Dead chain

Alternatively one chain radical may abstract a proton from the penultimate carbon atom of the other, giving one saturated and one unsaturated dead chain ... 

In equations 8 and 9yfis the initiator efficiency, the fraction of initiator radicals that actually initiates chain growth, kt = ktc + ktd, and is the number of dead chains formed per termination reaction = 2 for disproportionation, = 1 for combination. 

Lacroix-Desmazes and Guyot [13] applied Paine s model to the dispersion copolymerization of amphiphilic macromonomers and re-discussed this model in terms of possible incorporation of a new parameter - the chain transfer parameter (Css the chain transfer constant for transfer to solvent-alcohol). The relations for the rate of dead chains (kj) and chain length (CL) are as follows ... 

In a particular system, one, two, or the three termination mechanisms may be simultaneously present. But we assume that a termination step is always present (the treatment of living polymerizations is beyond our scope). The first two termination events have the same consequence the dead chain that is formed keeps the same length that it had at the time the termination event took place. In this sense, these termination mechanisms are statistically equivalent. On the contrary, the combination mechanism leads to a dead chain that has a length equal to the sum of the lengths of the two chains that were combined. 

Termination in this case produces a number, equal to the number of growing chains, of low molecular weight dead chains. This does not affect but halves . Hence / is doubled to 4.00. W n w n... 

Now one of two things can occur. A chain terminator can be added (e.g., a small amount of an alcohol) from which each chain will abstract a hydrogen ion and become a neutral polymer (a dead chain). This is the termination step shown in the preceding reaction sequence. Or, more monomer can be added and the polymerization will continue until the new sample of monomer has been consumed. In other words, these anionic polymerizations are living polymerizations, so named because the chains remain active until they are deliberately terminated (become dead ). (The terms living and dead describe relative states of chemical reactivity only and not any bio-... 

On the other hand, no difference in equilibrium concentration is expected between Models C and B. In the latter only the "dead chain segments are crystallized while the cationic active centers, at which depolymerization and polymerization of formaldehyde takes place, are in solution. 

From the start of the polymerization, the molecular mass distribution curve widens up to the total consumption of the transfer agent. The rate of the distribution changes depends on the intensity of the transfers and the starting conditions. The populations of various lengths in dead chains and in... 

A more formal derivation of Equation 4-39, useful when we get to chain transfer, is obtained starting from v = rjre (Remember the steady-state assumption, r, = r, ) To obtain the number average degree of polymerization instead of the kinetic chain length we then use the rate of dead chain formation instead of rt (Equations 4-40). 

Note that disproportionation results in the formation of two dead chains, hence the factor 2 in the equation. Dividing this term by the expression for the rate of termination we get Equation 4-38. 

Fig. 12 Instantaneous chain length distribution on a number and weight basis, where dead chains are formed by disproportionation termination. The value of n is increased by decreasing the bimolecular termination rate...

Whatever the living mechanism, an essential requirement for a successful LRP is the minimization of the fraction of dead chains. In a bulk or solution reaction, the final amount of dead chains is a function of the radical concentration only large polymerization rates correspond to high dead chain concentrations. 

According to the same bulk model as mentioned above, it can be shown that the time needed to obtain 90% conversion after proper tuning of the process parameters so as to obtain a defined fraction of dead chains, , is given by [1 la]... 

Bandermann and coworkers studied the MMA polymerization initiated by 37 . Whenever the initiator is contaminated by traces of diethyl 2-ethylmalonate, an inhibition period is observed, which was accounted for by a transfer reaction of the propagating enolate to diethyl 2-ethylmalonate. The polymerization cannot start until this contaminant is completely consumed. Consistently, no inhibition is observed when the initiator is highly pure. Finally, a Hoffman elimination in the propagating ammonium enolate (38) could occur with formation of dead chains (39) tri-n-butylamine and 1-butene (equation 43) . 

Inserting no = 30, Xo = 0.1 gives = 270. should be an upper hmit for the average chain length in the autocatalytic reaction regime, if for reasons to be discussed below any further limitation of the kinetic chain length is suspended and if dead chain ends are not revived by recombination with a running chain. 

Having spcdfied NJ, we now show how to compute the required MWD, or more specifically, the component of the MWD arising from the mechanisms considered in this section. This is the distribution of dead chains formed as a result of transfer, exit (desorption), and termination by disproportionation. We denote the components of the instantaneous MWD arising from each of these mechanisms by and S,g( e,M), where... 

Living polymerizations are limited to the realm of chain-growth polymerizations, in which a monomer is transformed to a polymer by a reactive species (an initiator, I) via a kinetic chain reaction (Scheme 15.1). An intrinsic limitation of a typical chain-growth process, such as free-radical polymerization, is the occurrence of termination reactions that lead to the formation of dead chains, chains that are incapable of further growth. 

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