Chain propagation constants

A better agreement between the theoretical and experimental data was obtained in79 where styrene oligomerization in carbon tetrachloride was studied. Five different variants of the functions interpolating the dependence of the chain propagation constant on chain length were computed, with kp regarded as a constant. Therefore, the relations were only empirical. 

The dependence of termination and chain propagation constants on the viscosity tj of the reaction medium was considered using the empirical equations ... 

Lachinov and co-workers [52] have performed a more detailed study of the kinetics of block radical polymerisation of perfluoroalkylmethacrylates (FMA) in the solid state. The main method of investigation of the kinetics of FMA polymerisation was isothermic calorimetry [58]. Due to the absence of data on the heat effects of their polymerisation in the reference literature, these values were measured [52]. The values of AQ and glass transition point (T ) of polymers formed are shown in Table 8.3. Obviously heat of polymerisation of monomers of the fluoroacrylate sequence is quite close to heat of polymerisation of non-substituted monomers of the AMA sequence [59], and a significant influence of the length of the fluoroalkyl radical on this parameter is absent [52]. In accordance with the Polyani-Semenov rule, the present result makes it possible to consider that chain propagation constant of FMA with the accuracy of the pre-exponential multiplicand being equal to each other [57]. 

Novel Determination of the Chain Propagation Constant by Means of the Distribution Development... 

Fig. 15 Novel determination of the chain propagation constant by means of the distribution development...

Fig. 16 Determination of the chain propagation constant kp via the longest formed alkane. Graphs show determination of kp from oligomer distribution as a function of time (above) and AlATi ratio (below)...

Inhibitors are characterized by inhibition constants which are defined as the ratio of the rate constant for transfer to inhibitor to the propagation constant for the monomer in analogy with Eq. (6.87) for chain transfer constants. For styrene at 50°C the inhibition constant of p-benzoquinone is 518, and that for O2 is 1.5 X 10. The Polymer Handbook (Ref. 3) is an excellent source for these and most other rate constants discussed in this chapter. 

Chain transfer to monomer is the main reaction controlling molecular weight and molecular weight distribution. The chain-transfer constant to monomer, C, is the ratio of the rate coefficient for transfer to monomer to that of chain propagation. This constant has a value of 6.25 x lO " at 30°C and 2.38 x 10 at 70°C and a general expression of 5.78 30°C, chain transfer to monomer happens once in every 1600 monomer... 

The rate of copolymerization often shows a strong dependence on the monomer feed composition. Many theories have been developed to predict the rate of copolymerization based on the terminal model for chain propagation (Section 7.3.1.1), This usually requires an overall rate constant for termination in copolymerization that is substantially different from that observed in homopolymerization of any of the component monomers. 

As shown by the data in Fig. 31, the chain transfer constant of this initiator, Q = 1.0. In this context it is of interest to remember that the effect of initiator concentration on the molecular weight of HSi-PaMeSt was negligible, probably because of unfavorable thermodynamics (Sect. III.B.3.b.iv.). In contrast, with isobutylene chain transfer from the propagating carbenium ion to initiator is thermodynamically favorable (see Sect. IH.B.4.b.i.). Thus it is not surprising to find a large Q. The chain transfer mechanism has been illustrated in Scheme 5. 

A similar association may result from intermolecular interaction of two growing chains. Of course, the degree of such an association should depend on the concentration of growing polymers, i.e. the observed propagation constant, kobs, is given then by the relation ... 

Radical addition to conjugated systems is an important part of chain propagation reactions. The rate constants for addition of cyclohexyl radical to conjugated amides have been measured, and shown to be faster than addition to styrene. In additions to RCH=C(CN)2 systems, where the R group has a chiral center, the Felkin-Ahn rule (p. 148) is followed and the reaction proceeds with high selectivity. Addition of some radicals, such as (McsSijaSi-, is reversible and this can lead to poor selectivity or isomerization. ... 

Note that equation 88 is based on the pseudo-homopolyirerlzatlon jproacli It reduces to liie sinple ptroduct of moncmer concentration by a suitably conposltlon averaged propagation constant and the total nuntoer of active chains in the particles. 

The results of chain transfer studies with different polymer radicals are compared in Table XIV. Chain transfer constants with hydrocarbon solvents are consistently a little greater for methyl methacrylate radicals than for styrene radicals. The methyl methacrylate chain radical is far less effective in the removal of chlorine from chlorinated solvents, however. Vinyl acetate chains are much more susceptible to chain transfer than are either of the other two polymer radicals. As will appear later, the propagation constants kp for styrene, methyl methacrylate, and vinyl acetate are in the approximate ratio 1 2 20. It follows from the transfer constants with toluene, that the rate constants ktr,s for the removal of benzylic hydrogen by the respective chain radicals are in the ratio 1 3.5 6000. Chain transfer studies offer a convenient means for comparing radical reactivities, provided the absolute propagation constants also are known. 

Table XVIL —Absolute Rate Constants for Chain Propagation and...

In the framework of this ultimate model [33] there are m2 constants of the rate of the chain propagation kap describing the addition of monomer to the radical Ra whose reactivity is controlled solely by the type a of its terminal unit. Elementary reactions of chain termination due to chemical interaction of radicals Ra and R is characterized by m2 kinetic parameters k f . The stochastic process describing macromolecules, formed at any moment in time t, is a Markov chain with transition matrix whose elements are expressed through the concentrations Ra and Ma of radicals and monomers at this particular moment in the following way [1,34] ... 

This is the simplest of the models where violation of the Flory principle is permitted. The assumption behind this model stipulates that the reactivity of a polymer radical is predetermined by the type of bothjts ultimate and penultimate units [23]. Here, the pairs of terminal units MaM act, along with monomers M, as kinetically independent elements, so that there are m3 constants of the rate of elementary reactions of chain propagation ka ]r The stochastic process of conventional movement along macromolecules formed at fixed x will be Markovian, provided that monomeric units are differentiated by the type of preceding unit. In this case the number of transient states Sa of the extended Markov chain is m2 in accordance with the number of pairs of monomeric units. No special problems presents writing down the elements of the matrix of the transitions Q of such a chain [ 1,10,34,39] and deriving by means of the mathematical apparatus of the Markov chains the expressions for the instantaneous statistical characteristics of copolymers. By way of illustration this matrix will be presented for the case of binary copolymerization ... 

The kernel (26) and the absorbing probability (27) are controlled by the rate constants of the elementary reactions of chain propagation kap and monomer concentrations Ma(x) at the moment r. These latter are obtainable by solving the set of kinetic equations describing in terms of the ideal kinetic model the alteration with time of concentrations of monomers Ma and reactive centers Ra. 

The obtained value of a indicates the proximity of the rate constant values of the addition of TBSM to the macroradicals MA and of MA to TBSM This can be explained by a similar influence of intermolecular coordination on chain propagation. The values of pt and p2 indicate that in free-radical copolymerization of TBSM with MA both free and complex-bound monomers are involved in chain propagation with a higher contribution of the latter. 

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