Principles of Fluorescence Spectroscopy

PRINCIPLES OF FLUORESCENCE SPECTROSCOPY 211
and is called the orientation polarizability. If the solvent has
no permanent dipole moment, ε n 2 and ∆f - 0. Table 6.1
lists representative values of ε, n and ∆f. From the magnitudes
of ∆f one may judge that spectral shifts ∆ν will be
considerably larger in water than in hexane.
The interactions of a fluorophore with solvent can be
described in terms of its ground- (µ G ) and excited-state (µ E )
dipole moments, and the reactive fields around these
dipoles. These fields may be divided into those due to electronic
motions (R el G and R el E) and those due to solvent
reorientation (R or G and R or E). Assuming equilibrium around
the dipole moments of the ground and excited states, these
reactive fields are
RG el 2 µ G
a3 f(n) REel 2µ E
a
R G or 2µ G
3 f(n)
a3 ∆f REel 2µ E
∆f 3 a
(6.8)
Consider Figure 6.7, which describes these fields during the
processes of excitation and emission. For light absorption
the energies of the ground (E G ) and nonequilibrium excited
(E E ) states are
Figure 6.7. Effects of the electronic and orientation reaction fields on
the energy of a dipole in a dielectric medium, µ E > µ G . The smaller circles
represent the solvent molecules and their dipole moments.
Energy E (absorption) E E V µ ER G or µ ER E el
Energy G (absorption) E G V µ GR G or µ GR G el
(6.9)
(6.10)
where E V represents the energy levels of the fluorophore in
the vapor state, unperturbed by solvent. The absorption
transition energy is decreased by the electronic reaction
field induced by the excited state dipole. This occurs
because the electrons in the solvent can follow the rapid
change in electron distribution within the fluorophore. In
contrast, the orientation of the solvent molecules does not
change during the absorption of light. Therefore, the effect
of the orientation polarizability, given by µ G R or G and µ E R or G,
contains only the ground-state orientational reaction field.
This separation of effects is due to the Franck-Condon principle.
Recalling that energy is related to the wavelength by
ν = ∆E/hc, subtraction of eq. 6.10 from 6.9 yields the energy
of absorption:
hcν A hc (ν A) V (µ E µ G)(R G or)
µ ER E el µ GR G el
(6.11)
where hc(ν A ) V is the energy difference in a vapor where solvent
effects are not present. By a similar consideration one
can obtain the energy of the two electronic levels for emission.
These are
Energy E (emission) E E V µ ER E or µ ER E el
Energy G (emission) E G V µ GR E or µ GR G el
(6.12)
(6.13)
To derive these expressions we assumed that the solvent
relaxed quickly in comparison to the lifetime of the excited
state, so that the initial orientation field (R or G) changed to
R or E prior to emission. The electronic field changed during
emission, but the orientation field remained unchanged. The
energy of the emission is given by
hcν F hc(ν F) V (µ E µ G)R E or µ ER E el µ GR G el
(6.14)
In the absence of environmental effects one may expect ν A
– ν F to be a constant for complex molecules that undergo
vibrational relaxation. Hence, subtracting eq. 6.14 from
6.11 yields