Monomolecular decay

Fig. 28. Potential energy for the nuclear motion along the reaction coordinate, (a) A monomolecular decay with the formation of radicals (b) a monomolecular decay with the formation of molecules with the paired electrons (E ) = n0a>, = n uj) (c) a monomolecular isomerization...

If monomolecular decay of the donor particles with the rate constant k is possible along with tunneling decay by the reaction with the acceptor particles, the following expression describes the change of the concentration of the donor particles with time... 

Depending on the kinetics of the excited state, the changes in AT as a function of the pump beam intensity I, when fitted to a power law equation —AT oc Ip, are indicative of the recombination mechanism of the species. For values of p close to unity, monomolecular decay of the excited species is assumed, whilst for p 0.5, a bimolecular decay mechanism is supposed. Excited state lifetimes can be determined by fitting the changes in transmission as a function of the modulation frequency lj to either the expression (1.12) for monomolecular decay or (1.13) for bimolecular decay [108] ... 

Here rm is the lifetime for monomolecular decay and g the efficiency of generation of the photoinduced species. The bimolecular decay constant (3 determines the intensity of the PIA signal via (1.13), where a = n/uTb and Tb — (gI/3) 05, the bimolecular lifetime under steady-state conditions. It is important to note that the bimolecular lifetime T > depends on experimental conditions such as concentration and pump beam intensity. 

The MP-CfioC i) state formed via the intramolecular singlet-energy transfer in the OPVn Cgo dyads is expected to decay predominantly via intersys-tem crossing to the MP-Cfjo(Ti) state, apart from some radiative decay. Consistent with this expectation, the PIA spectrum recorded for all four dyads in toluene solution shows the characteristic MP Cf,o T <— Tn absorption at 1.78 eV with a shoulder at 1.54 eV (Fig. 1.28a). The PIA bands increase in a near-linear fashion with the excitation intensity (—AT oc Ip, p = 0.80-1.00) consistent with a monomolecular decay mechanism. The lifetime of the triplet state lies in the range 140-280 ps. 

AT/T above 2 eV is an artefact caused by this correction. A monomolecular decay mechanism is inferred from the intensity dependence of the 1.80 eV PIA band (-AT oc Ip, p — 0.89-0.92). A lifetime of around 200 (is was determined by varying the modulation frequency between 30 and 3800 Hz. 

Consistently, the PIA spectra of toluene solutions containing MP-Ceo and OPVn (n = 2, 3 or 4) in a 1 1 molar ratio, recorded using selective photoexcitation of MP C60 at 528 nm (Fig. 1.28b), invariably exhibit an absorption at 1.78 eV with an associated shoulder at 1.54 eV, characteristic of MP-C6o(7i) [103]. The monomolecular decay (—AT oc Ip, p = 0.89-0.96) with lifetime 150-260 ps associated with these PIA bands supports this assignment. Furthermore, weak fullerene fluorescence at 1.73 eV (715 nm) is observed under these conditions for all three mixtures. No characteristic PIA bands of OP Vw+ radical cations or MP-Cg0 radical anions are discernible under these conditions. From these observations we conclude that electron transfer from the ground state of the OPVn molecules to the singlet or triplet excited state of MP-Cgo does not occur in toluene solution. 

Figure 38 Relative increase in the monomolecular decay rate constant (A/ // t) (decrease in the lifetime) of triplet excitons in three different anthracene crystals under the positive voltage applied to two different hole injecting electrodes Cul (a) and anthracene positive ions (A+) in nitromethane (b). jSt = t 1 is the triplet decay rate constant with no voltage jh = 239 s-1 for the d = 350 pm-thick crystal, / t = 175s 1 for anthracene with d = 625 pm (from Ref. 243) / t = 200s 1 for the d = 320 pm-thick crystal, A+ injecting contact (see Ref. 238). In the right-top scale in part (b) the Aji/U vs. j/U2 is presented (points) to be compared with Eq. (115) (solid line).

Figure 147 The relative cascade-like pattern of the increase of triplet exciton monomolecular decay rate constant (/ = t 1) as a function of charge-injecting voltage in anthracene crystal. Consecutive trap-filled limits are indicated by C/TFL (1), /TFL(2) and C/TFL (3). Dotted line indicates the averaged (linear) dependence of A/ // 0 as resulted from the standard interpretation assuming a continuous increase in the charge density proportional to the injecting voltage [334]. Adapted from Ref. 240.

