Dead polymer chain formation

In our illustrative calculated results, chain transfer reactions are neglected in order to highlight unique characteristics of emulsion polymerization. However, the radical entry rate into a polymer particle is often much smaller than the chain transfer frequency in emulsion polymerization usually. In such cases, dead polymer chain formation is dominated by chain transfer reactions, and the instantaneous weight fraction distribution is given by the following most probable distribution ... 

The chain-length-dependence of bimolecular termination reactions needs to be taken into account in order to be able to accurately estimate the MWD formed, except when very small polymer particles are formed and/or chain transfer reactions dominate over dead polymer chain formation. 

Since the nitroxide and the carbon-centered radical diffuse away from each other, termination by combination or disproportionation of two carbon-centered radicals cannot be excluded. This will lead to the formation of dead polymer chains and an excess of free nitroxide. The build-up of free nitroxide is referred to as the Persistent Radical Effect [207] and slows down the polymerization, since it will favor trapping (radical-radical coupling) over propagation. Besides termination, other side reactions play an important role in nitroxide-mediated CRP. One of the important side reactions is the decomposition of dormant chains [208], yielding polymer chains with an unsaturated end-group and a hydroxyamine, TH (Scheme 3, reaction 6). Another side reaction is thermal self-initiation [209], which is observed in styrene polymerizations at high temperatures. Here two styrene monomers can form a dimer, which, after reaction with another styrene monomer, results in the formation of two radicals (Scheme 3, reaction 7). This additional radical flux can compensate for the loss of radicals due to irreversible termination and allows the poly-... 

The probability of formation of dead polymer chains of length i is denoted as N (i) and N (i) where the subscripts d and r refer to disproportionation and recombination, respectively. 

However, the vinyl-terminated dead polymer chain opens the door to possible LCB-formation reactions if the correct catalyst is being used. These chains are called macromonomers and they can be considered to be very long a-olefins. If a catalyst that can copolymerize macromonomers is being used, they maybe reincorporated in the growing polymer chain, forming LCBs. As seen earlier, catalysts such as CGC are ideally suited for... 

The dead polymer chains generated via disproportionation carry an unsaturated end group which may be reactive during polymerization. Copolymerization of these macromonomers is a possible mechanism for the formation of long-chain... 

Moreover, the loss of radicals of course results in the formation of dead polymeric material. Here a crucial assumption is made and only termination by combination will be considered. Disproportionation reactions as well as chain tranfer reactions are ignored. Consequently, every termination event results in the formation of one dead polymer chain, hence ... 

The denominator of Eq. (12), the rate of dead chain formation, must be of the order 10 -10 chains s in order to produce polymer with a DPn of 10 -10. Individual polymer radicals exist on average only for a fraction of a second, as calculated by the expression t>/(fep[M]). Thus after the first few seconds of polymerization, the concentration of dead polymer chains is higher than that of polymeric radicals, and by the end of a typical polymerization the concentration of dead chains is orders of magnitude higher than [Ptot]. Final polymer MW and MWD (molecular weight distribution) are controlled by how the concentrations and kinetic coefficients in Eq. (12) vary with polymer conversion. 

No bimolecular termination reactions - termination by combination or disproportionation - as observed in free-radical polymerization take place with coordination catalysts. Some catalysts, under certain polymerization conditions, may polymerize dead polymer chains containing terminal vinyl unsaturations, leading to the formation of chains with long-chain branches. We will discuss the mechanism of long-chain branch formation with coordination catalysts in Section 8.3.4. 

The mechanism of long-chain branch (LCB) formation with coordination polymerization catalysts is terminal branching. In this mechanism, a dead polymer chain containing a terminal unsaturation - generally a vinyl group - is copolymerized with a growing polymer chain to form an LCB (Figure 8.27) [15]. We have already seen that dead polyethylene chains with terminal unsaturations will be formed by... 

Figure 8.29 shows how the chain length distribution of the whole polymer is affected by the value of the parameter a. First, notice that a belongs to the interval [0, 1]. All chains are linear when a = 0 since this implies that either / = 0 (without macromonomers, no LCBs can be formed) or s/ kicBY) oo. The latter condition is obeyed when either s —> oo (that is, the reactor residence time tends to zero) or kicB Y = 0. Both cases imply that no macromonomers are accumulated in the reactor. On the other hand, LCB formation is maximal when a = 1, a condition obeyed only when all dead polymer chains in the reactor contain terminal unsaturations, /" = 1, and the residence time in the reactor is infinite, s —> 0, or the rate of LCB formation is infinite, kicsY oo. Therefore, Eq. (32) captures, in a very elegant way, all the factors determining LCB formation with a coordination catalyst. 

A suitable cocatalyst is tris(pentaiiuorophenyl) borane. There is no evidence in the literature that methylaluminoxane cocatalysts are suitable for the synthesis of polyolefins containing long chain branches. It can be speculated that the presence of methylaluminoxane will promote transfer to aluminum and therefore produce dead polymer chains with saturated chain-ends which are unavailable for long chain branch formation. 

Note that in Eq. (7.6.1), the transfer reaction can occiu anywhere on the polymer chain. As a result, when the polymer radical P grows, it gives rise to branched chains, as seen in Figure 7.9. It is also observed that the disproportionation reaction [Eq. (7.6.le)] gives rise to dead polymer chains, which can react as in Eq. (7.6. Id). This also leads to the formation of branched polymers, as shown in Figure 7.9. 

