“Discrete shell model” for analysing time-resolved energy transfer in solids

We present a new mathematical method to describe the time-resolved fluorescence response of donors and acceptors for the case of energy transfer in crystals, taking into account energy diffusion within the donor system, direct donor-acceptor transfer with any arbitrary dependence of the transfer probability on distance, and the discrete crystal structure. For the first time we give the fluorescence responses for elevated temperatures including transfer of optical excitation energy from the acceptors back to the donors. Furthermore, the competition between neighbouring acceptors (excitation sinks), important for most real acceptor concentrations, is taken into account. The fluorescence responses of donors and acceptors to four commonly realized excitation conditions are given explicitly to any desired degree of precision as sums of exponential functions; they are based on the numerical solution of an eigenproblem. The method is designed to be used in computer analysis of time-resolved fluorescence data.