Termination rate

In any application of a copolymer the rate of formation of the product, its molecular weight, and the uniformity of its composition during manufacture are also important considerations. While the composition of a copolymer depends only on the relative rates of the various propagation steps, the rate of formation and the molecular weight depend on the initiation and termination rates as well. We shall not discuss these points in any detail, but merely indicate that the situation parallels the presentation of these items for homopolymers as given in Chap. 6. The following can be shown ... 

In the presence of any substantial amount of oxygen this reaction is extremely rapid, but the terminal peroxy radical formed reacts slowly with monomer and has a relatively rapid termination rate. 

Bulk Polymerization. This is the method of choice for the manufacture of poly(methyl methacrylate) sheets, rods, and tubes, and molding and extmsion compounds. In methyl methacrylate bulk polymerization, an auto acceleration is observed beginning at 20—50% conversion. At this point, there is also a corresponding increase in the molecular weight of the polymer formed. This acceleration, which continues up to high conversion, is known as the Trommsdorff effect, and is attributed to the increase in viscosity of the mixture to such an extent that the diffusion rate, and therefore the termination reaction of the growing radicals, is reduced. This reduced termination rate ultimately results in a polymerization rate that is limited only by the diffusion rate of the monomer. Detailed kinetic data on the bulk polymerization of methyl methacrylate can be found in Reference 42. 

Polymerization Kinetics of Mass and Suspension PVC. The polymerization kinetics of mass and suspension PVC are considered together because a droplet of monomer in suspension polymerization can be considered to be a mass polymerization in a very tiny reactor. During polymerization, the polymer precipitates from the monomer when the chain size reaches 10—20 monomer units. The precipitated polymer remains swollen with monomer, but has a reduced radical termination rate. This leads to a higher concentration of radicals in the polymer gel and an increased polymerization rate at higher polymerization conversion. 

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. 

The observed rate law is then three-halves order in the reagent A2. In most real systems, the situation is complicated because more than one termination reaction makes a contribution to the total termination rate. A more complete discussion of the effect of termination steps on the form of the rate law has been given by Huyser. ... 

Which mechanism of termination will be preferably applied depends largely on the monomer used. Thus, methyl methacrylate chains terminate to a large extent by disproportionation, whereas styrene chains tend to termination by combination. The ratios of termination rate constants 8 = ktJkic (for disproportionation, td, combination,, c) are 5 == 0 and 5 = 2 for styrene [95] and methyl methacrylate [96], respectively. In the case of styrene, however, the values of 8 reported in the literature are at variance. Berger and Meyerhoff [97] found 8 = 0.2, at 52°C. Therefore, it is possible that a fraction of styrene terminates by disproportionation. 

Center of mass or translational diffusion is believed to be the rate-determining step for small radicals33 and may also be important for larger species. However, other diffusion mechanisms are operative and are required to bring ihe chain ends together and these will often be the major term in the termination rate coefficient for the case of macromolecular species. These include ... 

In dealing with radical-radical termination in bulk, polymerization it is common practice to divide the polymerization timeline into three or more conversion regimes.2 "0 The reason for this is evident from Figure 5.3. Within each regime, expressions for the termination rate coefficient are defined according to the dominant mechanism for chain end diffusion. The usual division is as follows ... 

However, it has been pointed out that the value of kXo in the expressions eqs. 25-23 should not be confused with the small radical A, rather, the value of kt0 represents the termination rate constant of a single unit chain if the implied diffusion mechanism was the rate-determining process. 

Table 5.1 Parameters Characterizing Chain Length Dependence of Termination Rate Coefficients in Radical Polymerization of Common Monomers 1...

The concept of reaction diffusion (also called residual termination) has been incorporated into a number of treatments.7 7 Reaction diffusion will occur in all conversion regimes. However at low and intermediate conversions the process is not of great significance as a diffusion mechanism. At high conversion long chains are essentially immobile and reaction diffusion becomes the dominant diffusion mechanism (when i and j are both "large" >100). The termination rate constant is determined by the value of kp and the monomer concentration. In these circumstances, the rate constant for termination k - should be independent of the chain lengths i and j and should obey an expression of the form 75... 

Even though the chemical reactions are the same (i.e. combination, disproportionation), the effects of compartmentalization are such that, in emulsion polymerization, particle phase termination rates can be substantially different to those observed in corresponding solution or bulk polymerizations. A critical parameter is n, the average number of propagating species per particle. The value of h depends on the particle size and the rates of entry and exit. 

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 evaluating the kinetics of copolymerization according to the chemical control model, it is assumed that the termination rate constants k,AA and A,Br are known from studies on homopolymerization. The only unknown in the above expression is the rate constant for cross termination (AtAB)- The rate constant for this reaction in relation to klAA and kmB is given by the parameter . 

Vichutinsky, "Chemiluminescent Methods for the Determination of the Absolute Magnitude of the Termination Rate Constants of Peroxide Radicals in the Liquid Phase , PA Tech Translation 66(1967) 17) R. Czerepinski G.H. 

Achieving steady-state operation in a continuous tank reactor system can be difficult. Particle nucleation phenomena and the decrease in termination rate caused by high viscosity within the particles (gel effect) can contribute to significant reactor instabilities. Variation in the level of inhibitors in the feed streams can also cause reactor control problems. Conversion oscillations have been observed with many different monomers. These oscillations often result from a limit cycle behavior of the particle nucleation mechanism. Such oscillations are difficult to tolerate in commercial systems. They can cause uneven heat loads and significant transients in free emulsifier concentration thus potentially causing flocculation and the formation of wall polymer. This problem may be one of the most difficult to handle in the development of commercial continuous processes. 

Polymerizations Above Tg. Let the polymerization begin in pure monomer. As the concentration of polymer chains increases initially one observes a relatively small increase in the termination rate constant. This is related to the effect of polymer concentration on coil size. A reduction in coil size increases the probability of finding a chain end near the surface and hence causes an increase in k-. Soon thereafter at conversions 15-20 polymer chains begin to entangle causing a dramatic reduction in radical chain translational mobility giving a rapid drop in k-j. ... 

Figure 4. Bulk polymerization of MM A at 22.5° C with AIBN Ri = 8.36 X 10 mol/L sec. Effect of conversion on propagation and termination rate constants (6).

Development of a relationship which gives the decrease in the termination rate constant as a function of temperature and polymer molecular weight and concentration. 

In order to estimate the dependence of the termination rate constant on conversion, molecular weight and temperature, the following is assumed k- becomes diffusion controlled when the diffusion coefficient for a polymer radical Dp becomes less than or equal to a critical diffusion coefficient D ... 

It is further assumed that the termination rate constant beyond this conversion can he expressed by eq. (6a) and at the critical point (6h). 

TC = termination by combination rate constant T = ratio of the termination rate constant for combination to the rate constant for disproportionation CFM = ratio of the rate constant for monomer transfer to the constant for propagation... 

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