Kinetics of termination

The difficulties involved in the direct determination of the momentary concentration of active centres are the most serious shortcoming in studies of termination itself. With radical polymerizations we at least know the most probable method of centre decay, and thus the molecular scheme of the termination reaction. In ionic and coordination polymerizations, the termination mechanism is mostly unknown. Quite generally we can write 

The kinetics of termination is usually approximated by simple relations where a speculative reaction order is inserted into the rate equation1 

According to eqns. (105)—(107), the dependence of the decay of active centres on time is linear, exponential, and hyperbolic, respectively. The best approximation is obtained by a comparison of the observed course with the rate of monomer decay calculated for the assumed termination mode. This is, of course, a very rough method, which often does not reveal the effect of other components on termination, for example that of the monomer (its wrong addition etc.) 

These examples represent only a part of the possible situations. 

The calculated functional dependence for [Ac] is inserted into the rate equation. An agreement between calculation and experiment should not be overestimated. An exact kinetic analysis of polymerization requires proof of the partial steps, and is very difficult. 

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The kinetics of termination in suspension polymerization is generally considered to be the same as for solution or bulk polymerization under similar conditions and will not be discussed further. A detailed discussion on the kinetics... 

Table 2. Parameters of the hydroformylation kinetics of terminal olefins.

The polymerization kinetics of terminal alkynes have been determined. The reaction is initiated by tungsten carbene complexes (10) the chelating olefin is displaced by acetylene as the first step in the reaction, followed by formation of... 

Cationic Polymerization The kinetics of termination, chain transfer and macrocyclization processes in cationic ROP have been extensively reviewed in Chapter 5 of Ref. [3a] and also in Ref. [74]. Of particular value is Table 18 in Ref. [3a], which details the basic equations in nonstationary kinetics with chain transfer. Although, since these two reviews were published few new phenomena have been identified, we will at this point provide a brief description of activated monomer cationic polymerization. 

The kinetics of the reactions were complicated, but three broad categories were distinguished in some cases the rate of reaction followed an exponential course corresponding to a first-order form in others the rate of reaction seemed to be constant until it terminated abruptly when the aromatic had been consumed yet others were susceptible to autocatalysis of varying intensities. It was realised that the second category of reactions, which apparently accorded to a zeroth-order rate, arose from the superimposition of the two limiting kinetic forms, for all degrees of transition between these forms could be observed. 

Elsewhere in this chapter we shall see that other reactions-notably, chain transfer and chain inhibition-also need to be considered to give a more fully developed picture of chain-growth polymerization, but we shall omit these for the time being. Much of the argumentation of this chapter is based on the kinetics of these three mechanistic steps. We shall describe the rates of the three general kinds of reactions by the notation Rj, Rp, and R for initiation, propagation, and termination, respectively. 

A kinetic analysis of the two modes of termination is quite straightforward, since each mode of termination involves a bimolecular reaction between two radicals. Accordingly, we write the following ... 

As with the rate of polymerization, we see from Eq. (6.37) that the kinetic chain length depends on the monomer and initiator concentrations and on the constants for the three different kinds of kinetic processes that constitute the mechanism. When the initial monomer and initiator concentrations are used, Eq. (6.37) describes the initial polymer formed. The initial degree of polymerization is a measurable quantity, so Eq. (6.37) provides a second functional relationship, different from Eq. (6.26), between experimentally available quantities-n, [M], and [1]-and theoretically important parameters—kp, k, and k. Note that the mode of termination which establishes the connection between u and hj, and the value of f are both accessible through end group characterization. Thus we have a second equation with three unknowns one more and the evaluation of the individual kinetic constants from experimental results will be feasible. 

For counterions that can form esters with the growing oxonium ions, the kinetics of propagation are dominated by the rate of propagation of the macroions. For any given counterion, the proportion of macroions compared to macroesters varies with the solvent—monomer mixture and must be deterrnined independentiy before a kinetic analysis can be made. The macroesters can be considered to be in a state of temporary termination. When the proportion of macroions is known and initiation is sufftcientiy fast, equation 2 is satisfied. 

Polymerization Kinetics of Mass and Suspension PVC. The polymerization kinetics of mass and suspension PVC are considered together because a droplet of monomer in suspension polymerization can be considered to be a mass polymerization in a very tiny reactor. During polymerization, the polymer precipitates from the monomer when the chain size reaches 10—20 monomer units. The precipitated polymer remains swollen with monomer, but has a reduced radical termination rate. This leads to a higher concentration of radicals in the polymer gel and an increased polymerization rate at higher polymerization conversion. 

The overall rate of a chain process is determined by the rates of initiation, propagation, and termination reactions. Analysis of the kinetics of chain reactions normally depends on application of the steady-state approximation (see Section 4.2) to the radical intermediates. Such intermediates are highly reactive, and their concentrations are low and nearly constant throughout the course of the reaction ... 

The effect of temperature on the kinetics of the direct radiation method is quite complex. Increase in temperature increases the monomer diffusion rate but also increases transfer and termination reaction rates of the growing chains and reduces the importance of the gel effect. Solubility and radical mobility may also change as the temperature is varied [88,89]. 

In sharp contrast, Bartoli showed that the (salen) Co catalyst system could be applied to the kinetic resolution of terminal epoxides with unprotected tert-butyl carbamate as nucleophile with extraordinarily high selectivity factors (Scheme 7.40) [72]. Excellent yields and selectivities are also obtained with use of ethyl, Cbz,... 

One way of overcoming these problems is by kinetic resolution of racemic epoxides. Jacobsen has been very successful in applying chiral Co-salen catalysts, such as 21, in the kinetic resolution of terminal epoxides (Scheme 9.18) [83]. One enantiomer of the epoxide is converted into the corresponding diol, whereas the other enantiomer can be recovered intact, usually with excellent ee. The strategy works for a variety of epoxides, including vinylepoxides. The major limitation of this strategy is that the maximum theoretical yield is 50%. 

Illarionova, V. A., et al. (1997). Removal of essential ligand in N-terminal calcium-binding domain of obelin does not inactivate the photoprotein or reduce its calcium sensitivity, but dramatically alters the kinetics of the luminescent reaction. In Hastings, J. W., et al. (eds.), Biolu-min. Chemilumin., Proc. Int. Symp., 9th, 1996, pp. 431 —434. Wiley, Chichester, UK. 

If the amount of termination by radical-radical reaction is neglected the degree of polymerization and the kinetic chain length are given by eq. 29 ... 

Stein166 has indicated that the reactivity of the terminal double bond of the macromonomer (112) is 80% that of VAc monomer. The kinetics of incorporation of 112 have also been considered by Wolf and Burchard175 who concluded that 112 played an important role in determining the time of gelation in VAc homopolymerization in bulk. 

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