Excitonic annihilation processes

The femtosecond fluorescence up-conversion setup has been described elsewhere [13,14]. Briefly, a second harmonic (SH) of a home-made chromium-forsterite femtosecond laser tunable from 610 to 660 nm was used to excite the sample (Fig.2) [14]. The pulse duration of the SH pulses was about 50 fs at the full width at half maximum (FWHM). We were successful in the cavity-dumping operation of this laser [14] and kept the repetition rate as low as 4 MHz. Reduction of the repetition rate was necessary to avoid multiple hits of the same location of the sample as small as possible. The excitation intensity, controlled by a neutral density filter before the sample cell, was (0.5-l)xl012 photons/cm2/pulse. Special care was taken to work at the lowest excitation light intensity so that the effect of the exciton-exciton annihilation process was negligible. 

Webber and Swenberg (82) worked out a master equation theory for excitonic annihilation processes in low dimensional, finite lattices. This theory seems to describe well the process for polymers with few or shallow traps, as P2VN, but not for those containing many relatively deep traps, as PVCA. Finally, a list of those features which at the present time prevent a full understanding of T-T annihilation in dilute, solid solutions of aromatic polymers... 

With a sufliciently high total energy, this process can even cause the ejection of an electron from the crystal that is, the exciton annihilation leads to ionisation. In the case of anthracene, the ionisation limit of 5.75 eV lies lower than twice the Si energy, 2x3.15 = 6.30 eV. Measurement of the kinetic energy of the emitted photoelectrons permits the verification of the fusion process. In general, the fusion of two excitons allows higher excited states to be reached with smaller energy quanta. Table 6.4 contains numerical values of the rate constants for exciton annihilation processes. 

Of course, at high concentration, energy migration is also involved and one can view cross-relaxation as an exciton annihilation process. Because of the rrqrid multiphonon non-radiative relaxation between levels above p3/2, the most likely energy path for diffusion... 

One inevitable problem associated with the construction of artificial light harvesting complexes concerns energy dissipation via exciton annihilation processes. These reactions, which plague the natural organisms at high illumination intensities, compete with photon migration to the reaction center... 

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-... 

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. 

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,... 

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],... 

In addition to surface-enhanced exciton dissociation and geminate recombination, direct photoexcitation (Northrop and Simpson, 1956 Heilmeier et al., 1963 Harima et al., 1989) and exciton-exciton annihilation (Silver et al., 1963 Jortner et al., 1963 Braun, 1968 Johnston and Lyons, 1968 Foumy et al., 1968 Swenberg, 1969 Braun and Dobbs, 1970 Orlowski and Scher, 1983) arguments have been proposed. In direct photoexcitation, a free electron and free hole are created without the involvement of intermediate states. With the exception of the work of Harima et al. and Orlowski and Scher, there have been few references to direct or exciton-exciton photogeneration processes in the past one and a half decades. 

These results are strong evidence that excitons in polysilanes are highly mobile. The exciton concentration when the rate of loss by exciton-exciton annihilation equals the rate of loss by other nonannihilation processes can be determined by setting (3n = yn to give n = (3/y 10 excitons per cubic centimeter. At this concentration, the excitons are, on the average, about 400 A apart. 

Finally, because poly silanes show promise as photoresists (25, 26) and nonlinear optical materials (27), the fact that the rate of loss of excitons in poly(n-propylmethylsilane) by exciton-exciton annihilation becomes equal to the monomolecular loss rate at laser intensities of only 10 J/cm in a 5-ns pulse is significant. Because exposure levels are typically much higher for photoresist and nonlinear optical studies, exciton-exciton annihilation must be considered when attempting to understand the underlying photochemical reactions, because annihilation may dominate other photophysical and photochemical processes. 

A triplet exciton annihilation mechanism has been proposed for charge generation in molecularly doped polymers initiated with very fast, high-intensity, excitation [25b,c]. In this mechanism it is proposed that both charge separation, associated with the Onsager model, and the fusion process are very strongly field-dependent. This model has not been invoked in recent years. 

Excitons can, as we have seen in Sect. 6.9.2, react with one another and also with other excitation states. The most important processes are exciton annihilation or fusion and exciton splitting or fission. The annihilation of two triplet excitons, which leads to delayed fluorescence, takes place more precisely via the alternate reaction mechanism... 

If/represents the fraction of triplet-triplet annihilation processes which lead to singlet excitons - compare the reactions (6.29) - then for the time dependence of the singlet exciton density [Si], we find ... 

---