MODULE 19_03
The Deactivation of Excited Singlet States
As we have seen in earlier Modules the (stimulated) absorption (annihilation) of a photon by a
molecule causes an electronic transition to occur with the concomitant formation of an excited
electronic state.
Quantum mechanical laws govern the photon-molecule interaction.
In
photophysics and photochemistry, we focus on the physical and chemical properties of the
excited electronic state formed during the absorption process.
Excited electronic states have different electronic configurations from the ground states whence
they originated and are therefore different chemical species, even though their nuclear
framework may be identical or very similar to that of their ground state parent.
Excited
electronic states are intrinsically unstable and their excess energy can be dissipated in a variety
of ways, physical and chemical. We can conveniently categorize the various decay routes into
radiative and non-radiative (radiationless)
RADIATIVE DEACTIVATION PROCESSES BETWEEN STATES OF
LIKE MULTIPLICITY
UNLIKE MULTIPLICITY
S1  S0  hvF
T1  S0  hvP
Fluorescence
Spin-allowed and strong
Phosphorescence
Spin-forbidden and weak
NON-RADIATIVE DEACTIVATION PROCESSES BETWEEN STATES OF:
LIKE MULTIPLICITY
UNLIKE MULTIPLICITY
S2  S1  heat
S1 T1  heat
Internal conversion
Very rapid
Intersystem crossing
Usually less rapid since spin-forbidden
1
Energy relationships and rate processes between electronic states are often depicted on a
Jablonski diagram (Figure 19.1)
FIGURE 19.1
S2
Intersystem
crossing
T3
T2
internal
conversion
S1
Intersystem
crossing
internal
conversion
T1
absorption
phosphorescence
fluorescence
S0
2
S1 radiative lifetimes are in the range 1 to 100 ns, although some are found outside this range.
T1 radiative lifetimes are milliseconds and longer. Recall that the radiative lifetime is the
reciprocal of the radiative rate constant. Thus
 FM  1/ kFM
(19.1)
and
TM  1/ kTM
(19.2)
Since kFM is equal to the Einstein A coefficient, which is related to the Einstein B coefficient and
then to the transition dipole moment  fi , and then to the integrated extinction coefficient (J), it
should come as no surprise that there is a relationship between kFM and J, thus
1/  FM  2.88x10
9
n3f
na
 f3
1
av

 d

(19.3)
where nf and na are the mean refractive indices of the solvent over the fluorescence band and the
absorption band, respectively, and
 f3
1
av
is the reciprocal of the mean value of -3 over the fluorescence spectrum. Equation (19.3) is the
Strickler-Berg equation (1962). It allows a calculation of the radiative lifetime of fluorescence
from a measurement of the absorption spectrum of the fluor. 
The Jablonski method of presentation
20
(Figure 19.1) is useful but it is
energy
FIGURE 19.2
18
confined
16
relationships only. Other factors are
14
important when considering rates. An
12
alternative approach is to think in
10
terms of potential energy curves. For
to
showing
energy
a diatomic molecule we can construct
8
a potential energy curve such as
6
60
80
100
120
140
160
180
200
shown in Figure 19.2.
In such a
internuclear distance
molecule, quantized nuclear motions
along the inter-nuclear axis provide a series of vibrational energy levels given by
3
1
Ev  (v  ) 
(19.4)
2
For diatomics, every bound electronic state has a PE curve such as above. The curves are
separated from each other on the energy axis. Different PE curves can intersect with each other
depending on the curvature of the function (the force constant) and the value of r0.
It is not possible to characterize polyatomic molecules in the same precise manner as for
diatomics since they have more than one degree of vibrational freedom. A multi-dimensional
surface would be required for an equivalent characterization. However, an inaccurate, but very
useful physical picture can be gained for polyatomics, if we imagine that all the individual
nuclear oscillators in the molecule are reduced to a single dimension, viz., a generalized nuclear
coordinate. On this model we can represent a polyatomic in a Morse-type plot in an analogous
way to what we do for diatomics where
FIGURE 19.3
now the abscissa label become “general
nuclear coordinate”. Another device we
can employ is to regard the molecule in
question as having a particular bond as
the photochemically relevant entity, e.g.
alkyl carbonyls.
Then we can confine
our attention to a “local mode” on that
bond. This approximation is useful since
it allows for energy level juxtapositions
and curve crossings to be visualized.
Figure 19.3 shows an example of this
concept. Here we see the processes of
absorption, internal conversion in S1,
intersystem crossing and phosphorescence depicted. The vibrational cascade starts in S 1 and
continues until there is a curve crossing between S1 and T1. At that point, the isothermal
intersystem crossing process can occur and there is some probability that the system will leave
the crossing point on the triplet surface. Subsequent cascade takes the molecule to the v = 0 level
of the triplet state whence phosphorescence can occur.
In effect, absorption and fluorescence are inverse processes.
