Bimolecular annihilation

For a critical concentration of excitons 17 = 7/. the critical radius (, below which bimolecular annihilation process predominates over singlet exciton recombination can be expressed as [5],... 

At high excitation densities in the solid state, the decay of the singlet exciton becomes excitation dependant, bimolecular annihilation of the singlet exci-tons introduces a fast component to the decay [41,42,77,78], this is shown in Fig. 21. In a number of publications pump-probe spectroscopy has been used to study the phenomena surrounding this accelerated decay. The bimolecular annihilation reaction is effectively energy transfer from one excited singlet to... 

Daniel C, Herz LM, Silva C, Hoeben FJM, Jonkheijm P, Schenning A, Meijer EW (2003) Exciton bimolecular annihilation dynamics in supramolecular nanostructures... 

We are therefore left with the possibility that triplet excitons are formed in this polydiacetylene and that the 1.24 eV signal results from a triplet-triplet transition, in agreement with previous findings in other PDA single-crystals. The observed laser intensity dependence may in fact indicate the presence of both monomolecular and bimo-lecular decays. This is consistent with excited-states spontaneous relaxation of the triplet exciton and bimolecular annihilation processes of triplet excitons as observed in many organic molecular crystals as well as in PDA-TS single crystal... 

For a theoretical treatment we define a bimolecular annihilation rate constant y [6] and include it in a reaction scheme that accounts for a reversibility of trapping with k and k.- as the rate constants of trapping and detrapping, respectively [5]. The global analysis of ail dependences with one set of parameters (solid lines in Fig. 2) on this basis gives the following values ... 

The exciton interactions are described by an overall bimolecular annihilation rate constant 7 = 7-1 + 2 72 which accounts for the two singlet-singlet reactions ... 

A few free radicals are indefinitely stable. Entries 1, 4, and 6 in Scheme 12.1 are examples. These molecules are just as stable under ordinary conditions of temperature and atmosphere as typical closed-shell molecules. Entry 2 is somewhat less stable to oxygen, although it can exist indefinitely in the absence of oxygen. The structures shown in entries 1, 2, and 4 all permit extensive delocalization of the unpaired electron into aromatic rings. These highly delocalized radicals show no tendency toward dimerization or disproportionation. Radicals that have long lifetimes and are resistant to dimerization or other routes for bimolecular self-annihilation are called stable free radicals. The term inert free radical has been suggested for species such as entry 4, which is unreactive under ordinary conditions and is thermally stable even at 300°C. ... 

Bimolecular reaction between a pair of chain radicals accounts for annihilation of active centers. Two obvious processes by which this may occur are chain coupling (or combination)... 

Therefore, the sequence of reactions illustrated in Fig. 1 catalytically (the anthraquinone is regenerated) injects a radical cation into a DNA oligonucleotide that does not simultaneously contain a radical anion. As a result, the lifetime of this radical cation is determined by its relatively slow bimolecular reaction with H20 (or some other diffusible reagent such as 02- ) and not by a rapid intramolecular charge annihilation reaction. This provides sufficient time for the long distance migration of the radical cation in DNA to occur. 

A nonlinear plot of loge[ecd vs. T indicates that bimolecular processes such as triplet-triplet annihilation or triplet quenching are contributing to triplet state deactivation. 

Transient UV-vis absorption spectra showed that theTi02/Ru(II) films yield prompt electron injection upon photolysis ( >108s 1) These same films displayed photoluminescence decays with parallel first- and second-order components, the first-order component having a rate constant of about lxl06s-1. These two sets of results provide further support for the existence of at least two populations of adsorbed Ru(II), one of which injects electrons rapidly and another which does not inject electrons and is thus capable of luminescing on a longer time scale. The second-order component of the luminescence decay is attributed to bimolecular triplet-triplet annihilation of surface-bound Ru(II). (Note that the second-order rate constants reported for luminescence decay have units of s-1 because they are actually values for k2(Asi))... 

At present it is universally acknowledged that TTA as triplet-triplet energy transfer is caused by exchange interaction of electrons in bimolecular complexes which takes place during molecular diffusion encounters in solution (in gas phase -molecular collisions are examined in crystals - triplet exciton diffusion is the responsible annihilation process (8-10)). No doubt, interaction of molecular partners in a diffusion complex may lead to the change of probabilities of fluorescent state radiative and nonradiative deactivation. Nevertheless, it is normally considered that as a result of TTA the energy of two triplet partners is accumulated in one molecule which emits the ADF (11). Interaction with the second deactivated partner is not taken into account, i.e. it is assumed that the ADF is of monomer nature and its spectrum coincides with the PF spectrum. Apparently the latter may be true when the ADF takes place from Si state the lifetime of which ( Tst 10-8 - 10-9 s) is much longer than the lifetime of diffusion encounter complex ( 10-10 - lO-H s in liquid solutions). As a matter of fact we have not observed considerable ADF and PF spectral difference when Sj metal lo-... 

