Fluorescence emission rates

At high intensities of the exciting laser the linewidth and the fluorescence emission rate of a single molecule are subject to saturation effects. Before we outline the theo-... 

The Bloch equations (Eq. 5) can be solved under different conditions. The transient solution yields an expression for 0-22 (0> time-dependent population of the excited singlet state S. It will be discussed in detail in Section 1.2.4.3 in connection with the fluorescence intensity autocorrelation function. Here we are interested in the steady state solution (an = 0-22 = < 33 = di2 = 0) which allows to compute the line-shape and saturation effects. A detailed description of the steady state solution for a three level system can be found in [35]. From those the appropriate equations for the intensity dependence of the excitation linewidth Avfwhm (FWHM full width at half maximum) and the fluorescence emission rate R for a single absorber can be easily derived [10] ... 

F gre 7. Saturation behaviour of single pentacene molecules in p-terphenyl (site Oi r = 1.4 K). The (a) fluorescence excitation line width (FWHM) and (b) the fluorescence emission rate are shown as a fimction of laser intensity. The solid lines are fits to the data as described in the text The intensity is the free-space peak intensity at the molecule without local-field corrections (from Ref. 10). 

At low exciting intensities the linewidths (Fig. 7(a)) reach a value of 7.3 + 0.8 MHz in agreement with the lifetime-limited value, and the fluorescence emission rate increases almost linearly. In the high-intensity limit, the peak fluorescence emission rate saturates at 7.2 + 0.7 x 10 photons/s (Fig. 7(b)). As the peak emission rate saturates, the emission rate in the wings of the excitation spectrum continues to increase with intensity, and the linewidth broadens as shown in Fig. 7(a). Actually,... 

The solid curves in Figs. 7(a) and (b) are fits of Eqs. 6 and 7, respectively, to the data. They show that the functional form of the saturation behaviour is well reproduced by the theory. The fitting parameters in Eq. 7 are the saturation intensity and the fully saturated fluorescence photocount rate (Coo). The latter is given by the product of the fully saturated fluorescence emission rate 7 oo and the detection efli-ciency D Coa = Raa x D). For the case that i oo can be reliably calculated by Eq. 9 -i.e. all photophysical parameters are known from independent measurements - the detection efficiency of the optical setup can be determined. Conversely, if D is known independently, the measured value of Coo can be compared to the theoretical prediction from / Qo. 

With this difference of total irradiation how much fluorescence is actually collected This involves two aspects, the amount of emission photons and the efficiency of detection. In single beam scanning at 1 mW excitation intensity, fluorescein molecules in the region of peak intensity are 63% saturated, i.e. only 37% are not excited at any given time according to 1 and 2. The fluorescence emission rate k jjj amounts to 1.26x10 photons/s according to 3. 

The saturation level of fluorescein in such a mini-beam is 0.09% according to 1,2 and 7. The fluorescence emission rate is 1.72x10 photons/s according to 3. 

With the fluorescence emission rates of single and multi-beam scanning setups known, how many photons are actually emitted by a fluorophore in a... 

The fluorescence signal is linearly proportional to the fraction/of molecules excited. The absorption rate and the stimulated emission rate 1 2 are proportional to the laser power. In the limit of low laser power,/is proportional to the laser power, while this is no longer true at high powers 1 2 <42 j). Care must thus be taken in a laser fluorescence experiment to be sure that one is operating in the linear regime, or that proper account of saturation effects is taken, since transitions with different strengdis reach saturation at different laser powers. 

