Rate constant for propagation

In writing Eqs. (7.1)-(7.4) we make the customary assumption that the kinetic constants are independent of the size of the radical and we indicate the concentration of all radicals, whatever their chain length, ending with the Mj repeat unit by the notation [Mj ], This formalism therefore assumes that only the nature of the radical chain end influences the rate constant for propagation. We refer to this as the terminal control mechanism. If we wished to consider the effect of the next-to-last repeat unit in the radical, each of these reactions and the associated rate laws would be replaced by two alternatives. Thus reaction (7. A) becomes... 

Although there are a total of four different rate constants for propagation, Eq. (7.12) shows that the relationship between the relative amounts of the two monomers incorporated into the polymer and the composition of the monomer feedstock involves only two ratios of different pairs of these constants. Accordingly, we simplify the notation by defining... 

Note that this inquiry into copolymer propagation rates also increases our understanding of the differences in free-radical homopolymerization rates. It will be recalled that in Sec. 6.1 a discussion of this aspect of homopolymerization was deferred until copolymerization was introduced. The trends under consideration enable us to make some sense out of the rate constants for propagation in free-radical homopolymerization as well. For example, in Table 6.4 we see that kp values at 60°C for vinyl acetate and styrene are 2300 and 165 liter mol sec respectively. The relative magnitude of these constants can be understod in terms of the sequence above. 

Under these conditions, a component with a low rate constant for propagation for peroxy radicals may be cooxidized at a higher relative rate because a larger fraction of the propagation steps is carried out by the more reactive (less selective) alkoxy and hydroxy radicals produced in reaction 4. 

In the literature on radical polymerization, the rate constant for propagation, ( is often taken to have a single value (i.e. kp( I) - kv(2) - kvQ) - kp(n) - refer Scheme 4.45). However, there is now good evidence that the value of k is dependent on chain length, at least for the first few propagation steps (Section 4.5.1), and on the reaction conditions (Section 8.3). 

The allylic radicals that are formed are too stable to initiate polymerization, and the kinetic chain also terminates when the transfer occurs. The allylic radicals undergo termination by reaction with each other or, more likely, with propagating radicals [Litt and Eirich, I960], Reaction 3-155 is equivalent to termination by an inhibitor, which is the monomer itself in this case. In this polymerization the propagation and termination reactions will have the same general kinetic expression with first-order dependencies on initiator and monomer concentrations, since the same reactants and stoichiometry are involved. The degree of polymerization is simply the ratio of the rate constants for propagation and termination and is independent of the initiator concentration. 

The rate constants for propagation and termination have been determined for many monomers. Table 3-11 lists values for some of the common monomers. These data were based on rotating sector experiments. The monomers have been listed in order of decreasing kp values (which does not necessarily correspond to the exact order of decreasing kt values). The order of kp values is discussed in Sec. 6-3b, since kp is a function of both monomer reactivity and radical reactivity. 

It is usually assumed that the transfer coefficients, which are the ratios of rate constants for the transfer reactions concerned to that for the propagation reaction, are independent of conversion in estimating them from the dependence of MW averages or [rj] on conversion, this assumption is made implicitly. It is known (187) that the rate constants for propagation and termination vary with the conversion, especially at low temperatures the termination reaction, which... 

For N-vinylcarbazole in methylene chloride solutions cycloheptatrienyl ion has been shown to be a very efficient initiator, reacting by a rapid and direct addition to the olefin (82). A mechanistic scheme involving virtually instantaneous and quantitative initiation, rapid propagation (and transfer) and no true termination appears to operate, enabling rate constants for propagation kp, to be determined very simply from initial slopes of conversion/time curves. Under the experimental conditions used the initiators were almost totally dissociated and there seems every reason to suppose that the propagating cations are similarly dissociated (Section II.C.2). The derived rate constants therefore refer to the reactivity of free poly-(N-vinylcarbazole) cation, kp, and relevant data are summarised in Table 7. 

Table 8. Rate constants for propagation (fcp), in the polymerisation of alkyl vinyl ethers by stable carbocation salts in CH2C12...

Clearly s-cis conformers provide larger steric interference in forming the transition state for propagation (or reactions with electrophiles) than the other possible forms, and not surprisingly the methyl and /S-chloroethyl monomers yield data for the rate constant for propagation about one order of magnitude lower than the others, all of which exhibit comparable reactivity. 

In the case of polymerisations with SbFg counterion, addition of Ag0S02CF3 has predictably the reverse effect, producing significant proportions of dormant macroester molecules, and reducing the value of the apparent rate constant for propagation. 

Table 10. Rate constants for propagation by free ions (fc ) and ion pairs fc in the polymerisation of 3,3-dimethylthietan (53)...

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