Termination reactions, kinetics

Olefins can only be polymerized by metal halides if a third substance, the co-catalyst, is present. The function of this is to provide the cation which starts the carbonium ion chain reaction. In most systems the catalyst is not used up, but at any rate part of the cocatalyst molecule is necessarily incorporated in the polymer. Whereas the initiation and propagation of cationic polymerizations are now fairly well understood, termination and transfer reactions are still obscure. A distinction is made between true kinetic termination reactions in which the propagating ion is destroyed, and transfer reactions in which only the molecular chain is broken off. It is shown that the kinetic termination may take place by several different types of reaction, and that in some systems there is no termination at all. Since the molecular weight is generally quite low, transfer must be dominant. According to the circumstances many different types of transfer are possible, including proton transfer, hydride ion transfer, and transfer reactions involving monomer, catalyst, or solvent. 

Shortly after Plesch and Westermann s work was published, Jaacks et al. [132] also reported a study of the polymerization of 1,3-dioxolane by HCIO4 in CH2CI2 at 20°C. Again the need for the most rigorous absence of water is emphasized [133]. They found a gradual but quantitative initiation reaction with no kinetic termination reaction. Eventually from further studies [134] they concluded that the slow initiation involves two reactions... 

Intermolecular transfer reactions occur relatively frequently in cationic polymerizations. The cation from one growing chain is transferred to another in these transfer reactions. Thus, one individual growing chain is killed and another is started. Consequently, such reactions are of significance in the chemical sense for an individual chain, for which they represent a termination reaction, but these reactions are insignificant in the kinetic sense. Kinetically, termination reactions are defined as when a chain (or a pair of chains, see below) is killed and no new chain is formed. Genuine (kinetic) termination reactions are rare in cationic polymerization. 

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. 

It is possible to balance all of these thermodynamic, kinetic, and mechanistic considerations and to prepare well-defined PTHF. Living oxonium ion polymerizations, ie, polymerizations that are free from transfer and termination reactions, are possible. PTHF of any desired molecular weight and with controlled end groups can be prepared. 

The main reason that the decreases as the polymerization temperature increases is the increase in the initiation and termination reactions, which leads to a decrease in the kinetic chain length (Fig. 17). At low temperature, the main termination mechanism is polystyryl radical coupling, but as the temperature increases, radical disproportionation becomes increasingly important. Termination by coupling results in higher PS than any of the other termination modes. 

Termination. The conversion of peroxy and alkyl radicals to nonradical species terminates the propagation reactions, thus decreasing the kinetic chain length. Termination reactions (eqs. 7 and 8) are significant when the oxygen concentration is very low, as in polymers with thick cross-sections where the oxidation rate is controlled by the diffusion of oxygen, or in a closed extmder. The combination of alkyl radicals (eq. 7) leads to cross-linking, which causes an undesirable increase in melt viscosity. 

The overall rate of a chain process is determined by the rates of initiation, propagation, and termination reactions. Analysis of the kinetics of chain reactions normally depends on application of the steady-state approximation (see Section 4.2) to the radical intermediates. Such intermediates are highly reactive, and their concentrations are low and nearly constant throughout the course of the reaction ... 

The effect of temperature on the kinetics of the direct radiation method is quite complex. Increase in temperature increases the monomer diffusion rate but also increases transfer and termination reaction rates of the growing chains and reduces the importance of the gel effect. Solubility and radical mobility may also change as the temperature is varied [88,89]. 

Any understanding of the kinetics of copolymerization and the structure of copolymers requires a knowledge of the dependence of the initiation, propagation and termination reactions on the chain composition, the nature of the monomers and radicals, and the polymerization medium. This section is principally concerned with propagation and the effects of monomer reactivity on composition and monomer sequence distribution. The influence of solvent and complcxing agents on copolymerization is dealt with in more detail in Section 8.3.1. 