In solution phase at room
temperature, most molecules are in lowest vibrational state (v = 0). Thus, upward transitions
4
originate from v = 0 and terminate at v = 0,1,2,3…in S1 . The transition moments for the v = 0
to v = n set of transitions vary (via the Franck-Condon factors) throughout the series, thus the
efficiency of the individual absorption vibronic transitions varies through the series and the
observed spectrum is a convolution of the set.
At the instant of absorption, the ensemble of molecules in
FIGURE 19.3A
electronic state S1 will contain some in v  0 , some in v 1 ,
some in v  2 , and so on (Figure 19.3A).
A radiative
transition from S1 can therefore originate from any of the set of
vibrational states populated in the absorption process.
However, all states above v  0 (v  1, 2,3...) are capable of
undergoing internal conversion (vibrational cascade) to v  0 .
So a v  n state is confronted by a choice of competing deactivation channels:
Fluorescence: S1 (v  n)  S0 (v  m)
Internal conversion: S1 (v  n)  S1 (v  0)
In most molecules the non-radiative process is much more
rapid than the radiative one ( knr  1011 s 1 ; krad 108 s1 ). Therefore, as a general rule, the
fluorescence transition originates from
1.0
rule. One effect of this is to generate
fluorescence
chromophores.
example
of
spectra
of
many
Figure 19.4 shows an
this
for
a
silicon
phthalocyanine in toluene solution. This
absorbance (norm)
mirror symmetry between the absorption
and
1.0
FIG 19.4
0.9
symmetry is only found for molecules
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0.0
0.0
550
that undergo minimal nuclear geometry
600
650
700
wavelength / nm
change on excitation.
5
750
800
fluorescence (norm)
S1 (v  0) . This effect is called Kasha’s
FLUORESCENCE MEASUREMENTS
Electronically excited states of molecule M can deactivate in several ways, some intramolecular
and some bimolecular, as indicated in the accompanying scheme.
M + h
M(S1)
Bimolecular
processes
M + hF
M(S0) + 
M(T1) + 
N + 
N is the product of some intramolecular chemical change, e.g., cis-trans isomerization.
All the above processes (and more) may be competing in the de-activation of 1M*, and all are
characterized by a rate constant. Only one of the processes is radiative (fluorescence) and by
monitoring the fluorescence, either its intensity or lifetime, affords us a useful and convenient
way of measuring the rate of decay of 1M*, and thence information on its reactivity.
There are two basic experimental set-ups:
(1) Steady state:
FIGURE 19.5
Continuous light source
6
Measures the fluorescence intensity as a function of wavelength.
(2) Time resolved:
FIGURE 19.6
Pulsed light source
Time-resolved detector
Measures fluorescence intensity as a function of time.
Steady State Spectrofluorimetry
Instrument schematic:
FIGURE 19.7
EXCITATION
S
EMISSION
D
The source is a broadband lamp (usually Xe arc) operating in a continuous mode.
Monochromators are used to select narrow band of wavelengths from the excitation source and
the emitted radiation.
7
Such instruments are often used to obtain excitation and emission spectra.
Excitation spectrum: fluorescence intensity at fixed
EM and variable EX (comparison to
absorption spectrum.)
Fluorescence Spectrum: fluorescence intensity at fixed EX and variable
EM .
A typical observation may be seen in Figure 19.8.
The
FIGURE 19.8
excitation
spectrum
provides
information about the absorption spectrum
of the molecules present that fluoresce. In
Excitation
Fluorescence
a
pure,
uncomplicated
sample,
the
excitation spectrum closely resembles the
absorption spectrum. In a mixture where
only one component is fluorescent, the
excitation spectrum will be that of the
fluorescent
compound
only,
but
the
absorption spectrum will contain additional
bands. The excitation spectrum in this case
will not closely resemble the absorption
spectrum of the mixture.
Other factors also intervene to cause excitation and absorption spectra to differ.
Quantitative spectrofluorimetry:
FIGURE 19.9
Figure 19.9 shows a representation of a
fluorescence spectrum. The area under the
spectrum (GF) is proportional to the number
I
F
of photons emitted.
G
area
F
(GF) under the fluorescence intensity vs.
wavelength spectrum is proportional to the
 nm
concentration of fluorescent states:
GF  [ 1M  ]  qFM
8
where qFM is the molecular quantum efficiency of fluorescence. In many cases GF  I  max and in
such cases a measurement of the peak intensity can be used to follow changes in [ 1M  ] . Under
carefully controlled conditions, GF tracks the concentration of fluorescent states.
For example, consider the following experiment (Figure 19.10) in which a dilute solution of
tetraphenylporphine
(TPP)
in
benzene is examined with three
FIG. 19.10
0 mM
different concentrations of oxygen in
the solution, all under the same
conditions of excitation. It is clear
that the presence of oxygen causes
IF
an attenuation of the fluorescence
signal. A plot of I 650 vs. [o2 ] has the
2 mM
form shown in Figure 19.11.
10 mM
Oxygen is said to be a quencher of
 / nm
the fluorescence. The data obtained
can
N2 saturated
FIGURE 19.11
be
employed
to
extract
quantitative information about the
kinetic
properties
of
the
fluorescent species, as we see
IF
Air-saturated
below.
