Direct electronic energy transfer in the presence of static site-energy disorder–dipolar couplinga)

Abstract

The single-step energy transfer between randomly distributed donors and acceptors has been analyzed in the presence of static site-energy disorder. Exact expressions for the donor survival probability have been formulated with jump-frequencies that depend on both spatial and energy-coordinates. By using the factorization approximation and the continuum limit the procedure yields, for multipolar interaction, approximate, closed-form solutions of the Kohlrausch–Williams–Watts (KWW) functional form with a generalized energy-function λε ≳ 1, which influences the time-scale of the KWW-decay but does not affect the exponent α. For dipolar coupling and 3D transfer (α=1/2), both the energy-specific f(t;ε) and the energy-averaged donor relaxation 〈 f 〉 (t) have been Laplace inverted to yield the distributions of transition frequencies φ1/2(ν;ε) and Φ1/2(ν), respectively. The analysis of λε containing the energy-dependence of transition frequencies and the energetic spread of sites has been performed on the premises of a balance-equation for uphill processes and a Gaussian density-of-states function for the site-energy fluctuation. This allows the time and frequency-domain analogs of donor relaxation to be discussed as a function of the initial energy of excitation ε, the energetic width of fluctuating sites σ, and the energy gap δε̄ between the mean values of donor and acceptor distribution. The functional dependences of energy-specific responses, i.e., the characteristic deceleration of the KWW-profiles and the log frequency-shift of the corresponding frequency spectra as well as the pronounced deviation that may occur for broad-band excitation have been investigated in detail. Finally, the circumstances under which such relaxations are leading to the ordinary KWW-law (λε = 1) have been discussed by considering the exact limiting procedures.