Transport of optical excitations on dendrimers in the continuum approximation

We study the incoherent transport of optical excitations created at the rim of a dendritic molecule to a trap occurring at the core. The corresponding discrete random walk is treated in a continuum approximation, resulting in a diffusion-like process which admits semi-analytical solutions. The thus obtained arrival time distribution for the excitation at the trap is compared with the one for the original, discrete problem. In the case of an inward bias or even a weak outward one, the agreement is very good and the continuum approximation provides a good alternative description of the energy transfer process, even for small dendrimers. In the case of a strong outward bias, the mean trapping time, which sets the time scale for the entire distribution, depends exponentially on the number of generations in both approaches, but with a different base. The failure of the continuum approximation for this case is explained from the peaked behavior of the excitation density near the rim.