Radicals concentration, maximum

Now suppose we consider another extreme of the same type of experiment. This time we alternate extremely short light and dark periods of equal duration. If we again start with [M-] =0 when the light goes on, we expect the type of behavior shown in Fig. 6.5d, where the radical buildup is interrupted by the extinction of the light before it reaches [M-] We could use Eq. (6.43) to evaluate the maximum radical concentration achieved, if that were the... 

Chemisorption of oxygen on char has often been discussed previously in terms of free radical concentration in the char (1.5,6). For cellulose chars Bradbury and Shafizadeh (1) found that free spin concentration reached a sharp maximum at HTT 550°C, coinciding with maximum CSA and drew the obvious conclusion that the extent of CSA was at least partly related to free radical content of the char. However, in subsequent work on cellulose char, DeGroot and Shafizadeh (3) have found that unpaired spin concentration continues to increase up to HTT 700"C. Ihe CSA of the char must therefore depend on factors other than free radical concentration. 

In order to determine the errors that may be introduced by the Zeldovich model, Miller and Bowman [6] calculated the maximum (initial) NO formation rates from the model and compared them with the maximum NO formation rates calculated from a detailed kinetics model for a fuel-rich (isothermal system was assumed and the type of prompt NO reactions to be discussed next were omitted. Thus, the observed differences in NO formation rates are due entirely to the nonequilibrium radical concentrations that exist during the combustion process. Their results are shown in Fig. 8.1, which indicates... 

FIGURE 8.1 The effect of superequilibrium radical concentrations on NO formation rates in the isothermal reaction of 13% methane in air ( = 1.37). The upper curve is the ratio of the maximum NO formation rate calculated using the detailed reaction mechanism of Ref. [6] to the initial NO formation rate calculated using the Zeldovich model. The lower curve is the ratio of the NO concentration at the time of the maximum NO formation rate calculated using the detailed reaction mechanism to the equilibrium NO concentration (from Miller and Bowman [6]). 

One can estimate the maximum free radical concentration and, more important, calculate the number of crosslinks formed and chain scissions occurring for any particular time period of irradiation. These estimates are based on known or estimated G values for radical formation, crosslinks, or scissions. The G value is the magnitude of a particular reaction occurring per 100 e.v. of energy absorbed—e.g., G(scission) is the number of scissions that take place per 100 e.v. absorbed. G( crosslink) may be obtained from the sol-gel data presented earlier, while values of G(scission) and G(radicals) may be estimated from values in the literature—e.g., see (4). The former value may also be compared with established literature values—(e.g., see Ref. 14). For a 5.5-... 

Maximum Cation-Radical Concentration Mean Number of Cation Radicals to Generate One Additional... 

It s clear that all regions were passed during different time of day and night and measurement conditions varied in great extent. To reduce the diurnal change impact on the zoning results all calculated peroxy radicals concentrations were normalized on the maximum photo dissociation rate of N02. 

Figure 5.12 shows temperature dependencies of final and intermediate product accumulation or consumption for N2 hydroperoxide oxidation. Fixed nitrogen concentration in the reaction mixture reaches the maximum at 873 K and then decreases with a temperature increase to 923 K. Flence, hydrogen peroxide concentration decreases abruptly, which is associated with its consumption in the target reaction of nitrogen fixation HO and OH radical concentrations sharply increase with temperature. 

In these instances the rates of over-all reaction will not be simply proportional to the light intensity. During the period of illumination, when the radicals are at their maximum concentration, the termination steps will be relatively faster with respect to other steps than they are during the dark periods, when the radical concentrations have begun to fall off. This arises from the fact that the rate of a second-order reaction falls off more rapidly with decreasing concentration than does the rate of a first-order reaction. 

The reactivity of the char is related to a high concentration of trapped free radicals and a large surface area. Figure 24 shows the effect of temperature on the weight and free radical concentration of the chars produced by 1.5 min pyrolysis under nitrogen. The free radical concentration reaches a maximum for char produced at about 550 °C. 

The maximum radical concentration observed in cross-linked jwlybutadiene tested in tension below Jg is of the order of 4 x 10 spins/g and for cis-polyisoprene, which may be more highly crystalline at large pre-extensions, of the order of 11 x 10 spins/g. Chiang and Sibilia have reported 1.5 x 10 spins/g for PET and 0.76 X 10 spins/g for nylon 6 at their ultimate elongation. Pazonyi recorded a maximum of 8 x 10 spins/cm for nylon 6 and Becht and Fischer obtained 10 spins/cm for the same material at 17.4% strain. Other polymers commonly give significantly lower maximum radical concentrations, thus PMMA, PS < 10 spins/cm >... 

Fig. 22. Effects of pre-orientation and rate of testing on the maximum radical concentration observed in cts-polybutadiene tested at 83 K...

The effect of straining rate on maximum radical production in drawn fibres is not great, as Fig. 24 shows although we have already noted that under ste y load the number of radicals increases with time for periods of up to twenty minutes. In the plastic deformation of polycarbonate al ), radical (xrncentration increased only two-fold over two decades of strain rate Much la r effects have been observed in plastically deformed, cross-linked glasses, as Fig. 22 drows. Here, for cis-polybutadiene at 500% pre-strain, the radical concentration at fracture has a peak value of 7 X 10 spins/g at intermediate strain rates, and decreases to 5 x 10 at... 

For the initial conditions [R]o = [Y]o = 0, both radical concentrations increase at first linearly in time, [R] = rRt, [Y] = r t, but at later times the behavior diverges. If all rate parameters are different from zero, a stationary state is found12 where d[R]/dt = d[Y]/dt= 0. From this relation, the conditions on rR and rY emerge for which the selectivity for the formation of the cross-reaction product Pc is a maximum. This selectivity may be defined by the ratio of the rate of the cross-reaction to the sum of the rates of product formation by the self-terminations, that is, by... 

Found hysteresis of the dependenee of photolysis rate on light intensity is direetly connected with radicals concentration. At successive decreasing of light intensity radicals concentration, during the experiment, has remained invariable and equal to maximum stationary concentration of radicals, achieved at the greatest light intensity. 

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