Bimolecular recombination

The diffusion of H and D atoms in the molecular crystals of hydrogen isotopes was explored with the EPR method. The atoms were generated by y-irradiation of crystals or by photolysis of a dopant. In the H2 crystals the initial concentration of the hydrogen atoms 4x 10 mol/cm is halved during 10 s at 4.2 K as well as at 1.9 K [Miyazaki et al. 1984 Itskovskii et al. 1986]. The bimolecular recombination (with rate constant /ch = 82cm mol s ) is limited by diffusion, where, because of the low concentration of H atoms, each encounter of the recombinating partners is preceded by 10 -10 hops between adjacent sites. 

Flash photolysis has now been applied to a wide range of metal carbonyl species in solution, including Mn2(CO)10 (37), [CpFe(CO)2]2 (38), and [CpMo(CO)3]2 (39). In almost every case, interesting data have emerged, but, as with Cr(CO)5, the structural information is usually minimal. Thus, the radical Mn(CO)5 has been generated in solution by flash photolysis (37), the rate constant for its bimolecular recombination has been measured, but the experiments did not show whether it had Z>3h or Qv symmetry. Some experiments have been unsuccessful. Although the fragment Fe(CO)4 is well known in matrices (15), it has never been... 

Thus, according to this three-step mechanism, a bimolecular recombination reaction is second-order at relatively high concentration (cM), and third-order at low concentration. There is a transition from second- to third-order kinetics as cM decreases, resulting in a fall-off regime for kbi. 

Bimodal polymer, 20 165 Bimodal polymerization, 20 531 Bimodal reactor technology, for high density polyethylene, 20 170 Bimodal weight ratio, 70 17 Bimolecular reaction, 74 625 Bimolecular recombination coefficient, 74 833... 

Various methods are proposed (5, a—g), (6). Among these, the methods in which monomolecular recombination or bimolecular recombination of the carriers are assumed could not be used in our case, because the carrier transport in poly-N-vinylcarbazole is known to be the multi-trapping process of the hole carrier. The values of the trap depthaE of 5°C peak by these several methods are summarized in Tab. 1. Values are widely scattered and it seemed that this is due to the approximations involved in the method of analysis. Our value is calculated by the... 

A representative example for the information extracted from a TRMC experiment is the work of Prins et al. [141] on the electron and hole dynamics on isolated chains of solution-processable poly(thienylenevinylene) (PTV) derivatives in dilute solution. The mobility of both electrons and holes as well as the kinetics of their bimolecular recombination have been monitored by a 34-GHz microwave field. It was found that at room temperature both electrons and holes have high intrachain mobilities of fi = 0.23 0.04 cm A s and = 0.38 0.02 cm / V s V The electrons become trapped at defects or impurities within 4 ps while no trapping was observed for holes. The essential results are (1) that the trap-free mobilities of electrons and holes are comparable and (2) that the intra-chain hole mobility in PTV is about three orders of magnitude larger than the macroscopic hole mobility measured in PTV devices [142]. This proves that the mobilities inferred from ToF and FET experiments are limited by inter-chain hopping, in addition to possible trapping events. It also confirms the notion that there is no reason why electron and hole mobilities should be principally different. The fact... 

All the preceding mechanisms of the carrier packet spread and transit time dispersion imply that charge transport is controlled by traps randomly distributed in both energy and space. This traditional approach completely disregards the occurrence of long-range potential fluctuations. The concept of random potential landscape was used by Tauc [15] and Fritzsche [16] in their models of optical absorption in amorphous semiconductors. The suppressed rate of bimolecular recombination, which is typical for many amorphous materials, can also be explained by a fluctuating potential landscape. 

If we think of dyes as intrinsic semiconductors, each excitation gives an electron-hole pair (n = p) so that in the case of a bimolecular recombination process... 

In Table III we list the few values which have been obtained for the bimolecular recombination rate constants of radicals and we note again a rather pronounced uniformity of values this time in the range of 1010-6 liter/mole-sec. ... 

Some Rate Constants for the Bimolecular Recombination of Free Radicals... 

The second term on the right hand side accounts for the bimolecular recombination reaction (see, for example, Eqn. (1.2) //.). 

If there were no bimolecular recombination, we would get from equation (3.2.9) that... 

In this Section we consider the following problem. Defects B are mobile (A > 0) and interact with each other elastically as U (r) = — Xr 3 we call hereafter this interaction dynamical. Their counter-partners A involved into the bimolecular recombination, A + B — 0, could be both immobile, Da = 0, and mobile, Da = DB. Obviously to calculate the kinetics of this reaction, we have to go beyond the framework of the traditional approach, Section 4.1, which neglects the interaction of similar particles. 