At some point, the propagating polymer chain stops growing and terminates. Termination with the annihilation of the radical centers occurs by bimolecular reaction between radicals. Two radicals react with each other by combination (coupling) or, more rarely, by... 

Another example of simple bimolecular reaction is mobile exciton annihilation which is well studied in molecular crystals A + A —> 0 (zero means that usually we are not interested what is happening with reaction products) [10]. In this case the kinetic equation is obvious... 

The simplest class of bimolecular reactions involves only one type of mobile particles A and could result either in particle coagulation (coalescence, fusion) A + A —> A, or annihilation, A + A — 0 (inert product). Their simplicity in conjunction with the simple topology of d = 1 allows us to solve the problem exactly, which makes it very attractive for testing different approximations and computer simulations. In the standard chemical kinetics (i.e., mean-field theory, Section 2.1.1) we expect in d = 2 and 3 for both reactions mentioned trivial behaviour quite similar to the A+B — 0 reaction, i.e., tia( ) oc t-1, as t — oo. For d = 1 in terms of the Smoluchowski theory the joint density obeys respectively the equation (4.1.56) with V2 = and D = 2Da. 

These results are complemented by theoretical calculations and computer simulations [110, 111] ford = l,2and3 ofbimoleculartrapping/annihilation reaction A + A—>0, A + T — Ax and A + Ax —> T (T is an immobile trap making A particle to become immobile too) and unimolecular trapping/annihilation, A + A —> 0, A — Ay, A + Ax —> 0. It was found that the kinetics of trapped particles can be described by the mean-field theory for bimolecular but not for unimolecular reactions. The kinetics of free A s is described by mean-field theory at short times, but at long times and low trap concentrations the concentration of free A s decays as (2.1.106). 

Lattice models for four basic kinds of bimolecular reactions, A + B —> 0 and A + A —> 0, (annihilation) A+A —> A (coagulation) and A+B — B (energy transfer) were studied in [40] exploring the utility of using time-power series for determining the critical exponents of the kinetics. The particle concentration is presented in a form... 

The analysis conducted in this Chapter dealing with different theoretical approaches to the kinetics of accumulation of the Frenkel defects in irradiated solids (the bimolecular A + B —> 0 reaction with a permanent particle source) with account taken of many-particle effects has shown that all the theories confirm the effect of low-temperature radiation-stimulated aggregation of similar neutral defects and its substantial influence on the spatial distribution of defects and their concentration at saturation in the region of large radiation doses. The aggregation effect must be taken into account in a quantitative analysis of the experimental curves of the low-temperature kinetics of accumulation of the Frenkel defects in crystals of the most varied nature - from metals to wide-gap insulators it is universal, and does not depend on the micro-mechanism of recombination of dissimilar defects - whether by annihilation of atom-vacancy pairs (in metals) or tunnelling recombination (charge transfer) in insulators. 

Next we introduce the creation and annihilation process for a bimolecular step. In the previous model without energetic interactions discussed in Section 9.1.1 we have had the two-point transition rates K(aian -A Let us... 

A wide range of condensed matter properties including viscosity, ionic conductivity and mass transport belong to the class of thermally activated processes and are treated in terms of diffusion. Its theory seems to be quite well developed now [1-5] and was applied successfully to the study of radiation defects [6-8], dilute alloys and processes in highly defective solids [9-11]. Mobile particles or defects in solids inavoidably interact and thus participate in a series of diffusion-controlled reactions [12-18]. Three basic bimolecular reactions in solids and liquids are dissimilar particle (defect) recombination (annihilation), A + B —> 0 energy transfer from donors A to unsaturable sinks B, A + B —> B and exciton annihilation, A + A —> 0. 

Oxidized and reduced species can be produced when the excimer or exciplex is formed in a polar medium. The excited state-excited state annihilation reaction is another bimolecular process transforming the excited-state energy. An excited state of a higher energy, A in Equation 6.81, or charge separation (Equation 6.82) can be produced in the annihilation process. 

In case of interaction between excitations, exciton-exciton annihilations (or fusion) are the most likely mechanisms to be employed for an energy density dependence of the transient decays. The dynamics is reflected in a Riccatti rate equation including simultaneous monomolecular and bimolecular processes,... 

According to the Smoluchowski theory of diffusion-controlled bimolecular reactions in solutions, this constant decreases with time from its kinetic value, k0 to a stationary (Markovian) value, which is kD under diffusional control. In the contact approximation it is given by Eq. (3.21), but for remote annihilation with the rate Wrr(r) its behavior is qualitatively the same as far as k(t) is defined by Eq. (3.34)... 

It has been known for some time that bimolecular collisions between triplet states in solution leads to quenching of the triplet state by a diffusion controlled process.71 Recently Parker and Hatchard have shown that delayed fluorescence from solutions of compounds such as pyrene, naphthalene, and anthracene, is due to triplet-triplet annihilation, i.e.,... 

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