Most of the polymer is present in polymer particles and, in view of this, we must analyze the polymer formation therein if we want to determine the average chain length and the polydispersity index. We have already noted that initiator radicals are absorbed on the surface of polymer particles, initiating the formation of polymer radicals. These polymer radicals grow and terminate according to Eq. (7.6.1) or get desorbed. For the analysis presented in this section, we assume that dead polymer chains do not get desorbed, even though polymer radicals (i.e., P )... 

In some cases termination may be brought about by transfer reactions . In this type of reactions though the growth of one Polymer chain is stopped due to formation of dead polymer as in coupling or disproportionation reaction, yet there is a simultaneous generation of a new free radical that is capable of initiating a fresh Polymer chain growth. 

The theoretical molecular weight distributions for cationic chain polymerizations are the same as those described in Sec. 3-11 for radical chain polymerizations terminating by reactions in which each propagating chain is converted to one dead polymer molecule, that is, not including the formation of a dead polymer molecule by bimolecular coupling of two propagating chains. Equations 2-86 through 2-89, 2-27, 2-96, and 2-97 withp defined by Eq. 3-185... 

The conversion of an w-mer into an (n + l)-mer may be imagined to occur in two steps (1) fission of an M—M bond located in the middle of the chain (2) insertion of a monomer molecule into the broken linkage coupled with the formation of two new M—M bonds. Because the end groups are far away from the reaction center, their nature cannot influence the free energy of the process which is therefore independent of the magnitude of n and of the nature of X and Y. This remains true even if X and Y are some unreactive end groups of a dead polymer. 

The use of this phenomenon to control carbon-carbon bond-forming reactions relies on R being rapidly converted into another transient radical which, in the case of a polymerisation, occurs by repetitive addition to a monomer double bond to give the propagating polymer radical, P Thus, the PRE prevents dead polymer (P—P ) formation and the dormant concentration of P—T remains effectively constant. It follows that the excess of T ensures that reversible termination and addition of P to monomer are dominant reactions allowing all polymer chains to grow practically simultaneously (Section 10.5.4). 

The degree of polymerization (DP)—i.e., the average number of monomer units per polymer molecule—is given by the number of chain propagation steps for each reaction between a pair of polymer radicals—i.e., for each formation of a dead polymer molecule. Therefore, DP is equal to the rate of chain growth divided by half the rate of chain termination ... 

The rate of formation of dead polymer of chain length r is... 

Let us first consider the polymerization where each propagating chain results in the formation of one dead polymer molecule, that is, each polymer molecule consists of one kinetic chain. This happens when the chain radical is terminated by disproportionation and/or chain transfer (i.e., ktc = 0). The probability situation in this case is almost identical to that for linear, reversible step-growth polymerization described in Chapter 5. Thus if we select randomly an initiator fragment at the end of a polymer molecule, the probability that the monomer molecule added to this initiator (primary) radical has added another monomer molecule is P. Continuing in this way the probability that x monomer molecules have been added one after another is (see p. 253). Since the probability that the radical end of a growing chain has terminated is (1 - P), the probability that the polymer molecule under consideration consists of essentially x monomer units is P (1 - P). This probability can be equated to the mole fraction of polymer molecules of this size... 

Equation 6, where = 2FJ l+Ff) is the number fraction of dead chains formed by disproportionation and transfer, is just the so-called Mayo equation, which is much used because it affords control of average polymer size. Equation 7 gives a minimum value of PDI =1.5 for the case of all dead-chain formation by combination (F = 0) and a maximum value of PDI = 2 for the case of no combination (F, = 1). Thus the natural broadening of a conventional radical polymerization will be somewhere between these two PDI limits, depending on the balance between transfer/disproportionation and combination that one has. 

When we combine this observation with the autoaccelerating tendencies of the system, the chain-transfer reactions to both the monomer and the polymer on one of the several positions which leads to branched-chain formation, and the possible reactivation of dead polymer molecules by hydrogen abstraction with monomeric free radicals [78], the complexity of the kinetics of vinyl acetate polymerization may be appreciated. Similar factors may be involved not only in the polymerization of other vinyl esters, but also in the fiee-radical polymerization of other types of monomers. 

The general mechanism of an addition polymerization includes four steps initiation, propagation, chain transfer and termination. Initiation refers to the formation of a growing polymer chain, typically of length n = 1 but occasionally with n = 2 or 3. Propagation refers to the addition of monomer units to the chain as in equation (4.1). Propagation is the predominant means for consuming monomer and is approximately first order with respect to monomer concentration, [A/]. The active chain, R, can be converted to inactive (dead) polymer, P, by chain transfer. Chain transfer to monomer is common to most vinyl polymerization mechanisms ... 

In NMP, living macrospecies can be temporarily trapped by a nitroxide species X resulting in the formation of dormant macrospecies (RjX), which are the targeted polymer molecules for CRP, in contrast with the typical dead polymer product P in other chain-growth polymerizations. For a sufficiently fast deactivation (k eact, Scheme 10.2), this dormant state is favored and the contribution of dead polymer molecules is minimized. This favoritism is enhanced as X does not undergo self-termination. 

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