In early work, it was assumed that the rate constant for termination was determined by the monomer unit at the reacting chain ends. The kinetics of copolymerization were then dictated by the rate of initiation, the rates of the four propagation reactions (Scheme 7.1) and rales of three termination reactions... 

When the initiation and termination reactions are the reverse of one another, the kinetic form is usually simpler than when the two are independent. Also, the transition-state composition follows directly from the rate law, which is why the term well-behaved is applied. Imagine, for example, that the termination step in the system most recently presented was the recombination of two sulfate radical ions rather than Eq. (8-38) ... 

Taft equation, 229-230 Temperature, effect on rate, 156-160 Temperature-jump method, 256 Termination reaction, 182 Thermodynamic products, 59 Three-halves-order kinetics, 29... 

How does one know when the complete roster of reaction schemes that are consistent with the rate law has been obtained One method is based on an analogy between electrical circuits and reaction mechanisms.13 One constructs an electrical circuit analogous to the reaction scheme. Resistors correspond to transition states, junctions to intermediates, and terminals to reactants and products. The precepts are these (1) any other electrical circuit with the same conductance corresponds to a different but kinetically equivalent reaction scheme, and (2) these circuits correspond to all of the fundamentally different schemes. 

From complex kinetic studies the rate constants for the cross-termination reaction ... 

We should point out that one of the postulates on which the kinetic equations were derived is that the rate constant of the termination reaction between entangled radicals, k, is... 

It should be mentioned that there is no decrease in the peroxydisulphate current in the presence of both iron(ril) and arsenic(III). Presumably, the iron(II)-peroxydisulphate reaction is too slow to compete with the reduction of peroxydisulphate at the DME at the given concentration. However, iron(III) reduces the kinetic current in the presence of copper(II) and arsenic(ril). This can be accounted for by the termination reactions... 

Here, we see that the rate of the reaction depends on the square root of the concentration of the initiator and linearly on the concentration of the monomer. The steady state approximation fails when the concentration of the monomer is so low that the initiation reaction cannot occur at the same rate as the termination reaction. Under these conditions, the termination reaction dominates the observed kinetics. 

If equations 4.2.25 and 4.2.26 are substituted for equations 4.2.11 and 4.2.15, respectively, in the mechanism described above, the effect is to replace kx by k [M] and k5 by /c 5[M] everywhere that they appear. Since these quantities appear as a ratio in the final rate expression, the third body concentration will drop out and kjks) becomes identical with k /k 5 The necessity for the use of the third body concentration thus is not obvious in kinetic studies of the thermal reaction. However, from studies of photochemical reaction between hydrogen and bromine, there is strong evidence that the termination reaction is termolecular. This fact and... 

The orbital coefficients obtained from Hiickel calculations predict the terminal position to be the most reactive one, while the AMI model predicts the Cl and C3 positions to be competitive. In polyenes, this is true for the addition of nucleophilic as well as electrophilic radicals, as HOMO and LUMO coefficients are basically identical. Both theoretical methods agree, however, in predicting the Cl position to be considerably more reactive as compared to the C2 position. It must be remembered in this context that FMO-based reactivity predictions are only relevant in kinetically controlled reactions. Under thermodynamic control, the most stable adduct will be formed which, for the case of polyenyl radicals, will most likely be the radical obtained by addition to the C1 position. 

In this work, the kinetics of these reactions are closely examined by monitoring photopolymerizations initiated by a two-component system consisting of a conventional photoinitiator, such as 2,2-dimethoxy-2-phenyl acetophenone (DMPA) and TED. By examining the polymerization kinetics in detail, further understanding of the complex initiation and termination reactions can be achieved. The monomers discussed in this manuscript are 2-hydroxyethyl methacrylate (HEMA), which forms a linear polymer upon polymerization, and diethylene glycol dimethacrylate (DEGDMA), which forms a crosslinked network upon polymerization. 

