Propagation reactions, definition

Considering that for a steady system, the termination and initiation steps must be in balance, the definition of chain length could also be defined as the rate of product formation divided by the rate of termination. Such a chain length expression would not necessarily hold for the arbitrary system of reactions (3.1)—(3.6), but would hold for such systems as that written for the H2—Br2 reaction. When chains are long, the types of products formed are determined by the propagating reactions alone, and one can ignore the initiation and termination steps. 

By definition, a propagation step in a chain reaction is one in which products are formed, and the site of the reactive center changes but the number of active centers is not changed. (This statement is qualified in [2].) There are two major propagation reactions under the conditions of most free-radical polymerizations. These are addition and atom transfer reactions. 

Radicals can undergo other reactions such as rearrangements and fragmentations. These are also propagation reactions by definition but they do not concern us here because free-radical polymerizations are not usually performed under conditions in which these processes are significant. 

Many of the observations we have made on these data involve features barely more extended than our estimate of instrument response time. Conclusions reached from these data and observations are therefore quite tentative but do provide guidance on more definitive experiments that will be required to resolve the mechanistically complex curing of these resins. It seems quite likely that the apparent acceleration of the propagation reaction is real and requires further study. The nature of the two or three distinct populations needs resolution as does the origin of the observed acceleration. 

Each of the four propagation reactions has its own rate constant [ky], where subscript i refers to the nature of the propagating radical chain-end and subscript j denotes the nature of the adding monomer. In the mathematical description of copolymer composition as a function of comonomer feed composition, the individual propagation rate constants are not used. Instead, it is common practice to use so-called reactivity ratios. These reactivity ratios are defined as the ratio between the rate constant for homopropagation and that for aosspropagation. The definition of reactivity ratios is mathematically represented as shown in eqn [5] ... 

Lack of definition in the molecules of synthetic polymers may arise from a number of causes, two of the most important being the statistical nature of the polymerization process and the absence of specificity in the propagation reaction. The former leads to a distribution of molecular weights and the latter to distributions of iso- and syndiotactic placements of units along the chains and, in copolymerizations, to randomness in the sequence of different types of unit along the chains. 

In the sense of this definition, the associated species discussed above can also be called living, even if they do not participate in a propagation reaction, but they are in equilibrium vdth the active non-associated species on a much shorter time scale than the overall reaction. For simplicity, in the following discussion the association is not considered explicitly, but if it is known quantitatively it can be considered by making the rate coefficients a function of [P-Li]. 

Modified from the definition of chain-propagating reaction in [I]. 

It turned out that in many cases one uses the term of living polymerization for processes that only partially fell within the definition given by Szwarc. Therefore, introduce the concept of the pseudo-living or quasiliving polymerization. These concepts apply when the termination and transfer of chain rate constants are equal to zero and the condition ki>kw is not satisfied, or the propagation reaction is reversible, or a reversible chain transfer to polymer takes place. 

Definition of Dust E losion A dust explosion is the rapid combustion of a dust cloud. In a confined or nearly confined space, the explosion is characterized by relatively rapid development of pressure with a flame propagation and the evolution of large quantities of heat and reaction products. The required oxygen for this combustion is mostly supphed oy the combustion air. The condition necessaiy for a dust explosion is a simultaneous presence of a dust cloud of proper concentration in air that will support combustion and a suitable ignition source. 

Kinetic vs. material chain. Kinetically, a chain reaction exists throughout the "life" of the radical, that is, from the initiation of a radical up to its termination by recombination or by disproportionation. The lifetime of a radical determines the so-called kinetic chain length Lp defined as the number of monomers consumed per initiating radical. Lp, by definition, can be calculated from the ratio between the propagation rate Rp to the initiation rate R, or, using steady-state hypothesis (Equation (1)), from the ratio between propagation rate to the termination rate Rt (Equation (3)). 

The question whether this reaction is monoeidic or enieidic was not discussed by that author, but in view of the low polarity of bulk THF it seems likely that the principal propagating species is ion-pairs but since there is no definite evidence we will denote the rate constant by kp, but write the equations in terms of x rather than Exr. For this equilibrium polymerisation therefore... 

In the zirconocene-catalyzed polymerization of alkenes, Landis and coworkers [20] have reported in situ observation of a Zr-polymeryl species, 15, at 233 K (Figure 1.5). Complex 15 is formed by partial reaction of 14 with excess 1-hexene. Derivatives 16 and 17 are generated quantitatively from 15 by addition of ca. 10 equiv. of propene and ethene, respectively. No other intermediates, such as alkene complexes, secondary alkyls, diasteromers of 15 or 16, or termination products, accumulate to detectable levels. These NMR studies permit direct monitoring of the initiation, propagation and termination processes, and provide a definitive distinction between intermittent and continuous propagation behavior. 

CA 42, 5229(1948)(Theory of propagation of flame. States conditions in an expl chem reaction necesssry for propagation of the flame at a const rate. Calcs this rate for a definite relationship between diffusion and heat conductance. Evaluates the effect of chain reactions on the propagation of the flame) 4) B. Karlovitz, JChemPhys 19, 541-46(1951) Sc CA 45, 9341 (1951)(Theory of turbulent flames) 5) G. Klein, Phil-TransRoySocLondon 249, 389—415 (1957)... 

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