RET in three dimensions. Effect of viscosity

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 

1) 6Dr / r2 1 the donor and acceptor cannot significantly diffuse during the excited-state lifetime of the donor. This case is called the static limit. Distinction according to the mechanism of tranfer should be made. 

The survival probability Gs(t) 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 kT (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 R0, Gs(t) is given by 

4) According to classical equations of transla-tional Brownian motion in three dimensions, the mean diffusion distance of a particle during time t is (6 Dt)1 2. 

The solution of this differential equation, with the initial condition G(0) = 1, is 

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