Chain-ending step

These processes constitute a chain reaction. There are many possible chain-ending steps, which could account for some of the minor products observed in the pjorolysis. Certainly the pyrolyses of 3-ethylpent-l-ene and 3-ethylpent-2-ene do yield ethylbutadiene, but the rate of production of the diene is considerably slower than in the pyrolysis of the cyclopropane. Thus reaction (4) represents a sensitization of these latter processes. Further, unlike Chesick, we envisage the formation of the methyl radical from the cyclopropane to involve the rupture of the cyclopropane ring, and believe that this concerted process should be energetically favoured over the two-step mechanism. There are several simple experimental tests that could be used to decide between these mechanisms. 

The mechanism proposed by Calvert and Hanst88 originally used ozone as a chain carrier in the methyl oxidation. This has now been shown to be unlikely. They agree with McDowell et al.81 that reaction of a radical with acetaldehyde to give acetyl radicals ends the initiation sequence. The propagation steps are also identical with those proposed by McDowell et al.81 Chain ending steps include... 

The absence of methyl hydroperoxide in the results of Hanst and Calvert38 cannot be considered conclusive and it is very likely that methyl radicals will be oxidized to methyl hydroperoxide, in this system as in other systems (e.g., CH3I photooxidation), where a readily available hydrogen atom is present. Decomposition to give methanol and/or formaldehyde might quickly follow and Hanst and Calvert say that under their conditions formaldehyde would quickly be converted to formic acid. The chain ending steps that they postulate [(96) and (21)] are quite possible, but if one accepts the reaction between hydroxyl radicals and methyl peroxy radicals as put forward for CHSI photooxidation,10 one might equally accept a similar reaction... 

It is, however, quite plausible to assume that under these conditions the recombinations of H atoms (reaction 23), H + C2H5 (reaction 12), and probably CH3 + H (reaction 22) arc negligible compared to the other processes, since the latter undoubtedly require three-body collisions for stabilization. In this case, II is unimportant in chain-ending steps and Fa. (XIII.11.4) reduces to... 

In view of the small number of degrees of freedom involved in reactions (1), (4), (5) and (6) these processes will be in their pressure-dependent regions. Both H and CH3 are p radicals, so that the choice of any chain-ending step leads to recombination, which with second-order initiation corresponds to three-halves-order reaction (cf. Table 11), in disagreement with experiment. For example, the mechanism... 

It is easily calculated on the basis of the known rates of these reactions that the ethyl radicals are present at much higher concentrations than hydrogen atoms under usual pyrolysis conditions, so that the predominant chain-ending step is almost certainly... 

The overall first-order kinetics is thus accounted for. This interpretation of the kinetics, in terms of a three-halves order for reaction (3), was first suggested by Quinn . The initiation and chain-propagating steps were originally suggested in 1934 by Rice and Herzfeld . However, until the matter of the order of reaction (3) became clarified there remained considerably uncertainty about the nature of the chain-ending step. Because reaction (3) is in its intermediate pressure region the ethyl radical is neither a p nor a fi radical, but is about half-way between. First-order initiation with im termination leads to half-order kinetics, and with pp termination to three-halves order if the radicals are half-way between p and /i the result is first-order kinetics. 

The methyl and propyl radicals predominate in this reaction scheme, so that the most likely chain-ending steps are... 

The methyl-radicals are p radicals, and if their recombination were the predominant chain-ending step the kinetics would be three-halves order (cf. Table 11). On the other hand, if reaction (9) were predominant the recombination would be of the Pfi type, and the overall kinetics would be first order. The experimental result that the order is between unity and three-halves - is thus explained if both of these chain-ending steps play some part, with perhaps some smaller contribution from reaction (10). The result that the order is closer to at lower pressures and higher temperatures, and closer to unity at higher pressures and lower temperatures, is also explicable on this basis. Since methyl radicals are removed bimole-cularly and propyl radicals by unimolecular processes the ratio [CH3]/[C3H7] will be higher at lower pressures, so that reaction (8), leading to f-order kinectics, will... 

Reactions (l)-(5) are the ones that occur in the absence of NO in its presence reaction (5) becomes unimportant since the C2H5 concentration is low. Reaction (6) is the one suggested in the Laidler-Wojciechowski mechanism it must be admitted, however, that the ethane results do not provide unequivocal evidence for this reaction, since reaction (8) explains the behavior equally satisfactorily. Most of the remaining reactions have already been discussed. Reaction (10) represents a likely fate for HNO, which can also dissociate into H + NO. Reaction (17) is included as an additional chain-ending step to (16). Not enough acetonitrile is produced to permit us to conclude that reaction (16) is the main termination step, and little C4H10 is formed reaction (17) seems a reasonable possibility. 

