Rate coefficient with radicals

Conditions of laser power and precursor concentration are chosen such that very low initial radical concentrations ( 3 x 10 molecules cm ) are generated so that radical recombination reactions are minimized. The absence of such reactions is verified by the invariance of the observed radical disappearance rate coefficient with radical concentration. 

A parameter which determines the atmospheric lifetime of DDT and, hence, long-range transport is the reaction rate coefficient with the OH radicals. In a recent... 

A subsequent reaction is the recombination of the benzyl radicals to form dibenzyl, so that the rate of formation of dibenzyl measures the rate of reaction (1). Szwarc evaluated his results in terms of first-order kinetics for the overall process, since he could not find a systematic variation of his first-order rate coefficients with total pressure (varied from 5 to 15 torr). However, in view of the fact that only one... 

One of the most important parameters in the S-E theory is the rate coefficient for radical entry. When a water-soluble initiator such as potassium persulfate (KPS) is used in emulsion polymerization, the initiating free radicals are generated entirely in the aqueous phase. Since the polymerization proceeds exclusively inside the polymer particles, the free radical activity must be transferred from the aqueous phase into the interiors of the polymer particles, which are the major loci of polymerization. Radical entry is defined as the transfer of free radical activity from the aqueous phase into the interiors of the polymer particles, whatever the mechanism is. It is beheved that the radical entry event consists of several chemical and physical steps. In order for an initiator-derived radical to enter a particle, it must first become hydrophobic by the addition of several monomer units in the aqueous phase. The hydrophobic ohgomer radical produced in this way arrives at the surface of a polymer particle by molecular diffusion. It can then diffuse (enter) into the polymer particle, or its radical activity can be transferred into the polymer particle via a propagation reaction at its penetrated active site with monomer in the particle surface layer, while it stays adsorbed on the particle surface. A number of entry models have been proposed (1) the surfactant displacement model (2) the colhsional model (3) the diffusion-controlled model (4) the colloidal entry model, and (5) the propagation-controlled model. The dependence of each entry model on particle diameter is shown in Table 1 [12]. 

Comparison of the computed profiles with experiment may in principle be used to establish values of some of the unknown rate coefficients. The radical pool in this computation includes molecular oxygen as a bi-radical. The validity of the partial equilibrium assumptions will be discussed in Sect. 5.4.4. 

Mercaptans are oxidised to disulphides by peroxodisulphate. Eager and Winkler studied the kinetics of the oxidations of n-butyl, n-octyl, and n-dodecyl mercaptans in acetic acid/water solvent (80 ml acid-I-20 ml water) and found first-order kinetics with respect to peroxodisulphate. The first-order rate coefficient increases with increase of mercaptan concentration, and reaches a limit at about 5 x 10 Af mercaptan. A decrease in the first-order rate coefficient with increase of the initial peroxodisulphate concentration was observed and attributed to a salt effect. Eager and Winkler suggested a mechanism involving sulphate radical ions. Levitt proposed a mechanism involving sulphur te-troxide, but there is no evidence for its formation in peroxodisulphate oxidations. 

Recently, Ugelstad et al. l969i proposed a semiempirtcal rate coefficient for radical desorption in vinyl chloride emulsion polymerization. On the other hand, Nomura et al. (1971, 1976) have derived a rate coefficient for radical desorption theoretically with both stochastic and deterministic approaches and have successfully applied it to vinyl acetate emulsion polymerization. They also pointed out that radical desorption from the particles and micelles played an important role in micellar particle formation, Fiiis et al. 1973 also derived the rate coefficient for radical desorption in a different way. Lift et al. (1981) discussed in more detail the chemical reactions incorporated in the physical process of radical desorption in the emulsion polymerization of vinyl acetate. 

Changes in the population of propagating species and the increase in the polymer concentration mean that the rate coefficient for radical-radical termination will decrease with conversion. The moderate conversion regime is characterized by the autoacceleration phenomenon known as the gel or Norrish-Trommsdorf effect. Various empirical relationships defining or the rate of diffusion of long chains in terms of either the viscosity or the free volume have been proposed which enable the onset of the gel effect (Figure 5.3) to be predicted for a number of polymer systems. 

A number of esters [10], ethers [11, 12] and alcohols [13] were investigated with respect to reactivity with nitrate radicals. Both absolute and relative rate methods were employed. Rate coefficients for the reaction of NO3 are given in Table 1. The rate coefficients for aliphatic esters may be predicted from available group reactivity factors for alkanes provided that formate carbonyl hydrogen atoms are treated as primary hydrogen atoms. The rate coefficients with temperature dependence for ethers and alcohols are valid between 268 to 363 K. 

RAFT agent. The growing radicals produced from the fragmentation of the RAFT agent exit the particles and reenter into the continuous phase to form new particles before the precipitation of the existing particles, thus increased the exit rate coefficient with RAFT concentration. This induces the retardation of the polymerization due to the transfer of the RAFT agent to the particles and so the particle size decreases with the RAFT concentration. In the emulsion polymerization of styrene, the particle diameter decreased and the size distribution became narrower with the RAFT concentration. However, a partial... 

The H atom reacts (with diffusion-controlled rate coefficient) with dissolved oxygen according to O Eq. (23.42) forming perhydroxyl radical... 

Several groups investigated the reactions of radical cations in liquid alkenes. In pulse radiolysis studies the radical cations show a strong absorption band around 280 nm, which is attributed to the n-n transition of the alkene monomer radical cation. Monomer radical cations dimerize with diffusion-controlled rate coefficients with the olefin molecules the dimer cations have broad absorption bands in the 600-800 nm range (Mehnert et al. 1981, 1985 Alfassi 1989). Dimerization may proceed via a hydride ion (H ) transfer in the transition-state of radical-molecule reaction (O Fig. 23.7) ... 

The reaction dynamics of the internal quantum states of molecules is also relevant to understanding the kinetics of reactions such as the temperature dependence of rate constants. Furthermore, reactions such as those considered here between diatomic free radicals often have very large rate coefficients with unusual temperature dependences that are not explained using simple theories that do not treat the full reaction dynamics of the chemical reaction [7]. 

Chain-transfer reactions to monomers and chain-transfer agents lead to the formation of small and mobile radicals that can exit the polymer particle. Radical desorption leads to a decrease in the average number of radicals per particle. Equation (10), where is the rate coefficient for radical exit [Eq. (11)] [25], gives the rate of radical exit from a population of particles with an average number of radicals per particle n. In Eq. (11), X is an overall mass-transfer rate coefficient, y/rj the ratio between the rate of generation of small radicals by chain transfer and the rate of consumption of these radicals (mostly by propagation), m the partition coefficient of the small radicals between the polymer particles and the aqueous phase, [M] the concentration of monomer in the aqueous phase, km, the termination rate constant in the aqueous phase, and [R] the concentration of radicals in the aqueous phase. 

In dealing with radical-radical termination in bulk, polymerization it is common practice to divide the polymerization timeline into three or more conversion regimes.2 "0 The reason for this is evident from Figure 5.3. Within each regime, expressions for the termination rate coefficient are defined according to the dominant mechanism for chain end diffusion. The usual division is as follows ... 

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... 

Attempts have been made to trap the intermediate radical with a monomer, particularly in the reduction of benzyl chloride by Cr(II) to benzylchromium ion (and ultimately to toluene and dibenzyl). The results were ambiguous, however, as benzylchromium ion itself reacts with butadiene and acrylonitrile. This reduction shows second-order kinetics with E — 14.6 kcal.mole and = 14.3 eu. The rate coefficients for benzyl chloride, bromide and iodide follow the expected sequence ... 

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