O2 saturated
[O2]
A KINETIC SCHEME FOR FLUORESCENCE QUENCHING
Assume we have a solution of a fluorophore (such as the TPP above) in some solvent and there
are no complications. Singlet states are populated in a continuous way by absorption of photons
from the excitation light beam at the appropriate wavelength.
9
The S1 states are depopulated via a variety of competing pathways:
hv A
M
 1M *
REX
1
M*
 M  hvF
k FM
1
M*

kTM
1
M*
 M 
kGM
1
M* Q
 M Q'
kQM
3
M* 
Q represents a quencher of S1 such as oxygen, and Q’ represents the effects of the quenching act
(non-specific). This quenching interaction is a bimolecular process. The excitation parameter,
Rex, is a measure of the rate at which photons are absorbed into the sample. Since each photon
absorbed generates one 1M* state, it also gives the rate of S1 production (in molecules per
second).
For a fixed REX ( you must be aware of the need for this) the amplitude of the fluorescence
signal will depend on the competition between the fluorescence process (via k FM ) and all the
other deactivation routes.
In the absence of quenchers, i.e., [Q] = 0
d 1 *
[ M ]  REX  (kFM  kTM  kGM ) [1 M * ]
dt
(19.5)
 REX  i ki [1 M * ]
(19.6)
Under continuous, low-intensity irradiation, the concentration of 1 M * rapidly builds up to a
low constant level and the steady-state approximation can be used, i.e.,
d 1 *
[ M ]0
dt
when
[1 M * ]ss  REX / i ki
(19.7)
10
and since
GF  [1 M * ]  b[1 M * ]
then
GF0  b REX / i ki
(19.8)
The superscript '0' is used to indicate that [Q] = 0, and b is a proportionality (instrument)
constant that takes into account light absorption, light gathering power, and detector sensitivity,
etc.
When the quencher is present, i.e., [Q] > 0, another deactivation channel is added and
d 1 *
[ M ]  REx  (i ki  kQM [Q])[1 M * ]
dt
(19.9)
and proceeding as above and using the steady-state approximation:
GF  b REX / (i ki  kQM [Q])
(19.10)
and with b and REX arranged to be constant
 k  k [Q]
GF0
 i i QM
 1  kQM  M [Q]
GF
i ki
(19.11)
where  M1  i ki
It is usual to replace the product kQM  M by KSV, the Stern-Volmer constant. Then,
GF0
 1  K sv [Q]
GF
(19.12)
The procedure is named the Stern-Volmer kinetic analysis, after the originators.
The Stern-Volmer Equation
The quantity GF0 / GF is an observable, and is a linear function of the concentration of the
quencher. Figure 19.12 represents a
FIGURE 19.12
Stern-Volmer plot of the data in
Figure 19.11.
G0/G
Note that the intercept is unity as
required by the S-V equation.
1.0
[O2]
11
Whenever you make a S-V plot and it is not linear or does not have an intercept of unity you must
suspect that the kinetic scheme you are using is incorrect.
Since
K sv  kQM  M  kQM / i ki
this competition kinetics approach evaluates a ratio of rate constants (bimolecular/unimolecular).
Even though kQM and i ki can be very large, (approaching the theoretical limit), their relative
magnitudes are available through the technique of competition kinetics. There is no requirement
for time-resolved equipment to evaluate K sv . The Stern-Volmer constant informs us how
effectively the quencher can compete with the combination of the unimolecular deactivation
pathways.
RELATIVE QUENCHING EFFICIENCIES
In a series of molecules, all of which will quench a given fluorescent S1 state, their individual
kQM values express the different quenching efficiency.
Since kQM  M  K sv , for quenchers Q1, Q2, Q3,...., we can write:
kQ1M : kQ2 M : kQ3M ...  K sv (1) : K sv (2) : K sv (3) ...
(19.13)
(  M is an intrinsic property of the fluorescent state and is independent of the quencher.)
Thus, we can evaluate the SV coefficient ratios and, if we can obtain an absolute value for one
kQM value, we can obtain the absolute values of the others.
What is
M ?
We defined i ki as the sum of the rate constants that relate to intrinsic decay processes of 1 M * .
Further more we defined its inverse as being equal to a quantity we labeled M. The dimensions
of k i are s 1 , thus those of  are s.
Suppose a collection of S1 states is produced by a brief flash of light incident upon a solution of
M. After the end of the flash, REX  0 , thus, when [Q] = 0
d 1 *
[ M ]   i ki [1 M * ]   k M [1 M * ]
dt
12
(19.14)
1
(Here kM  i ki  M )
The above is a linear first-order differential equation, the solution of which can be written down,
viz.,
[1 M * ]  [1 M * ]0 e kM t
(19.15)
[1 M * ]  [1 M * ]0 et / M
(19.16)
or
After the flash, the population of excited states decays exponentially with time.
