RET in ensembles of donors and acceptors

We have considered so far the energy transfer from a donor to a single acceptor. Extension to ensembles of donor and acceptor molecules distributed at random in an infinite volume will now be considered, paying special attention to the viscosity of the medium. Then, the effect of dimensionality and restricted geometry will be examined. Homotransfer among the donors or among the acceptors will be assumed to be negligible. 

The viscosity of the medium plays an important role in the dynamics of energy transfer because the mean distance diffused by the donor and acceptor relative to 

D is the mutual diffusion coefficient of the donor and acceptor (given by Eq. 4.12), depends on viscosity. This diffusion distance is thus to be compared with the mean distance r between donors and acceptors, so that the criterion will be EDr /r. Three regimes can be distinguished  

1) 6Dr / 1 the donor and acceptor cannot significantly diffuse during the 

The survival probability Gft) of the donor molecule (i.e. the probability that when excited at t = 0, it is still excited at time t) is obtained by summation over all possible rate constants kj (given by Eq. 9.1), each corresponding to a given donor-acceptor distance r. For a donor molecule surrounded with n acceptor molecules distributed at random in a spherical volume whose radius is much larger than the Forster critical radius Rq, G (t) is given by 

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