Propagation reactions rate constants

Two steady state conditions apply one to the total radical concentration and the other to the concentrations of the separate radicals Ml- and M2-. The latter has already appeared in Eq. (2), which states that the rates of the two interconversion processes must be equal (very nearly). It follows from Eq. (2) that the ratio of the radical population, Mi - ]/ [Msteady-state condition as applied to the total radical concentration requires that the combined rate of termination shall be equal to the combined rate of initiation, i.e., that... 

The range of chain propagation reaction rate constants kp differs practically in two orders without essential differences in molecular characteristics (M. Mn, Mw/Mn) of synthesized oligopiperylene (Table 5.2). This determines necessity of use in technological scheme of liquid oligopiperylene rubber synthesis of chemical reactors constructions of various types in dependence on catalytic systems activity. 

The principle of equal chemical reactivity applies, i.e., the propagation reaction rate constant is independent of molar mass. 

The kinetic chain length gives the number of monomer molecules added on to an initiator radical before the polymer radical is destroyed by a termination reaction. Thus, the kinetic chain length is given as the ratio of the propagation reaction rate constant to the sum of rate constants for all termination reactions ... 

The parameter f is the initiator efficiency factor, is the initiator decomposition rate constant, is the propagation reaction rate constant, and [ST]a,o and [STlo are the initial monomer concentrations in microemulsion droplets and in the polymerization system, respectively. This kinetic model was based on the assiunption that (i) all the free radicals generated in the continuous aqueous... 

Equation (l) shows the rate of polymerization is controlled by the radical concentration and as described by Equation (2) the rate of generation of free radicals is controlled by the initiation rate. In addition. Equation (3) shows this rate of generation is controlled by the initiator and initiator concentration. Further, the rate of initiation controls the rate of propagation which controls the rate of generation of heat. This combined with the heat transfer controls the reaction temperature and the value of the various reaction rate constants of the kinetic mechanism. Through these events it becomes obvious that the initiator is a prime control variable in the tubular polymerization reaction system. 

The same reaction rate constant kp is written for each propagation step under the assumption that the radical reactivity is independent of the chain length, in accordance with the conclusion reached in the preceding chapter. 

There are several guidelines that should be followed in order to increase the chemoselectivity of the monoadduct. Firstly, radical concentration must be low in order to suppress radical termination reactions (rate constant of activation [fcal and fca2] < < rate constant of deactivation kd t andfcd2]). Secondly, further activation of the monoadduct should be avoided ( al> >kd2). Lastly, formation of oligomers should be suppressed, indicating that the rate of deactivation (kd 2[Cu"LmX]) should be much larger than the rate of propagation ( [alkene]). Alkyl halides for copper-catalyzed ATRA are typically chosen such that if addition occurs, then the newly... 

Table I. The Reaction Rate Constants for Propagation and Termination Expressed as a Function of Turnover Frequencies, Probability of Chain Growth, Steady-State Surface Coverage of the Precursor A, and the Equilibrium Constant K.

Table II. Minimum Reaction Rate Constants for Propagation Caknlated from the Data of Turnover Frequency and Probability of Chain Growth Published in the...

Secondly, the modified S-F model(II) was constructed. The chain growth of readsorbed olefins was assumed to take place independently from the S-F propagation path. The numerical simulation was made, assuming that the reaction rate constants Are not... 

Substituting the semiclassical propagator of Eq. (367) into Eq. (359), one obtains the following semiclassical reaction rate constant [80] ... 

The branched sulfonium ions are not reactive, thus Reaction (130) is an irreversible termination. The measured ratios of rate constants kp/k, [(rate constant of propagation to rate constant of termination according to Eq. (130)] reflect the general phenomenon that by increasing the number and size of the substituents the contribution of chain transfer to polymer may be considerably reduced [161] (Table 12). 

Inserting experimental data for (bpC) — bp)/(b — bp) from Fig. 7, (5AE/5n)x=o = 9 10 eV (see above), k, = 10 s, and t = 7.3 10 s at 295 K allows calculating absolute numbers for n(X). Note that no adjustable parameter enters. Figure 4, which shows the result of the calculation, demonstrates that Eq. (9) provides an excellent fit to the experimental data of Albouy et al. This documents that chain propagation in TS can be consistently interpreted by taking into account the variation of the reaction rate constant with reaction distance. 

In the quadruple-barrier case one needs to distinguish whether dissociation/ neutralization or propagation are the rate-limiting steps. Furthermore, a parameter a is needed describing the ratio of the forward reaction rate constants of the anion and the cation propagation, i.e. 

The results of the simulations indicate that the most effective channel propagation occurs when the reactions are transport-controlled (reaction rate constants faster than transport) since in these cases, the channel maximizes its own rate of growth by restricting permeability change to its walls and tip. 

Error limits on the rate constants are estimated as follows. The reproducibility of the rate constants is typically <10%. Sources of error include the above reproducibility ( 10%), measurement of temperature ( 2%), pressure ( 1%), ion flight time ( 5%), an end correction related mainly to reactant gas mixing ( 2 cm or 4%), buffer gas flow rate (relative, 1%, or absolute, 2%), and neutral reactant gas flow rate (relative, 3%, or absolute, 15%). Propagation of errors leads to a net relative uncertainty of 13% and a net absolute uncertainty of 19%. The reaction rate constants measured with the HTFA apparatus are quoted with relative and absolute uncertainties of 15% and 25%, respectively, to account for the possibility of systematic errors not treated in the above analysis. 

The effectiveness of catalytic cycles in destroying stratospheric ozone depends on the efficiency of the chain propagation reactions in the cycles [i.e., reactions (71)-(79)] versus the rates of the chain termination reactions. In the proposed cycles the reactions of CF3O and CF3O2 radicals with ozone are critical to assessing how propagation reactions compete with termination reactions. Rate constants for these reactions are summarized in Table 10. 

Aj Michaelis constant see equation (3-74) k reaction rate constant, a for first order kj deactivation rate constant see equation (4-152) ki initiation rate constant, normally second order k() pre-exponential factor, a for first order kp propagation rate constant... 

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