Rate of termination

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 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. 

Setting the rate of initiation equal to the rate of termination and assuming that is the dominant termination process gives ... 

This shows that the rate of initiation equals the rate of termination. Thus,... 

Even within the small numbers of studies conducted to date, we are already seeing potentially dramatic effects. Free radical polymerization proceeds at a much faster rate and there is already evidence that both the rate of propagation and the rate of termination are effected. Whole polymerization types - such as ring-opening polymerization to esters and amides, and condensation polymerization of any type (polyamides, polyesters, for example) - have yet to be attempted in ionic liquids. This field is in its infancy and we look forward to the coming years with great anticipation. 

The rate of termination reaction is slower than that observed in the homogenous bulk or solution polymerization since the limited number of free radicals exists in the polymerization loci having a reasonably small volume (i.e., monomer swollen forming latex particle). Higher degree of polymerizations can be achieved in an emulsion system relative to the homogenous polymerization due to the existence of this limitation. 

In contrast to /3-PCPY, ICPY did not initiate copolymerization of MMA with styrene [39] and AN with styrene [40]. However, it accelerated radical polymerization by increasing the rate of initiation in the former case and decreasing the rate of termination in the latter case. The studies on photocopolymerization of MMA with styrene in the presence of ICPY has also been reported [41], /8-PCPY also initiated radical copolymerization of 4-vinylpyridine with methyl methacrylate [42]. However, the ylide retarded the polymerization of N-vinylpyrrolidone, initiated by AIBN at 60°C in benzene [44]. (See also Table 2.)... 

The SP-PLP817 18 and PS-PLP171 techniques involve following the monomer conversion induced by a single laser pulse or a sequence of laser pulses. These experiments are usually conducted at high pressure beeause rates of termination are lower and sensitivities are somewhat higher. 7... 

It remains a common misconception that radical-radical termination is suppressed in processes such as NMP or ATRP. Another issue, in many people s minds, is whether processes that involve an irreversible termination step, even as a minor side reaction, should be called living. Living radical polymerization appears to be an oxymoron and the heading to this section a contradiction in terms (Section 9.1.1). In any processes that involve propagating radicals, there will be a finite rate of termination commensurate with the concentration of propagating radicals and the reaction conditions. The processes that fall under the heading of living or controlled radical polymerization (e.g. NMP, ATRP, RAFT) provide no exceptions. 

It is important to realize that, even if the rate of termination is determined by the rates of chain diffusion, the chain end composition and the ratio of combination to disproportionation are not. Knowledge or prediction of the overall rate of termination offers little insight into the detailed chemistry of the termination processes not involved in the rale-determining step. 

Heterogeneous polymerization processes (emulsion, miniemulsion, non-aqueous dispersion) offer another possibility for reducing the rate of termination through what are known as compartmcntalization effects. In emulsion polymerization, it is believed that the mechanism for chain stoppage within the particles is not radical-radical termination but transfer to monomer (Section 5.2.1.5). These possibilities have provided impetus for the development ofliving heterogeneous polymerization (Sections 9.3.6.6, 9.4.3.2, 9.5.3.6). 

Transfer constants of the macromonomers arc typically low (-0.5, Section 6.2.3.4) and it is necessary to use starved feed conditions to achieve low dispersities and to make block copolymers. Best results have been achieved using emulsion polymerization380 395 where rates of termination are lowered by compartmentalization effects. A one-pot process where macromonomers were made by catalytic chain transfer was developed.380" 95 Molecular weights up to 28000 that increase linearly with conversion as predicted by eq. 16, dispersities that decrease with conversion down to MJM< 1.3 and block purities >90% can be achieved.311 1 395 Surfactant-frcc emulsion polymerizations were made possible by use of a MAA macromonomer as the initial RAFT agent to create self-stabilizing lattices . 

Some of the issues associated with RAFT emulsion polymerization have been attributed to an effect of chain length-dependent termination.528 In conventional emulsion polymerization, most termination is between a long radical and a short radical. For RAFT polymerization at low conversion most chains are short thus the rate of termination is enhanced. Conversely, at high conversion most chains are long and the rate of termination is reduced. 