At time t = M,
[1 M * ] M [1 M * ]0 e1
(19.17)
Thus  M corresponds to that time at which the concentration of excited states has fallen to 1/e of
the initial value.
(19.18)
 M 1/ i ki 1/ kM
is termed the FLUORESCENCE LIFETIME of the molecule M (absence of any bimolecular
processes).
Even though we have defined  through a consideration of excited state concentrations, it could
equally well have been arrived at by considering fluorescence intensity time profiles, hence the
name fluorescence lifetime. Note that, in general, the reciprocal of any unimolecular rate
constant (s-1) has the dimensions of time and can be referred to as a lifetime. For example,
 FM 1/ kFM
(19.19)
is termed the RADIATIVE LIFETIME.
We can employ fluorescence lifetime measurements in a similar way to the intensity
measurements. Thus when [Q] = 0
and when [Q] > 0
 M 1/ kM 1/ i ki
(19.20)
 1/ (kM  kQM [Q])
(19.21)
then
k
M
1  QM [Q]

kM
1  kQM  M [Q] 1  K sv [Q]
(19.22)
(19.23)
 is here defined as the measured lifetime when Q is present.
Values of M are usually in the range of 10-11 s to 10-7 s, with the largest representation being in
the 1 to 10 ns range.
13
Examples covering the range are:
Rose Bengal in water
80 ps
Rose Bengal in CH 3CN
2 ns
Anthracene in cyclohexane
4 ns
Naphthalene in cyclohexane
95 ns
Pyrene in cyclohexane
450 ns
Some practicalities of quenching kinetics
From the above table it is apparent that fluorescence lifetimes are short and any technique that
intends to measure such lifetimes must have a high time resolution. This is even more necessary
when quenchers are present because then the lifetimes are even shorter.
Moreover, any
bimolecular reaxn that is to effectively quench fluorescence must possess a high bimolecular rate
constant, since, from above
  1/(kM  kQM [Q])
(19.24)
kM'  kM  kQM [Q]
(19.25)
kM  kM'  kM  kQM [Q]
(19.26)
or
and
kM is the rate constant difference caused by the presence of Q. Effective quenching can be said
to occur when kM' / kM  5 , or more. If kM is 108 s-1 (10 ns lifetime), then kM = 4x108 s-1, or
kQM[Q] = 4x108 s-1.
The product kQM [Q] can be varied for a given Q by changing [Q] within the limits of solubility.
Thus, when [Q]=
102 M, the above kQM [Q] product requires kQM  4 1010 M 1s1
It turns out that such a value for a bimolecular rate constant between normal-sized molecules in a
mobile solvent represents the "diffusion-limited" value. Molecules that are free to diffuse in
fluids will collide with each other at a rate which is governed by molecular size, solvent size,
solvent viscosity, and temperature, if the species are uncharged; when charged, a Coulombic
factor is involved (see a later Module). In solvents such as cyclohexane at RT, this diffusionlimited rate parameter has a value of ca 2 1010 M 1 s 1 (bimolecular, since collisional). This
14
defines the upper limit of bimolecular rate constants for reactions that require collision. Many
reactions have k values less than this because there are energy or entropic factors, which cause
the efficiency on collision to be less than unity.
QUANTUM EFFICIENCIES AND QUANTUM YIELDS
The molecular quantum efficiency of fluorescence (qFM) is defined as the ratio of the number of
photons emitted by an ensemble of molecular fluorophores to the number of molecules excited
into the fluorescent (S1) state (which is equal to the number of photons absorbed).
qFM  k FM [1 M * ]/ I a
 k FM /  i ki
(19.27)
 k FM  M
Under conditions when some of the fluorescent states are quenched (by quencher Q) the
fluorescence intensity is less than qFM and we use the term molecular fluorescence quantum yield
(FM) to express this. In general
X
= Number of molecules of X converted per photon absorbed
=
Rate of X conversion
Rate of light absorption
=
Rate of X conversion
Rate of all processes involved
FM  kFM [1 M * ]/{kFM  kNR  kQM [Q]}[1 M * ]
e.g.,
= k FM / (kFM  k NR  kQM [Q])  kFM 
qTM  kTM / (kFM  kNR )  kTM  M
(19.28)
(19.29)
(19.30)
when quencher is absent.
The combination of quantum yield and lifetime measurements allows evaluation of the
individual rate constants.
SIGNIFICANCE OF FLUORESCENCE STUDIES
Fluorescence arises from S1  S0 transition, i.e., is a property of an electronically excited state of
a molecule. Thus we can learn about how the state deactivates and how it reacts with other
molecules.
Fluorescence spectra give information on:
15
'
Vibrational spacing in S 0 ; efficiency of v  0 to v  0,1, 2... transitions (through FM).
Fluorescence lifetimes give information on:

Effectiveness of the radiative process.

Bimolecular rate constants and the reactivity of S1
(towards energy transfer, electron transfer, proton transfer, atom transfer, and
other physical quenching processes)
SPECTROFLUORIMETRY: Practical considerations
As we saw above, under steady state excitation
With [Q ]  0
[1 M * ]0ss  REX / (k F  k NR )
With [Q ]  0
[1 M * ]ss  REX / (kF  kNR  kQM [Q])
Where k NR  kTM  kGM
The most often used detector is a photomultiplier tube (PMT).
