Effect of Temperature on the Triplet–Triplet Annihilation Rate in Anthracene Crystals

Abstract

Jortner, Rice, Katz and Choi have recently shown that triplet–triplet annihilation leading to delayed fluorescence in crystalline anthracene can be adequately described in terms of a random walk diffusion model when the effects of charge transfer interactions are included¹. This model is valid if the scattering of the triplet excitation wave by lattice phonons is so strong that the mean free path of the triplet exciton is of the same order of magnitude as the crystal lattice spacing. On the basis of the random walk model the triplet–triplet interaction rate constant (γ) is given by where D is the triplet excitation diffusion constant and R is the triplet–triplet interaction distance, taken to be 10⁻⁷ cm for crystalline anthracene². The value of γ calculated by Jortner et al. for anthracene is 4 × 10⁻¹¹/cm³/sec, and is in good agreement with the experimental values² which range from 1 × 10⁻¹¹ to 5 × 10⁻¹¹/cm³/sec. (Moore and Munro³ have recently reported γ = 2.1 × 10⁻¹¹/cm³/sec for a carefully purified anthracene crystal.) The value of D calculated using equation (1) is 30 × 10⁻⁶/cm²/sec which shows quite good agreement with the value of 6 × 10⁻⁶/cm²/sec obtained by King and Voltz². (In calculating the value of D, Jortner et al.¹ assume a pure anthracene crystal; King and Voltz², however, analysed the slow scintillation component obtained from anthracene crystals of commercial grade. They suggest that the ionizing radiation may perturb the crystal lattice, thus giving a value of D which may be different from diffusion in the perfect lattice.)