Decay second-order

Even though the model was derived based on first order deactivation of active centres, it was found that the model is equally capable of fitting data generated from a distribution of active sites undergoing second order decay. 

For second order decay, the concentration of species i is given by... 

Second Order Deactivation. All simulations described thus far are based on first order deactivation. As mentioned previously, the model is capable of fitting second order decay data. To assess the effect of second order decay, simulations were carried out with similar distributions of activities and termination rates with the active sites undergoing second order decay. 

Using a hybrid blmodal distribution, with the HAFD sites undergoing first order decay and the LASD sites undergoing second order decay, one can generate 8 values spanning the full... 

Evaluation of F(x) for Second Order Deactivation. As mentioned earlier for the case of second order decay F(x) cannot be derived analytically, however numerical calculation of F(x) or Its evaluation from simulated rate data Indicates that the function defined In Equation 11 provides an excellent approximation. This was also confirmed by the good fit of model form 12 to simulated polymerization data with second order deactivation. Thus for second order deactivation kinetics the rate expression Is Identical to Equation 12 but with 0 replacing 02. 

Electron-releasing groups facilitate the oxidation of a series of / ara-substituted toluenes, although determination of the rate coefficients again depended on a second-order decay plot of the concentration of Cr(VI) . ... 

The second-order decays of the uncharged neutral radicals are very similar to those of the radical anions so that, perhaps surprisingly, the negative charge does not hinder the radical-radical interaction. 

Figure 7. The rate of loss of Mn(C0)5 is plotted as a second order decay. The data were obtained at 2004.3 cm"1. The inset is a transient waveform at this frequency which covers a 2 ms time range.

Matheson and Rabani (1965) measured the rate of the reaction eh + eh— H2 + 20H at pH 13 under 100 atmospheres H2 pressure, where all radicals are converted to eh. From a pure second-order decay, the rate constant was determined as 6 x 109 M 1s 1. There are contradictory views on this reaction. According to some, this rate is too low for a diffusion-controlled reaction between like charges, by a factor of -4 (see Farhataziz, 1976). This factor of 4 can be accounted for by spin considerations, since each electron is a doublet but the end product H2is a singlet. To be consistent, then, one has to consider the rate of reaction eh + O—-O2- as normal for diffusion control. 

An alternative electrochemical method has recently been used to obtain the standard potentials of a series of 31 PhO /PhO- redox couples (13). This method uses conventional cyclic voltammetry, and it is based on the CV s obtained on alkaline solutions of the phenols. The observed CV s are completely irreversible and simply show a wave corresponding to the one-electron oxidation of PhO-. The irreversibility is due to the rapid homogeneous decay of the PhO radicals produced, such that no reverse wave can be detected. It is well known that PhO radicals decay with second-order kinetics and rate constants close to the diffusion-controlled limit. If the mechanism of the electrochemical oxidation of PhO- consists of diffusion-limited transfer of the electron from PhO- to the electrode and the second-order decay of the PhO radicals, the following equation describes the scan-rate dependence of the peak potential ... 

Figure 10.14 Integrated rate law plot of the second-order decay of QH radical species...

Fig. 1.6 Decay of (NH3)jCo(mbpy ) + at pH 7.2 and 25 °C. The transient was generated by using equivalent amounts (10 pM) of (NHjljCofmbpy) and CO5. The decay of the transient was nicely second-order up to 85% reaction (a). After this, when the Co(III) radical concentration is small (1-2 pM), there is a slight deviation for the expected second-order plot (not shown) and a first-order reaction (b) remains k = 5.4 X lO s ). The difference between the (steep) second-order decay and the (extrapolated) first-order loss is apparent.

The second-order decay of the three-coordinate transient (to form a dimer, k = 2 X lO M s ) can be accelerated in the presence of substrates, Ph3P, CO etc. The second-order rate constant for reaction with CO, 1.0 x 10 M s is consistent with an early... 

The results obtained in this work are summarized in Table I. The rate constants were obtained from good second-order decays in all cases. The absolute values of the rate constants given in Table I are probably correct to within a factor of 2 to 3 in most cases. The ceric results should be somewhat more reliable than the photolytic results because more time was devoted to their study. It seems likely that more accurate rate constants will be obtained by both methods as more experience is gained in the use of the ESR technique. 