Each dynode stage contributes an
FIG.19.13
amplification factor or 3-4 depending
on applied voltage.
With 11 stages of gain (typical)
 311  411 , i.e., 2 105  4 106
thus I anode  I cathode
You could check out these web sites for information about optics, instruments, etc.
(1) www.oriel.com
(2) www.acton-research.com
The PMT acts as a current source, which is run to ground via a load resistance ( RL ). A voltagemeasuring device (CRO, digital device, etc) registers the voltage developed across RL .
Thus VL  I a RL (Ohm’s Law), and VL is the measured quantity.
Now
I anode  I cathode  Fcollected  Femitted
photon flux (cm2 s 1 )
16
 VL  m Femitted RL
m’ is an instrument constant
V  mFem
i.e.,
For a fluorescent sample under S-S illumination for [Q] = 0:
[1 M * ]0ss  REX / i ki
Fem0  [1 M * ]0ss k FM
Fem0 
REX k FM
 REX k FM  M
 i ki
and
Vss0  mREX k FM  M
REX is the rate at which 1M* species are generated by the absorption of light
REX ( )  I a ( )
[The excitation source usually has a  distribution]
REX ( )  I a ( )  I 0 ( )(1 10 A( ) )
Vss0  mk FM  M I 0 ( ) (1  10 A(  ) )
[remember that A( )   ( ) C ]
For non-monochromatic light sources and broadband absorbers, this needs summing over
overlap region.
 1  10
For small values of A(
A
A
And thus
Vss0  mk FM  M I 0  ( ) cM
or
Vss0   k FM  M   . qFM
(19.31)
where  = mI 0 ( )CM and can be kept constant in a particular experiment.
Thus the quantum efficiency of fluorescence is directly proportional to the measured steady state
voltage when the instrument conditions are carefully controlled.
17
Also, when a quencher is present:
Vss0 / Vss  qFM /  FM
 M / 
1  K SV [Q]
(19.32)
Thus, the ratios Vss0 / Vs s for a series of [Q] measured in a spectrofluorimeter under constant
irradiation and absorption conditions allow ratios of quantum yields to be determined and K SV
values to be extracted.
SOURCES OF ERROR IN SPECTROFLUORIMETRY
Self-absorption (inner filter effect)
The emitted photons must pass through the sample to reach the detector and will thus need to
pass absorber molecules, when they have a chance of being reabsorbed. The probability of reabsorption will depend on the extent of the spectral overlap (see red segment of Figure 19.14).
The higher the absorbance in the overlap region, the more the blue edge of the fluorescence will
be distorted
FIG.19.14
.
The rule of thumb is to minimize absorbance in the overlap region by working at Aexc < 0.05 per
cm.
18
Poor energy distribution-see schematic
SAMPLE
Optics are designed for maximum excitation at
and light collection from the center of cuvette.
If the absorbance at the excitation wavelength >
EXCITATION
1, very little exciting radiation reaches center of
sample and weak and distorted signals result.
In
all
fluorescence
experiments
keep
the
absorbance at the excitation wavelength as low as
possible, consistent with sensitivity.
EMISSION
19
FLUORESCENCE LIFETIME INSTRUMENTATION124-126
Part of the following material has been excerpted and adapted from a review (hence the nonstandard reference numbering) entitled “Photochemical Techniques” written by Kevin Henbest
and myself for the series Electron Transfer in Chemistry, edited by Vincenzo Balzani and
published by VCH in 2001
Introduction
Photon absorption by molecules can generate excited states that are fluorescent. The spinallowed radiative process of fluorescence will be in competition with non-radiative deactivation
modes and any bimolecular reactions and thus several processes will contribute to the overall
decay of the excited state. The intrinsic lifetimes of fluorescent molecular states are typically in
the range from 10-11 s to >10-8 s.
The occurrence of bimolecular reactions involving the
fluorescent state will shorten its lifetime , and thus measurement of changes of this quantity as a
function of reactant concentration allows a computation of the rate constant for bimolecular
reactions such as electron transfer.
The kinetic scheme describing this situation has been
discussed extensively above and in this addendum we focus on measurement techniques. In the
past twenty years, time resolved measurements for fluorescence lifetime determination have
become highly developed and they have been much used in electron transfer, energy transfer,
proton transfer and other areas of research.
Sensitivity and specificity of fluorescence detection
Fluorescence detection is a very sensitive technique capable of measuring concentrations as low
as one part in 1010. In comparison, absorption spectrophotometry is ca 103 times less sensitive.
The superior sensitivity of fluorescence arises because fluorescence signals are measured relative
to a zero background. The photomultiplier (or other detector) measures either photon arrival or
no photon.
In absorption spectrophotometry, the signal is determined from the difference
between two light intensity measurements, one the test and one the reference.
