Excitonic Funneling in Extended Dendrimers with Nonlinear and Random Potentials

Abstract

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.Dendrimers constitute a new class of nanomaterials with unusual tree-like geometry and interesting chemical, transport, and optical properties [1][2][3][4][5]. Two families of Phenylacetylene dendrimers have received considerable recent attention. In the compact family, the length of the linear segments is fixed, whereas in the extended family it increases towards the center creating an energy funnel in that direction (Fig. 1). This latter family may, therefore, serve as artificial light-harvesting antennas, as has been demonstrated experimentally [6]. It has been conjectured by Kopelman et. al., based on optical absorption spectra [1], that electronic excitations in these dendrimers are localized on the linear segments. This has been confirmed in theoretical studies which showed that the relative motion of photogenerated electron-hole pairs is confined to the various segments and energy-transfer may then be described by the Frenkel exciton model. The time it takes for an excitation that starts at the periphery to reach the center, and its dependence on the molecular size (number of generations g) and the funneling force, were calculated. The latter results from the interplay of entropic (or geometric, i.e. the branching ratio c = 2) and energetic factors [7].These pioneering studies, however, assumed the funneling force to be constant since the energy ǫ(n) varied linearly with n. (n=1,2,. . . ,g is the generation number, at which the segment length is l = g − n + 1 monomers. See Fig. 1.) In addition, ε(n) were assumed to be fixed. In reality, interactions with other degrees of freedom (solvent and intramolecular vibrations), induce fluctuations in ε(n) which may span many different timescales. Here we consider slow (quenched) fluctuations compared with the exciton trapping times which are typically in the picosecond range [6,8]. Nonlinear [9] and single molecule [10] spectroscopy in liquids, glasses and proteins typically show nanosecond to millisecond bath motions responsible for spectral diffusion. Slow vibrational motions that can be treated as static disorder dominate the photoinduced energy transfer dynamics of photosynthetic antenna complexes [11]. Fast (annealed) fluctuations do not change the behavior qualitatively. In addition, we explore different degrees of correlations among the various energy fluctuations. In the absence of correlations, we obtain the standard diagonal disorder (random energy) model. If the e...

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“…Of particular interest in this study is their use as light-harvesting complexes and artificial antennae in the context of energy storage and transfer [1,2,3,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37].…”