Bimolecular termination reaction

In termination reactions, all mesomeric structures may contribute. Cases in point, where one would not immediately expect this to play a significant role are the a-carboxymethyl radicals (Wang et al. 2001). For some of the nucleobase radicals also more than one mesomeric structure maybe written (Chap. 10), and it is not unlikely that also here this aspect has to be taken into account. 

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. 

Adams GE, Willson RL (1969) Pulse radiolysis studies on the oxidation of organic radicals in aqueous solution. Trans Faraday Soc 65 2981-2987 

Akhlaq MS, Al-Baghdadi S, von Sonntag C (1987) On the attack of hydroxyl radicals on polyhydric alcohols and sugars and the reduction of the so formed radicals by 1,4-dithiothreitol. Carbo-hydr Res 164 71-83 

Akhlaq MS, Murthy CP, Steenken S, von Sonntag C (1989) The reaction of a-hydroxyalkyl radicals and their anions with oxidized dithiothreitol. A pulse radiolysis and product analysis study. J Phys Chem 93 4331-4334 

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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. 

Of the six possible bimolecular termination reactions which HO2, SO4, and OH radicals might undergo only reactions (87), (88), (64) and (65) appear to be of importance under the experimental conditions covered... 

It should be clear from Section IV. B that a major difficulty involved in preparing monomeric iron-dioxygen adducts is the prevention of bimolecular termination reactions, leading via autoxidation to the formation of a ju-oxo dimer, thus... 

We saw previously that a major factor in inhibiting the bimolecular termination reaction was the presence of sufficiently bulky ligands so that a monomeric dioxygen adduct could be isolated 135). A number of synthetic metal porphyrins 239) have been prepared recently which satisfy the above requirement, and bind molecular oxygen we shall now proceed to discuss these. 

Where B = pyridine, piperidine or 1-methylimidazole, in methylene chloride solution, but under normal conditions rapid irreversible autoxidation takes place 232) leading to the formation of the well characterised 247, 248) fi-oxo product, (TPP)Fe(IlI)—0—Fe(III) (TPP) and since the rate of oxidation decreases 249, 250) with increasing excess of axial base, B, it follows 232, 251) that a five co-ordinate species, Fe(II) (Base)TPP, is probably involved as an intermediate which can then undergo a bimolecular termination reaction with Fe(II) (Base)02TPP, followed by autoxidation. Firstly 251),... 

The polymerization reaction was found to develop both faster and more extensively as IQ was increased, up to a certain value above which identical RTIR curves were recorded. Consequently, the (Rp)max value reaches an upper limit, as shown in Figure 5 where (Rp)max was plotted versus Iq on a logarithmic scale. The slope of the straight line obtained at low light intensities, 0.55, is close to the 0.5 value expected for a photoinitiated radical polymerization involving bimolecular termination reactions. 

We assume that only free ions propagate the reaction and take part in the transfer and the bimolecular termination reactions, we neglect the unimolecular termination, characterised by kt, which can only occur in an ion-pair, since the very small value of kf kfl hardly exceeds the experimental uncertainty. 

In consideration of the kinetic law obtained, Rp i0 of magnitude range, one can conclude that the common polymerization mechanism, based on bimolecular termination reactions, is no longer valid for these multifunctional systems when irradiated in condensed phase. Indeed, for conventional radical-induced polymerizations, the termination step consists of the interaction of a growing polymer radical with another radical from the initiator (R), monomer (M) or polymer (P) through recombination or disproportionation reactions ... 

The bimolecular termination reaction can be neglected at low conversions since no linear sulphide residues are present initially, enabling a simpler interpretation of initial conversion/time curves to be made. In the earlier work the concentration of active centres was equated with the initial catalyst salt concentration, but later an XH NMR method of analysis was employed (137). As in the polymerisation of tetrahydrofuran it was anticipated that both free ions and ion pairs were likely to contribute to the propagation reaction and the calculated rate constant kP.pp e t, was described by... 

It is reasonable to expect that in a viscous monomer such as trimethylol-propane triacrylate (>/ = 65 cp), bimolecular termination reactions proceed more slowly than in monofunctional monomers. However, considering the long lifetime observed for the polymer radicals in these monomers, caution must be exercised in the interpretation of the linear intensity dependence. Long-lived radicals are more likely to terminate by chain transfer and... 

This source of peroxyl radicals has been used to study the peroxyl radical reactions with nucleobases (Simandan et al. 1998) and thymidine (Martini and Termini 1997 Chap. 10). The slow H-abstraction reactions of peroxyl radicals prevents their reaction with DNA in dilute aqueous solution unless they are positively charged and thus bound to DNA by electrostatic forces (Paul et al. 2000). Otherwise, their competing bimolecular termination reactions are much faster (Chap. 8). 

The time required to reach equilibrium very much depends on the pKd value of the acid. An acid with a pKa value of 4, for example, deprotonates with a rate of 106 s Thus, the equilibrium is established within a few microseconds. On the other hand, an acid with a pKa value of 7 dissociates with a rate of ca. 103 s"1, and the equilibrium becomes established only on the millisecond time range. In a pulse radiolytic experiment, a large part of the radicals will thus have disappeared in bimolecular termination reactions, before an equilibrium is reached. Buffers speed-up the protonation/deprotonation reactions, and their addition can overcome this problem. Yet, they deprotonate acids and protonate their corresponding anions typically two to three orders of magnitude more slowly than OH and H+ (for a DNA-related example, see Chap. 10.4 for potential artifacts in the determination of pKa values using too low buffer concentrations, see, e.g., von Sonntag et al. 2002). 

