Chain transfer reactions rate constants

Table 3.7 Isoprene polymerisation by TiCl4-Al(t-C4H9)3 catalyst, kp is the chain growth reaction rate constant is the concentration of AC k, are chain-to-monomer and chain-to-aluminium-organic compound transfer reaction rate constants respectively, w is the initial polymerisation rate, method 1) traditional, 2) hydrodynamic impact on a separately prepared catalytic system, 3) catalytic system formation in a turbulent mode, and 4) preliminary formation of a reaction mixture in a turbulent mode...

Uo A1 Chain-to-aluminium-organic compound transfer reaction rate constant... 

Comparing Eqs, (12) and (11), we obtain dependence of chain transfer to low-molecular RAFT-agent constant on the constant of radical s addition to macro-molecular RAFT-agent and chain growth reaction rate constant ... 

Figure 1 shows the reactions of AH, and it can be seen that major processes using up AH are the formation of trimer, the MAH process, and chain transfer. The rate constants for all three of these reactions can be estimated in the following way (6,6a) If it is assumed that all of the trimeric product A-Sty is produced by an ene reaction (eq in Figure lA) rather than by radical recombination, reaction j, then the rate constant for the ene reaction of AH can be calculated from the rate of appearance of the trimer A-Sty measured by Buchholz and Kirchner (22) The rate constant for transfer of AH can be calculated from its transfer constant, obtained from our computer simulation (23), and the known value of k for styrene. And finally, the rate constant of the MAH reaction of AH can be calculated from the rate at which radicals are formed in styrene (calculated from the observed rate of thermal polymerization), assuming that all radicals come from this postulated MAH reaction. The steady state concentration of AH was measured by Kirchner, and is 6 x 10M at about 60 . 

For addition-fragmentation chain transfer, the rate constants for the forward and reverse reactions are defined as shown in eqns [98] and [99], respectively ... 

Chain transfer is an important consideration in solution polymerizations. Chain transfer to solvent may reduce the rate of polymerization as well as the molecular weight of the polymer. Other chain-transfer reactions may iatroduce dye sites, branching, chromophoric groups, and stmctural defects which reduce thermal stabiUty. Many of the solvents used for acrylonitrile polymerization are very active in chain transfer. DMAC and DME have chain-transfer constants of 4.95-5.1 x lO " and 2.7-2.8 x lO " respectively, very high when compared to a value of only 0.05 x lO " for acrylonitrile itself DMSO (0.1-0.8 X lO " ) and aqueous zinc chloride (0.006 x lO " ), in contrast, have relatively low transfer constants hence, the relative desirabiUty of these two solvents over the former. DME, however, is used by several acryhc fiber producers as a solvent for solution polymerization. 

The thiol ( -dodecyl mercaptan) used ia this recipe played a prominent role ia the quaUty control of the product. Such thiols are known as chain-transfer agents and help control the molecular weight of the SBR by means of the foUowiag reaction where M = monomer, eg, butadiene or styrene R(M) = growing free-radical chain k = propagation-rate constant = transfer-rate constant and k = initiation-rate constant. 

Intramolecular hydrogen abstraction by primary alkyl radicals from the Si—H moiety has been reported as a key step in several unimolecular chain transfer reactions [11]. In particular, the 1,5-hydrogen transfer of radicals 8-11 (Reaction 3.4), generated from the corresponding iodides, was studied in competition with the addition of primary alkyl radicals to the allyltributylstannane and approximate rate constants for the hydrogen transfer have been obtained. Values at 80 °C are in the range of (0.4-2) x 10" s, which correspond to effective molarities of about 12 M. 

Values of Ca from eqn. (113) can be used in eqn. (83) to obtain instantaneous values for P at particular times (when chain transfer reactions are unimportant). If the initiation rate is taken as constant and no chain transfer reactions occur, then, using equations given by Tadmor and Biesenberger [62], it can be shown that... 

Chain-transfer reactions would be expected to increase in rate with increasing pressure since transfer is a bimolecular reaction with a negative volume of activation. The variation of chain-transfer constants with pressure, however, differ depending on the relative effects of pressure on the propagation and transfer rate constants. For the case where only transfer to chain-transfer agent S is important, Cs varies with pressure according to... 

