Polymerization with Simultaneous Propagation and Termination

Let us now consider an anionic polymerization where propagation and termination reactions occur simultaneously and polymerization follows in a manner similar to free-radical polymerizations. An example is the potassium amide initiated polymerization in liquid ammonia. This is one of the few anionic systems in which all active centers behave kinetically as free ions. The initiation step in this case consists of dissociation of potassium amide followed by addition of amide ion to monomer (Ghosh, 1990 Odian, 1991)  

In general terms, the propagation reactions can be represented by H2N-M- + M H2N-M M-with the rate of propagation expressed as 

Problem 8.12 Justify the steady-state assumption of lij. (8.84) considering the fact that the chain transfer reaction [Eq. (8.82)] is truly not a termination reaction since the amide ion is regenerated. 

The second step of initiation [Eq. (8.77)], being slower than the rst [Eq. (8.76)], is rate-determining for initiation (unlike in the case of free-radical chain polymerization) and so though the amide ion produced upon chain transfer to ammonia can initiate polymerization, it can be only at a rate controlled by the rate constant, ki. Therefore, this chain transfer reaction may be considered as a true kinetic-chain termination step and the application of steady-state condition gives Eiq. (8.84). 

The average kinetic chain length ( 0 or degree of polymerization (DP) is expressed as 

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