Fluorescence lifetime

The fluorescence lifetime , formerly also fluorescence decay time , indicates the mean time that a molecule remains in an excited state during fluorescence before it emits a photon and thus returns to the ground state . ${\displaystyle \tau }$

Typical fluorescence lifetimes are on the order of 10 ⁻⁹ to 10 ⁻⁷  s. It should be noted that the fluorescence is a spin- allowed process. In contrast, the spin- forbidden phosphorescence results in longer lifetimes in the range from milliseconds to hours.

meaning

The fluorescence lifetime is an important measurement parameter in spectroscopy and microscopy ( fluorescence lifetime microscopy ), which serves to differentiate between different fluorophores (also of the same color). In addition, the fluorescence lifetime provides important information about the chemical environment of a fluorophore and can reveal energy transfer mechanisms such as Förster resonance energy transfer .

For example, the fluorescence lifetime in a cell is influenced by the vicinity of the fluorophore, i.e. H. the fluorophores can serve as measuring probes for the environment.

definition

The decay of the fluorescence follows an exponential law:

${\displaystyle I(t)=I_{0}\exp \left(-{\frac {t}{\tau }}\right)}$.

With

• the fluorescence intensity immediately after an excitation flash (e.g. a laser pulse ) ${\displaystyle I_{0}}$
• the elapsed time . ${\displaystyle t}$

The following applies to the fluorescence lifetime

${\displaystyle \tau ={\frac {1}{k_{\mathrm {r} }+k_{\mathrm {nr} }}}}$

With

• the rate at which radiant processes disintegrate (engl. radiative ) ${\displaystyle k_{\mathrm {r} }}$
• the rate at which non-radiative processes decay ( non-radiative ). ${\displaystyle k_{\mathrm {nr} }}$

With strongly fluorescent substances such as fluorescent dyes, the following is negligible: ${\displaystyle k_{\mathrm {nr} }}$

${\displaystyle k_{\mathrm {r} }\gg k_{\mathrm {nr} }\Rightarrow \tau \approx {\frac {1}{k_{\mathrm {r} }}}}$

In the case of non-fluorescent substances, on the other hand (i.e. most things in our environment) is much smaller than : ${\displaystyle k_{\mathrm {r} }}$ ${\displaystyle k_{\mathrm {nr} }}$

${\displaystyle k_{\mathrm {r} }\ll k_{\mathrm {nr} }\Rightarrow \tau \approx {\frac {1}{k_{\mathrm {nr} }}}}$

Experimental determination

The determination of fluorescence lifetimes requires the time-resolved recording of the intensity of the emitted radiation.

Time correlated single photon counting

Histograms of the time- correlated single photon count in a fluorescence (lifetime) spectrometer . The diagram shows the intensity profile of the excitation light flashes over time and the numerically unfolded histogram of the photon count of the luminescent light of a solution of the dye rhodamine  6G.
Result: ${\displaystyle \tau \approx 4{,}3\,\mathrm {ns} }$

A common method for this is time- correlated single photon counting  (TCSPC). The sample is excited periodically with monochromatic light flashes of low intensity ( laser , nanosecond flash lamp, monochromator on the emission side of the test arrangement ). The fluorescence is detected at a wavelength that is greater than that used for excitation, using a secondary electron multiplier ( photomultiplier / PMT) that can register individual photons . If the light from the excitation light source is weakened to such an extent that a signal is only registered after one to five percent of the light flashes, it can be assumed that it is the registration of individual photons.

With an electronic circuit time measurements are carried out, which are started by an additional detector ( photodiode ) directly at the light source and stopped by the signal from the fluorescence detector. By discretising the time signal, after running through many excitation / measuring cycles, a histogram is obtained ( depending on the resolution of the analog-digital converter used ) (see figure). Its envelope corresponds to the signal of an analog recording of the time-resolved intensity curve of the fluorescence after a single high-power excitation pulse. The fluorescence lifetime can be determined graphically or by regression analysis from the histogram . ${\displaystyle \tau }$

Phase fluorometry

Another method is measurement in the frequency domain (phase fluorometry). The sample is irradiated with a light , the intensity of which is modulated with the angular frequency (symbol E for excitation : excitation). The emitted fluorescent light is detected , which is modulated with the same frequency but with a reduced amplitude . A phase shift occurs. ${\displaystyle E(t)}$ ${\displaystyle \omega }$ ${\displaystyle F(t)}$

The system can be described as a linear response function :

${\displaystyle {\begin{aligned}F(t)&=\chi (\omega )\,E(t)\\&=|\chi (\omega )|\,E_{0}\ \mathrm {exp} \left(-i[\omega t-\phi (\omega )]\right)\end{aligned}}}$

With

• the susceptibility , which is composed of a dispersion and an absorption term ${\displaystyle \chi \left(\omega \right)}$
• the phase . ${\displaystyle \phi }$

If a Debye relaxation is now assumed as the answer to a delta perturbation in the time domain :

${\displaystyle {\overline {\chi }}\left(t\right)=\mathrm {exp} \left(-{\frac {t}{\tau _{M}}}\right)}$

with the decay time for the demodulation , ${\displaystyle \tau _{M}}$

then it follows for the frequency range after a Fourier transformation :

${\displaystyle \chi (\omega )={\frac {1+i\,\omega \,\tau _{M}}{1+({\omega }\,{\tau _{M}})^{2}}}}$

The cooldown time for the phase results in : ${\displaystyle \tau _{P}}$

${\displaystyle {\begin{aligned}\phi (\omega )&=\arctan {(\omega \,\tau _{P})}\\\Leftrightarrow \tau _{P}&={\frac {1}{\omega }}\cdot \tan {\phi (\omega )}\end{aligned}}}$

and for demodulation:

${\displaystyle {\begin{aligned}M=|\chi (\omega )|&={\sqrt {\frac {1}{1+({\omega }\,{\tau _{M}})^{2}}}}\\\Leftrightarrow \tau _{M}&={\frac {1}{\omega }}\cdot {\sqrt {\left({\frac {1}{M}}\right)^{2}-1}}\end{aligned}}}$

In the case of only one fluorophore, and are the same and independent of frequency: the fluorescence lifetime. ${\displaystyle \tau _{P}}$ ${\displaystyle \tau _{M}}$

literature

• Joseph R. Lakowicz : Principles of Fluorescence Spectroscopy . Plenum Publishing Corporation, 2nd Edition, 1999
• K. Suhling et al. - Imaging the Environment of Green Fluorescent Protein, Biophysical Journal (2002) 83 , 3589-3595
• Primer on Time-Correlated Single Photon Counting , PicoQuant GmbH, Berlin.