Reaction loci

The First Stage. The preferential polymerization of AA at the initial stage of copolymerization means that the main reaction locus is the aqueous phase just as Juang and Krieger pointed it out for the aqueous copolymerization of St with sodium styrenesul-fonate ( SSS ) (9). In the St-SSS system, SSS polymerized preferentially up to a few percent conversion under the condition of SSS/St (w/w) - 0.014. Copolymerization of hydrophobic monomer with a large amount of hydrophilic comonomer was considered to yield a greater amount of information with respect to the reaction mode. By use of a relatively large amount of AA or its derivatives the characteristic reaction mode of the copolymerization of St with acrylamides could be clarified. 

These phenomena must result from alteration of the main reaction locus from the particles to the aqueous phase. 

No clear evidence was obtained about the alteration of the main reaction locus for the copolymerization of St with MA. This would be attributed to the difference in the partition coefficient between MA and AA (see above) and the difference in the number of latex particles formed in their copolymerization systems with St. (The number of particles in St-AA copolymer latex was about a third of that in St-AA latex. The small number for St-MA system is considered to result from the lower particle-stabilizing ability of MA due to its lower hydrophilicity.) These factors would alter the balance of the polymerization in two reaction loci, that is, the aqueous phase and the particles, and consequently serve to change the reaction mode. 

N-(hydroxymethyl)acrylamide, N,N-dimethylacrylamide, and methacrylamide) were carried out in emulsifier-free aqueous media. When either of the former three acrylamides were used, the copolymerization course was divided into three srages on the basis of the main reaction locus. At first acrylamides polymerized preferentially in the aqueous phase. After the particle formation styrene... 

The theory of compartmentalised free-radical polymerisation reactions of the type considered in this paper is of interest primarily because it is believed that most of the polymer which is formed in the course of an emulsion polymerisation reaction is formed by way of reactions of this type. The objective of the theory is to calculate the relative proportions of the reaction loci which at any instant contain 0, 1, 2,. .., r,. .. propagating radicals, and also such properties of the locus population distribution as the average number of propagating radicals per reaction locus, and the variance of the distribution of locus populations. 

It is then a straightforward matter to write down an expression for the overall rate of polymerisation in the reaction system, once an expression has been obtained for the average number of propagating radicals per reaction locus. 

The reaction model assumed is one in which free-radical polymerisation is compartmentalised within a fixed number of reaction loci, all of which have similar volumes. As has been pointed out above, new radicals are generated in the external phase only. No nucleation of new reaction loci occurs as polymerisation proceeds, and the number of loci is not reduced by processes such as particle agglomeration. Radicals enter reaction loci from the external phase at a constant rate (which in certain cases may be zero), and thus the rate of acquisition of radicals by a single locus is kinetic-ally of zero order with respect to the concentration of radicals within the locus. Once a radical enters a reaction locus, it initiates a chain polymerisation reaction which continues until the activity of the radical within the locus is lost. Polymerisation is assumed to occur almost exclusively within the reaction loci, because the solubility of the monomer in the external phase is assumed to be low. The volumes of the reaction loci are presumed not to increase greatly as a consequence of polymerisation. Two classes of mechanism are in general available whereby the activity of radicals can be lost from reaction loci ... 

In this set of equations, n is the number of reaction loci per arbitrary volume of reaction system which contain i propagating radicals, cr is the average rate of entry of radicals into a single reaction locus, xr is the volume of the reaction locus, A. is the rate coefficient for the mutual termination of radicals, and k is a composite constant which quantifies the rate at which radicals are lost from reaction loci by first-order processes. For convenience we put kju s x ... 

Attempts have also been made to provide approximate solutions by truncating the infinite set of differential difference equations to a small set which is then amenable to solution by standard methods for simultaneous linear differential equations. The most usual truncations which have been adopted are those which correspond to two- and three-state models in which each reaction locus can contain at most either one or two propagating radicals respectively. 

The average number of propagating radicals per reaction locus can be found from... 

In reviewing the cases for which explicit analytic solutions have so far been obtained, it is helpful to recall that the Smith-Ewart differential difference equations are derived on the assumption that the state of radical occupancy of a reaction locus can change as a result of three distinct types of process ... 

Introduction of a reactive group adjacent to the reaction locus has proven to be a very effective approach to irreversible inhibitors of many pyridoxal phosphate (PLP) dependent... 

