Yokota and Tanimoto

Elkana et al. [138], Steinberg [139], and Yokota and Tanimoto [140]), with specific attention given to dipole—dipole transfer of energy. These theories will be considered in more detail in the following subsections. 

Yokota and Tanimoto [140] have developed this procedure and from their compact Pade approximant formulae, the rate coefficient is given by... 

This is a much more severe condition than those discussed by Yokota and Tanimoto [140] or by Birks [6]. In the rate coefficient equation (83), x has an upper bound of (t/r0)2/3/10, which practically means thatx < 0.1, since for times longer than t r0 natural decay of the donor masks any long-range transfer effects. The term in square brackets and raised to the three quarter power in eqn. (83) is 1.15 for x 0.1. Consequently, the Yokota and Tanimoto [140] expression is only strictly valid under circumstances where it differs from the Forster [12] expression [that is where D = 0 in eqn. (83)] by little more than likely experimental errors The decay law of excited donor molecules concentration [D ], is... 

It is not unreasonable that the steady-state rate coefficient [eqn. (80)] and the time-independent component of Yokota and Tanimoto s [140] rate coefficient expression (83) do not agree very well. Perhaps the similarity might be described as surprising ... 

If the donor and acceptor molecules are unable to rotate in the solvent during the donor fluorescence time, the value of R0 considered above is too large. Steinberg [139] has analysed Forster kinetics in this limit. Allinger and Blumen [153] have developed a more detailed analysis of dipole—dipole energy transfer from excited donors to acceptors in liquids and obtained essentially similar results to those of Yokota and Tanimoto. 

Yokota and Tanimoto O have solved Eq. (59) for the special case of weak diffusion and strong host-activator interaction. They used an operator expansion and Fade approximant technique to obtain... 

The efficiency remains high. For both compounds a diffusion coefficient of 10 —10 i2 cm s has been found applying Yokota and Tanimoto s theory ). 

Yokota and Tanimoto (39) have worked out the expected fluorescence decay when both quenching and diffusion are active and the diffusion is not fast enough to maintain the initial distribution of excitation. In such a case the decay function of the excited sensitizers is given by (39)... 

At shorter times, the Yokota and Tanimoto [140] expression is valid for larger diffusion coefficients (e.g. at t Tq/IO, D quasi-static transfer could be described by eqns. (83) and (85), but only for times [Pg.84]

Energy transfer in the case of interaction between donor ions The diffusion of energy in the donor-system ion occurs in concentrated systems and is of the same magnitude as the transfer between donors and acceptors. The general case of diffusion in the donor system has been treated by Yokota and Tanimoto (1967). When energy transfer occurs by a dipole-dipole mechanism, their equation takes the form under uniform distribution... 

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