Anti-Smoluchowski time dependence of the delayed fluorescence from anthracene in viscous solution due to triplet-triplet annihilation: Effect of Förster energy transfer S1 + T1 → S0 + Tn on the initial spatial distribution of molecules in T1 Original Rese

The delayed S1 → S0 fluorescence from the first electronically excited singlet state S1 of an aromatic compound in liquid solution is caused by diffusion-controlled triplet-triplet annihilation (TTA) T1 + t1 → S1 + S0. For a random spatial distribution of triplet state molecules at time t = 0, Smoluchowskiʹs theory for a diffusion-controlled reaction predicts a time-dependent rate constant kd(t) of TTA with kd(0) ⪢ kd(∞). If the triplet state is populated by optical excitation S0→S1 and subsequent intersystem crossing S1 → T1, it is principally impossible to generate a random distribution of triplet state molecules. Since the pair S1⋯ T1 is an intermediate during the creation of a triplet pair T1⋯ T1, Förster energy transfer S1 + T1 → S0 + Tn may compete with the generation of T1⋯T1 at short intermolecular distances. As a consequence, one expects an anti-Smoluchowski behavior of TTA with kd(0)⪡kd(∞), or with respect to the intensity of the delayed fluorescence, a strong initial rise. The anti-Smoluchowski behavior of a delayed fluorescence has been observed for the first time (with anthracene in a viscous alkane mixture as solvent). The anti-Smoluchowski behavior can be quantitatively described with a simple kinetic model, which contains only four parameters: the diffusion coefficient of molecules in T1, the Förster radius for the S1-T1 energy transfer, and two parameters specifying an exponential distance dependence of the annihilation rate constant for a triplet pair.