Termination reactions rate constants

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... 

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. 

The presence of several different ionic particles and therefore, centres with different reactivity, should contribute to the values of the chain growth and chain termination reaction rate constants. The presence of associated, nonassociated and isomeric forms of catalyst particles, the influence of electrolytic dissociation, intramolecular and intermolecular interaction, leading to the formation of catalytic complexes is the reason for the presence of different centres in ionic catalytic systems. 

The authors model the quantity k g. This quantity is the termination reaction rate constant which accounts for the gel effect as soon as the critical degree of conversion is reached, the gel effect occurs. The termination reaction rate constant in the gel region is much smaller than that in the region where the gel has not yet formed, and, thus, is a function of the degree of conversion t] = (Mo — Mj/Mg. This dependence is modeled by an ad hoc function... 

In the introduced kinetic scheme I, R(0), R(i), R , M, RAFT(i, j), Int(i, j, k), P(i, j, k, m) - reaction system s components (refer to Table 10.1) i, j, k, m-a number of monomer links in the chain kd-a real rate constant of the initiation reaction kil, ki2, ki3, -thermal rate constants of the initiation reaction s kp, ktr, kal, ka2, kf, ktl, kt2 are the values of chain growth, chain transfer to monomer, radicals addition to low-molecular RAFT-agent, radicals addition to macromolecular RAFT-agent, intermediates fragmentation, radicals quadratic termination and radicals and intermediates cross termination reaction rate constants, respectively. 

The decomposition of acetaldehyde has Eq. (8-6) as the rate-controlling step, this being the one (aside from initiation and termination) whose rate constant appears in the rate law. In the sequence of reactions (8-20)—(8-23), the same reasoning leads us to conclude that the reaction between ROO and RM, Eq. (8-22), is rate-controlling. Interestingly, when Cu2+ is added as an inhibitor, rate control switches to the other propagating reaction, that between R and O2, in Eq. (8-21). The reason, of course, is that Cu2+ greatly lowers [R ] by virtue of the new termination step of reaction (8-30). 

The inhibition method has found wide usage as a means for determining the rate at which chain radicals are introduced into the system either by an initiator or by illumination. It is, however, open to criticism on the ground that some of the inhibitor may be consumed by primary radicals and, hence, that actual chain radicals will not be differentiated from primary radicals some of which would not initiate chains in the absence of the inhibitor. This possibility is rendered unlikely by the very low concentration of inhibitor (10 to 10 molar). The concentration of monomer is at least 10 times that of the inhibitor, yet the reaction rate constant for addition of the primary radical to monomer may be less than that for combination with inhibitor by only a factor of 10 to 10 Hence most of the primary radicals may be expected to react with monomer even in the presence of inhibitor, the action of the latter being confined principally to the termination of chain radicals of very short length. ... 

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 - ]/ [Mpropagation reaction rate constants. The steady-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 termination constants kt found previously (see Table XVII, p. 158) are of the order of 3 X10 1. mole sec. Conversion to the specific reaction rate constant expressed in units of cc. molecule" sec. yields A f=5X10". At the radical concentration calculated above, 10 per cc., the rate of termination should therefore be only 10 radicals cc. sec., which is many orders of magnitude less than the rate of generation of radicals. Hence termination in the aqueous phase is utterly negligible, and it may be assumed with confidence that virtually every primary radical enters a polymer particle (or micelle). Moreover the average lifetime of a chain radical in the aqueous phase (i.e., 10 sec.) is too short for an appreciable expectation of addition of a dissolved monomer molecule by the primary radical prior to its entrance into a polymer particle. 

The above models describe a simplified situation of stationary fixed chain ends. On the other hand, the characteristic rearrangement times of the chain carrying functional groups are smaller than the duration of the chemical reaction. Actually, in the rubbery state the network sites are characterized by a low but finite molecular mobility, i.e. R in Eq. (20) and, hence, the effective bimolecular rate constant is a function of the relaxation time of the network sites. On the other hand, the movement of the free chain end is limited and depends on the crosslinking density 82 84). An approach to the solution of this problem has been outlined elsewhere by use of computer-assisted modelling 851 Analytical estimation of the diffusion factor contribution to the reaction rate constant of the functional groups indicates that K 1/x, where t is the characteristic diffusion time of the terminal functional groups 86. ... 

As a model experiment to see the effect of orthoesters in reducing the content of terminal carboxyl, aliphatic long-chain dicarboxylic acid and a large excess of various additives reacted in biphenyl at 250°C, and the rate constants of the pseudo-first-order reaction were compared. The reaction rate constant decreases in the order of tetraphenyl... 

