Molecular Radicals Radical Concentrations

This important equation shows that the stationary-state free-radical concentration increases with and varies directly with and inversely with. The concentration of free radicals determines the rate at which polymer forms and the eventual molecular weight of the polymer, since each radical is a growth site. We shall examine these aspects of Eq. (6.23) in the next section. We conclude this section with a numerical example which concerns the stationary-state radical concentration for a typical system. 

Reactions with Parting of Radicals. The one-electron oxidation of cationic dyes yields a corresponding radical dication. The stabihty of the radicals depends on the molecular stmcture and concentration of the radical particles. They are susceptible to radical—radical dimerization at unsubstituted, even-membered methine carbon atoms (77) (Fig. 6). 

The radical concentration, when coupled with information on the rate of polymerization, allows k (and k,) to be calculated. The EPR methods have been applied to various polymerizations including those of B, DMA, MMA,361 566 S 67 368 and VAc.369 Values for kp are not always in complete agreement with those obtained by other methods (e.g. PLP, SIP) and this may reflect a calibration problem. Problems may also arise because of the heterogeneity of the polymerization reaction mixture,365 and insufficient sensitivity for the radical concentrations in low conversion polymerizations 63 or very low molecular weights. Some data must be treated with caution. However, the difficulties are now generally recognized and are being resolved. 60... 

On the other hand, the limiting conversion in a reactor of fixed size is dependent on the temperature and the radical concentration in the reactor and results from a predominating radical-radical interaction precipitated by an increased initiator concentration and the accompanying temperature excursion. At this point the solvent concentrations have little effect on the molecular... 

Trace-gas Lifetimes. The time scales for tropospheric chemical reactivity depend upon the hydroxyl radical concentration [HO ] and upon the rate of the HO/trace gas reaction, which generally represents the slowest or rate-determining chemical step in the removal of an individual, insoluble, molecular species. These rates are determined by the rate constant, e,g. k2s for the fundamental reaction with HO, a quantity that in general must be determined experimentally. The average lifetime of a trace gas T removed solely by its reaction with HO,... 

The rate expressions have been written in generalized fashion with the terms fp, fb, fst, and fgt containing the reaction rate constants, stoichiometric coefficients, and concentrations of the various stable species present in the reaction mixture. If one also wished to consider bi-molecular radical processes, these could also be lumped into the / parameters. 

Successful application of radical polymerization requires the appropriate choice of the specific initiator to achieve the desired initiation rate at the desired reaction temperature and the realization that higher polymerization rates achieved by increasing the initiation rate (either by increasing [I] or kmolecular weights. Higher radical concentrations result in more propagating chains but each propagates for a shorter time. 

The relative importance of these three mechanisms in NO formation and the total amount of prompt NO formed depend on conditions in the combustor. Acceleration of NO formation by nonequilibrium radical concentrations appears to be more important in non-premixed flames, in stirred reactors for lean conditions, and in low-pressure premixed flames, accounting for up to 80% of the total NO formation. Prompt NO formation by the hydrocarbon radical-molecular nitrogen mechanism is dominant in fuel-rich premixed hydrocarbon combustion and in hydrocarbon diffusion flames, accounting for greater than 50% of the total NO formation. Nitric oxide formation by the N20 mechanism increases in importance as the fuel-air ratio decreases, as the burned gas temperature decreases, or as pressure increases. The N20 mechanism is most important under conditions where the total NO formation rate is relatively low [1],... 

The time needed to suppress normal bimolecular termination is shortened by deliberately adding the deactivator at the start of polymerization, instead of waiting until its concentration builds up from the reaction of initiator and activator. Reaction variables that yield faster rates (e.g., higher initiator and activator concentrations and higher temperatures) increase normal bimolecular termination because the radical concentrations are higher. Another consideration is the suppression of normal bimolecular termination by the decrease in k, with conversion (increasing molecular weight). 

Other spectral regions are also important because the detection and quantification of small concentrations of labile molecular, free radical, and atomic species of tropospheric interest both in laboratory studies and in ambient air are based on a variety of spectroscopic techniques that cover a wide range of the electromagnetic spectrum. For example, the relevant region for infrared spectroscopy of stable molecules is generally from 500 to 4000 cm-1 (20-2.5 /Am), whereas the detection of atoms and free radicals by resonance fluorescence employs radiation down to 121.6 nm, the Lyman a line of the H atom. 

The free radical concentration is quite small relative to the number of chains present. Also, the number of crosslinks formed are sufficient to gel the network, which could lead only to a decrease in creep rate. Finally, the crosslinks exceed the scissions, and the latter could not reduce the molecular weight sufficiently—even temporarily—to yield the significant increases in creep noted in the glassy polystyrene. Recombination of chain scission radicals has also been neglected. 

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