Chain transfer constants reversible

Chain transfer constant, Reversible transfer constant, Cg Intrinsic molecular weight, Formula weight of monomer, F, ... 

The situation becomes more complex for semi-reversible chain transfer, where kcl and /cRT are both positive, but kCT > kRT As demonstrated in Fig. 7, MJMn can be greater than, less than, or equal to 2.0, depending on the conversion and the magnitudes of the chain transfer constants. The Mn of the polymer is simply a function of C ° the value of C has no effect on M up to C = C °. However, M is dramatically affected by lower values of Ct. If C° Ca > 0, then the initial increase in M IM is dramatic, and M IM does not dip below 2 until high conver-sion. However, as C approaches C 0, the initial increase in MJMn is negligible, and MJMn drops below 2.0 at low conversion. In any case, if Ca > 0, then MJMn asymptotically approaches two from the low side. 

The chain-transfer constant of about 105 L/mol s172,175 makes it difficult to study the properties of (DH)2CoH. Equation 16 is reversible, and under basic conditions the equilibrium is shifted to the left. LCoH complexes are weakly acidic and are dissociated easily according to eq 17. 

The /fd. /fex. and kp are the rate constant tor reversible termination (RT) (Scheme 7(a)), degenerative transfer (DT) (Scheme 7(b)), and propagation, respectively. Cex is the degenerative chain transfer constant (=kjkp). 

Quinn JF, Bamer L, Davis TP, Thang SH, Rizzardo E Living free radical polymerisation under a constant source of gamma Radiation—an example of reversible addition-fragmentation chain transfer or reversible termination Macromol Rapid Commun 23 717-721, 2002. 

Figure 6.3 Predicted dependence of (a) degree of polymerization and (b) dispersity on conversion in pol5merizations involving reversible chain transfer as a function of the chain transfer constant (Ctr). Predictions are based on equations proposed by Muller et with a = 10 (the concentration...

This equation can be solved numerically to give values of Clr and Ctr.404 For reversible addition-fragmentation chain transfer (RAFT) (Scheme 6.5), the rate constant for the reverse reaction is defined as shown in eq. 22 ... 

For addition-fragmentation chain transfer, the rate constants for the forward and reverse reaclions are defined as shown in eqs. 21 and 22 respectively. 

Fig. 4 Simulated M IM vs. conversion as a function of chain shuttling constant for reversible chain transfer, with C° = C,...

The polymerization proceeds without termination or chain transfer to give poly-norbomene with a narrow molecular weight distribution [35], After an induction period, the rate of monomer consumption (rate of polymerization) becomes constant, indicating a zero-order dependence on the monomer concentration. The induction period is caused by part of titanacycle 7 undergoing non-productive, but rapidly reversible, cleavage to norbornene and the titanium methylene complex, Eq. (17 a). 

In many systems, however, the analysis of the cationic copolymerization of heterocyclic monomers is complicated by two factors (1) at least some of the homo- and cross-propagation reactions may be reversible (2) redistribution of the sequences of comonomers within the chain may occur as a result of chain transfer to polymer. Therefore, the conventional treatment involving four irreversible propagation steps is rarely applicable in cationic ring-opening copolymerization. Instead, the diad model should involve four reversible reactions, i.e., eight rate constants... 

Both reactions, namely tte intermolecular process (131) and the intramolecular one (132) can be either reversible or irreversible (termination). In the case of reversible reactions true chain transfer takes place vdien the rate constant of the backward reaction (kj ) becomes comparable with the rate constant of M-opaptun. This applies to the polymerization of cyclic acetals where the product of chain traiKfer is equally active in propaption. 

Gordon and Roe paid their attention mainly to chain transfer rather than chain propagation process. Thus, in a hypothetical model the termination rate constant depends on the chain length (due to control of the termination reaction by reversible desorption of the polymer macromolecule from the catalyst surface). A two parameter expression for the MWD function was derived which, with a chain transfer agent, should imply a Q decrease toward an asymptotic value of 2 On the other hand, according to Roe, no modification of MWD could be expected if catalyst non-uniformity were responsible for the broad distribution. More recent data seem to support this latter hypothesis rather than the mechanism of Gordon and Roe. 

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. 

This technique for controlling radical polymerizations is based on one of the oldest technique, that of chain transfer, and has often been used in telomeriza-tion [83]. Similar to the concept of degenerative transfer with alkyl iodides [50, 51, 84], reversible addition fragmentation chain transfer with dithio esters (RAFT) [52-55, 85] is successful because the rate constant of chain transfer is faster than the rate constant of propagation. Analogous to both nitroxide-medi-... 

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