Step A in Figure 4 shows that after a second reaction with an ethylene molecule a butyl branch is formed. The polymerization reaction may continue propagating along the ehain or, step c, the radical chain-end may back-bite to form a tertiary radical. This tertiary radical then decomposes into a propyl radical and an unsaturated polymer chain-end. Step B in Figure 4 shows two potential back-bitingroutes which result in formation of either double ethyl brarKhing ora 2-elhylhexyl braiKh. 

Reactions (2) and (3) constitute chain-propagating reactions. Reaction (1) is referred to as chain-initiation process and reaction (—1) as a chain-ending step. Application of the steady-state treatment to the Br atoms gives... 

Let us incorporate the numbers n, of chain end steps in the i direction of the d-dimensional lattice with cell size equal to the statistical length of the chain link ... 

At partial pressures near one atmosphere, ethane decomposes by a simple Rice-Herzfeld mechanism, with combination or disproportionation of ethyl radicals as the predominant chain-ending step. However, at a total pressure ot 100 mm., or at a partial pressure of 0.01 atm. another chain-ending step predominates. Unlike butane formed from ethyl, the products of this step cannot be distinguished analytically from the major products of the reaction chain. It is therefore believed to involve reaction of H and C2H5, either homogeneously or at the reactor wall. Quantitative rate and yield data are given, as are methods of correction for secondary reactions and of extrapolation to zero reaction time. 

The next step in the development of a model is to postulate a perfect network. By definition, a perfect network has no free chain ends. An actual network will contain dangling ends, but it is easier to begin with the perfect case and subsequently correct it to a more realistic picture. We define v as the number of subchains contained in this perfect network, a subchain being the portion of chain between the crosslink points. The molecular weight and degree of polymerization of the chain between crosslinks are defined to be Mj, and n, respectively. Note that these same symbols were used in the last chapter with different definitions. 

A reaction analogous to the alkylation step of reaction (7.Q) can account for the association of an aluminum species with chain ends ... 

The requirements for a polymerisation to be truly living are that the propagating chain ends must not terminate during polymerisation. If the initiation, propagation, and termination steps are sequential, ie, all of the chains are initiated and then propagate at the same time without any termination, then monodisperse (ie, = 1.0) polymer is produced. In general, anionic polymerisation is the only mechanism that yields truly living styrene... 

Rea.CtlVltyRa.tlO Scheme. The composition of a copolymer at any point in time depends on the relative rates that each monomer can add to a chain end. If it is assumed that the chemical reactivity of a propagating chain depends only on the terminal unit and is not affected by any penultimate units, then four possible propagation steps in the copolymerisation of two monomers, and M2, with two growing chain ends, M and M2, can be written as follows ... 

At each Monte Carlo step (MCS), either a dimer is formed from two adjacent monomers or a monomer is added or deleted from the chain end. The transition probabilities are... 

The four steps of the /3-oxidation pathway, resulting in the cleavage of an acetyl group from the end of the fatty-acid chain. The key chain-shortening step is a retro-Claisen reaction of a /3-keto thioester. Individual steps are explained in the text. 

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 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... 

It is important to realize that, even if the rate of termination is determined by the rates of chain diffusion, the chain end composition and the ratio of combination to disproportionation are not. Knowledge or prediction of the overall rate of termination offers little insight into the detailed chemistry of the termination processes not involved in the rale-determining step. 

Table 2 shows a list of collagen model peptides which have teen prepared. Many efforts have been made to prevent racemization. The polycondensation reaction seemed to be more sensitive to racemization than the coupling steps preparing the monomeric tripeptide. Therefore, the sequence of the monomer was selected with Gly or Pro at the C-terminal chain end, because racemization is mostly favored at the carboxy-activated amino acid, and these amino acids cannot racemize. 

The Alexander model is based on two assumptions that enable simple expressions for these two terms (1) The concentration profile of the layer is step-like. That is, the monomer volume fraction within the layer, (p Na3/d2L, is constant, independent of position (2) The chains are uniformly stretched. That is, all chain ends are positioned on a single plane at a distance L from the surface. [In this paper, we use the symbol to mean approximately equal to or equal to within a numerical factor of order one we use to mean proportional to .] The first assumption simplifies the calculation of Fin, while the second yields a simple expression for Fel. 

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