Radical chain length

The importance of the secondary reactions can be expressed as a radical chain length, which is the total rate of all reactions involving a particular radical divided by the primary rate of formation of that radical. For a particular set of conditions chosen in the modeling studies, chain lengths of about 4 for the hydroperoxy radical and about 8 for the alkyl-peroxy and hydroxyl radicals were calculated early in the irradiation period. After further irradiation, the chains became shorter. 

If the NO concentration is appreciable, the efficiency of trace gas oxidation (free radical chain length) is high for this species, In remote air masses, very low NO concentrations limit recycling of HO, and the HO oxidation rate approaches the prime HO generation rate, for instance by these reactions ... 

Right) Luminescence lifetimes of tris and ternary Nd111 complexes as a function of the fluorinated radical chain length. Filled and opened triangles stand for tris complexes with benzoylacetonate and thienylacetonate derivatives, respectively filled and opened circles for the corresponding ternary complexes formed with phen. 

The set of differential equations (13.53) and (13.54) describing the evolution of each radical chain length can be reduced to the following set of differential equations for the moments ... 

The radical chain length depends on the mechanism of chain breaking. The most common of these is coupling. Here, the chain-breaking (and termination) rate is... 

With this and eqns 10.33, 10.34, and 10.23 the radical chain length becomes... 

Similarly, for chain-breaking predominantly by chain transfer to solvent or an agent, the chain-breaking rate and radical chain length are... 

The radical chain lengths resulting from the various chain-breaking mechanisms can be summarized as follows ... 

While the radical chain length as the ratio of the propagation and chain-breaking rates refers to conditions existing at the moment, the degree of polymerization and the molecular weight characterize a polymer that may have been produced over a span of time during which the conditions varied. Here, only some idealized situations with conditions held constant can be described in any detail. 

According to the assumptions [(ii) and (iv)3 givoi above, we can regard the values of and defined by Eqs. (49) and (50) to be constant and equal to and regardless of radical chain length, /, respectively. Moreover, no radicals longer than s monomer units will be found m the water phase according to the assumption of (ii). Thus, Eqs. (49) and (50) can be rewritten as... 

The chain-length dependence of the propagation rate coefficient is of a more chemical nature in that it is caused by differences in the activation energy and the frequency factor of the actual, intrinsic, rate coefficients of the addition reaction for different size radicals. chain-length averaged propagation rate coefficient is defined by Eq. 4,... 

The unique attributes of the RAFT mediated FRP (i.e., a linear increase in the average radical length (i) and a nearly monodisperse radical chain length distribution (i ) allows for the chain-length averaged ki to be related directly to the... 

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