As the
concentration of absorber is reduced, the test and reference signals will approach each other in
magnitude and eventually the measurement of the small difference between two nearly equal
large signals will become subject to large random error.
20
Instrumentation
Fluorescence Time Profiles
IF
ideal
not so clean
time
The ideal has an instantaneous rise because the excitation pulse is very short compared to the
decay lifetime. The “not so clean” has excitation and decay proceeding in the same time
window. We seek the ideal but sometimes have to compromise. The shorter the timescale,
usually the worse things become.
Photoelectric DC Recording
In this method (see schematic) we use
a light source that produces a short
pulse to
generate a fluorescence
profile, then we pick up the emitted
light in a collection system (lens),
select a wavelength of interest and
finally steer the fluorescence beam to a
detector/signal processing unit.
The needs are for
1) A generating impulse of zero width (a  -function).
2) A detection system of infinite temporal bandwidth and zero noise.
21
Generating impulse:
These days unbelievably short pulses are available from lasers (the current record is about 6 fs).
So given the necessary financial resources, the generating function is not a problem. We discuss
the technicalities later.
Detection system:
Three important factors:
1) Detector sensitivity.
2) Detector time response.
3) Processor time response.
Sensitivity:
The detector has to convert photons to electrons thus the quantum efficiency of the photocathode
(how many photons per photoelectron?) needs to be high and the noise background has to be low
(Signal-to-Noise ratio). Photomultipliers are excellent in these respects and the Oriel website has
lots of detail on response, noise and so forth.
Time response of PMT:
Approximate electron energy is 500 V, or a
10 cm
velocity of 4x106 ms-1
If distance traveled ~10 cm (cathode
 anode), time taken is 2x10-8 s = 20 ns.
Thus, the transit time for PMT is ca 20 ns.
This can be improved somewhat by good design, but few ns is typical.
Thus the input light pulse produces a replica electron pulse at anode,
delayed by the transit time, of the PMT, tTr. Transit time per se is not the
problem, since all it does is delay the appearance of the anode signal.
What really matters is the dispersion
of transit times that arises from differences in the electron
trajectories. Since the electron speeds are finite, different
trajectories will result in different arrival times at the anode,
even though they start at the same time. This represents
degradation in information content.
22
dynode
h
Anode electron pulse
This transit time dispersion is
the
Tr
limiting
determining
factor
the
in
time
resolution of the detector.
time
Time Constant of the Signal Processor
The current output of the PMT is processed in an amplifier where a voltage is generated. The
simplest amplifier is a resistor since VL = IaRL (Ohm’s Law). Thus for a given value of Ia we can
increase output voltage by simply increasing RL.
But all electrical circuits have an intrinsic capacitance
(C), which has to be charged by Ia. This leads to a phase
lag in the voltage waveform.
The rise time of a voltage signal caused by the impedance
of the circuit is given by  R  RLC . Thus, amplification
by increasing RL leads to longer time constants which
in turn reduces our capability of resolving rapidly
changing signals. Typical minimum values of C are in
the region of 20 pF and the industry standard for the
input impedance of amplifiers is 50 Then  R  50 x 20 pF  1000 ps 1ns 
This tells us that the laws of physics impose a nanosecond barrier for properly resolving
temporal changes in voltage waveforms and this time constant consideration limits the use of
direct photoelectric recording to fluorescent signals with lifetimes of a few nanoseconds. In
order to resolve more rapid voltage changes we somehow have to defeat the laws of physics!
Time Correlated Single Photon Counting,125-131
Time correlated single photon counting (TCSP) has proven to be a much-used method for
measuring fluorescence lifetimes. It is highly sensitive inasmuch as it requires only one photon
to be incident on the detector per excitation cycle and statistical analysis of the experimental data
23
gives lifetimes with well-defined error limits. Commercial systems are available which allow
lifetimes from 50ps to many tens of nanoseconds to be measured with relative ease and high
precision.
Figure 19.15 shows a typical schematic diagram of a TCSP system.
Power
Supply
Lamp power
Supply
Start
photodiode
lamp
Sample
Cell
Monochromator
Monochromator
Thyratron
gate
Fast (stop)
phototube
Start
pulse
Discriminator
Stop
Pulse
Delay
Time -to
amplitude
converter
Delay
Amplifier
Dual input
counter
MCA
Figure 19.15
Discriminator
2-pen
plotter
IBM-PCXT
A schematic presentation of a time-correlated single photon counting instrument (see text).
The experimental set-up requires an excitation source, sample chamber, a sensitive
photomultiplier detector, and electronics that allow precise timing of the interval between the
arrival of the pulse from the excitation source and the arrival of first fluorescence photon at the
detector. In a typical experiment, a hydrogen flash lamp excitation source produces low intensity
light pulses of a few nanoseconds duration (in many systems today mode-locked laser sources
24
are replacing flash lamps). Each pulse produces a fluorescence pulse, the fluorescence photons
are emitted over a range of times after excitation with more photons being emitted earlier, and
fewer emitted later as the excited state decays. Single photon counting relies on the fact that
highly sensitive photomultipliers are able to give measurable current output pulses after a single
photon strikes the photocathode. This allows the delay time between the excitation pulse and the
arrival of individual photons to be determined. The key to the precise timing is the time to
amplitude converter (TAC). The TAC is a device that starts to charge a capacitor linearly upon
command from the start pulse generated by a photodiode that senses the excitation pulse. It
ceases to charge when commanded by the arrival of the fluorescence (stop) pulse.
