Excitonic Funneling in Extended Dendrimers with Non-Linear and Random Potentials

The mean first passage time (MFPT) for photoexcitations diffusion in a funneling potential of artificial tree-like light-harvesting antennae (phenylacetylene dendrimers with generation-dependent segment lengths) is computed. Effects of the non-linearity of the realistic funneling potential and slow random solvent fluctuations considerably slow down the center-bound diffusion beyond a temperature-dependent optimal size. Diffusion on a disordered Cayley tree with a linear potential is investigated analytically. At low temperatures we predict a phase in which the MFPT is dominated by a few paths.Comment: 4 pages, 4 figures, To be published in Phys. Rev. Let

Disorder and Funneling Effects on Exciton Migration in Tree-Like Dendrimers

The center-bound excitonic diffusion on dendrimers subjected to several types of non-homogeneous funneling potentials, is considered. We first study the mean-first passage time (MFPT) for diffusion in a linear potential with different types of correlated and uncorrelated random perturbations. Increasing the funneling force, there is a transition from a phase in which the MFPT grows exponentially with the number of generations $g$, to one in which it does so linearly. Overall the disorder slows down the diffusion, but the effect is much more pronounced in the exponential compared to the linear phase. When the disorder gives rise to uncorrelated random forces there is, in addition, a transition as the temperature $T$ is lowered. This is a transition from a high-$T$ regime in which all paths contribute to the MFPT to a low-$T$ regime in which only a few of them do. We further explore the funneling within a realistic non-linear potential for extended dendrimers in which the dependence of the lowest excitonic energy level on the segment length was derived using the Time-Dependent Hatree-Fock approximation. Under this potential the MFPT grows initially linearly with $g$ but crosses-over, beyond a molecular-specific and $T$-dependent optimal size, to an exponential increase. Finally we consider geometrical disorder in the form of a small concentration of long connections as in the {\it small world} model. Beyond a critical concentration of connections the MFPT decreases significantly and it changes to a power-law or to a logarithmic scaling with $g$, depending on the strength of the funneling force.Comment: 13 pages, 9 figure