Dead polymers

The kind of reaction which produces a dead polymer from a growing chain depends on the nature of the reactive intermediate. These intermediates may be free radicals, anions, or cations. We shall devote most of this chapter to a discussion of the free-radical mechanism, since it readily lends itself to a very general treatment. The discussion of ionic intermediates is not as easily generalized. 

Termination. By some reaction, generally involving two polymers containing active centers, the growth center is deactivated, resulting in dead polymer ... 

This mode of termination produces a negligible effect on the molecular weight of the reacting species, but it does produce a terminal unsaturation in one of the dead polymer molecules. Each polymer molecule contains one initiator fragment when termination occurs by disproportionation. 

The compound R X is a chain-transfer agent, with X usually H or Cl. The net effect of chain transfer is to kill a growing chain and start a new one in its place, thus shortening the chains. Mercaptan chain-transfer agents ate often used to limit molecular weight, but under appropriate conditions, almost anything in the reaction mass (solvent, dead polymer, initiator) can act as a chain-transfer agent to a certain extent. 

A number of examples have been studied in recent years, including liquid sulfur [1-3,8] and selenium [4], poly(o -methylstyrene) [5-7], polymer-like micelles [9,11], and protein filaments [12]. Besides their importance for applications, EP pose a number of basic questions concerning phase transformations, conformational and relaxational properties, dynamics, etc. which distinguish them from conventional dead polymers in which the reaction of polymerization has been terminated. EP motivate intensive research activity in this field at present. 

Eventually, one should also note that even in the case of dead polymers one has also observed a variation of the gyration radius (i g) with D, which goes through a minimum as D —> 0 [48] although the contour length of the chains L does not change. Thus computer simulations, being capable of... 

Thus, in order to reproduce the effect of an experimentally existing activation barrier for the scission/recombination process, one may introduce into the MC simulation the notion of frequency , lo, with which, every so many MC steps, an attempt for scission and/or recombination is undertaken. Clearly, as uj is reduced to zero, the average lifetime of the chains, which is proportional by detailed balance to Tbreak) will grow to infinity until the limit of conventional dead polymers is reached. In a computer experiment Lo can be easily controlled and various transport properties such as mean-square displacements (MSQ) and diffusion constants, which essentially depend on Tbreak) can be studied. 

The termination step of a polymerization involves a reaction which destroys the activity of the growing end and thus leads to cessation of its growth. The resulting polymeric molecule is frequently referred to as a dead polymer. If the activity of a growing chain is transferred to another molecule, the process is referred to as chain transfer if it is lost entirely, a normal termination step is involved. 

Chain transfer, the reaction of a propagating radical with a non-radical substrate to produce a dead polymer chain and a new radical capable of initiating a new polymer chain, is dealt with in Chapter 6. There are also situations intermediate between chain transfer and inhibition where the radical produced is less reactive than the propagating radical but still capable of reinitiating polymerization. In this case, polymerization is slowed and the process is termed retardation or degradative chain transfer. The process is mentioned in Section 5.3 and, when relevant, in Chapter 6. 

Inactive (Dead) Polymer in Micro-mixed CFSTR... 

Segregated CFSTR Micro-mixed CFSTR With Dead Polymer Fraction D D /D D D /D... 

TABLE VII. FRACTION DEAD POLYMER REQUIRED TO MATCH EXPERIMENTAL DEGREES OF POLYMERIZATION USING A MICRO-MIXED REACTION WITH DEAD POLYMER... 

Run Number Fraction Dead Polymer, (j) Run Number Fraction Dead Polymer, (f)jj... 

TABLE VIII. AVERAGE FRACTION DEAD POLYMER FOR SEED MIXTURES... 

Seed Number CFSTR Run Number Average Fraction Dead Polymer,... 

Calculated Molecular Weight Distributions. The calculated weight fraction distributions for the micro-mixed, segregated, and micro-mixed reactor with dead-polymer models for Runs 2, 5,... 

The micro-mixed reactor with dead-polymer model was developed to account for the large values of the polydispersity index observed experimentally. The effect of increasing the fraction of dead-polymer in the reactor feed while maintaining the same monomer conversion is to broaden the product polymer distribution and therefore to increase the polydispersity index. As illustrated in Table V, this model, with its adjustable parameter, can exactly match experiment average molecular weights and easily account for values of the polydispersity index significantly greater than 2. 

The fair degree of consistency observed in the values of <()j) for Seeds II and III and the excellent agreement between the experimental molecular weight distribution and those calculated with, lends credibility to the dead-polymer model. The... 

To differentiate between the micro-mixed reactor with dead-polymer and the by-pass reactor models in this investigation, the effect of mixing speed on the value of "( )" was observed. As illustrated in Table V, the value (j>" is not observed to increase with decreasing mixing speed as would be expected for a by-pass reactor. This rules out the possibility of a by-pass model and further substantiates the dead-polymer model. 

The effect of dead-polymer and by-passing on the micro-mixed reactor for the same degree of monomer conversion is to broaden the product polymer distribution and thus allow values of the polydispersity index much larger than 2. 

The micro-mixed reactor with dead-polymer model simulated the product of the laboratory reactor well within experimental accuracy. 

Autocatalytic rate constant for initiation Fraction active polymer in CFSTR with dead polymer Fraction by-pass in by-pass CFSTR... 

In contrast to chain transfer, termination reactions destroy free radicals. Two mechanisms are considered. Termination by combination produces a single molecule of dead polymer ... 

Chain lifetimes are small and the concentration of free radicals is low. To a reasonable approximation, the system consists of unreacted monomer, unreacted initiator, and dead polymer. The quasi-steady hypothesis gives... 

The dynamic chain length is the number average length of the growing chains before termination. The dead polymer will have the same average length as live polymer if termination is by disproportionation and will have twice this length if termination is by combination. 

Note that n= 1 gives mi/Mo = In, and n = 2 gives ti2ltio = lNlw for the dead polymer. For the case at hand. 

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