Cationic polymerization steady-state assumption

The steady-state assumption that is helpful in simplifying the analysis of free-radical kinetics is not valid in many, if not most, cationic polymerizations, which proceed so rapidly that steady-state is not achieved. Some of these reactions (e.g., isobutylene polymerization by AICI3 at -100°C) are essentially complete in a matter of seconds or minutes. Even in slower polymerizations, the steady-state may not be achieved if > Rt- The expressions given above can only be employed if there is assurance that steady-state conditions exist, at least during some portion of the overall reaction. Steady state is implied if Rp is constant with conversion, except for changes due to decreased monomer and initiator concentrations. A more rapid decline in Rp with time than what is expected or an increase in Rp with time would signify a nonsteady state. Thus many of the experimental expressions reported in the literature to describe the kinetics of specific cationic polymerizations are not valid since they are based on data where steady-state conditions do not apply. 

Experimental verification of the foregoing kinetic scheme has been obtained in the case of the cationic polymerization of styrene (Pepper, 1949) and vinyl alkyl ethers (Eley and Richards, 1949), where the polymerization rate was indeed found to be dependent on the first power of the initiator and on the square of the monomer concentration. However, it should be noted that this simple kinetic scheme is not general for cationic polymerizations even the steady-state assumption is not valid in many cationic polymerizations (Odian, 2004b). 

The validity of the steady-state assumption in many cationic polymerizations may be questioned, because many reactions occur at such high rates that a steady state is not achieved. Nevertheless, the above equations were shown to be generally followed. ... 

We pause here to note that the steady-state assumption that is so helpful in simplifying the analysis of free-radical kinetics (Section 6.3.4) will not apply to many cationic polymerizations of vinyl monomers, because propagation through free carbenium ions is so much faster than any of the other reactions in the kinetic chain. 

The determination of the various rate constants (ki, kp, kt, kts, ktr) for cationic chain polymerization is much more difficult than in radical chain polymerization (or in anionic chain polymerization). It is convenient to use Rp data from experiments under steady-state conditions, since the concentration of propagating species is not required. The Rp data from non-steady-state conditions can be used, but only when the concentration of the propagating species is known. For example, the value of kp is obtained directly from Eq. (8.143) from a determination of the polymerization rate when [M J is known. The literature contains too many instances where [M" "] is taken equal to the concentration of the initiator, [IB], in order to determine kp from measured Rp. (For two-component initiator-coinitiator systems, [M" ] is taken to be the initiator concentration [IB] when the coinitiator is in excess or the coinitiator concentration [L] when the initiator is in excess.) Such an assumption holds only if Ri > Rp and the initiator is active, i.e., efficiency is 100%. Using this assumption without experimental verification may thus lead to erroneous results. 

For a long time the only known steady-state processes involved initiation balanced by termination. This was the first postulate of Bodenstein (see Section 3.02.3) when in the reaction GI2 + H2, Gl is formed in the initiation step by GI2 dissociation and either 2G1 GI2 and Gl + H HGl or 2H H2 terminates the kinetic chains. A large number of reactions of inorganic or organic compounds have been analyzed in this way. This approach has also been adapted for the chain polymerizations. There were several attempts to analyze not only radical polymerizations but also ionic polymerizations by using this assumption, for example, cationic... 

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