Equal reactivity assumption

Suppose that the reactivity of the A and B endgroups is independent of the chains to which they are attached. This is a form of the equal reactivity assumption that is needed for almost all analytical solutions to polymer kinetic problems. If it is satisfied, we can ignore the details of the polymerization and just concentrate on the disappearance of the endgroups. For a batch system. 

Example 13.5 Determine the instantaneous distributions of chain lengths by number and weight before and after termination by combination. Apply the quasi-steady and equal reactivity assumptions to a batch polymerization with free-radical kinetics and chemical initiation. 

Solution The equal reactivity assumption says that kp and kc are independent of chain length. The quasi-steady hypothesis gives d R /dt = 0. Applying these to a material balance for growing chains of length / gives... 

Ray [31] details the continuous variable approximation by considering equations (3.13)-(3.16), and using the equal reactivity assumption. If the chain length j is taken to be a continuous variable then the Taylor s series expansion for Pj j about Pj results in... 

In order to simplify a kinetic expression for the rate of polymerization, it is necessary to assume that both the k and fc, are independent of the size of the radical, as well as the "equal-reactivity assumption" of the growing radicals. Very small radicals are more reactive than the propagating radicals with longer chains, but this effect is not important due to the fact that the effect of size vanishes at the dimer or trimer size.[13] The rate of polymerization is expressed by the following equation ... 

Solution The equal reactivity assumption says that kp and... 

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