Grafting Temperature Effect. Temperature can influence the reaction rates in different ways initiation, propagation, transfer, termination. For grafting reaction, the length and number of grafted chains depend on rate constant of these reactions. However for radiochemical grafting, the initiation rate is not temperature dependent (2, 3, 4). 

In recent years, considerable work has been devoted to polymerization reactions of vinyl monomers at higher conversions which permit useful quantitative interpretation of the results. A useful review of studies of the gel effect, chain transfer reactions, and new theoretical postulates and studies at elevated conversions has been presented by Gladyshev and Rafikov (24). This accumulated work has demonstrated the effects of conditions at elevated conversions not only on the termination rate constant, but on initiator efficiency, propagation rate constants, and therefore, the concentration of macroradicals. A rigorous quantitative theory, however, has not yet been developed. 

It was proposed to determine the rate constants of transfer and termination or their ratios to that of propagation for polymerization systems that allow synthesis of well-defined polymers [6]. This information will be useful for the reproducible synthetic efforts and also for setting limits for the preparation of well-defined high polymers. The direct determination of transfer/termination rate constants may be facilitated by working under "difficult reaction conditions such as those which usually disallow preparation of well-defined polymers (higher temperatures, lower [I]0, longer chains, etc.), and the obtained results extrapolated to the "usual living conditions. 

One of the big difficulties in unraveling the individual rate constants of polymer reactions is caused by the reaction of the polymer with other species in the solution or even by nonadditive reaction with monomer. Of these reactions, those which lead to termination of the radical chain and the production of a new radical are spoken of as chain transfer reactions. A typical example is found in the polymerization of styrene in CCI4 solution. The final polymer is found to contain chlorine, and the reaction is... 

During the parameter estimation, it was noted that the model is relatively insensitive to changes in k, and therefore it should not be taken as a reliable prediction of the Diels-Alder reaction rate constant. Effectively, the rate R is very large compared with the rates of initiation and chain transfer, and therefore the DH ratio calculation could be simplified without significantly changing the model results ... 

Table 11. Rate constants of chain transfer reactions in the olefin polymerization on catalysts containing titanium chlorides 2 .in-n9)...

In systems where termination is quantitative and there are no significant side reactions it is clear that the measurements will involve all polymer molecules containing reactive metal—carbon bonds, including non-propagating chains attached to aluminium after transfer. No entirely satisfactory correction procedure has been found, but the usual method is to extrapolate the linear region of the increase in metal—carbon bond concentration with time to zero time. Provided the transfer reactions are constant in rate the concentration of metal bonds [N] is given by... 

This transfer reaction with the formation of the monomer P1 is governed by the propagation rate constant kp and is more common than other reactions for many polymers. More general types of chain transfer reactions followed by radical decompositions can be written as follows ... 

Comprehensive Models. This class of detailed deterministic models for copolymerization are able to describe the MWD and the CCD as functions of the polymerization rate and the relative rate of addition of the monomers to the propagating chain. Simha and Branson (3) published a very extensive and rather complete treatment of the copolymerization reactions under the usual assumptions of free radical polymerization kinetics, namely, ultimate effects SSH, LCA and the absence of gel effect. They did consider, however, the possible variation of the rate constants with respect to composition. Unfortunately, some of their results are stated in such complex formulations that they are difficult to apply directly (10). Stockmeyer (24) simplified the model proposed by Simha and analyzed some limiting cases. More recently, Ray et al (10) completed the work of Simha and Branson by including chain transfer reactions, a correction factor for the gel effect and proposing an algorithm for the numerical calculation of the equations. Such comprehensive models have not been experimentally verified. 

To give a specific example, the advantages of styrene as a substrate for peroxyl radical trapping antioxidants are well known" (i) Its rate constant, kp, for chain propagation is comparatively large (41 M s at 30 °C) so that oxidation occurs at a measurable, suppressed rate during the inhibition period and the inhibition relationship (equation 14) is applicable (ii) styrene contains no easily abstractable H-atom so it forms a polyper-oxyl radical instead of a hydroperoxide, so that the reverse reaction (equation 21), which complicates kinetic studies with many substrates, is avoided and (iii) the chain transfer reaction (pro-oxidant effect, equation 20) is not important with styrene since the mechanism is one involving radical addition of peroxyls to styrene. 

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