Polymerization rate represents the instantaneous status of reaction locus, but the whole history of polymerization is engraved within the molecular weight distribution (MWD). Recently, a new simulation tool that uses the Monte Carlo (MC) method to estimate the whole reaction history, for both hnear [263-265] and nonlinear polymerization [266-273], has been proposed. So far, this technique has been applied to investigate the kinetic behavior after the nucleation period, where the overall picture of the kinetics is well imderstood. However, the versatility of the MC method could be used to solve the complex problems of nucleation kinetics. 

The MC method is a powerful technique for investigating complicated phenomena that are difficult to solve by the conventional differential equation approach. In the MC approach, all one needs are the individual probabilities of various kinetic events. It is easy to understand the advantages of applying the MC method to emulsion polymerization if we note that it is possible to simulate the formation processes of all polymer molecules in each polymer particle directly because the volume of the reaction locus is very small. One... 

If all of these species exist in the same reaction locus as in Fig. 17a, it would be highly probable that all of the radicals would attack the largest chain. In other words, the chain transfer rate of the polymer chain with chain length P, Vfp Pp, is proportional to its chain length ... 

The number of reaction loci is assumed not to vary with time. No nucleation of new reaction loci occurs as polymerization proceeds, and the number of loci is not reduced by processes such as particle agglomeration. The monomer is assumed to he only sparingly soluble in the external phase (a typical examide is styrene as monomer and water as the external phase), and thus polymerization is assumed to occur exclusively within the reaction loci and not within the external phase. The monomer is assumed to be present in sufficient quantity throughout the reaction to ensure that monomer droplets are present as a separate phase, and the rate of transfer of monomer to the reaction loci from the droplets is assumed to be rapid relative to the rate of consumption of moncuner in the loci by polymerization. The monomer concentration within the reaction loci is then taken to be constant throughout the reaction. This assumption is important if an attempt is made to relate the overall rate of polymerization to the average number of propagating radicals per reaction locus. The assumption will therefore be examined in further detail below. 

Once a radical enters a reaction locus, it is presumed to initiate a chain polymerization reaction which then continues at a constant rate until the activity of the radical is lost. The processes whereby the activity of the propagating radicals is lost from the reaction loci can be classified into two broad types ... 

Processes that are kinetically of first order with respect to the concentration of radicals within the reaction locus. These processes include exit from the locus into the external phase, termination by reaction with monomer within the locus, termination by reaction with adventitious impurities in the locus, and spontaneous deactivation. 

A related matter concerns the physical mechanism by which radicals (primary or oligomeric) are acquired by the reaction loci. One possibility, first proposed by Garden (1968) and subsequently developed by Fitch and Tsai (1971), is that capture occurs by a collision mechanism. In this case, the rate of capture is proportional to, inter alia, the surface area of the particle. Thus, if the size of the reaction locus in a compartmentalized free-radical polymerization varies, then a should be proportional to r, where r is the radius of the locus. A second possibility (Fitch, I973) is that capture occurs by a diffusion mechanism. In this case, the rate of capture is approximatdy proportional to r rather than to r. A fairly extensive literature now exists concerning this matter (see, e.g., Ugelstad and Hansen, 1976, 1978. 1979a, b). The consensus of present opinion seems to favor the diffusion theory rather than the collision theory. The nature of the capture mechanism is not. however, relevant to the theory discussed in this chapter. It is merely necessary to note that both mechanisms predict that the rate of capture will depend on the size of the reaction locus constancy of a therefore implies that the size of the locus does not change much as a consequence of polymerization. 

Whatever may be the exact nature of the molecular processes that lead to exit, the rate of loss of radicals from a single reaction locus by exit is written simply as ki, where i is the number of radicals in the locus and k is a... 

Little needs to be said here except to note that (i) the rate of propagation is unlikely to be appreciably dependent on the size of the reaction locus, whereas the rate of termination is likely to be appreciably size-dependent and (ii) the rate of both propagation and termination will be reduced if the viscosity of the reaction medium rises, but the rate of termination wiU be reduced more than that of propagation. 

The physical reason why the rate of propagation is not appreciably size dependent is simply that a propagating radical is always surrouoded by the same concentration of monomer molecules wherever the radical is in the reaction locus and, to a first approximation, whatever the size of the locus. However. to the extent that the monomer/polymer ratio in the reaction locus depends on the size of the locus (see Section then some... 

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