Termination Free-radical initiators, rates

As for any chain reaction, radical-addition polymerization consists of three main types of steps initiation, propagation, and termination. Initiation may be achieved by various methods from the monomer thermally or photochemically, or by use of a free-radical initiator, a relatively unstable compound, such as a peroxide, that decomposes thermally to give free radicals (Example 7-4 below). The rate of initiation (rinit) can be determined experimentally by labeling the initiator radioactively or by use of a scavenger to react with the radicals produced by the initiator the rate is then the rate of consumption of the initiator. Propagation differs from previous consideration of linear chains in that there is no recycling of a chain carrier polymers may grow by addition of monomer units in successive steps. Like initiation, termination may occur in various ways combination of polymer radicals, disproportionation of polymer radicals, or radical transfer from polymer to monomer. 

The reaction sequence for a typical vinyl polymer has four steps. In the first step, a free radical must be produced from the initiator such as those shown in Figs. 2.18 and 2.19. These radical formation reactions are typically first order in rate and are promoted by the elevated temperature of the reaction. For some free radical initiators, light can also promote the reaction. Then a sequence of events in the reaction mixture occurs, including initiation of a chain, followed by propagation, and finally termination of the chain. Termination of the chain will be discussed later. The schematic steps to produce an addition polymer from bulk or solvent polymerization are detailed in Fig. 2.19. The radical produced from the initiator reacts with the monomer in Step 2 to produce a new free radical by opening the double bond of a... 

As indicated earlier, G=0.7 for free radical initiation and about 0.1 for the free ions. The termination rate constants are 3 X 10 M sec for free radicals and 2 x 10 M sec for the free ions. The propagation rate constants have been determined to be 30, 4 X 10 and about 10 sec for free radical, cationic and anionic polymerization, respectively. 

In polyethylene, the tertiary carbon atom, which dominated the chemistry of the oxidative degradation of PP, is present only at branch points. This suggests that there may be a difference among LDPE, LLDPE and HDPE in terms of the expected rates of oxidation. This is complicated further by the presence of catalyst residues from the Ziegler-Natta polymerization of HDPE that may be potential free-radical initiators. The polymers also have differences in degree of crystallinity, but these should not impinge on the melt properties at other than low temperatures at which residual structure may prevail in the melt. Also of significance is residual unsaturation such as in-chain tra s-vinylene and vinylidene as well as terminal vinyl, which are defects in the idealized PE strucmre. 

Problem 6.21 A vinyl monomer of molecular weight 132 is polymerized by a free-radical initiator in the presence of dodecyl mercaptan (C12H25SH). The rate of polymerization is not depressed by the mercaptan. The purified polymer has a sulfur content of 0.02% (w/w) and its DP is 450. If 80% of the kinetic chains are terminated by coupling and 20% by disproportionation, what should be the extent of terminal unsaturation of the chains ... 

For long chain lengths, many molecules of hydroperoxide are formed per free radical initiating the reaction before termination occurs and hence variations of over-all rate constant K essentially reflects changes in the rate of propagation, i.e. in eq. (8)... 

Whether initiated by radiation or by the thermal decomposition of free radical initiators, and whether in the bulk or in the imbibed state, the mechanisms of free radical polymerizations of monomers in wood should be essentially similar. As with any free radical polymerization, three basic steps must be involved initiation, propagation, and termination also, chain transfer reactions may occur, depending on the monomer, additives, and on the mode of initiation (Chapiro, 1962 Siau et al, 1965a see also Appendix A, Chapter 1). In such cases, the rate of polymerization should depend on the square root of the concentration of initiating radicals, which, in turn, should depend on the dose or on the concentration of free radical initiator ... 

The radical mechanism of OA occurs only for polar substrates. A free radical initiator (I) is made, typically by photolysis or electrochemical means. The initiator reacts with the metal complex to oxidize it by one electron, as shown in Figure 19.10. The species can then react with RX to generate R-. The R- radical undergoes a chain reaction with a second metal complex to make R-M " -X and another R- radical. This continues until chain termination by two R radicals coupling together or by radical trapping. The propagation step in the mechanism competes with isomerization or racemization of R-, so that the product is almost always a racemic mixture of optical isomers when a chiral C atom is used. Unlike the S 2 mechanism, the rate of the reaction is independent of steric bulk on the transition metal. Furthermore, the reaction sequence with respect to 3°>2°> I >CH3 (which maps with the... 

In pol)mierization kinetic, steady state conditions must obtain, i.e. where the rate of generation of free radicals (initiation) is equal to the rate at which they disappear (termination). This implies a constant overall concentration of propagating free radicals, [M ]. The equation for the steady state conditions is ... 

Most emulsion polymerisations are free radical processes (318). There are several steps in the free radical polymerisation mechanism initiation (324), propagation and termination (324, 377, 399). In the first step, an initiator compound generates free radicals by thermal decomposition. The initiator decomposition rate is described by an Arrhenius-type equation containing a decomposition constant ( j) that is the reciprocal of the initiator half-life (Ph). The free radicals initiate polymerisation by reaction with a proximate monomer molecule. This event is the start of a new polymer chain. Because initiator molecules constantly decompose to form radicals, new polymer chains are also constantly formed. The initiated monomeric molecules contain an active free radical end group. 

While the SNR-mediated polymerization process comprises heating a mixture of monomer(s) and P-N adduct (that acts both as an initiator and a controlling agent), or a mixture of monomer(s), free-radical initiator, and SNR (or P-N adduct), the best temperature of polymerization, determined by experiments, is the one that leads to (i) a fast initiation rate as compared to the propagation rate (ii) a fast equilibrium between the active species and the dormant ones (iii) a low concentration of active species in order to minimize the termination and/or transfer reactions and (iv) a negligible thermal polymerization (of styrenic monomers). For example, the rate of formation of thermal radicals in styrene is equal to 1.6x10 mol L s at 100°C, 0.6x10 mol L... 

Data pertaining to the initiation process must be considered briefly, before the evaluation of the rate constants for propagation and termination can be attempted. A free-radical initiated polymerization, carried out under steady-state conditions and with an initiator which follows... 

Polymer propagation steps do not change the total radical concentration, so we recognize that the two opposing processes, initiation and termination, will eventually reach a point of balance. This condition is called the stationary state and is characterized by a constant concentration of free radicals. Under stationary-state conditions (subscript s) the rate of initiation equals the rate of termination. Using Eq. (6.2) for the rate of initiation (that is, two radicals produced per initiator molecule) and Eq. (6.14) for termination, we write... 

The completion stage is identified by the fact that all the monomer has diffused into the growing polymer particles (disappearance of the monomer droplet) and reaction rate drops off precipitously. Because the free radicals that now initiate polymerization in the monomer-swollen latex particle can more readily attack unsaturation of polymer chains, the onset of gel is also characteristic of this third stage. To maintain desirable physical properties of the polymer formed, emulsion SBR is usually terminated just before or at the onset of this stage. 

The result of the steady-state condition is that the overall rate of initiation must equal the total rate of termination. The application of the steady-state approximation and the resulting equality of the initiation and termination rates permits formulation of a rate law for the reaction mechanism above. The overall stoichiometry of a free-radical chain reaction is independent of the initiating and termination steps because the reactants are consumed and products formed almost entirely in the propagation steps. 

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