Triplet—Triplet Annihilation and Delayed Fluorescence in Molecular Aggregates

This paper deals with triplet—triplet annihilation in pure and mixed organic crystals. In crystals containing a small concentration of impurity traps, triplet excitation migration may proceed from trap to trap on a time scale which is short compared with the long triplet state lifetime but which is long compared with the normal fluorescence lifetime. Nearest-neighbor and long-range mutual annihilation of two triplets may then take place giving rise to delayed fluorescence. The rates of long-range triplet excitation migration and annihilation show a concentration dependence, a temperature dependence, and a solvent dependence. Providing the triplet—triplet annihilation rate is not too fast, the intensity of the delayed fluorescence can be shown to depend upon the square of the intensity of the exciting light. This expectation is borne out by experiments, briefly reported here, on delayed fluorescence in dilute isotopic mixed crystals. In crystals containing high concentrations of such impurity traps, or in pure crystals, the annihilation rate becomes extremely rapid and this mechanism effectively quenches phosphorescence in many, but not all, classes of pure organic crystals. The kinetics of the over-all process are discussed in both the limits of fast and slow annihilation rates. A theoretical investigation of the origin of the annihilation matrix element is carried out, and it is shown that exchange interactions play the largest role in determining annihilation rates. Past work [H. Sponer, Y. Kanda, and L. A. Blackwell, J. Chem. Phys. 29, 721 (1958); N. W. Blake and D. S. McClure, ibid., p. 722] on delayed fluorescence of assumed pure naphthalene crystals containing very small amounts of β-methyl naphthalene (traps) can be understood within the framework of this paper. The need in organic crystals for the major delayed fluorescence mechanism to be based upon ionization and electron trapping seems now to be considerably lessened.