Molecular rotors are useful as reporters of their microenvironment, because their fluorescence emission allows to probe TICT formation and solvent interaction. Measurements are possible through steady-state spectroscopy and time-resolved spectroscopy. Three primary effects were identified in Sect. 2, namely, the solvent-dependent reorientation rate, the solvent-dependent quantum yield (which directly links to the reorientation rate), and the solvatochromic shift. Most commonly, molecular rotors exhibit a change in quantum yield as a consequence of nonradia-tive relaxation. Therefore, the fluorophore s quantum yield needs to be determined as accurately as possible. In steady-state spectroscopy, emission intensity can be calibrated with quantum yield standards. Alternatively, relative changes in emission intensity can be used, because the ratio of two intensities is identical to the ratio of the corresponding quantum yields if the fluid optical properties remain constant. For molecular rotors with nonradiative relaxation, the calibrated measurement of the quantum yield allows to approximately compute the rotational relaxation rate kor from the measured quantum yield [Pg.284]

Fluorescence Lifetimes. The fluorescence decay times of TIN in a number of solvents (11.14.16.18.19), low-temperature glasses (12.) and in the crystalline form (15.) have been measured previously. Values of the fluorescence lifetime, Tf, of the initially excited form of TIN and TINS in the various solvents investigated in this work are listed in Table III. Values of the radiative and non-radiative rate constants, kf and knr respectively, are also given in this table. A single exponential decay was observed for the room-temperature fluorescence emission of each of the derivatives examined. This indicates that only one excited-state species is responsible for the fluorescence in these systems. 

When a molecule is in the S v = 0) state, fluorescence emission is only one of the several competing physical processes by which the molecule can return to the ground state. A molecule in Si(v = 0) can undergo fluorescence, intersystem crossing or internal conversion, which have rate quantum yields < >f, (j) sc and respectively and ... 

P-type delayed fluorescence is so called because it was first observed in pyrene. The fluorescence emission from a number of aromatic hydrocarbons shows two components with identical emission spectra. One component decays at the rate of normal fluorescence and the other has a lifetime approximately half that of phosphorescence. The implication of triplet species in the mechanism is given by the fact that the delayed emission can be induced by triplet sensitisers. The accepted mechanism is ... 

Now, the rate of fluorescence emission is Jf = kf [Si], and since the fluorescence quantum yield was shown in Section 3.5 to be equal to the ratio of the rate of fluorescence to the total rate of deactivation, the fluorescence quantum yields in the presence and absence of a quencher, Q( )f and < )f respectively, are ... 

Two principal ways exist to use a dye as a sensor of local polarity (or of microscopic electric fields) (1) monitoring the polarity-induced shift of the energy levels, e.g., the red shift of the fluorescence and (2) monitoring changes in fluorescence intensity induced by the polarity- or field-induced modulation of nonradiative rates. As these compete with the fluorescence emission, the fluorescence intensity (and lifetime) is correspondingly modulated. (3) In some cases, the radiative rates are also solvent sensitive this is usually connected with the formation of luminescent products. 

One may consider the relaxation process to proceed in a similar manner to other reactions in electronic excited states (proton transfer, formation of exciplexes), and it may be described as a reaction between two discrete species initial and relaxed.1-7 90 1 In this case two processes proceeding simultaneously should be considered fluorescence emission with the rate constant kF= l/xF, and transition into the relaxed state with the rate constant kR=l/xR (Figure 2.5). The spectrum of the unrelaxed form can be recorded from solid solutions using steady-state methods, but it may be also observed in the presence of the relaxed form if time-resolved spectra are recorded at very short times. The spectrum of the relaxed form can be recorded using steady-state methods in liquid media (where the relaxation is complete) or using time-resolved methods at very long observation times, even as the relaxation proceeds. 

Note that this expression differs from the more familiar t = qx0 applicable to systems in which the rate constant of the fluorescence emission path to the... 

To test the above ideas, Weitz etal.(i2) performed experiments on the fluorescence decay from a thin layer of europium(III) thenoyltrifluoracetonate (ETA) deposited on a glass slide covered with Ag particles approximately 200 A in diameter. The fluorescence decay rate was found to increase by three orders of magnitude in comparison with that of ETA in solid form. In addition to the large increase in decay rate, there was also evidence for an increase in overall fluorescence quantum efficiency. It is not possible from Eq. (8.11) to say anything about the manner in which is partitioned between radiative and nonradiative processes, y should be written in terms of a radiative part yr and a nonradiative part ynr y = yr + y r. Since the radiative rate for dipole emission is given by... 

EMISSION SPECTRUM ACTION SPECTRUM EXCITATION SPECTRUM FLUORESCENCE Empirical rate equations,... 

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