RET in the Rapid-Diffusion Limit

The theory for en gy transfer in restricted geometries is obviously complex. Hence, one may question how we can consider the further complications of combining restricted geometries with D-A difriision. In fact, such theory has not yet appeared in the literature. Howev. if the donor decay time is very long, then one reaches the rapid-diffusion limit/ whCTe the theory once again becomes relatively simple. 

TaUe 15.2. Numerkal Parameters ta Calculate the Relative Donor Quantum Yidds in Mnnbranes  

If the donor lifetime is near I its, then the transfra efficiency becomes sensitive to diffiision. Such decay tames are available using transition-metal-Ugand complexes, as described in Chapter 20 As the donor lifetime becomes longer, 1 ms-1 s, die transfer efficiency reaches an uppo-limit. This is the lapid-diffiision limit, which can be reached for diffusion coefficients exceeding 10 cmVs if the donmr lifetimes are on the millisecond timescale. 

Sudi decay times are found in die landianides sudi as europium and terbium, which diq Iay lifetimes near 2 ms. 

Because ol diffiisive averaging, it is relatively simple to calculate predicted values of kr- The precise form ol kr depends on the geometric model. Many such models have been described in detail. For sphoical donors and acceptors, the diffiision-limited valueof iris given by  

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