ANTI-SMOLUCHOWSKI TIME-DEPENDENCE OF THE DELAYED FLUORESCENCE FROM ANTHRACENE IN VISCOUS SOLUTION DUE TO TRIPLET-TRIPLET ANNIHILATION - EFFECT OF FORSTER ENERGY-TRANSFER S(1)-]S(0)+T(N) ON THE INITIAL SPATIAL-DISTRIBUTION OF MOLECULES IN T(1)(T(1))

The delayed S1 --> S0 fluorescence from the first electronically excit ed singlet state S1 of an aromatic compound in liquid solution is caus ed by diffusion-controlled triplet-triplet annihilation (TTA) T1 + T1 --> S1 + S0. For a random spatial distribution of triplet state molecu les at time t = 0, Smoluchowski's theory for a diffusion-controlled re action predicts a time-dependent rate constant k(d)(t) of TTA with k(d )(0) must-greater-than k(d)(infinity). If the triplet state is populat ed by optical excitation S0 --> S1 and subsequent intersystem crossing S1 --> T1, it is principally impossible to generate a random distribu tion of triplet state molecules. Since the pair S1 ... T1 is an interm ediate during the creation of a triplet pair T1 ... T1, Forster energy transfer S1 + T1 --> S0 + T(n) may compete with the generation of T1 ... T1 at short intermolecular distances. As a consequence, one expect s an anti-Smoluchowski behavior of TTA with k(d)(0) much-less-than k(d )(infinity), or with respect to the intensity of the delayed fluoresce nce, a strong initial rise. The anti-Smoluchowski behavior of a delaye d fluorescence has been observed for the first time (with anthracene i n a viscous alkane mixture as solvent). The anti-Smoluchowski behavior can be quantitatively described with a simple kinetic model, which co ntains only four parameters: the diffusion coefficient of molecules in T1, the Forster radius for the S1-T1 energy transfer, and two paramet ers specifying an exponential distance dependence of the annihilation rate constant for a triplet pair.