The biperoxy radical produced by the ceric ion oxidation of 2,5-di-methylhexane-2,5-dihydroperoxide decays rapidly with first-order kinetics [k = ioio.e exp( -11,500 1000)/RT sec.1 = 180 sec."1 at 30°C. (30)]. After the first-order decay has run to completion, there is a residual radical concentration (—4% of the initial hydroperoxide concentration) which decays much more slowly by a second-order process. The residual second-order reaction cannot be eliminated or changed even by repeated recrystallization of the dihydroperoxide. This suggests that a small fraction of the biperoxy radicals react intermolecularly rather than by an intramolecular process and thus produce monoperoxy radicals. The bimolecular decay constant for this residual species of peroxy radical is similar to that found for the structurally similar radical from 1,1,3,3-tetra-methylbutyl hydroperoxide. Photolysis of the dihydroperoxide gave radicals with second-order decay kinetics which are presumed to be 2,5-hydroperoxyhexyl-5-peroxy radicals. 

The postirradiation decay of the radical concentration at room temperature has been followed for the 10 and 18% methanol solutions. The actual rates of decay are shown in Figures 13 and 14, and the values plotted as a second-order decay reaction are shown graphically in Figure... 

A systematic dependence of reaction order on temperature and pH is not visible, n varies between one and two. Different experimental conditions and/or missing details about these conditions as well as different analytical methods make a comparison of these results impossible. Staehelin and Hoigne (1985) proposed a possible explanation for the second order reaction (n = 2). Since in clean water ozone not only reacts with the hydroxide ions but also with the intermittently produced hydroxyl radicals (see Chapter A 2), it behaves like a promoter and the decay rate increases with the square of the liquid ozone concentration. This is supported by the results obtained by Gottschalk (1997). She found a second order decay rate in deionized water, compared to a first order decay rate in Berlin tap water, which contains about 4 mg L DOC and 4 mmol LT1 total inorganic carbon. Staehelin and Hoigne (1982) also found first order in complex systems. 

Increasing the solvent polarity results in a red shift in the -t -amine exciplex fluorescence and a decrease in its lifetime and intensity (113), no fluorescence being detected in solvents more polar than tetrahydrofuran (e = 7.6). The decrease in fluorescence intensity is accompanied by ionic dissociation to yield the t-17 and the R3N" free radical ions (116) and proton transfer leading to product formation (see Section IV-B). The formation and decay of t-17 have been investigated by means of time resolved resonance Raman (TR ) spectroscopy (116). Both the TR spectrum and its excitation spectrum are similar to those obtained under steady state conditions. The initial yield of t-1 is dependent upon the amine structure due to competition between ionic dissociation and other radical ion pair processes (proton transfer, intersystem crossing, and quenching by ground state amine), which are dependent upon amine structure. However, the second order decay of t-1" is independent of amine structure... 

The mechanism of this reaction shows that excitation of the substrate gave an n,n triplet state, but this excited state was unable to dissociate the carbon-iodine bond. This was demonstrated by showing that the n,n triplet state, when sensitized by chrysene, did not produce coupling products. Probably, the reaction occurred in an excited a,a triplet state mainly localized on the carbon-iodine bond, and the interaction between this triplet state and aromatic compounds led to homolytic cleavage of the C-I bond with the formation of both a 5-thienyl radical and a complex between the aromatic compound and the halogen atom. The formation of this complex was demonstrated by the presence of a short-lived transient with Amax = 510 nm, showing a second-order decay kinetics and a half-life of ca. 0.4 (is in laser flash photolysis. The thienyl radical thus formed... 

Figure 3. Decay curve for the flash photolysis of RhCl(CO) (PPI13)2 in 25° benzene under Ar showing the formation of another intermediate species (B) as a product of the second-order decay of the initial transient (A).

All of the molecules in this study have triplet states which are easily detectable by the technique of nanosecond transmission laser flash photolysis. (11) The triplet state of acetoveratrone has a lifetime in excess of 15 ps in ethanol (Figure 2) under conditions of laser excitation the decay involves a mixture of first and second order kinetics, with the latter dominating at high laser powers. This second order decay demonstrates that the triplet state is decaying at least partly by triplet-triplet annihilation. 

II 5.1 Pseudo-First-Order Decay of Reactive Species, 130 111 5.2 Second-Order Decay of Reactive Species, 131 111 5.3 Time Dependent Radical Concentration by Consecutive Reactions, 133... 

The EPR spectra of the NHC boryl radicals that were generated through HAT to the ferf-butoxyl radical clearly show the delocalized 7i-type nature of these intermediates postulated to be essential by calculations [10, 12]. It was also demonstrated that the decay of the EPR signals could be fitted to a second-order decay having 2kt = 9 x 106 M-1 s-1. In agreement with this kinetic analysis, the NHC boryl radicals ultimately dimerize to give bis-NHC diborane derivatives. With the aid of EPR spectroscopy it was also established that the NHC boryl radicals readily abstract bromine atoms from primary, secondary, and tertiary alkyl bromides. However, chlorine atom abstraction is much slower and useful only for benzyl chloride. 

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