Primary Photonic Processes in Energy Harvesting: Quantum Dynamical Analysis of Exciton Energy Transfer over Three-Dimens
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Primary Photonic Processes in Energy Harvesting: Quantum Dynamical Analysis of Exciton Energy Transfer over Three-Dimensional Dendrimeric Geometries David L. Andrews and Garth A. Jones School of Chemistry, University of East Anglia, Norwich NR4 7TJ, U.K. ABSTRACT In molecular solar energy harvesting systems, quantum mechanical features may be apparent in the physical processes involved in the acquisition and migration of photon energy. With a sharply declining distance-dependence in transfer efficiency, the excitation energy generally takes a large number of steps en route to the site of its utilization; quantum features are rapidly dissipated in an essentially stochastic process. In the case of engineered dendrimeric polymers, each such step usually takes the form of an inward hop between chromophores in neighboring generation shells. A physically intuitive, structure-determined adjacency matrix formulation of the energy flow affords insights into the key harvesting and inward funneling processes. A numerical method based on this analytic approach has now been developed and is able to deliver results on significantly larger dendrimeric polymers, with the help of large multi-processor computers. Central to this study is the interpretation of key features such as the relevance of a spectroscopic gradient and the presence of traps or irregularities due to conformational changes and folding. With the objective of fine-tune the funneling process, this model now allows the incorporation of parameters derived from quantum chemical calculations, affording new insights into the detailed operation of the harvesting process in a variety of dendrimer systems. INTRODUCTION The technology of energy harvesting materials is experiencing dramatic growth in the development of molecular materials designed to emulate some of the organizational and mechanistic principles that operate in photosynthetic systems.1-6 Dendrimers are repeatedly branched nanoscale polymers, also known as nanostars or functional cascade molecules5-16, whose quasi-fractal geometry and large number of chemically similar chromophores built around a core approach an ideal type of structure for solar energy harvesting, expediting highly efficient, ultrafast energy transport10,16. In any such dendrimer the synthetic route generally builds outwards through successive generations, each further expanded to form a new outer shell by peripheral functionalization with additional groups. The resulting proliferation of chromophores on the outermost shell supports a high photon capture efficiency, though the associated generation-dependence in the distribution of inter-chromophore distances can reduce the efficiency of energy transfer.18 A typical example of a dendrimer is shown in Fig. 1 (though this and similar representations should be viewed with a caveat: such commonplace planar depictions misrepresent the three-dimensional folding that increasingly takes place with successive generations). In ideal cases a spectroscopic gradient that is directed towards the core assist
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