These chain reactions are generally terminated by a bimolecular combination of two propagating radicals, so that their whole rate depends on two quantities the initiation rate (initiation being generally the most expensive step in terms of energy) and a combination of propagation, kp, and termination, kt, rate constants, generally of the form kp/yjq, that depend sharply on the type of radicals and molecular mobility. For example, in the case of oxidation, kp decreases in the series ... 

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.

Explicit termination steps do not have to be considered in this approximate kinetic analysis. A termination step has already been implicitly considered as the reversal of the starting reaction (rate constant k2). As soon as all halogen atoms have been converted back into halogen molecules, the chain reaction comes to a stop. 

The kinetic parameter for the radical dissociation of a carbon—halogen terminal was obtained with the use of an isolated polystyrene with a terminal C—Br bond in the presence of a copper catalyst and a conventional radical initiator with a long half-life.282-283 The result was compared with that of low molecular weight compounds of similar carbon-halogen bonds.163 The second-order rate constant of the model compound 1-13 (X = Br), an effective initiator for styrene, is comparable to that of the polymer terminal. Alternatively, rate constants can be obtained by using a combination of nitroxide-exchange reactions and HPLC analysis.242... 

The rate constants for the reaction of carbon-centred radicals with various substrates such as alkenes424,425 and dioxygen426,427 vary over many orders of magnitude depending on thermodynamic, steric and stereoelectronic effects. Radical recombination reaction rate constants krcc are often close to the diffusion-controlled limit, kr = kj4 58 the factor of one-quarter is due to spin statistics (Section 2.2.1). The observed second-order rate constant for self-termination reactions is 2kr... 

The data obtained for the broadening of the product MWD in the course of the reaction, combined with the theoretical calculations of the effect of various elementary reactions on MWD, made it possible to conclude that the reaction taking place in the system is that of transfer with polymer chain termination. The rate constant of this reaction is (8 + 3) x 10-s 1 mol-1 s l. 

Numerical calculations using a computer showed the difference between the solutions obtained in steady- and nonsteady-state approximations as depending mainly on the magnitude of Q/(cp) (where Q is the reaction thermal effect, c is thermal capacity and p is the reaction medium density), activation energy, and pre-exponential factors of initiation ( ) and termination ( t) rate constants. 

Copolymer composition can be predicted for copolymerizations with two or more components, such as those employing acrylonitrile plus a neutral monomer and an ionic dye receptor. These equations are derived by assuming that the component reactions involve only the terminal monomer unit of the chain radical. This leads to a collection of N x N component reactions and x 1) binary reactivity ratios, where N is the number of components used. The equation for copolymer composition for a specific monomer composition was derived by Mayo and Lewis [74], using the set of binary reactions, rate constants, and reactivity ratios described in Equation 12.13 through Equation 12.18. The drift in monomer composition, for bicomponent systems was described by Skeist [75] and Meyer and coworkers [76,77]. The theory of multicomponent polymerization kinetics has been treated by Ham [78] and Valvassori and Sartori [79]. Comprehensive reviews of copolymerization kinetics have been published by Alfrey et al. [80] and Ham [81,82], while the more specific subject of acrylonitrile copolymerization has been reviewed by Peebles [83]. The general subject of the reactivity of polymer radicals has been treated in depth by Jenkins and Ledwith [84]. 

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. 

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 ... 

When the absolute reaction rate constants are not available, the ratio k(R02 + N02)/ (R02 + NO) is an important parameter, giving the relative importance of the terminating and the nomterminating reaction channels. This ratio has been determined for a few typical radicals (Becker). 

The processes of reaction and diffusion occur at the same time in a variety of systems. These issues are particularly important in the formation of blend systems and are central issues in the performance property enhancement of such systems. A study of the competitive effects of the rates of the two processes can be easily carried out using FTIR microspectroscopy. The rate of diffusion can be monitored by the time evolution of the absorbance (concentration) profiles while the rate of reaction can be monitored as a time evolution of the reactant (or product) absorbance (concentration). Reaction of a random copolymer of styrene and maleic anhydride (SMA) with bis(amine)-terminated poly(tetrahydrofuran) (PTHF) is one such studied system [73]. Temperature was varied while studying the effects of two different PTHF molecular weights. The reaction rate constants were obtained from the initial slope of conversion-time plots. In addition, it was shown that the rate of diffusion was faster as diffusion of PTHF into the SMA phase occurred prior to the imide formation. The imide was formed in the SMA phase and quantitatively estimated. A corresponding decrease in the carbonyl stretching vibration of the maleic anhydride peak was seen. 

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