A typical effect observed in the synthesis of linear polymers by a free-radical mechanism is the auto-acceleration process. At a particular conversion, when sufficient polymer has accumulated in the system for the viscosity to reach a certain level, the rate of the bimolecular termination reaction begins to fall because of diffusional restrictions to the encounter of two chain ends. However, the initiation and growth rates are hardly affected. 

To obtain a behavior similar to case 2 for free-radical polymerizations, it is necessary to decrease the influence of the bimolecular termination reaction by decreasing the concentration of active centers. This is possible by producing a reversible combination between a growing chain (a polymer radical P ) with a stable radical N to form an adduct P-N, which behaves as a dormant species ... 

The bimolecular termination reaction in free-radical polymerization is a typical example of a diffusion controlled reaction, and is chain-length-depen-dent [282-288]. When pseudobulk kinetics appUes, the MWD formed can be approximated by that resulting from bulk polymerization, and it can be solved numerically [289-291]. As in the other extreme case where no polymer particle contains more than one radical, the so-caUed zero-one system, the bimolecular termination reactions occur immediately after the entrance of second radical, so unique features of chain-length-dependence cannot be found. Assuming that the average time interval between radical entries is the same for all particles and that the weight contribution from ohgomeric chains formed... 

On the other hand, however, it is not straightforward to calculate the MWDs for intermediate cases using the conventional approach. A notable advantage of using an MC simulation technique is that it can be applied to virtually any type of emulsion polymerization, and can account for the chain-length-dependent bimolecular termination reactions in a straightforward manner [265]. Sample simulation results for instantaneous MWDs were shown [265] that were obtained using parameters for styrene polymerization that were reported by Russell [289]. 

The chain-length-dependence of bimolecular termination reactions needs to be taken into account in order to be able to accurately estimate the MWD formed, except when very small polymer particles are formed and/or chain transfer reactions dominate over dead polymer chain formation. 

The traditional method of determining the monomer transfer constant is the Mayo method [294,295], where the inverse of the number average chain length Pn is extrapolated to zero polymerization rate. To obtain reliable values, one needs to measure rather large P values to high precision that can then be extrapolated to zero polymerization rate. In addition, linear extrapolation is not guaranteed if bimolecular termination reactions are chain-length-dependent [296]. 

The compartmentalization of radicals may produce another important effect when large-sized branched polymer molecules are formed by chain transfer to polymer plus combination termination. As clarified in Sect. 4.1, when the n value is small, the frequency of bimolecular termination reactions between large polymer radicals drops significantly compared to models that do not account for compartmentalization of radicals. From this fact, it is easy to see that the size of branched polymer molecule is smaller than that calculated without considering compartmentalization effects [281]. 

Analytic solutions for Eq. (5) provide the most direct path of the prediction of PSD evolution. For batch polymerizations in Interval II, however, analytic solutions have only been achieved for the so-called zero-one system (Lichti et al., 1981). These are systems wherein negligibly few particles contain two or more free radicals because of the rapidity of the bimolecular termination reaction (e.g., in styrene emulsion polymerizations with small latex particles). In this case, Eq. (5) may be written as follows ... 

Disulfonyl halides such as MI-22 to MI-26 are effective bifunctional initiators for various monomers including methacrylates, acrylates, and styrenes, because the sulfonyl halide part, as pointed out for their monofunctional versions, can induce fast initiation without a bimolecular termination reaction between the sulfonyl radicals.240-343... 

Equations (6.25) and (6.26) have the significant conclusion that the rate of polymerization depends directly on the monomer concentration and on the square root of the rate of initiation. Thus doubling the rate of initiation or initiator concentration does not double the polymerization rate, but the polymerization rate is increased only by the factor /2. This behavior is a consequence of the bimolecular termination reaction between radicals. It is further evident from Eqs. (6.25) and (6.26) that the polymerizability of a monomer in a free radical polymerization is related to the ratio kp/kt rather than to kp alone. This ratio will appear frequently in the relations we develop for radical polymerization. 

The two propagation reactions form a chain of conversion events that, in principle, can continue until all the ethane molecules are converted. In fact this does not happen. There is a finite probability that some two radicals will collide and either recombine or disproportionate. Which of a number of such bimolecular termination reactions possible in this system will dominate at given conditions is not easily guessed, but it is possible to find this out by studying the overall kinetics of ethane conversion. This case therefore gives us an example in which the mechanism of the reaction can be identified by observing the overall kinetics of the reaction. 

The differences between the step-growth and the chain polymerization mechanisms are summarized in Table 1.2. Notice that chain polymerizations may include bimolecular termination reactions (as in the free radical mechanism) or may not (as in living anionic or cationic polymerizations). 

The most conventional kinetic scheme of FRP includes initiation, propagation, and bimolecular termination reaction steps. Additional reactions such as chain transfer are introduced to improve the process description. Free radicals are highly reactive chemical species produced by the homolytic dissociation of covalent bonds. Such species are produced through physical (thermoexcitation, radiation) or chemical methods (oxidation-reduction, addition, etc.). Generally, their survival time is less than a second, except for those radicals highly stabilized by specific chemical groups the hybridization state is sp. ... 

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