Electronic excited state transport and trapping as a probe of intramolecular polymer structure

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Abstract
A theory is presented for the incoherent transport and trapping of electronic excitations among chromophores attached to two specific sites on a macromolecule, such as the ends of a polymer chain. Two problems are considered: (a) the donor and trap chromophores are randomly distributed on the sites; (b) each macromolecule has exactly one donor and one trap chromophore. The formalism includes the possibility of a statistical distribution of intersite distances within the macromolecule, and allows transport between chromophores on different molecules, as well as intramolecular transport and trapping processes. In the dilute limit (isolated macromolecules) the theory is exact, and for large intramolecular site separations or high densities the self‐consistent formalism of Loring, Andersen, and Fayer is recovered. The theory can be applied to any transfer rate, any distribution of intramolecular intersite distances and transition moments, and is well behaved at all polymer densities and site occupancy probabilities. Sample calculations are performed for the Förster rate and a Gaussian distribution of distances between sites on the same molecule. The theory will allow fluorescence depolarization and trap fluorescence experiments to be used as a probe of the distribution of end to end distance for end‐tagged polymer chains in viscous solution, or in solid noncrystalline materials. Applications to structural studies in biological systems are likely.