It
subsequently outputs a voltage pulse whose amplitude is derived from the stored charge and is
thus proportional to the time interval between start and stop pulses.
The voltage pulse produced by the TAC is fed to the multichannel analyzer (MCA), and stored in
a specific channel according to its amplitude, and hence time post-excitation. The probability of
a single photon event being counted is high at early times post-excitation and decreases with
time. Repetitive operation of the TAC produces a probability histogram for the detection of
fluorescence photons, which is identical to the fluorescence decay curve.
The fluorescence lifetime is obtained from this curve by an iterative curve-fitting program that
deconvolutes the lifetime from the instrument response profile (IRF). This latter describes how
the instrument responds to scattered excitation pulses. A typical scattering solution used to
obtain an IRF is colloidal silica, or even a weak suspension of coffee creamer. The results of a
typical experiment are shown in Figure 19.16. The plot consists of three traces, the instrument
response function, the raw experimental data, and the numerical fit obtained from the fitting
program. The data are usually displayed with a logarithmic ordinate in order to scale the
intensity response that is usually arranged to cover over four decades and to clearly show any
deviations between data and fit.
The deviations between the experimental data and the
calculated best fits are often too small to be seen by eye and an assessment of the best fit is
normally carried out using statistical tests such as point by point weighted-residuals and
autocorrelation functions. Full details of data analysis and evaluation can be found in the
relevant literature.125,126,131
25
Figure 19.16
1000
Co 100
unt
s
10
1
0
20
Time / ns
40
The time profile for the decay of fluorescence from a solution of anthracene in degassed hexane. The data were
obtained with a time-correlated single photon counting instrument such as shown in Figure 8. The figure shows the
raw data with a super-imposed linear fit and the instrument response function. The extracted lifetime was 5.14 ns..
(Courtesy of Dr. F. N. Castellano).
Fluorescence up-conversion132
Fluorescence up-conversion (also called fluorescence sum frequency mixing) is a technique used
to measure fluorescence lifetimes with time resolution in the sub-picosecond time scale. The upconversion method allows significant improvements in time resolution over the above-discussed
time correlated single photon counting (TCSPC) method. The latter has time resolution (with
deconvolution) approaching 20ps. Barbara and co-workers have described an up-conversion
instrument with a minimum 300-fs full-width-half-maximum (FWHM) response function.132
Up-conversion is an all-optical method of time resolving fluorescence, analogous to an optical
boxcar and akin to the pump-probe absorption method (see later). It involves frequency mixing
of non-coherent fluorescence from a sample with a coherent probe pulse. This is accomplished
in a non-linear crystal such as KDP or LiIO3. Time resolution is obtained by delaying the probe
pulse relative to the excitation pulse, using an optical delay stage.
The apparatus can be divided into three main sections, laser pulse production, amplification and
fluorescence up-conversion. The ultrafast lasers employed for up-conversion will be described
later. The experiment is a cross-correlation between the fluorescence pulse and the laser pulse.
26
At time t = 0, the sample is excited by the ultrafast laser pulse. The resulting incoherent
fluorescence (frequency = fl) is collected and mixed in a non-linear crystal (such as KDP) with
the gating pulse (frequency = 1) derived from the excitation source and arriving at time t = .
This frequency mixing of the fluorescence and probe beams generates light at the sum frequency,
sum
sum = 1 + fl
(19.33)
The theory of sum frequency conversion of incoherent light can be found in the literature. 133-134
The intensity of the sum frequency light at a given delay time is proportional to the correlation
function of the fluorescence intensity with the intensity of the 1 beam. A time profile of the
fluorescence intensity is obtained by changing the arrival time of one of the pulses using an
optical delay line.
Frequency Domain (Phase Shift) Method 91,135
Over a substantial number of years the phase shift or frequency domain method has been
employed for the measurement of fluorescence lifetimes. The technique requires the continuous
excitation of a fluorescent sample with a source of varying intensity. The fluorescence response
would normally be expected to increase and decrease to reflect the changes in excitation
intensity. However, in a frequency domain experiment the excitation beam is modulated at a
high frequency, =2f, to produce a sinusoidally changing intensity given by:
I0 (t) =A + Bcos( t)
(19.34)
If the fluorescence from the sample has a lifetime much shorter than a half period, the
fluorescence signal will vary in a sinusoidal manner, without phase shift. If the decay time is
comparable with that half period, the sinusoidal signal from the sample emission is phase shifted
with respect to the excitation. For a single exponential lifetime , the fluorescence response from
the sample is
I(t) = C .[A+
Bcos( t- )
]
(1+ 2 t 2 )1/2
(19.35)
The value  can be obtained directly from the measurement of the phase angle, , between
excitation and fluorescence.
