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Free radical concentration

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. [Pg.363]

This low level of concentration is typical of free-radical polymerizations. Next we inquire how long it will take the free-radical concentration to reach 0.99[M-]5, liter" in this case. Let a = (16fk jkj [1] q) ... [Pg.363]

The superpositioning of experimental and theoretical curves to evaluate a characteristic time is reminiscent of the time-tefnperature superpositioning described in Sec. 4.10. This parallel is even more apparent if the theoretical curve is drawn on a logarithmic scale, in which case the distance by which the curve has to be shifted measures log r. Note that the limiting values of the ordinate in Fig. 6.6 correspond to the limits described in Eqs. (6.46) and (6.47). Because this method effectively averages over both the buildup and the decay phases of radical concentration, it affords an experimentally less demanding method for the determination of r than alternative methods which utilize either the buildup or the decay portions of the non-stationary-state free-radical concentration. [Pg.379]

In this example the number of micelles per unit volume is exactly twice the stationary-state free-radical concentration hence the rates are identical. Although the numbers were chosen in this example to produce this result, neither N nor M are unreasonable values in actual emulsion polymerizations. [Pg.402]

Electron spin resonance (esr) (6,44) has had more limited use in coal studies. A rough estimate of the free-radical concentration or unsatisfied chemical bonds in the coal stmcture has been obtained as a function of coal rank and heat treatment. For example, the concentration increases from 2 X 10 radicals/g at 80 wt % carbon to a sharp peak of about 50 x 10 radicals/g at 95 wt % carbon content and drops almost to zero at 97 wt % carbon. The concentration of these radicals is less than that of the common functional groups such as hydroxyl. However, radical existence seems to be intrinsic to the coal molecule and may affect the reactivity of the coal as well as its absorption of ultraviolet radiation. Measurements from room... [Pg.220]

Note that the quasi-steady hypothesis is applied to each free-radical species. This will generate as many algebraic equations as there are types of free radicals. The resulting set of equations is solved to express the free-radical concentrations in terms of the (presumably measurable) concentrations of the long-lived species. For the current example, the solutions for the free radicals are... [Pg.52]

The free-radical concentrations will be small—and the quasi-steady state hypothesis will be justified— whenever the initiation reaction is slow compared with the termination reaction, kj /f[CH3CHO]. [Pg.52]

The quasi-steady hypothesis allows the diflficult-to-measure free-radical concentrations to be replaced by the more easily measured concentrations of the long-lived species. The result is... [Pg.52]

Solution The procedure is the same as in the acetaldehyde example. ODEs are written for each of the free-radical species, and their time derivatives are set to zero. The resulting algebraic equations are then solved for the free-radical concentrations. These values are substituted into the ODE governing RCl production. Depending on which termination mechanism is assumed, the solutions are... [Pg.53]

The free-radical concentrations are small and are ignored in this equation for the overall reaction. [Pg.74]

Apply the pseudo-steady hypothesis to the free-radical concentrations to determine a functional form for the reaction rate. Note that M represents any molecule. Use the combined data in Problem 7.6 to fit this mechanism. [Pg.252]

Such reactions have only been investigated on their role in the processes of ageing and carcinogenesis to a large extent (Dizdaroglu 1991), their effects on environmental contaminants and organisms have not been fully realized. Because of the short time and difficulties in chemical analyses for transitory presence of free radicals, relationship between free radical concentrations and effects on pollutants or natural microorganisms has not been fully established. It is clear that further... [Pg.179]

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. [Pg.363]

For an ideal case Fj should be equal to Xj. If we assume steady state for free radical concentrations, i.e., rate of conversion of M1 to -Mj M2 is equal to rate of conversion of M2 to M2 Mj. Then we have,... [Pg.230]

Jones, 1. T. N., and K. D. Bayes. Detection of steady-state free-radical concentrations by photoionization. J. Amer. Chem. Soc. 94 6869-6871, 1972. [Pg.42]

The rate of propagation in the micelles is similar to that described for other free radical chain growth, but since the free radical concentration is equal to the number of active micelles, the value of N/1 is used instead of [M ]. Thus, the rate of propagation is dependent on the number of micelles present. [Pg.189]

Multiplication by [M2] gives what are generally referred to as the copolymerization equations, Equations 7.17 and 7.19, which gives the copolymer composition without the need to know any free radical concentration, and which gives the composition of the growing polymer as a function of monomer feed (Equation 7.19). [Pg.209]

A steady-state approximation allows us to solve for the intermediate free-radical concentration, [R02 ], to obtain... [Pg.264]

Chemical structure and compositional changes Free radical concentration Quantitative gases up to mol. wt. of C6 hydrocarbons Same as above Secondary effect occurence or correlation not established... [Pg.243]

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-... [Pg.107]

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. [Pg.108]

Figure 10. Variation of free radical concentration with dose for dry wool... Figure 10. Variation of free radical concentration with dose for dry wool...
ESR Studies of Wool in Styrene Grafting Solution. The variation of free radical concentration of wool irradiated in styrene-dioxane contain-... [Pg.244]


See other pages where Free radical concentration is mentioned: [Pg.34]    [Pg.363]    [Pg.375]    [Pg.316]    [Pg.513]    [Pg.220]    [Pg.134]    [Pg.249]    [Pg.93]    [Pg.138]    [Pg.299]    [Pg.136]    [Pg.143]    [Pg.428]    [Pg.185]    [Pg.133]    [Pg.490]    [Pg.89]    [Pg.49]    [Pg.237]    [Pg.48]    [Pg.244]    [Pg.245]    [Pg.314]    [Pg.155]    [Pg.8]   
See also in sourсe #XX -- [ Pg.228 ]




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