Chain propagation probability

An analogous homopolymerisation can be initiated by strong bases, including for example tert-amines. In this case chain propagation probably proceeds through an oxyanion ... 

Reduction and chain propagation probably occur in a manner described earlier for unsupported Ziegler catalysts. 

Introducing the rate of thermal chain generation Wq, chain generation in the course of the reaction and the probability of path 1 referred to (according to [427]) as the chain propagation probability, co = a, the rate of the stationary reaction in terms of the scheme in Fig. 51 is... 

Effects of compounds observable at lower concentrations ai e probably connected with the effect on the initiation/termination stages (transition metals in TMB-0, reaction with photoinitiation, UDMH in the same reaction with chemical initiation), while the compounds influencing only at higher concentrations may affect chain propagation stages. 

The kernel (26) and the absorbing probability (27) are controlled by the rate constants of the elementary reactions of chain propagation kap and monomer concentrations Ma(x) at the moment r. These latter are obtainable by solving the set of kinetic equations describing in terms of the ideal kinetic model the alteration with time of concentrations of monomers Ma and reactive centers Ra. 

Chain propagation is started from a methylene group and terminated by desorption of 1-alkenes or alkanes. Propeller-type mobility of the olefin ligand renders possible CH3 branching of the growing chain, as demonstrated by the scheme. The growth probability is determined by the ratio of rates of formation of the alkyl intermediate and of the desorption of 1-alkenes, and to a minor extent of alkanes. 

In addition to two peroxyl radicals, H02 and R1R2C(0H)00 , participating in chain propagation in the oxidized alcohols, there are three reactions that are guilty of chain termination in the oxidized alcohols. The most probable reaction between them is disproportionation. 

The opposite of the stabilisation of an ester is its activation. If we include in the concept ester the alkyl halides, their Friedel-Crafts reactions provide familiar examples of this phenomenon. An unusual example especially relevant to our present considerations is provided by some results made available to me in advance of publication by Giusti and Andruzzi. Their results [38] on the polymerisation of styrene by iodine and hydrogen iodide can be interpreted in terms of an organic iodide derived from styrene, probably 1-phenylethyl iodide, being activated by the co-ordination of one or two molecules of iodine. This process appears to polarise the C—I bond to such an extent that the normally stable ester becomes activated to a chain-propagating species and induces a pseudocationic polymerisation ... 

Step 2 represents the chain origin, step 3 is nitrite-ion oxidation, steps 4-6 are the chain propagation, and steps 8 and 10 show the chain termination at the expense of radical dimerization. Steps 4 and 5 can probably be nnited into one stage, as Scheme 4.38 points out. 

An increase in the cA-stilbene concentration favors the chain propagation and decreases the probability of termination when the DCNA anion-radicals react with the stilbene cation-radicals. A decrease in the irradiation intensity has a similar effect The chain propagation is the first-order process, whereas termination of the chains is the second-order process. A temperature rise accelerates the accumulation of the stilbene cation-radicals. In this system, the free energy of electron transfer is -53- —44 kJ moD (the cation-radical generation is in fact an endothermal process). If a polar solvent is substituted for a nonpolar one, the conversion of the cii-stilbene cation-radical into the trani-stilbene cation-radical deepens. Polar solvents break ion pairs, releasing free ion-radicals. The cA-stilbene cation-radicals isomerize more easily on being released. The stilbene cation-radical not shielded with a counterion has a more positive charge, and therefore, becomes stabilized in the... 

An inhibition mechanism involving electron transfer between a chain-propagating radical and the antioxidant has frequently been suggested but has rarely been identified with any certainty. This process remains one of the least understood of all inhibition mechanisms. Probably the most clear-cut example of inhibition by one electron transfer (either partial or complete) has come from studies of metal-catalyzed oxidations. Many workers have reported that under certain conditions transition metals may inhibit rather than catalyze oxidations. Cobalt, manganese, and copper are particularly prominent in this respect. 

However, our fast oxidations were obtained under conditions where the concentration of free hydrogen bromide was extremely low. The following observations suggest that free hydrogen bromide is probably not responsible for chain propagation. 

If the rates of combination of radicals or atoms are so fast, you might well wonder how chain propagation ever could compete. Of course, competition will be possible if the propagation reactions themselves are fast, but another important consideration is the fact that the atom or radical concentrations are very low. Suppose that the concentration of Cl - is 10 UM and the CH4 concentration 1M. The probability of encounters between two Cl atoms will be proportional to 10-11 x 10 u, and between CH4 and Cl - atoms it will... 

An increase in the ra-stilbene concentration favors the chain propagation and decreases the probability of termination when the dicyanoanthracene anion radicals react with the stilbene cation radicals. A decrease in the irradiation intensity has a similar effect The chain propagation is the first-order process, whereas termination of the chains is the sec-... 

Fig. 14. The probabilities Pi, and of formation of isotactic, syndiotactic, and heterotactic triads, respectively, as a function, of o, the probability of isotactic placement of monomer units during chain propagation. Experimental points at the left are for methyl methacrylate polymers prepared with free radical initiators . those at the right for polymers prepared with anionic initiators ( O) t peaks ...

In lithium alkyl-initiated polymerizations only chain initiation and propagation steps need be considered in hydrocarbon solvents. Both reactions are strongly influenced by extensive association of all lithium compounds. The reactive species in chain propagation is the small amount of dissociated material which probably exists as an ion pair. Association phenomena disappear on adding small amounts of polar additives, and the aggregates are replaced by solvated ion pairs. In polar solvents of relatively high dielectric constant (e.g. tetrahydrofuran), some dissociation of the ion pairs to free ions occurs, and both species contribute to the propagation step. The polymerizations are often complicated in tetrahydrofuran by two side reactions, namely carbanion isomerization and reaction with the solvent. 

The reaction probably involves a cationic chain reaction involving hydride transfer, and indeed the rate-limiting step in the oxidation of trityl benzyl ether was shown to be a chain-propagating step (equation I). 

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