The strongly acceleratory character of the exponential law cannot be maintained indefinitely during any real reaction. Sooner or later the consumption of reactant must result in a diminution in reaction rate. (This behaviour is analogous to the change from power law to Avrami—Erofe ev equation obedience as a consequence of overlap of compact nuclei.) To incorporate due allowance for this effect, the nucleation law may be expanded to include an initiation term (kKN0), a branching term (k N) and a termination term [ftT(a)], in which the designation is intended to emphasize that the rate of termination is a function of a, viz. 

Effect of Counteranion Nucleophilicity on the Rate of Termination in Isobutylene Polymerization... 

Though increased G nucleophilicity tends to decrease the rate of transfer, it is also expected to increase the rate of termination. For the systems characterized by AEmv = —1.8 1.0 kcal/mole, however, transfer is negligible and termination controls molecular weights. 

In sum, a relation of counteranion nucleophilicity and the molecular weight in isobutylene polymerization is discovered, according to which an increase in G nucleophility leads to an increase in the rate of termination but a decrease in the rate of chain transfer to monomer. Thus, an increase in G6 nucleophilicity leads to increased termination and hence decreased molecular weight for systems in which termination is molecular weight governing. Similarly, it leads to a decrease in rate of transfer and hence to an increase in molecular weights for systems in which chain transfer controls molecular weight. The nucleophilicity of G is determined by the... 

In the above reactions, I signifies an initiator molecule, Rq the chain-initiating species, M a monomer molecule, R, a radical of chain length n, Pn a polymer molecule of chain length n, and f the initiator efficiency. The usual approximations for long chains and radical quasi-steady state (rate of initiation equals rate of termination) (2-6) are applied. Also applied is the assumption that the initiation step is much faster than initiator decomposition. ,1) With these assumptions, the monomer mass balance for a batch reactor is given by the following differential equation. 

Two steady state conditions apply one to the total radical concentration and the other to the concentrations of the separate radicals Ml- and M2-. The latter has already appeared in Eq. (2), which states that the rates of the two interconversion processes must be equal (very nearly). It follows from Eq. (2) that the ratio of the radical population, Mi - ]/ [Mpropagation reaction rate constants. The steady-state condition as applied to the total radical concentration requires that the combined rate of termination shall be equal to the combined rate of initiation, i.e., that... 

The diffusion constant of a primary radical must be of the order of 10 cm.2 sec.- the radius r is about 5X10 cm., and as we have seen 1 10 " per second. Hence ]ag l0 radicals per cc. But the radicals are being generated at a rate of 10 cc. sec. hence the average lifetime of a radical from generation to capture by a polymer particle will be only 10 sec. " The rate of termination by reaction between two radicals in the aqueous phase at the calculated equilibrium concentration, 10 radicals per cc., will be given by... 

The termination constants kt found previously (see Table XVII, p. 158) are of the order of 3 X10 1. mole sec. Conversion to the specific reaction rate constant expressed in units of cc. molecule" sec. yields A f=5X10". At the radical concentration calculated above, 10 per cc., the rate of termination should therefore be only 10 radicals cc. sec., which is many orders of magnitude less than the rate of generation of radicals. Hence termination in the aqueous phase is utterly negligible, and it may be assumed with confidence that virtually every primary radical enters a polymer particle (or micelle). Moreover the average lifetime of a chain radical in the aqueous phase (i.e., 10 sec.) is too short for an appreciable expectation of addition of a dissolved monomer molecule by the primary radical prior to its entrance into a polymer particle. 

We turn next to consideration of the concentration of radicals in a polymer particle. The rate of termination in a particle of volume V may be written... 

Most workers are in agreement with the suggestion of Marks (25) and others (22) that the increased formation of gel content with increasingHCl concentration is due to an increased rate of termination by inter-chain reactions leading to cross links. Hjertberg and Sorvik though (17) believe that the termination rate constant is unaffected hut that the increased... 

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