ISSN:
1089-7690
Source:
AIP Digital Archive
Topics:
Physics
,
Chemistry and Pharmacology
Notes:
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 (approximately-greater-than) 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 cursive-phi1/2(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 δε¯ 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.463908
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