Cationic chain polymerization steady-state

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. 

As in the case with cationic polymerizations, the number of growing chains is constant so that a steady state exists such as the Ri = R. This is useful because it is difficult to determine the concentration of [M ] so that it can be eliminated as follows ... 

We pause here to note that the steady-state a.ssumption 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. 

Dreyfuss and Dreyfuss (13) showed that the cationic polymerization of cyclic ethers has the characteristics of a "living" polymerization, in that there appears to be a lack of termination except through reaction of the cationic growing chain end with impurities and that eventually a steady state is attained where the living polymer is in equilibrium with its monomer. 

It has been noted (Odian, 1991) that the steady-state approximation cannot be applied in many cationic polymerizations because of the extreme rate of reaction preventing the attainment of a steady-state concentration of the reactive intermediates. This places limitations on the usefulness of the rate expressions but those for the degree of polymerization rely on ratios of reaction rates and should be generally applicable. The molar-mass distribution would be expected to be very narrow and approach that for a living polymerization (with a poly-dispersity index of unity), but this is rarely achieved, due to the chain-transfer and termination reactions discussed above. Values closer to 2 are more likely. 

Termination reactions cannot be eliminated in radical polymerizations because termination reactions involve the same active radical species as propagation therefore, eliminating the species that participates in termination would also result in no polymerization. Termination between active propagating species in cationic or anionic processes does not occur to the same extent because of electrostatic repulsions. Equation (1) represents the rate of polymerization, Rp, which is first order with respect to the concentration of monomer, M, and radicals, P, while Eq. (2) defines the rate of termination, Rt, which is second order with respect to the concentration of radicals. To grow polymer chains with a degree of polymerization of 1000, the rate of propagation must be at least 1000 times faster than the rate of termination (which under steady state condition is equal to the rate of initiation). This requires a very low concentration of radicals to minimize the influence of termination. However, termination eventually prevails and all the polymer chains produced in a conventional free radical process will be dead chains. Therefore they cannot be used in further reactions unless they contain some functional unit from the initiator or a chain transfer agent. 

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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