}} \sum\limits_y {F \left( {x,y} \right)} \prod\limits_{i = 1}^y {\alpha _i }} \right]^{ - 1} = \left[{\rm R} _x \right]/\left[{\rm R} _{x - 1} \right]$$\end{document} with F(x,y) giving the functional dependence of kt = kto F(x, y) on the lengths x and y of the two radicals involved in the termination process. As, in addition, αx links the stationary concentrations of radicals of adjacent length, [Rx-1] and [Rx], solving for the set of αx allows to build up the complete chain length distribution of polymer radicals from which all relevant kinetic quantities may be calculated. The following types of functional dependence have been used in practice \documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{l} F_1 \left( {x,y} \right) = \left[ {2xy/\left( {x + y} \right)} \right]^{ - b} \left( { = {\rm harmonic \ mean}} \right) \\ F_2 \left( {x,y} \right) = \left[ {xy} \right]^{ - b/2} \left( { = {\rm geometic \rm mean}} \right) \\ \end{array}$$\end{document}The case of F2, which is the slightly less realistic one, allows to separate the variables x and y in the equation for αx, thus leading to an immediate comfortable solution. Irrespective of the type of F(x, y) chosen (the differences being quantitative in nature rather than qualitative) it can be shown that nearly all the familiar relationships known from “classical” polymerization kinetics with chain length independent termination (b = 0) break down. The new relationships, however, can be cast into comparatively simple power laws. The general consequences of the concept of chain length dependent termination are discussed in some detail.
Additional Material:
9 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/macp.1986.021870426
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