Application of Smoluchowski's generalized theory to the kinetics of triplet-triplet annihilation of anthracene in viscous solution after long-pulse excitation

The validity of Smoluchowski's theory is demonstrated by its application to the bimolecular triplet-triplet annihilation (TTA) T₁ + T ₁ → S₀ + S¹ in viscous solution. For that purpose the delayed S₁ → S₀ fluorescence of anthracene in cis-1,3-dimethylcyclohexane/trans-1,4-dimethylcyclohexane (1:1) was measured after UV excitation with long laser pulses (∼30 μs) in a temperature range where TTA is completely diffusion controlled. Through the adequate treatment of the kinetics of TTA upon spatially homogeneous and spatially periodic excitation (which is partially based on the results of previous publications) absolute values for the diffusion coefficients D of triplet molecules, for the effective annihilation distance R_A and for the Förster radius R_ST of heterogeneous annihilation S ₁ + T₁ → S₀ + T_n were determined. The temperature dependence of all three parameters (D, R_A and R_ST) is discussed. From the decrease of R_A with increasing temperature, the parameters A and L can be determined, which define the exponential distance dependence of the annihilation of a triplet pair in the kinetic model of Butler and Pilling (1977). Differences of the two models and applicability criteria are discussed.