It can be observed that the initial rate of polymerization decreases and the autoacceleration peak is suppressed as the TED concentration is increased. The TED molecules generate dithiocarbamyl (DTC) radicals upon initiation. As a result, termination may occur by carbon-carbon combination which leads to a dead polymer and by carbon-DTC radical reaction which produces a reinitiatable ( living ) polymer. The cross-termination of carbon-DTC radicals occurs early in the reaction (with the carbon-carbon radical termination), and this feature is observed by the suppression of the initial rate of polymerization. As the conversion increases, the viscosity of the system poses mass transfer limitations to the bimolecular termination of carbon radicals. As has been observed in Figure 3, this effect results in a decrease in the ktCC. However, as the DTC radicals are small and mobile, the crosstermination does not become diffusion limited, i.e., the kinetic constant for termination of carbon-DTC radicals, ktCS, does not decrease. Therefore, the crosstermination becomes the dominant reaction pathway. This leads to a suppression of the autoacceleration peak as the carbon-DTC radical termination limits the carbon radical concentration to a low value, thus limiting the rate of polymerization. This observation is in accordance with results of previous studies (10) with XDT and TED, where it was found that when there was an excess of DTC radicals, the carbon radical concentration was lower and the cross-termination reaction was the dominant termination pathway. 

The role of water is two-fold. It is a co-catalyst, and its consumption during the reaction is, or is associated with, a kinetic termination. Moreover, there is evidence that the reaction in which water is consumed is of a lower order with respect to monomer than the propagation reaction, which therefore is most probably of first order with respect to monomer. 

Once a compound has been shown to polymerise, the most interesting question for me is What is stopping the chains from growing When that question has been answered we must know much about the kinetics of the system and at least a little about its chemistry. Before entering into an account of the reactions which stop chains from growing, it is important to make once again a clear distinction between termination and transfer reactions. There is no reason for not adhering to the radical chemist s definition of termination a reaction in which the chain-carrier is destroyed. In cationic polymerizations there are two main types of termination reaction ... 

No general discussion of the multitude of behaviour patterns, especially as regards dependence on concentration of catalyst, or of components of a syncatalyst, can be profitable at this stage. As for the termination reactions - our special concern here - this kinetic pattern implies that Vt is of first order, Vt of zero order, with respect to monomer. This means that k3 or k4 contain a term k iplky, they may also contain one or more equilibrium constants - depending on the nature of the catalytic system. 

The rate constants for reaction of Bu3SnH with the primary a-alkoxy radical 24 and the secondary ce-alkoxy radical 29 are in reasonably good agreement. However, one would not expect the primary radical to react less rapidly than the secondary radical. The kinetic ESR method used to calibrate 24 involved a competition method wherein the cyclization reactions competed with diffusion-controlled radical termination reactions, and diffusional rate constants were determined to obtain the absolute rate constants for the clock reactions.88 The LFP calibrations of radical clocks... 

Recently proof has been reported for a heterometallic bimolecular formation of aldehyde from a manganese hydride and acylrhodium species [2], Phosphine free, rhodium carbonyl species show the same kinetics as the cobalt system, i.e. the hydrogenolysis of the acyl-metal bond is rate-determining. Addition of hydridomanganese pentacarbonyl led to an increase of the rate of the hydroformylation reaction. The second termination reaction that takes place according to the kinetics under the reaction conditions (10-60 bar, 25 °C) is reaction (3). The direct reaction with H2 takes place as well, but it is slower on a molar basis than the manganese hydride reaction. 

Figure 9.3 pictures the oligomerisation reaction Ni is an abbreviation for the nickel-ligand moiety, kg stands for the rate of the growth reaction, and kt for the rate of the termination reaction. These rate constants are the same for all intermediate nickel alkyls, except perhaps for the first two or three members of the sequence owing to electronic and steric effects. Interestingly, a simple kinetic derivation leads to an expression for the product distribution. One can... 

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