Rate of radical

The following conditions are stipulated the catalyst decomposition rate constant must be one hour or greater the residence time of the continuous reactor must be sufficient to decompose the catalyst to at least 50% of the feed level the catalyst concentration must be greater than or equal to 0.002 x Q, where the residence time, is expressed in hours. An upper limit on the rate of radical formation was also noted that is, when the rate of radical formation is greater than the addition rate of the primary radicals to the monomers, initiation efficiency is reduced by the recombination of primary radicals. 

New radicals are introduced by thermolysis of the hydroperoxide by chain-branching decomposition (eq. 4). Radicals are removed from the system by chain-termination reaction(s) (eq. 5). Under steady-state conditions, the production of new radicals is in balance with the rate of radical removal by termination reactions and equation 8 appHes for the scheme of equations 1—5 where r. = rate of new radical introduction (eq. 4). 

An expression for the number of particles formed during Stage I was developed, assuming micellar entry as the formation mechanism (13), where k is a constant varying from 0.37 to 0.53 depending on the relative rates of radical adsorption in micelles and polymer particles, r is the rate of radical generation, m is the rate of particle growth, is the surface area covered by one surfactant molecule, and S is the total concentration of soap molecules. 

During Stages II and III the average concentration of radicals within the particle determines the rate of polymerization. To solve for n, the fate of a given radical was balanced across the possible adsorption, desorption, and termination events. Initially a solution was provided for three physically limiting cases. Subsequentiy, n was solved for expHcitiy without limitation using a generating function to solve the Smith-Ewart recursion formula (29). This analysis for the case of very slow rates of radical desorption was improved on (30), and later radical readsorption was accounted for and the Smith-Ewart recursion formula solved via the method of continuous fractions (31). 

In practice it is found that the concentration of radicals rapidly reaches a constant value and the reaction takes place in the steady state. Thus the rate of radical formation Ej becomes equal to the rate of radical disappearance V. It is thus possible to combine equations (2.1) and (2.3) to obtain an expression for [M—] in terms of the rate constants... 

An increase in the rate of radical production in emulsion polymerisation will reduce the molecular weight since it will increase the frequency of termination. An increase in the number of particles will, however, reduce the rate of entry of radicals into a specific micelle and increase molecular weight. Thus at constant initiator concentration and temperature an increase in micelles (in effect in soap concentration) will lead to an increase in molecular weight and in rate of conversion. 

Table 12.8. Relative Rates of Radical Addition as a Function of Alkene Substitution"...

Until the early 1970s, the absence of suitable techniques for probing the detailed microstructure of polymers or for examining the selectivity and rates of radical reactions prevented the traditional view front being seriously questioned. In more recent times, it has been established that radical reactions, more often than not, are under kinetic rather than thermodynamic control and the preponderance of... 

For a long time, this finding was correlated with the observation that substituents at a radical center tend to enhance its stability (Section 1.1.2). This in turn led to the belief that the degree of stabilization conferred on the product radical by the substituents was the prime factor determining the orientation and rate of radical addition to olefins. That steric, polar, or other factors might favor the same outcome was either considered to be of secondary importance or simply ignored. ... 

The rate of radical addition is most dramatically affected by substituents either at the site of attack or at the radical center. Remote substituents generally have only a small influence on the stereochemistry and regiospecificity of addition unless these groups are very bulky or the geometry of the molecules is constrained (e.g. intramolecular addition - Section 1,2.4). 

If the reaction with monomer is not the rate determining step, the rate of radical generation in pholoinitiated polymerization is given by eq. 9... 

In other cases, the cage reaction may simply lead to reformation of the initiator. This process is known as cage return and is important during the decomposition of BPO (Section 3.3.2.1.1) and DTBP (Section 3.3.2.4). Cage return lowers the rate of radical generation but does not directly yield byproducts. It is one factor contributing to the solvent and viscosity dependence of kA and can lead to a reduced at high conversion. 

However, while it is generally accepted that the rate of radical-radical reaction is dependent on how fast the radical centers of the propagating chains (Pp and Pj ) come together, there remains some controversy as to the diffusion mechanism(s) and/or what constitutes the rate-determining step in the diffusion process. The steps in the process as postulated by North and coworkers30 3" arc shown conceptually in Scheme 5.5. 

Even though the rate of radical-radical reaction is determined by diffusion, this docs not mean there is no selectivity in the termination step. As with small radicals (Section 2.5), self-reaction may occur by combination or disproportionation. In some cases, there are multiple pathways for combination and disproportionation. Combination involves the coupling of two radicals (Scheme 5.1). The resulting polymer chain has a molecular weight equal to the sum of the molecular weights of the reactant species. If all chains are formed from initiator-derived radicals, then the combination product will have two initiator-derived ends. Disproportionation involves the transfer of a P-hydrogen from one propagating radical to the other. This results in the formation of two polymer molecules. Both chains have one initiator-derived end. One chain has an unsaturated end, the other has a saturated end (Scheme 5.1). 

