Termination rate constant, determination

However, it has been pointed out that the value of kXo in the expressions eqs. 25-23 should not be confused with the small radical A, rather, the value of kt0 represents the termination rate constant of a single unit chain if the implied diffusion mechanism was the rate-determining process. 

The concept of reaction diffusion (also called residual termination) has been incorporated into a number of treatments.7 7 Reaction diffusion will occur in all conversion regimes. However at low and intermediate conversions the process is not of great significance as a diffusion mechanism. At high conversion long chains are essentially immobile and reaction diffusion becomes the dominant diffusion mechanism (when i and j are both "large" >100). The termination rate constant is determined by the value of kp and the monomer concentration. In these circumstances, the rate constant for termination k - should be independent of the chain lengths i and j and should obey an expression of the form 75... 

Vichutinsky, "Chemiluminescent Methods for the Determination of the Absolute Magnitude of the Termination Rate Constants of Peroxide Radicals in the Liquid Phase , PA Tech Translation 66(1967) 17) R. Czerepinski G.H. 

Diffusion of the macroradicals controls can be assumed to be the termination reaction. However, that is not the case the termination rate constant is absolutely independent of the degree of polymerization, as shown in Table I. Therefore, the assumption must be that the diffusion of the segment at the end of the radical chain controls the termination process (as long as the Trommsdorff effect is not rate-determining). 

In a series of papers, Chateauneuf and Brennecke (Roberts et al., 1993b, 1995) reported absolute rate constants for the dimerization of benzyl radical determined using laser flash photolysis (LFP). The termination rate constant (2 kj) was diffusion-controlled and, thus, decreased slightly with increasing pressure (e.g., 2 fcT = 4 x 1010 and 2 x 1010 s 1 at 80 and 100 bar,... 

Traditionally, linear pharmacokinetic analysis has used the n-compartment mammillary model to define drug disposition as a sum of exponentials, with the number of compartments being elucidated by the number of exponential terms. More recently, noncompartmental analysis has eliminated the need for defining the rate constants for these exponential terms (except for the terminal rate constant, Xz, in instances when extrapolation is necessary), allowing the determination of clearance (CL) and volume of distribution at steady-state (Vss) based on geometrically estimated Area Under the Curves (AUCs) and Area Under the Moment Curves (AUMCs). Numerous papers and texts have discussed the values and limitations of each method of analysis, with most concluding the choice of method resides in the richness of the data set. 

The overall rate of autoxidation of a substrate is determined not only by the propagation rate constant, kp, but also by the termination rate constant, kt, as given in Eq. (7). Table IV lists approximate rate constants for various peroxy radical terminations. Examination of Table IV reveals that the lower rates of autoxidation for primary and secondary hydrocarbons compared to tertiary... 

It was proposed to determine the rate constants of transfer and termination or their ratios to that of propagation for polymerization systems that allow synthesis of well-defined polymers [6]. This information will be useful for the reproducible synthetic efforts and also for setting limits for the preparation of well-defined high polymers. The direct determination of transfer/termination rate constants may be facilitated by working under "difficult reaction conditions such as those which usually disallow preparation of well-defined polymers (higher temperatures, lower [I]0, longer chains, etc.), and the obtained results extrapolated to the "usual living conditions. 

As indicated earlier, G=0.7 for free radical initiation and about 0.1 for the free ions. The termination rate constants are 3 X 10 M sec for free radicals and 2 x 10 M sec for the free ions. The propagation rate constants have been determined to be 30, 4 X 10 and about 10 sec for free radical, cationic and anionic polymerization, respectively. 

The chain length dependence of termination rate constants (Section 5.2.1.4) should not be ignored when considering copolymerization kinetics. It has been pointed out that average chain lengths in copolymerization will be a function of the monomer feed composition especially in copolymerizations with disparate propagation rate constants. Factors determining the rate of copolymerizalion are not fully resolved and copolymerization kinetics remains a topic of discussion and an area in need of further study. 

There is no precise method for the measurement of the termination rate. Major difficulties in rate constant determination arise from the diffusion control of this reaction. Termination rate may depend on segmental and translation diffusion (and reaction diffusion) of radical species occurring in an increasingly viscous medium that change with monomer conversion. In other words, because of the decrease of the diffusion coefficient with molecular size, the termination rate coefficient is lower at higher chain lengths. 

Although single-source experiments are not satisfactory for determining rate constants as a function of time, it is quite obvious from the above-mentioned study that the reaction rate constant will vary with the energy of collision in the source and that, as a consequence, the only meaningful statement that can be made about a rate constant determined with continuous ion extraction must include a statement of the terminal energy. Many investigators now do express reaction rate constants in this form. 

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