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Resonance energy transfer (RET), both radiative and nonradiative, is a well-known process in the molecular fluorescence field. On the other hand, RET has been much less explored in connection with phosphorescent systems. We have recently studied in detail phosphorescence reabsorption (radiative transfer) of polycyclic aromatic hydrocarbons in the presence of excited-state absorption. In this case, reabsorption of phosphorescence results from triplet-triplet (T-T) absorption overlapping the emission spectrum, i.e. Tn ← T1 radiative transitions, and not from absorption by ground state molecules, owing to the forbidden nature of the Tn←S0 radiative transitions. In this way, all absorbing molecules are already in the T1 state, and are generated in the first place by the external source, whose intensity and spatial distribution completely determines the set of allowed sites for excitation diffusion. The excitation moves from one triplet, that returns to the ground state, to another, that undergoes the fast sequence T1→Tn→T1 and thus remains unchanged, hence the elementary process for radiative transfer is T1 + T1 → S0 + T1. The process may take place a number of times. In this mechanism there is no radiation imprisonment, only a peculiar type of inner filter effect, as the emitted photon is lost and does not reach the detector. Unlike the fluorescence reabsorption process, phosphorescence reabsorption depends significantly on the excitation intensity, which determines the number and spatial distribution of triplets. Furthermore, the reabsorption probability is time-dependent, as the T-T absorption contribution to the optical thickness of the medium continuously decreases with time, after excitation cut-off: For sufficiently long times, the phosphorescence absorption probability is negligible, and the decay becomes exponential. However, for shorter times the decay has a distinctive form, displaying an initial concavity when reabsorption is significant [3,4]. For sufficiently high concentrations (typically around 0.01 M), nonradiative transfer of the type T1 + T1 → S0 + Tn (the final triplet state after relaxation being T1) by the dipole-dipole mechanism can also occur. Here, the phosphorescence decay is affected owing to an increase of the nonradiative decay rate. This process is sometimes called long-range triplet-triplet annihilation. For even higher concentrations (typically around 0.1 M) a significant fraction of molecules is so close that the exchange interaction is now operative. In this way, for high excitation intensities short-range triplet-triplet annihilation, T1 + T1 → S0 + S1, eventually preceded by triplet energy migration, T1 + S0 → S0 + T1, comes into play. The phosphorescence decay is again affected and delayed fluorescence may be observed. In this work, we discuss radiative and nonradiative transfer of energy owing to triplet-triplet absorption, including the effect of dimensionality.
[1] D. L. Andrews and A. A. Demidov eds., Resonance Energy Transfer, Wiley, Chichester, 1999.
[2] B. Valeur and M. N. Berberan-Santos, Molecular Fluorescence. Principles and Applications, Wiley-VCH, Weinheim, 2nd ed., 2012.
[3] T. Palmeira, M. N. Berberan-Santos, J. Lumin. 158 (2015) 510-518.
[4] T. Palmeira, A. Fedorov, M. N. Berberan-Santos, ChemPhysChem 16 (2015) 640-648.
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