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The non-radiative process is described by:
Energy T ransfer : S ∗ + Q −→ S + Q ∗
υet = ket[S ∗ ]
Introduction
The acceptor does not need to be fluorescent, but when it is, it’s emission band
will be observed at longer wavelength. It is important to note that RET does not
involve emission of light by the donor, i.e., there is no emission and reabsorption of a
photon in the RET processes. The distance at which energy transfer is 50% efficient
(i.e., 50% of excited donors are deactivated by RET) is defined by the Förster radius
(R0). The magnitude of R0 is dependent on the spectral properties of the donor and
acceptor ‘fluorophores. The Förster radius R0 is given by:
R0 = [8.8 × 10 23 · κ 2 · n 4 · φ · J(λ)] 1/6˚A (1.10)
where κ 2 is the dipole orientation factor, φ is the quantum yield of the donor
in the absence of an acceptor, n is the refractive index, J(λ) is the spectral overlap
integral (see Figure 1.12). The spectral overlap is calculated from: ɛA(λ) · FD(λ) ·
λ 4 dλ cm 3 M −1 where ɛA is the extinction coefficient of the acceptor and FD is the
fluorescence intensity of the donor as a fraction of the total integrated intensity.
The rate of energy transfer ket is given by:
ket(r) = 1
τd
6 R0
r
(1.11)
where r is the distance between the donor and the acceptor molecules, and τd is the
lifetime of the donor in the absence of energy transfer.
Non-Radiative Processes: If all the non-radiative processes (quenching, energy
transfer etc) are taken into account, the expression for the observed fluorescence
lifetime is then given as :
τ =
1
kf + kic + kisc + kq[Q] + ket
=
1
kf + knr
(1.12)
where knr represents the sum of the non-radiative processes competing with the
fluorescence decay.
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