Fluorescence Study of the
Kinetics of Energy
Transfer Between Dyes
1. Introduction
Coumarin 1 and Sodium fluorescein are two dyes which absorb and emit light in the visible region. By using a spectrophotometer we are recording an absorption spectrum and then determining the molar decadic absorption coefficients, which will be used later to interpret and analyse the fluorescence spectra.

For fluorescence spectra, there are two kinds, the excitation and the emission spectrum.
The excitation spectrum is obtained by measuring the intensity of the emission as the excitation wavelength is altered by scanning a monochromator. The emission spectrum is obtained by measuring the emission intensity as a function of wavelength for excitation at a fixed wavelength.

An absorption spectrum and an excitation spectrum are by their nature actually equivalent.

The two dyes exhibit energy transfer properties. The donor is coumarin and the acceptor the fluorescein. When the donor is excited, it is naturally decaying to the ground state. However in presence of an acceptor, this process is enhanced trough energy transfer. We will distinguish between collisional energy transfer and dipole-dipole transfer. From here we will try to determine the quenching constant and the distance at which decay and energy transfer are equally probable, as well as prove that Stern-Volmer’s law and Frster’s theory are obeyed.

2. Results
2.1. Electronic Absorption Spectra
We made up stock solutions for both salts and diluted them down to use in the UV/vis spectrometer.

Coumarin 1
C = 8 x10-5 mol dm -3
We obtained a spectrum with a maximum at 376.5nm at an absorbance of 1.4573, using Beer-Lambert’s law, we deduced the molar decadic absorption coefficients.

Sodium fluorescein
C = 2.425 x10-5 mol dm -3
Here max was 500.5 nm at an absorbance of 2.0922
Summary of the results obtained.

max (nm)
max (m2 mol-1)
(m2 mol-1)
‘ (m2 mol-1)
D (Coumarin)
1.82 x 109

1.25 x 106
A (Fluorescein)
5.17 x 107
1.41 x 106
8 x 106
2.2. Fluorimetry
a) Perylene standard
Emission Spectrum4384.063EX = 434nm
Excitation Spectrum4102.755EX = 438nm
These are the values for the maxima in both spectrum, for the graphs, see attached sheet.

b) Coumarin 1 C = 4 x10-6 mol dm -3
Emission Spectrum3741.050EX = 377nm
Excitation Spectrum3734.156EX = 443 nm
b) Sodium fluorescein C = 1.212 x10-6 mol dm -3
Emission Spectrum5167.453EX = 501nm
Excitation Spectrum5017.516EX = 516 nm
On the graphs of the standard and the two dyes, we can nicely see that the excitation and emission spectra are mirror images of each other overlaid.
The excitation wavelength in one is the highest emitting one in the other.

2.3. Energy Transfer
Stern-Volmer equation
0 /= 1 + K A(1)
with 0 /being the ratio of quantum yield and
K being the Stern-Volmer quenching constant
a) Experimental study
To test the Stern-Volmer equation, as well as to prove the dipole-dipole transfer, we did fluorimetric measurements with mixtures of different concentrations of D and A.

0.003 070.238 1.001188 0.9883
0.003 8.084E-04 38.766 1.003237 1.806
0.003 1.617E-03 25.816 1.005285 2.7064
Table 1: Results from D-A mixtures experiments.

withIbeing the intensity of light emitted
m being a geometric correction factor
and ratio the ratio of the quantum yields
Those values were used to fit the model expression (1),
using the following program
* NonLinear Regression.


COMPUTE PRED_ = 1+K*conc.

NLR ratio

Non-linear Regression
Iteration Residual SSK
1.0089160488 1000000.00
1.1.0031167306 1034392.20
2.0031167306 1034392.20
2.1.0031167306 1034392.20
Run stopped after 4 model evaluations and 2 derivative evaluations.

Iterations have been stopped because the relative difference between
successive parameter estimates is at most PCON = 1.000E-08
Nonlinear Regression Summary StatisticsDependent Variable RATIO
SourceDF Sum of Squares Mean Square
Regression 1 18.55731 18.55731
Uncorrected Total 5 18.56043
(Corrected Total) 4 1.79521
R squared = 1 – Residual SS / Corrected SS =.99826
Asymptotic 95 %
AsymptoticConfidence Interval
ParameterEstimateStd. ErrorLowerUpper
K1034392.1957 12606.399781 999391.21871 1069393.1726
The crosses are marking the values obtained and the line is the fit based on (1).

So the best fit value for K is 1.034×106, with at confidence limit of +/- 3.5×104.

So K , the Stern-Volmer quenching constant is 1.034×103 mol-1 dm 3.

Parent variance 2ratio = 2.43×10-4.

The mean square residual s2ratio is 7.79×10-4
Reduced chi-square 2v = 3.20.
A value under 3 indicates a good fit, hence this shows that our data, is not really fitted onto the model.

b) Energy transfer rate constant
For coumarin, =0.64
Its intrinsic fluorescence lifetime is 0s = 1/(1.822×108)
ktots = 1/ (0s)
=2.846 s-1
ket = K ktots
= 2.943x1011mol-1 dm 3 s-1
This value as an error estimation of +/- 9.961 x109mol-1 dm 3 s-1
And as ket kdiff , we can see that 98% of the total energy transfer is due to dipole-dipole transfer.

c) Frster energy transfer
A1/2 = 9.67 x10-4 mol dm -3
Transformation of the raw data through SPSS gives us the following graph.

Values obtained:
JDA = 6.897×1031 nm mol -1
R0 = 0.14 nm
(R0)eff = 0.584 nm based on equation (A3-13)
So we see that those are very clearly quite different, and that could show that it does not obey to Forster’s theory.

3. Conclusion
So we have shown that the quenching of Coumarin 1 by Sodium fluorescein is obeyed by Stern-Volmer kinetics, that there is mainly dipole-dipole transfer, but could not agree with Forster’s theory.