Polymerization chains, ideal free-radical

If ideal free-radical polymerization chains are formed very quickly with respect to the total time of monomer conversion, then any given propagating chain sees an environment (concentration of radicals, monomers, solvent, etc.) that changes httle during its formation. It is of interest to know after N free-radical events, what the probability is that there were N-l consecutive events (j=N - 1) that chained monomers to the free radical, and a final chain killing event that terminated the chain by a radical-radical encounter. Although there are A/ /[(A/-l) l ]=A different sequences of events that give N-1 monomers and one terminated radical in a chain, the only physically possible sequence is when the terminated radical is at the end of the chain. 

Ideally, free-radical polymerization involves three basic steps initiation, propagation, and termination, as discussed above. However, a fourth step, called chain transfer, is usually involved. In chain-transfer reactions, a growing polymer chain is deactivated or terminated by transferring its growth activity to a previously inactive species, as illustrated in Equation 2.17. 

The polymerization rate is directly proportional to the monomer concentration for ideal free radical polymerization kinetics. Deviations from this first-order kinetics can be caused by a whole series of effects which must be checked by separate kinetic experiments. These effects include cage effects during initiator free radical formation, solvation of or complex formation by the initiator free radicals, termination of the kinetic chain by primary free radicals, diffusion controlled termination reactions, and transfer reactions with reduction in the degree of polymerization. Deviations from the square root dependence on initiator concentration are to be primarily expected for termination by primary free radicals and for transfer reactions with reduction in the degree of polymerization. 

Free-radical polymerization ideally follows the preceding sequence of reaction steps. However, there are also slow but important steps that complicate this simple model. These involve chain transfer steps. We assumed that the only termination involves two radical species reacting with each other to form a stable dead molecule,... 

The ideal free-radical kinetics without chain transfer culminate in Eiqs. (6-64) and (6-65) in which termination of the growth of polymeric radicals is accounted for only by mutual reaction of two such radicals. Chain transfer can also end the physical growth of macroradicals, and the polymerization model will now be amended to include the latter process. This can be easily done by changing Eq. (6-62) to include transfer reactions in the rate of polymer production, <7[polymer]/[Pg.209]

The nature of free-radical polymerization has traditionally hindered attempts to produce an ideal living free radical polymerization technique. It is very difficult to prevent chain transfer and termination reactions in free-radical polymerizations and although several methods have afforded polymers with very low polydispersities < 1.1), these approaches are often referred... 

Equations (6.105) and (6.106) for apply to free-radical polymerization following ideal kinetics in which termination of chain growth occurs only by mutual reaction (coupling and disproportionation) of chain radicals. Combining Eqs. (6.100) and (6.105) one may write... 

Practical free-radical polymerizations often deviate from Eq. (6.126) because the assumptions made in the ideal kinetic scheme are not fuUy satisfied by the actual reaction conditions or because some of these assumptions are not valid. For example, according to the ideal kinetic scheme that leads to Eq. (6.126), the initiation rate (Rf) and initiator efficiency (/) are independent of monomer concentration in the reaction mixture and primary radicals (i.e., radicals derived directly from the initiator) do not terminate kinetic chains, thoughrifi reality R may depend on [M], as in the case of cage effect (see Problem 6.7) and, at high initiation rates, some of the primary radicals may terminate kinetic chains (see Problem 6.25). Moreover, whereas in the ideal kinetic scheme, both kp and kt are assumed to be independent of the size of the growing chain radical, in reahty k[ may be size-dependent and diffusion-controlled, as discussed later. 

Additional well-defined side-chain liquid crystalline polymers should be synthesized by controlled polymerizations of mesogen-ic acrylates (anionic or free radical polymerizations), styrenes (anionic, cationic or free radical), vinyl pyridines (anionic), various heterocyclic monomers (anionic, cationic and metalloporphyrin-initiated), cyclobutenes (ROMP), and 7-oxanorbornenes and 7-oxanorbornadienes (ROMP). Ideally, the kinetics of these living polymerizations will be determined by measuring the individual rate constants for termination and... 

In the RAFT mechanism, the chain equilibrium process is based on a transfer reaction thus, no radicals are formed or destroyed [15, 16]. When the RAFT agents behave ideally, the kinetics can be compared to the one of a conventional free radical polymerization. The release of initiating radicals through... 

Most vinyl and acrylic compounds more or less obey ideal polymerization kinetics during free radical polymerization. Drastic deviations, however, occur for allyl polymerizations since a chain termination by monomer dominates in this case [see Equation (20-41)]. For this case, the formation of polymer free radicals is given analogously to Equation (20-51) as... 

RAFT agent molecule is transformed into the end group of one polymer chain. Hence, the final chain lengths of the polymeric material can easily he controlled via vaiying the ratio of RAFT agent concentration to conversion. It should he noted that the free radical concentration—at least in principle—is not reduced in the RAFT process. Hence, the overall rate of polymerization is imchanged in an ideal RAFT polymerization compared to a conventional free radical polymerization. 

Transition metal complexes functioning as redox catalysts are perhaps the most important components of an ATRP system. (It is, however, possible that some catalytic systems reported for ATRP may lead not only to formation of free radical polymer chains but also to ionic and/or coordination polymerization.) As mentioned previously, the transition metal center of the catalyst should undergo an electron transfer reaction coupled with halogen abstraction and accompanied by expansion of the coordination sphere. In addition, to induce a controlled polymerization process, the oxidized transition metal should rapidly deactivate the propagating polymer chains to form dormant species (Fig. 11.16). The ideal catalyst for ATRP should be highly selective for atom transfer, should not participate in other reactions, and should deactivate extremely fast with diffusion-controlled rate constants. Finther, it should have easily tunable activation rate constants to meet sped c requirements for ATRP monomers. For example, very active catalysts with equilibrium constants K > 10 for styrenes and acrylates are not suitable for methacrylates. 

In polyolefins, the chain is propagated by an intermediate free-radical species or by an alkyl species adsorbed onto a solid. Both the free radical and the alkyl have the possibility of termination, and this creates the possibility of growth mistakes by chain transfer and chain-termination steps that create dead polymer before all reactants are consumed. The presence of termination steps produces a broader molecular-weight distribution than does ideal addition polymerization. 

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