Diffusion-controlled termination radical polymerization

A new rate model for free radical homopolymerization which accounts for diffusion-controlled termination and propagation, and which gives a limiting conversion, has been developed based on ft ee-volume theory concepts. The model gives excellent agreement with measured rate data for bulk and solution polymerization of MMA over wide ranges of temperature and initiator and solvent concentrations. 

If ki and k.i are much larger than kj, the reaction Is controlled by kj. If however, ki and k.i are larger than or comparable to kz, the reaction rate becomes controlled by the translational diffusion determining the probability of collisions which Is typical for specific diffusion control. The latter case Is operative for fast reactions like fluorescence quenching or free-radical chain reactions. The acceleration of free-radical polymerization due to the diffusion-controlled termination by recombination of macroradicals (Trommsdorff effect) can serve as an example. 

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. 

Herein is reported a summary of recent studies of diffusion-controlled termination and propagation reactions in free-radical polymerization which are pertinent to emulsion polymerization kinetics. Also included are discussions of the effects of diffusion-controlled termination and propagation on molecular weight and branching development with particular reference to the synthesis of poly (vinyl chloride) at high conversions and to the significant reduction of thermal stability of PVC which occurs. 

Bulk polymerization eliminates solvents and suspending fluids other than monomer. It has the highest volume efficiency. However, the viscosity inaeases rapidly with the increase in polymer concentration and molecular weight, thereby reducing the mixing efficiency and heat transfer rate. Low heat transfer coefficient at high monomer conversions can cause safety problem with a mnaway reaaion. This is particularly tme with the kinetics characteristic of significant gel effect due to diffusion-controlled bimolecular radical termination. In bulk polymerization, monomer conversions beyond 65% are unusual for stirred reactor vessels. 

Most radicals are transient species. They (e.%. 1-10) decay by self-reaction with rates at or close to the diffusion-controlled limit (Section 1.4). This situation also pertains in conventional radical polymerization. Certain radicals, however, have thermodynamic stability, kinetic stability (persistence) or both that is conferred by appropriate substitution. Some well-known examples of stable radicals are diphenylpicrylhydrazyl (DPPH), nitroxides such as 2,2,6,6-tetramethylpiperidin-A -oxyl (TEMPO), triphenylniethyl radical (13) and galvinoxyl (14). Some examples of carbon-centered radicals which are persistent but which do not have intrinsic thermodynamic stability are shown in Section 1.4.3.2. These radicals (DPPH, TEMPO, 13, 14) are comparatively stable in isolation as solids or in solution and either do not react or react very slowly with compounds usually thought of as substrates for radical reactions. They may, nonetheless, react with less stable radicals at close to diffusion controlled rates. In polymer synthesis these species find use as inhibitors (to stabilize monomers against polymerization or to quench radical reactions - Section 5,3.1) and as reversible termination agents (in living radical polymerization - Section 9.3). 

Before any chemistry can take place the radical centers of the propagating species must conic into appropriate proximity and it is now generally accepted that the self-reaction of propagating radicals- is a diffusion-controlled process. For this reason there is no single rate constant for termination in radical polymerization. The average rate constant usually quoted is a composite term that depends on the nature of the medium and the chain lengths of the two propagating species. Diffusion mechanisms and other factors that affect the absolute rate constants for termination are discussed in Section 5.2.1.4. 

It is appropriate to differentiate between polymerizations occuring at temperatures above and below the glass transition point(Tg) of the polymer being produced. For polymerizations below Tg the diffusion coefficients of even small monomer molecules can fall appreciably and as a consequence even relatively slow reactions involving monomer molecules can become diffusion controlled complicating the mechanism of polymerization even further. For polymerizations above Tg one can reasonably assume that reactions involving small molecules are not diffusion controlled, except perhaps for extremely fast reactions such as those involving termination of small radicals. 

As the polymerization reaction proceeds, scosity of the system increases, retarding the translational and/ or segmental diffusion of propagating polymer radicals. Bimolecular termination reactions subsequently become diffusion controlled. A reduction in termination results in an increase in free radical population, thus providing more sites for monomer incorporation. The gel effect is assumed not to affect the propagation rate constant since a macroradical can continue to react with the smaller, more mobile monomer molecule. Thus, an increase in the overall rate of polymerization and average degree of polymerization results. 

A copper-based ATRP catalyst that is sufficiently stable and active can be used at very low concentrations. However, it is very important to mention that a copper(I) complex is constantly being converted to the corresponding copper(II) complex as a result of unavoidable and often diffusion-controlled radical termination reactions (k=l.0-4.0 x 109 M 1 s 1). Therefore, the deactivator (copper(II) complex) will accumulate as the reaction proceeds resulting in slowing down of the polymerization rate and limiting high monomer conversions. 

The bulk polymerization of acrylonitrile in this range of temperatures exhibits kinetic features very similar to those observed with acrylic acid (cf. Table I). The very low over-all activation energies (11.3 and 12.5 Kj.mole-l) found in both systems suggest a high temperature coefficient for the termination step such as would be expected for a diffusion controlled bimolecular reaction involving two polymeric radicals. It follows that for these systems, in which radicals disappear rapidly and where the post-polymerization is strongly reduced, the concepts of nonsteady-state and of occluded polymer chains can hardly explain the observed auto-acceleration. Hence the auto-acceleration of acrylonitrile which persists above 60°C and exhibits the same "autoacceleration index" as at lower temperatures has to be accounted for by another cause. 

The rate of copolymerization, unlike the copolymer composition, depends on the initiation and termination steps as well as on the propagation steps. In the usual case both monomers combine efficiently with the initiator radicals and the initiation rate is independent of the feed composition. Two different models, based on whether termination is diffusion-controlled, have been used to derive expressions for the rate of copolymerization. The chemical-controlled termination model assumed that termination proceeds with chemical control, that is, termination is not diffusion-controlled [Walling, 1949]. But this model is of only historical interest since it is well established that termination in radical polymerization is generally diffusion-controlled [Atherton and North, 1962 Barb, 1953 Braun and Czerwinski, 1987 North, 1963 O Driscoll et al., 1967 Prochazka and Kratochvil, 1983] (Sec. 3-10b). 

Tcrminadon is commonly diffusion-controlled, i.c., it is governed by the rate at which the reactive sites in growing radicals can come together rather than by chemical factors. In viscous media, termination may be so seriously impeded that both the overall rate of polymerization and the degree of polymerizadon increase markedly. In systems where the polymer is insoluble in the reacdon medium, polymer radicals may be trapped in the precipitated material and be able to grow but unable to participate in temunation processes. 

C olvents have different effects on polymerization processes. In radical polymerizations, their viscosity influences the diffusion-controlled bimolecular reactions of two radicals, such as the recombination of the initiator radicals (efficiency) or the deactivation of the radical chain ends (termination reaction). These phenomena are treated in the first section. In anionic polymerization processes, the different polarities of the solvents cause a more or less strong solvation of the counter ion. Depending on this effect, the carbanion exists in three different forms with very different propagation constants. These effects are treated in the second section. The final section shows that the kinetics of the... 

Anionic polymerization differs from radical polymerization in that no chain termination of the propagating polymers with each other occurs ( living polymers ). Furthermore, the rate constant of the propagation kp is not so high that this process is controlled by diffusion. 

The rates of these bimolecular termination reactions are usually close to diffusion controlled except for equally charged radicals (Ulanski et al. 1997), notably polymeric radicals (Chap. 9.3). DNA belongs to this group. 

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