In order to arrive at meaningful (exponential) decay rates in such experiments, non-linear triplet quenching by diffusion, has to be avoided. For example, the initial accelerated decay in Fig. 7 is caused by bimolecular triplet-triplet annihilation dominating the decay of the triplets. Similarly, a faster decay is observed at higher temperature, where triplet exciton diffusion to quenching sites is faster than monomolecular decay. Nevertheless, by using low temperatures and low excitation doses exponential decay kinetics are observed yielding radiative decay rates as low as 1 s x, which sets an upper limit for the triplet excited state lifetime [28,34],... 

At low temperature, it is reasonable to neglect radiative and non-radiative monomolecular decay and to assume that annihilation is the dominating decay mechanism for the triplets in the time domain much shorter than the triplet lifetime, i.e. for t < 100 ms ... 

For low excitation conditions, i. e. where the monomolecular decay prevails 7tta[ ]2<< / o[T ]> time dependence of the phosphorescence intensity derived from Eq. (16) is ... 

From Eq. (3.19) it is apparent that the DF intensity varies quadratically with the triplet concentration and hence with excitation light intensity as long as the singlet state is deactivated by monomolecular decay. The DF intensity decays exponentially with a lifetime half of the phosphorescence lifetime rphos. 

Studies of intramolecular ET in oxidases provide interesting examples of how pulse radiolysis is employed to obtain insights into both (1) these enzymes respective mechanisms of action and (2) electron transfer along protein polypeptide matrices that were most probably selected by evolution (9,10, 30-32). Thus, early attempts to study the electron uptake mechanism by the blue oxidase, ceruloplasmin, showed that a diffusion-controlled decay process of the eaq in solutions of this protein is paralleled by the formation of transient optical absorptions due to electron adducts of protein residues, primarily of cystine disulfide bonds (30). The monomolecular decay of the latter absorption was found to have the same rate constant as that at which the type 1 Cu(II) absorption band was reduced. These results were interpreted as being the combined result of the high reactivity of the e q and the relatively inaccessible type 1 Cu(II) site, yielding an indirect, intramolecular electron transfer pathway from surface-exposed residues (30). 

Pulse radiolysis of some scavenger solutions in water, intermediates spectra, and kinetics of their decay in liquid ammonia are investigated. Rate constant and activation energy are calculated for the latter. The dependence of the disappearance of intermediates on concentration is analyzed. It is shown that rate constant of reactions of pseudo-first order is not proportional to acceptors concentration. One of the possible reasons is that first order reaction was not taken into consideration. On this basis, rate constants of reactions with acceptors and these of monomolecular decay are calculated. It is revealed the decay of intermediates in 10 5-10 3M perchloric acid solutions does not depend upon HsO+ ion concentration. This fact is contrary to the present day theories about the nature of intermediates. 

The experimental results in aqueous and ammonium solutions show that the process of intermediates decay in the presence of acceptors follows a first-order law. However, a proportionality between the calculated rate constant of the pseudo-first order reaction and the concentration is not observed. Under these conditions no influence of dose rate on the kinetics of intermediates decay is found, so recombination interactions play a rather small role. By kinetic treatment of the results, satisfactory agreement with experimental data can be obtained by supposing that the intermediates disappear in a monomolecular decay which simultaneously proceeds with scavenger reactions. 

In this expression, c = yy Fjf/Ytotj This limiting case was observed for anthracene in about the first 4 ms after the end of the excitation [48]. In the further course of the decay of the triplet excitons, the relative fraction of the bimolecular decay continues to decrease until the limit of long times is reached, in which the monomolecular decay predominates (fer[Ti > ot [Ti] ). The solution of Eq. (6.30) is then given by [Ti] = [Ti]ooe r . With this and Eq. (6.33b), the decay of the delayed fluorescence in the hmit of very small triplet exciton concentration, i.e. in the later part of the decay curve, is found to be... 

The observed behaviour of the PA signals at 0.80 eV and at 0.95 eV (which is probably the vibronic satellite of the 0.80 eV peak) is in agreement with the predictions for bipolarons. On the contrary, the chopper frequency dependence of the 1.24 eV band is consistent with the photogeneration of a defect with lifetime values of the order of ms at 20K and substantially lower at 77K. The laser intensity dependence rules out the photocreation of defects with a simple monomolecular decay. On the other hand, this signal cannot be attributed to the photocreation of polarons and bipolarons, which are expected to recombine bimolecularly. ... 

The lifetime derived fi om the best fit to this equation is 175 ms. This specific evidence of monomolecular decay behavior is indicative of an excitation with a well-defined lifetime in contrast to the power law dependence of n(co) typically found for trapped. 

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