tan   t
27
(19.36)
The modulation ratio M is another valuable parameter that describes the modulation of the
fluorescence intensity relative to the excitation intensity:
1
(19.37)
(1  ( t ) 2 )1/ 2
Most commercial spectrometers contain a Debye-Sears Cell,136 which employs a quartz crystal
M  cos  
oscillating at a specified frequency to modulate the intensity of the excitation beam. A crosscorrelation detection technique is generally used to measure phase angles at a frequency  with
the gain of the photomultiplier modulated at a frequency  + , where  is of the order of a
few hertz. The detector signal contains a component at frequency , which is filtered and used
to obtain  with high precision using digital signal-processing techniques. At a single modulation
frequency, a single  value is obtained and only single exponential lifetimes can be determined.
However, if the excitation intensity is modulated at two different frequencies in consecutive
experiments, the  and M values should yield the same lifetime if the fluorescence decay is truly
exponential. Alternately the two sets of  and M values can be used to obtain 1 and 2 for the
sample exhibiting bi-exponential decay. The laboratories of Lakowicz and Gratton have both
been very active in developing frequency domain fluorometry.91,137-139
An important development in the phase shift technique is the use of a radio-frequency
synthesizer as the driver for the Pockels cell modulator. In this way the excitation beam can be
modulated at any frequency between 1 and 200 MHz.137-139 This approach allows use of CW
lasers such as He-Cd laser and even mode locked lasers139 to be used as an excitation source. If 
and M are measured at six to ten suitably spaced frequencies, least squares curve fitting
techniques can be employed to obtain lifetimes with greatly enhanced precision. Typical data
obtained by this multi frequency technique has the ability to measure decay times as short as
10ps. Gratton and co-workers have developed other curve fitting procedures to analyze data
obtained on a multi-frequency phase-shift fluorimeter.
These experiments include the
construction of time resolved spectra,140 measurements of rotational relaxation times from
fluorescence anisotropy data141 multi exponential analyses142-143 and determination of
distributions of lifetimes as continuous functions143-144 and greatly increase the power of the
phase shift technique.
28
References
[124] G. R. Fleming, in Light, Chemical Change and Life: a source book in Photochemistry,
(Eds.: J.D. Coyle, R.R. Hill, D.R. Roberts), Open University Press, Milton Keynes, 1982, chapter
4.
[125] J. N. Demas, Excited State Lifetime Measurements, Academic Press, New York, 1983.
[126] D. V. O’Connor, D. Phillips, Time-Correlated Single Photon Counting, Academic
Press, London, 1984.
[127] W. R. Ware, in Creation and Detection of the Excited State, Vol. 1., (Ed.: A. A. Lamola),
Marcel Dekker, New York, 1971, chapter 5.
[128] I. Isenberg, in Biochemical Fluorescence, Vol. 1, (Eds.: R.H. Chen, H. Edelhoch), Marcel
Dekker, New York, 1975, p. 43.
[129] M. G. Badea, L. Brand, Methods Enzymol., 1979, 61, 378.
[130] L. J. Cline Love, L. A. Shaver, Anal. Chem., 1976, 48, 364A-371A.
[131] D. A. Holden, in Handbook of Organic Photochemistry Vol.1. (Ed.: J. C. Scaiano), CRC
Press Inc, Boca Raton, Florida. 1989.
[132] M. A. Kahlow, W. Jarzeba, T.P. DuBrull, P. F. Barbara, Rev.Sci. Instum. 1988, 59, 10981109.
[133] F. Zernicke, J. E. Midwinter, Applied Nonlinear Optics, 1973, Wiley, New York.
[134] Y. R. Shen, The Principles of Nonlinear Optics, 1984, Wiley, New York.
[135] F. W. Teale, NATO Adv. Sci. Inst. Ser. A, 1983, 69, 59.
[136] P. Debye, F. W. Sears, On the scattering of light by supersonic waves, Proc Natl, Acad.
Sci. U.S.A., 1932, 18, 409.
[137] E. Gratton, M. Limkeman, Biophys. J. 1984.44, 315.
[138] J. R. Lakowicz, B. P. Maliwal, E. Gratton Anal. Instrum., 1985, 14 193.
[139] J. R. Alcala, E. Gratton, D. M. Jameson, Anal. Instrum., 1985, 14, 225.
[140] T. Parasassi, F. Conti, E. Gratton, Cell Mol. Biol., 1986, 32, 103.
[141] J. Lakowicz, H. Cherek, B. P. Maliwal, E. Gratton. Biochemistry, 1985, 24, 376.
[142] T. Parasassi, F. Conti, E. Gratton, Biochemistry, 1984, 23, 5660.
[143] T. Parasassi, F. Conti, M. Glaser, E. Gratton, J. Biol. Chem., 1984, 239, 14011.
[144] E. Gratton, Anal. Chem., 1985, 57, 1694.
29