Termination rate constants

Fourier transform infrared spectroscopy glycidyl methacrylate group transfer polymerization 2-hydroxyethyl methacrylate hydrophobic-lipophilic-balance hydroxypropylcellulose 2-hydroxypropyl methacrylate initiator concentration decomposition rate constant propagation rate constant termination rate constant... 

It is assumed that kp is independent of the size of the growing radical (given above by the index n in terms of monomer units). k is the absolute termination rate constant. Termination may occur by combination or disproportionation ... 

Combination and disproportionation are competitive processes and do not occur to the same extent for all polymers. For example, at 60°C termination is virtually 100% by combination for polyacrylonitrile and 100% by disproportionation for poly (vinyl acetate). For polystyrene and poly (methyl methacrylate), both reactions contribute to termination, although each in different proportions. Each of the rate constants for termination individually follows the Arrhenius equation, so the relative amounts of termination by the two modes is given by... 

Table 6.3 lists the activation energies for termination (these are overall values, not identified as to mode) of several different radicals. The rate constants for termination at 60°C are also given. We shall see in Sec. 6.6 how these constants are determined. 

Table 6.3 Rate Constants at 60 C and Activation Energies for Some Termination Reactions...

This situation is expected to apply to radical termination, especially by combination, because of the high reactivity of the trapped radicals. Only one constant appears which depends on the diffusion of the polymer radicals, so it cannot cancel out and may be the source of a dependence of the rate constant on the extent of reaction or degree of polymerization. 

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... 

In writing Eqs. (7.1)-(7.4) we make the customary assumption that the kinetic constants are independent of the size of the radical and we indicate the concentration of all radicals, whatever their chain length, ending with the Mj repeat unit by the notation [Mj ], This formalism therefore assumes that only the nature of the radical chain end influences the rate constant for propagation. We refer to this as the terminal control mechanism. If we wished to consider the effect of the next-to-last repeat unit in the radical, each of these reactions and the associated rate laws would be replaced by two alternatives. Thus reaction (7. A) becomes... 

Droplet trajectories for limiting cases can be calculated by combining the equations of motion with the droplet evaporation rate equation to assess the likelihood that drops exit or hit the wall before evaporating. It is best to consider upper bound droplet sizes in addition to the mean size in these calculations. If desired, an instantaneous value for the evaporation rate constant may also be used based on an instantaneous Reynolds number calculated not from the terminal velocity but at a resultant velocity. In this case, equation 37 is substituted for equation 32 ... 

The two main termination steps for neutral solutions are HO + HO — H2O2 + 2 O3 and HO + HO3 — H2O2 + O3 + O2. An alternative mechanism has been proposed that does not involve HO and HO but has a different initiation step (26). Three ozone molecules are destroyed for each primary event. In the presence of excess HO radical scavengers, ie, bicarbonate, the pseudo-first-order rate constant at 20°C for the initiation step is 175 X. This yields an ozone half-hfe of 66 min at pH 8. In distilled water = 50 mmol/L), the half-hfe is significantly lower, ie, 7 min. 

The piC values of polymethine dyes depend on terminal group basicity (64) thus the protonation abHity diminishes if the basic properties of the residues decrease, passing from benzimidazole, quinoline, benzothiazole, to indolenine. On the other hand, the piC of higher homologues increases with chain lengthening. The rate constant of protonation is sensitive to other features, for example, substituents and rings in the chain and steric hindrance for short-chain dyes. 

Thus the thiol 0 2 25511 is capable of terminating a growiug chain and also initiating a new chain. If the initiation-rate constant, k is not much slower than the propagation-rate constant, the net result is the growth of a new chain without any effect on the overall polymerization rate (retardation). That represents a tme chain transfer, ie, no effect on the rate but a substantial decrease iu molecular weight (12). 

In this equation, Mp is the monomer concentration within forming particles, pa is the adsorption rate of oligomeric radicals by the forming particles, Vp is the volume fraction of forming particles within the system, and kp and k, are the rate constants of propagation and termination, respectively. 

Photoinitiation is an excellent method for studying the pre- and posteffects of free radical polymerization, and from the ratio of the specific rate constant (kx) in non-steady-state conditions, together with steady-state kinetics, the absolute values of propagation (kp) and termination (k,) rate constants for radical polymerization can be obtained. 

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. 

The rate constants for benzoyloxy and phenyl radicals adding to monomer are high (> KF M-1 s for S at 60 CC - Table 3.7). In these circumstances primary radical termination should have little importance under normal polymerization conditions. Some kinetic studies indicating substantial primary radical termination during S polymerization may need to be re-evaluated in this light.161 Secondary benzoate end groups in PS with BPO initiator may arise by head addition or transfer to initiator (Section 8.2.1). 

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. 

Even though the absolute rate constant for reactions between propagating species may be determined largely by diffusion, this does not mean that there is no specificity in the termination process or that the activation energies for combination and disproportionation are zero or the same. It simply means that this chemistry is not involved in the rate-determining step of the termination process. 

The overall rate constant for radical-radical termination can be defined in terms of the rate of consumption of propagating radicals. Consider the simplified mechanism for radical polymerization shown in Scheme 5.4. 

Ideally, as long as the rate constants for reinitiation (AjT, AiM) are high with respect to that for propagation (kv), the transfer reactions should not directly affect the rate of polymerization and they need not be considered further in this section. The overall rate constant for radical-radical termination (A,) can be defined in terms of the rate of consumption of propagating radicals as shown in eq. I ... 

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