Effect of molecular reorientation on excitation decay due to incoherent energy transfer

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Abstract
A complete study is presented of the excitation decay ρ(t) due to incoherent energy transfer in a system of randomly distributed donor molecules, following a flash excitation at t=0. In particular the dipole–dipole interaction is considered, which causes the well‐known anisotropic Förster transfer, and thus makes the transfer process sensitive to molecular reorientations. The general case of a finite reorientation time scale τa and an arbitrary orientational distribution is considered here, from which the static and dynamic limits are obtained as limiting cases for τa →∞ and τa →0, respectively, for arbitrary degree of orientational order. In the isotropic case, these reduce to well‐known results. In our approximation the influence of reorientational motion on log ρ(t) can be fully contained in a time dependent factor g(t/τa). From a general expression, g(t/τa) is evaluated for the isotropic case by numerical techniques for different models of reorientation, viz. reorientation through large uncorrelated steps and diffusion type reorientation. By means of a rigorous scaling procedure of t, based on the exact expression of g(t/τa) for small t/τa, it is shown, that in principle, experimental determination of g(t) can be used to estimate τa and determine the amount of diffusive behavior in the reorientational motion.