Diffusion-controlled chain termination

On the basis of the free volume model in Ref. [70] the diffusion-controlled chain termination constant is described via all processes as follows ... 

Such a dependence was interpreted within the scope of the model of chain oxidation with diffusionally controlled chain termination on the surface of solid antioxidant (for example, Mo or MoS2). According to the Smolukhovsky equation, the diffusion velocity of radical R02 at the distance //2 is v = 0.2DkS13, where S is the surface of the solid inhibitor and k is the coefficient of proportionality between the surface and number n of the solid particles (S=k x ). The function F for such diffusionally controlled chain termination is the following ... 

From the observation that diffusion-controlled wall termination seems to be the important termination step for most chain explosions at the low-pressure limit, which usually falls between 1 and 10 mm Hg, it appears that for these systems e must be of the order of 10 or higher. ... 

When the bimolecular terminations are highly diffusion controlled, the termination reactions are dominated by interactions between radicals with short and long chain lengths even in bulk polymerization, and the MWD of the longer polymer radicals tends to follow the most probable distribution [287, 292]. Under such conditions, oligomeric chains that can be observed only in the number fraction distribution may be formed via disproportionation termination irrespective of particle size. Figure 13 shows the effect of particle size on the instantaneous chain length distribution where the bimolecular terminations are from disproportionation [265]. 

When terminations are diffusion controlled, most termination events involve two highly entangled chains whose ends move by the reaction-diffusion process [119]. In this process, terminations occur because of the propagation-induced diffusion of the chain ends of growing macroradicals. This means that the rates of terminations depend upon the chain lengths [113]. 

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. 

More recent work has shown that the observed variation in propagation rate constants with composition is not sufficient to define the polymerization rates.5" 161,1152 There remains some dependence of the termination rate constant on the composition of the propagating chain. Thus, the chemical control (Section 7.4.1) and the various diffusion control models (Section 7.4.2) have seen new life and have been adapted by substituting the terminal model propagation rate constants (ApXv) with implicit penultimate model propagation rate constants (kpKY -Section 7.3.1.2.2). 

In the classical diffusion control model it is assumed that propagation occurs according to the terminal model (Scheme 7.1). The rate of the termination step is limited only by the rates of diffusion of the polymer chains. This rate may be dependent on the overall polymer chain composition. However, it does not depend solely on the chain end.166,16... 

More complex models for diffusion-controlled termination in copolymerization have appeared.1 tM7j Russo and Munari171 still assumed a terminal model for propagation but introduced a penultimate model to describe termination. There are ten termination reactions to consider (Scheme 7.1 1). The model was based on the hypothesis that the type of penultimate unit defined the segmental motion of the chain ends and their rate of diffusion. 

Reaction scheme, defined, 9 Reactions back, 26 branching, 189 chain, 181-182, 187-189 competition, 105. 106 concurrent, 58-64 consecutive, 70, 130 diffusion-controlled, 199-202 elementary, 2, 4, 5, 12, 55 exchange, kinetics of, 55-58, 176 induced, 102 opposing, 49-55 oscillating, 190-192 parallel, 58-64, 129 product-catalyzed, 36-37 reversible, 46-55 termination, 182 trapping, 2, 102, 126 Reactivity, 112 Reactivity pattern, 106 Reactivity-selectivity principle, 238 Relaxation kinetics, 52, 257 -260 Relaxation time, 257 Reorganization energy, 241 Reversible reactions, 46-55 concentration-jump technique for, 52-55... 

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. 

Anticipating the discussion on acetylene polymerization [98], extensively reported in Section IV, a value of n = 0.6 has been found, which implies a linear diffusion-controlled growth where the molecular librational and translational oscillations control the approach of the monomers to the active sites (chain terminations). 

Then, they depend also on the viscosity of the system. Specific diffusion control is characteristic of fast reactions like fluorescence quenching. In polymer formation, specific diffusion control is responsible for the acceleration of chain polymerization due to the retardation of the termination by recombination of two macroradicals (Trommsdorff effect). Step reactions are usually too slow to exhibit a dependence on translational diffusion also, the temperature dependence of their rate constants is of the Arrhenius type. 

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 chain-termination reactions are expected to be exceedingly fast because atoms and radicals have electrons in unfilled shells that normally are bonding. As a result, bond formation can begin as soon as the atoms or radicals approach one another closely, without need for other bonds to begin to break. The evidence is strong that bond-forming reactions between atoms and radicals usually are diffusion-controlled, that there is almost no barrier or activation energy required, and the rates of combination are simply the rates at which encounters between radicals or atoms occur. 

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... 

Diffusion of the macroradicals controls can be assumed to be the termination reaction. However, that is not the case the termination rate constant is absolutely independent of the degree of polymerization, as shown in Table I. Therefore, the assumption must be that the diffusion of the segment at the end of the radical chain controls the termination process (as long as the Trommsdorff effect is not rate-determining). 

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. 

---