Combination rate constants

TC = termination by combination rate constant T = ratio of the termination rate constant for combination to the rate constant for disproportionation CFM = ratio of the rate constant for monomer transfer to the constant for propagation... 

Here, is the rate constant for radiative decay (fluorescence), while k r is the combined rate constant for aU non-radiative decay processes, is virtually constant and is an inherent property of the material in question, and for this material is significantly greater than k r, given the high fluorescence efficiency. When a fluorescence quencher, such as TNT, is introduced, km increases because an additional efficient non-radiative pathway now exists. This, via Eq. (4), makes r smaller. 

Despite its significance, N02 has not received nearly as much attention as NO in kinetic and mechanistic studies in solution (217). The reason probably lies in the short lifetime of N02, which rapidly disproportionates to nitrite and nitrate, see Scheme 12, Eqs. (54)—(55), with an overall combined rate constant k = 6.5 x 107 NT1 s 1, Eq. (57). Direct kinetic studies are thus limited to rapid reactions and require the use of absorbing reactants or kinetic probes. 

They have also obtained a combination rate constant of 5 x 10 12 cm3 molec sec for CF3... 

Tedder and Walton (964) report a combination rate constant of 5.3 x 10 11 cm3 molcc 1 see -1 by a rotating-sector method... 

K = hydrate formation growth rate constant, representing a combined rate constant for diffusion (mass transfer) and adsorption (reaction) processes... 

In so far as values of pATn2o for the hydration of alkenes are known or can be estimated,47 values of pATR can be derived by combining rate constants for protonation of alkenes with the reverse deprotonation reactions of the carbocations. The protonation reactions seem much less likely to be concerted with attack of water on the alkene than the corresponding substitutions. Indeed arguments have been presented that even protonation of ethylene in strongly acidic media involves the intermediacy of the ethyl carbocation.97,98... 

MPT reacts somewhat more slowly with singlet oxygen than PTH. The combined rate constants of physical quenching (e.g. Equation 32) and chemical reaction (e.g. Equation 27) have been calculated from photooxidation experiments in bromobenzene/methanol (2/1) to be 1.2x10 M s-1 for MPT and 4.2x10 for PTH (26). Hovey has calculated... 

Decomposition experiments for these CPs listed in Table 14.11 were carried out by the simultaneous action of UV radiation and Fenton s reagent (Benitez et al., 2000). Table 14.11 shows the first-order rate constants and half-lives. During the photo-Fenton s reagent reaction, the single photodecomposition rate constant, ku decreased as the number of chlorine substituents increased. In addition, combined rate constants, ku are much greater than the radical reaction constants, k,. Therefore, this confirms the additional contribution of the radical reaction due to generation of the hydroxyl radicals by Fenton s... 

Because / esc is directly proportional to / difn the in-cage combination product yield can be related directly to the solvent micro viscosity, rjm- Thus, plots of In [100/(2 x (5)-3b + 2-BN + 4-BN)in cage-l] versus In (l/r)n using data from irradiations of (/ )-3b in the -alkanes are linear, with positive slopes, 0.47 0.10 at 296K and 0.6 0.1 at 333K. Unfortunately, the number of data points is too small to determine whether the two slopes are truly different. Regardless, the positive slopes indicate that the sum of the in-cage combination rate constants, kj, + k, is less sensitive to micro-... 

The first-order combination rate constants from in-cage processes, 3 x 10 s, were determined from the initial slopes of the fast components of the kinetic curves. They remain nearly constant in films with 30-100 wt% of PCV. The activation energy of Iq-i is very small, 8 kJ/mol, suggesting that geminal recombination in the PVC films is limited only by the rotational mobility of the radicals in their cages. Furthermore, was insensitive to the application of a strong external magnetic field... 

On closer inspection, the combination rate constants are about 1/4 of the estimated diffusion-controlled rate constant. For acetonitrile, for example, fcjj - 2.9 X 10 L mol" s from the von Smoluchowski equation wiA a diffusion coefficient from a modified version of the Stokes-Einstein relation, D - fcT/4jiT r. Owing to the restriction to singlet state recombination, an experimental rate constant 1 /4 of is quite reasonable. On the other hand, for these heavy metals, the spin restriction may not apply, in which case one would argue that the geometrical and orientational requirements of these large species could well give recombination rates somewhat below the theoretical maximum. 

The combination rate constant ks, is known , so that the v and b measurements lead to a value of k. Lin and Back carried out such measiurements over a range of temperatures and pressures. They found a considerable pressure-dependence of the first-order rate coeflBcient for the ethyl radical decomposition. In the temperature range 823 to 893 °K and the pressure range 200 to 600 torr the rate is in fact approximately proportional to [C2Hg]. At higher pressures the rate of (3) becomes independent of the ethane concentration, and the first-order rate coefficient can then be represented by... 

The combination rate constant k was derived from the exchange rate constant which was measured by dynamic NMR line shape analysis. The combination rate constant Is about 3 x 10 H s l at 20 with a low enthalpy of activation, about 2 kcal/mole (see Experimental for more details). The high rate of exchange In the 2-alkoxy-... 

The oxonlum Ion Is an Intermediate In the exchange reaction, and because of Its symiaetry the exchange rate constant Is equal to k /2 (combination rate constant). If the exchange occurs In equimolar solution of 2-metho]qr and 2-ethoxy l,3-dloxolane, the pseudo first order rate constant of exchange may be expressed as... 

Using these combined rate constants, the Solomon equations can be written... 

This process is called termination by combination (or coupling). In general terms, this is written as Eq. (6.7a), where ktc is the rate constant for termination by combination (or coupling) or simply the combination rate constant. 

This is the design equation for a PER with total reflux and, not surprisingly, is reminiscent of the conventional PER equation where k is defined as a combined rate constant (Equation 21.33) and the electrode area appears as a parameter. 

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