Kinetics anionic chain polymerization

The kinetic picture of anionic chain polymerization also depends mostly upon the specific reaction. For those that are initiated by metal amides in liquid anunonia, the rate of initiation can be shown to be as follows ... 

Thus the growing anionic chain can assume at least two identities the free anion and the anion-cation ion pair (several types of solvated ion-pairs can also be considered). Furthermore, the kinetics of these propagation reactions, which generally show a fractional dependency on chain-end concentration ranging from one-half to unity, can best be explained by assuming that the monomer can react with both the free anion and the ion-pair (4, 5, 60, but at different rates. Thus, for example, in the polymerization of styrene by organosodium, the rate of polymerization (Rp) can be expressed as... 

The macromolecular silyl chloride reacts with sodium in a two-electron-transfer reaction to form macromolecular silyl anion. The two-electron-trans-fer process consists of two (or three) discrete steps formation of radical anion, precipitation of sodium chloride and generation of the macromolecular silyl radical (whose presence was proved by trapping experiments), and the very rapid second electron transfer, that is, reduction to the macromolecular silyl anion. Some preliminary kinetic results indicate that the monomer is consumed with an internal first-order-reaction rate. This result supports the theory that a monomer participates in the rate-limiting step. Thus, the slowest step should be a nucleophilic displacement at a monomer by macromolecular silyl anion. This anion will react faster with the more electrophilic dichlorosilane than with a macromolecular silyl chloride. Therefore, polymerization would resemble a chain growth process with a slow initiation step and a rapid multistep propagation (the first and rate-limiting step is the reaction of an anion with degree of polymerization n[DP ] to form macromolecular silyl chloride [DP +J, and the chloride is reduced subsequently to the anion). 

The simple kinetics of anionic polymerization described earlier exists because the initiator is converted completely from the inactive form, CA, to the active form, C "A" (or C -bA ) before any propagation reactions take place. However, some initiators (e.g, lithium alkyls and aryls) maintain an equilibrium between the active form and the inactive form. Moreover, this equilibrium may extend to the growing anionic chains also. In such a situation we must write the initiation steps as... 

The aforesaid complexities make it virtually impossible to write explicit general equations for the rate of polymerization, kinetic chain length, average degree of polymerization as has been done above for a completely dissociated ionic initiator. With the exception of those simple cases discussed above, each system in anionic polymerization represents a kinetically unique problem and must be solved separately. 

Free-Radical Chain Polymerization. In contrast to the typically slow stepwise polymerizations, chain reaction polymerizations are usually rapid with the initiated species rapidly propagating until termination. A kinetic chain reaction usually consists of at least three steps, namely, initiation, propagation, and termination. The initiator may be an anion, cation, free radical, or coordination catalyst. 

As mentioned previously, most continuous anionic polymeri tion studies have been conducted at relatively low temperatures ( < 50 °C). Even then, mixing kinetics have been of considerable concern due to the fast polymerization kinetics. In the recent anionic polymerization studies of Priddy and Pirc [1,73], the polymerization temperature range of 80-140 °C was studied (typical free radical temperature range). At these temperatures, the polymerization kinetics are extremely fast Also, the high polymerization temperature results in significant thermal termination of active polystyryl chains. Kem et aL [74] found that the termination reaction involved liberation of lithium hydride (1) and was first order. They found the apparent rate constant K at 65, 93, and 120°C are 0.15, 0.78, and 1.3 h respectively. 

Cationic surfactants, in contrast to anionic surfactants, usually reduce both the number of particles involved in the polymerization and the rate of polymerization. The nature of the stabilizing emulsifier has a marked effect on the polymerization kinetics. For example, addition of a non-ionic stabilizer [e.g., poly(vinyl alcohol), a block copolymer of carbowax 6000 and vinyl acetate, or ethylene oxide-alkyl phenol condensates] to a seed polymer stabilized by an anionic surfactant decreased the rate of polymerization to 25% of the original rate. The effect was as if the nonionic stabilizer (or protective colloid) acted as a barrier around the seed particles to alter the over-all kinetics. It may be that the viscosity of the medium in the neighborhood of the nonionic surfactant coating of the polymer particle is sufficiently different from that of an anionic layer to interfere with the diffusion of monomer or free radicals. There may also be a change in the chain-transfer characteristics of the system [156]. 

It is important to emphasize that this kinetic treatment is valid for any chain polymerization mechanisms, i.e., free radical, cationic, anionic, and coordination. However, in the case of the ionic mechanisms, the type of initiator used and the nature of the solvent medium may influence the ri and r2 values. This is due to the fact that the growing chain end in ionic systems is generally associated with a counterion, so that the structure and reactivity of such chain ends can be expected to be affected by initiator and the solvent. This will be discussed in Section 2.8.3. 

CHAIN POLYMERIZATION BY ANIONIC MECHANISM 2.8.1 Mechanism and Kinetics... 

The kinetic scheme outlined in section 3.3 for anionic chain-growth polymerization resulted in the following mathematical representation for the evolution of monomer and polymeric species ... 

A general description of anionic polymerization kinetics is complicated by the associations that may occur, particularly in nonpolar (hydrocarbon) solvents. The rate of propagation is proportional to the product of the monomer concentration and the concentration of active living chains [Pj] ... 

Often the transferred reactive species i.e., radical, cation, anion, etc.) rapidly re-initiates monomer. In this case, the polymerization kinetics are unaffected, and each chain transfer event creates one additional polymer chain. Thus, the total number of chains in the system, P]tot, is given by ... 

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