Chemiluminescence can occur when a thermal (dark) reaction is so exothermic that its energy exceeds that of the electronically excited state of one of the product molecules. The major pathway for these reactions is the decomposition of cyclic peroxides, and this is at the basis of most bioluminescence processes. There are some other physico-chemical processes which can lead to the formation of excited states and thereby to the emission of light these are based on the bimolecular recombination of high-energy species such as free radicals and radical ions. 

The mechanism presented here is somewhat at variance with that proposed by the authors (Yamamoto et al. 1995) who suggested that the /BuOI I-derived radical adds to the primarily formed electron-adduct radical. Since this has been shown above to have only a very short lifetime, it will not be capable of undergoing bimolecular recombination reactions. An isomerization of C(8)-H -adduct [reaction (183)] followed by an addition of the tert-butanol-derived radical and water elimination [reactions (184) and (185)] is not in conflict with the above pulse radiolysis results [note that the tautomerization reaction (183) cannot be excluded on the basis of the pulse radiolysis data]. 

A number of recent investigations have been concerned with the mobility of heavy atoms in rare gas matrices. Although not directly related to tunneling processes, they are concerned with important fundamental dynamics of atoms and small molecules in low-temperature solids, so we shall briefly review selected examples here. A typical experiment of this type includes the photolytic formation of atoms (see the review by Perutz [1985]) with subsequent detection of the decrease in atom concentrations due to bimolecular recombination. In most cases the rates are diffusion limited, and the temperature dependences are characteristic of thermally activated transfer. 

The conclusion drawn from Worked Problem 6.14 is that changing the type of termination step from gas to surface alters the kinetics. This is because the order with respect to the radical differs between the second order recombination of the gas phase termination and surface termination where diffusion to the surface or adsorption on the surface is rate determining and first order. If, however, the rate-determining step in surface termination were bimolecular recombination on the surface, the order would not change between gas and surface termination. This is because both recombinations would now have the same order, i.e. 2 4[R ]2 and 2 7[R ]2, with the total rate of termination if both contributed being 2(k + 7)[R ]2. 

Table 2 also reveals that the bimolecular recombination rate, Eq. (16), of the hydrophobic photoproduct, C8V+ is retarded by a factor of 37 as compared to the hydrophilic intermediate, C4V+. Thus, the microheterogeneous water-in-oil... 

The last term in the same equation describes the subsequent bimolecular recombination. The general solution to this equation shows the complex interplay between geminate and bimolecular recombination (Fig. 3.29). When... 

If excitation is weak or partner concentration is small, then the free ions are produced in low concentration and their bimolecular recombination is too slow to be seen in the timescale of the geminate reaction. Therefore the kinetics of the latter is often studied separately with a fast time-resolved technique. Alternatively, the free-ion quantum yield found from the initial concentration of ions participating in the slow bimolecular recombination can be used to calculate

charge separation quantum yield tp is the usual subject of numerous investigations. Here we will concentrate only on two of them, where this quantity was studied as a function of not only the recombination free energy but of the solvent viscosity as well. These investigations were carried out on the following systems ... 

The Laplace transformations of the kernels, representing the bimolecular recombination to the ground and excited states, are... 

Figure 3.58. Decay of the excited donor concentration (solid line) accompanied by ion accumulation/recombination (dashed line) and depletion of neutral acceptors (dotted line) at Wi = wr = 1000 ns-1 andrD = oo (the remaining parameters are the same as in Figs. 3.57 and 3.58). The shortest stage of excited donor decay is shown in the insert in comparison to the excitation decay without bimolecular recombination in the bulk (dashed-dotted line). The charge separation quantum yield (p = 6.2%,A (0) = 10-2M,c = 10-4M. (From Ref. 195.)...

Initially, the concentration of excited molecules goes down approximately to the level shown in the insert by a dashed-dotted line, which is obtained by ignoring the bimolecular recombination. This level does not equal N (0) c as one might expect, but is much lower. The reason is that only a

geminate pair, restoring the c(l — cp) neutral particles that are ready to accept electrons once again. Hence, in the absence of bimolecular recombination, the concentration of excitations approaches the following limit... 

The spinless variant of the present theory was already discussed in Section V.D and its interrelationship with IET and a number of other theories of exciplexes or stable complexes was disclosed. In the next Section XI.D we also consider not an excited-state but a ground-state particle. It is subjected to thermal dissociation to radicals followed by their geminate and subsequent bimolecular recombination into the fluorescent product. 

At the beginning, the number of separated radicals was N(0) = Nrip tp, but they disappear with time as a result of bimolecular recombination in the bulk. The current number of free radicals N(t) obeys the conventional rate equation ... 

According to Eqs. (3.617) and (3.624) the total yield of excited singlets jointly produced by geminate and bimolecular recombination is... 

At fast bimolecular recombination of RIPs to the triplet products, the fluorescence quenching by electron transfer becomes irreversible. 

The first kernel represents the biexciton ionization, the second one controls the geminate recombination of charged products, and the last one governs the bimolecular recombination of separated ions. 

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