Solvent effects on the reactions of small radicals have been discussed in general terms in Chapter 2 (see 2.3.6.2 2.4.5). Small, yet easily discernible, solvent effects have been reported for many reactions involving neutral radicals. These effects on the rates of radical reactions often appear insignificant when... 

In combination ATRP, the catalyst is again present in its more stable oxidized form. A slow decomposing conventional initiator e.g. AIBN) is used together with a normal ATRP initiator. Initiator concentrations and rate of radical generation arc chosen such that most chains arc initiated by the ATRP initiator so dispersities can be very narrow.290 The conventional initiator is responsible for generating the activator in situ and prevents build up of deactivator due to the persistent radical effect. Reverse or combination ATRP are the preferred modes of initiation for ATRP in emulsion or miniemulsion (Section 9.4.3.2).290 291... 

Recombination reactions between two different macroradicals are readily observable in the condensed state where molecular mobility is restricted and the concentration of radicals is high. Its role in flow-induced degradation is probably negligible at the polymer concentration normally used in these experiments (< 100 ppm), the rate of radical formation is extremely small and the radicals are immediately separated by the velocity gradient at the very moment of their formation. Thus there is no cage effect, which otherwise could enhance the recombination efficiency. 

Rate of Formation of Primary Precursors. A steady state radical balance was used to calculate the concentration of the copolymer oligomer radicals in the aqueous phase. This balance equated the radical generation rate with the sum of the rates of radical termination and of radical entry into the particles and precursors. The calculation of the entry rate coefficients was based on the hypothesis that radical entry is governed by mass transfer through a surface film in parallel with bulk diffusion/electrostatic attraction/repulsion of an oligomer with a latex particle but in series with a limiting rate determining step (Richards, J. R. et al. J. AppI. Polv. Sci.. in press). Initiator efficiency was... 

The rates of radical-forming thermal decomposition of four families of free radical initiators can be predicted from a sum of transition state and reactant state effects. The four families of initiators are trarw-symmetric bisalkyl diazenes,trans-phenyl, alkyl diazenes, peresters and hydrocarbons (carbon-carbon bond homolysis). Transition state effects are calculated by the HMD pi- delocalization energies of the alkyl radicals formed in the reactions. Reactant state effects are estimated from standard steric parameters. For each family of initiators, linear energy relationships have been created for calculating the rates at which members of the family decompose at given temperatures. These numerical relationships should be useful for predicting rates of decomposition for potential new initiators for the free radical polymerization of vinyl monomers under extraordinary conditions. 

The linear free energy equations generated in this study are useful for reasonably accurate predictions of rates of radical forming decompositions of Irons-symmetric bisalkyl diazenes (1),... 

One of the most challenging aspects of modeling turbulent combustion is the accurate prediction of finite-rate chemistry effects. In highly turbulent flames, the local transport rates for the removal of combustion radicals and heat may be comparable to or larger than the production rates of radicals and heat from combustion reactions. As a result, the chemistry cannot keep up with the transport and the flame is quenched. To illustrate these finite-rate chemistry effects, we compare temperature measurements in two piloted, partially premixed CH4/air (1/3 by vol.) jet flames with different turbulence levels. Figure 7.2.4 shows scatter plots of temperature as a function of mixture fraction for a fully burning flame (Flame C) and a flame with significant local extinction (Flame F) at a downstream location of xld = 15 [16]. These scatter plots provide a qualitative indication of the probability of local extinction, which is characterized... 

Rate of radical generation in the aqueous phase during emulsion polymerization (Chap. V). 

Fig. 2. Stored charge (as calculated from conductivity changes) as a function of irradiation time. Concentration of the silver sol 2.5 x 10 M. J rate of charging the microelectrode (i.e. rate of radical generation divided by Faraday s equivalent)...

Baldwin, R.C., Pasi, A., MacGregor, T.J. and Hine, C.H. (1975). The rates of radical formation fixjm the dipyridylium herbicides paraquat, diquat and morfemquat in homc nates of rat lung, kidney and liver an inhibitory effect of carbon monoxide. Tox. Appl. Pharmacol. 32, 298-304. 

In the second limiting case, the rate of reaction with H20 is presumed to be much slower than the rate of radical cation migration and independent of the specific base pair sequence surrounding the GG step. Under these circumstances, each GG step will be equally reactive, and just as much strand cleavage will be observed at the GG step farthest from the AQ as at the one closest to it. 

In the intermediate circumstance where the rate of reaction with H20 and the rate of radical cation migration are comparable, then the amount of reaction detected is somehow related to the distance from the AQ to the GG step. 

Therefore, analysis of the efficiency and pattern of strand cleavage provides information on the relative rate of radical cation migration through different DNA sequences. This is powerful information for analysis of the charge migration mechanism. 

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