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Introduction
where υ is the rate of each of the four processes listed, S is the ground state, S ∗
is the excited singlet state, T ∗ the excited triplet state, and hνex and hνex are the
energies of the incident and fluorescent photons respectively. If the absorbance of
the sample is low and the incident light intensity is relatively high, the steady-state
approximation for the change in concentration of S ∗ can be given as:
d[S ∗ ]
dt = Iabs − kf[S ∗ ] − kic[S ∗ ] − kisc[S ∗ ] = Iabs − (kf + kic + kisc)[S ∗ ] = 0
it follows that:
Iabs = (kf + kic + kisc)[S ∗ ]
Bringing in the quantum yield term from Equation 1.2 yields:
φ =
kf
kf + kic + kisc
(1.3)
In steady state experiments the sample is illuminated with a constant beam of
light. Because of the short (typically nanosecond) timescale of fluorescence, a steady
state is reached almost immediately. If the fluorophore is exposed to a pulse of light
that generates the excited state, the intensity decays exponentially according to:
[S ∗ ]t = [S ∗ ]0e −t/τ
where the average time that the excited state exists is given by the fluorescence
lifetime, τ.
The observed fluorescence lifetime(τ) is comprised of the non-radiative (kic+kisc)
and the radiative (kf) parts and is given by:
τ =
1
kf + kic + kisc
18
= φ
kf
(1.4)