Recombination constant

The mathematical processing of co-oxidation curves can be oriented to determine, independently of any hypothesis about the recombination constants, the three relative parameters ... 

Previously, it was mentioned that the steric characteristics of the carbon atom (primary, secondary, tertiary) should be considered it becomes clear with the new classes of compounds studied that the electronic characteristic of the substituent groups—aryl, hydroxyl, alkoxyl— must also be taken into account. Thus, whereas trisalkylperoxy radicals have weak recombination constants, dialkylhydroxy or dialkylalkoxy have much higher recombination constants, occasionally similar to values observed for secondary alkyl radicals. 

The conclusion that the photocurrents are limited by recombination has been verified recently by Karl and Sommer (1971) who also determined the value of the bimolecular electron-hole recombination constant. The shapes of the transients observed in these experiments are similar to those which are characteristic of damaged surface layers (see p. 181). In a similar way many workers have observed non-linear field dependences of the collected charge. In their study of durene, Burshtein and Williams (1977) show that a consideration in terms of Onsager s (1938) theory of geminate surface recombination appears to be unsatisfactory the results are best explained in terms of efficient deep trapping and/or recombination in a narrow region near the illuminated surface. 

Recombination constants kr of a pair of primary products of PET at the inner membrane // water interface were also measured for the system of Fig. 4d using flash photolysis in the absence of EDTA and Fe(CN). The values kt, kr and q for a series of membrane-bound viologens are listed in Table 2. Taking into account that 0 amounts to 15%-20%, it is easy to calculate (using Eq. (32)) that even in the absence of an irreversible electron donor, the value of <5 for PET across the membrane can achieve several percent. 

This expression is represented by a small intermediate step with height 0.25 seen on the thick line. However, with a further increase in AG, the triplet recombination constant is not as high any more, but falls down to zero, giving way to the alternative recombination channel backward to the excited singlet state. Therefore % rises further on with AG, up to x = 1 ... 

Such a complex behavior of x(AG ) in the presence of the triplet channel is smoothed at faster diffusion when ko is closer to the maximal value of the recombination constants. In this case there is a single step border [dashed line in Fig. 3.81(a)] between the irreversible (to the left) and reversible (to the right) reactions. The position of this border essentially depends on the true height of k,. In Figure 3.81 (Vi) one can see how the border marked by this line is shifted to the right with the increasing rate of triplet recombination. 

The dependence of the dissociation constant kj) and the recombination constants kjt in the reaction (a) on the optical polarization of the atoms A was predicted by Bernheim [65] and Kastler [225] and later demonstrated experimentally [7, 363]. The dependence can be understood from the obvious fact that only hydrogen-like atoms with opposite electronic spins may recombine and form a molecule A2(X1E+). Hence we have kR = kft(l — S2), where S is the degree of electron spin polarization of the atoms. A convenient indicator of dimer formation is provided by the kinetics of the laser-induced molecular fluorescence after switching on magnetic resonance which destroys the polarization of the atoms, as performed by Huber and Weber [201] for a Na — Na2 mixture. The se-... 

Solution of these equations eventually gives an expression fornj (0), the concentration of electrons at the surface, in terms of the parameters already defined, together with kCT, the rate constant for charge transfer across the interface (see Fig. 10.21) and two recombination constants, one for the bulk and one for the surface. Recombination of hole-electron pairs is taken into account in the development, as is also the formation of surface states by a surface-dependent anion adsorption at a degree of coverage, 9. 

The situation is similar to the success of the traditional Poisson—Boltzmann approach its ability in describing, at least qualitatively, and many times even quantitatively, the behavior of most colloidal systems probably resides in the use of at least one adjustable parameter (surface charge, surface potential, recombination constant and so on) in the fitting of the experimental results. If that parameter could be accurately measured, one would have to address the inaccuracies generated by the mean field treatment itself. 

II R = np l ntcxv + Recombination constant assuming a Boltzmann distribution... 

Thermal excitation out of the traps is neglected in these expressions and band-to-band recombination is also not included. The Cs are the recombination constants for the four transitions shown in Fig. 8.24. According to Eqs. (8.54) and (8.56), C, = 6kToJea and the four cross-sections differ by less than a factor 10 (see Table 8.1). N +, and N -are the concentrations of the different charge states of the defect. By charge neutrality. 

If it is assumed that the interradical recombination constants are given by twice the geometric mean of the recombination constants for each free radical, which is not too unreasonable an assumption, then the eijuation can be linearized and solved explicitly. This implies that kvi = 2[W 23(M)T kio — 2(A. jA 24) et( ., so that E(p (XIII.11.4) becomes a perfect square which can be extracted to give... 

Under such conditions it is possible to compute a value of the first recombination constant by assuming equal diffusion coefficients and using the approximate equation (29) ... 

Note that in the case of a Qio-pool, either reaction route (a) or (b) would yield a recombination constant (P-Qio). The measured value of 0.84 0.04 s" is in excellent agreement with the calibration value. In the case of a Qo-pool, the rate constant A (P Qo) is expected if an exchange between Q10H2 and Qo in the pool has taken place. The measured recombination rate constant of 1.7 0.2 s confirms that a molecular exchange between Q10H2 and Qo has indeed taken place per route (a) discussed on p. 123. 

This rule has the obvious advantage of drastically reducing the number of useful recombination constants simply related to the self-recombinations. The kcoii evaluation deserves some further consideration. First of all, the Stokes-Einstein theory suggests that when molecules are not too long (the exclusion regards the case of polymers or that one of solvents with extended linear backbones), the diffusion coefficient is... 

By applying the given formulas at 450 K, the recombination constant of macro-radicals in molten polymethylene becomes... 

Until 1950s, radiation-induced polymerization was considered to proceed only by the free-radical mechanism. In fact, the rate of ion generation by ionizing radiation is one to two orders of magnitude lower than that of free-radical formation. In contrast, the recombination constants for ions (ion and counter-ion) are approximately two orders of magnitude higher than those for free radicals. Hence, the stationary concentration of ions is approximately 100 times lower than that of free radicals. Consequently, radiation polymerization proceeds mainly by a free-radical mechanism. 

Here np and ngp are the concentrations of the charged excitations, G(t) is the generation term and B is the bimolecular recombination constant. Under steady state conditions for the polarons, eq. (2) becomes... 

Recombination constant, direct recombination Recombination constant of electrons, recombination via gap states Recombination constant of electrons, recombination via surface states Recombination constant of holes, recombination via gap states... 

The rate of formation of ions is a factor of approximately 10-100 times smaller than that for free radicals. Conversely, the recombination constants are about 100 times larger for ions than for free radicals. Thus, it follows that the steady state concentration of ions is about 100 times smaller than that for free radicals. Consequently, the majority of radiation-initiated polymerizations proceed by a free radical mechanism. 

Here the rate of the ion dissociation is on the left-hand side (a is the degree of ionization), and the rate of their bimolecular recombination is on the right-hand side (otc = nY=ny is a volume concentration of ions), and are corresprMiding dissociation and recombination constants. The temperamre dependent ionization confident can be written as follows ... 

The temperature dependence of conductivity (2.1) is controlled by the temperature dependence of ion mobilities and ionization-recombination constants and, in general, assumes an activation character... 

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