Principles of Fluorescence Spectroscopy

466 ENERGY TRANSFER
Figure 13.33. Fluorescence microscopy of lipid mixing between giant unilamellar vesicles. Reprinted from [80] and courtesy of Dr. Robert
MacDonald, Northwestern University.
13.10. ENERGY TRANSFER IN SOLUTION
Energy transfer also occurs for donors and acceptors randomly
distributed in three dimensional solutions. In this
case the theory is relatively simple. Following δ-function
excitation the intensity decay of the donor is given by 88–90
ID(t) I0 D exp [ t/τD 2γ ( t ) τD 1/2
]
(13.29)
with γ = A/A 0 , where A is the acceptor concentration. If R 0
is expressed in cm, the value of A 0 in moles/liter is given by
(13.30)
The relative steady-state quantum yield of the donor is
given by
F DA
F D
A 0 3000
2π 3/2 NR 3 0
1 √π γ exp(γ 2 )1 erf(γ)
(13.31)
where
erf(γ) 2
√π γ
0
(13.32)
These expressions are valid for immobile donors and acceptors
for which the orientation factor is randomized by rotational
diffusion, κ 2 = 2/3. For randomly distributed acceptors,
3 where rotation is much slower than the donor decay,
κ 2 = 0.476. Still more complex expressions are necessary if
the donor and acceptor diffuse during the lifetime of the
excited state (Chapters 14 and 15). The complex decay of
donor fluorescence reflects the time-dependent population
of D–A pairs. Those donors with nearby acceptors decay
more rapidly, and donors more distant from acceptors decay
more slowly.
The term A 0 is called the critical concentration and represents
the acceptor concentration that results in 76% energy
transfer. This concentration in moles/liter (M) can be
calculated from eq. 13.30, or from a simplified expression 14
A 0 447/R 3 0
exp(x 2 ) dx
(13.33)