The trapping of excitons by impurities and its dependence on the impurity concentration

When excitons migrate through molecular crystals containing impurities the relative probabilities of their decay at a site of the host lattice or at an impurity can often be deduced experimentally from the material's luminescence spectrum. Theoretically, the mean probability K that an exciton will be captured by an impurity can be calculated by solving a diffusion equation with a term that takes account of the exciton-impurity interaction. The results of such calculations are reported, with particular emphasis on the dependence of K on the impurity concentration c for small values of c. It is found that if the impurities behave as absorbing spheres K is proportional to c, but if the interaction potential is of the multipole-multipole form then d(logK)/d(logc) depends on the exciton's mean free path and on c, and can be much less than unity. The physical reasons for these results are discussed.