Radiative lifetime, fluorescence

Certain features of light emission processes have been alluded to in Sect. 4.4.1. Fluorescence is light emission between states of the same multiplicity, whereas phosphorescence refers to emission between states of different multiplicities. The Franck-Condon principle governs the emission processes, as it does the absorption process. Vibrational overlap determines the relative intensities of different subbands. In the upper electronic state, one expects a quick relaxation and, therefore, a thermal population distribution, in the liquid phase and in gases at not too low a pressure. Because of the combination of the Franck-Condon principle and fast vibrational relaxation, the emission spectrum is always red-shifted. Therefore, oscillator strengths obtained from absorption are not too useful in determining the emission intensity. The theoretical radiative lifetime in terms of the Einstein coefficient, r = A-1, or (EA,)-1 if several lower states are involved,... 

Since is greater than kf, the observed excited singlet-state lifetime is less than the excited singlet-state radiative lifetime. h only approaches ho as intersystem crossing and internal conversion from Si become much slower processes than fluorescence. 

F. Perrin Theory of fluorescence polarization (sphere). Perriris equation Indirect determination of lifetimes in solution. Comparison with radiative lifetimes... 

If the only way of de-excitation from Sj to S0 was fluorescence emission, the lifetime would be l/krs this is called the radiative lifetime (in preference to natural lifetime) and denoted by rf. The radiative lifetime can be theoretically calculated from the absorption and fluorescence spectra using the Strickler-Berg relation6 . 

Using the radiative lifetime, as previously defined, the fluorescence quantum yield can also be written as... 

There are many molecular interactions which influence the fluorescence decay times. The measured fluorescence lifetime r is usually shorter than the radiative lifetime tr because of presence of other decay rates which can be dependent on intramolecular processes and intermolecular interactions (Figure 10.3). The measured fluorescence lifetime (r) is given by the inverse of the total rate of dynamic processes that cause deactivation from the excited (mostly singlet Si) state... 

EXAMPLE 1.7 The fluorescence lifetime measured from the metastable state Ej/2 ofNd + ions in the laser crystal yttrium aluminum borate (YAl3(B03)4) is 56 lus. If the quantum efficiency from this state is 0.26, determine the radiative lifetime and the radiative and nonradiative rates. 

The yttrium aluminum garnet crystal, Y3 AI5O12, doped withNd + ions, is a well-known solid state laser material (abbreviated to Nd YAG). If the fluorescence lifetime of the main laser emission is 230 /rs and the quantum efficiency of the corresponding emitting level is 0.9, determine (a) the radiative lifetime and... 

Recall that the radiative lifetime, tq = 1 /A, can be determined from Equation (1.20) by measuring the fluorescence lifetime t from a luminescence decaytime experiment, and provided that the nom-adiative rate Am is known. Eor pro-ces ses where the nom-adiative rate is negligible (Am 0), t = tq and so we will measure lifetimes in the range of nanoseconds for electric dipole transitions and lifetimes in the range of microseconds for magnetic dipole transitions. 

Cr + ions in aluminum oxide (the ruby laser) show a sharp emission (the so-called Ri emission line) at 694.3 nm. To a good approximation, the shape of this emission is Lorentzian, with Av = 330 GHz at room temperature, (a) Provided that the measured peak transition cross section is c = 2.5 x 10 ° cm and the refractive index is = 1.76, use the formula demonstrated in the previous exercise to estimate the radiative lifetime, (b) Since the measured room temperature fluorescence lifetime is 3 ms, determine the quantum efficiency for this laser material. 

In Table E7.5, the fluorescence lifetimes and quantum efficiencies measured from different excited states of the Pr + ( Po and D2) and Nd + (" Fs ji) ions in a LiNbOs crystal are listed, (a) Determine the multiphonon nonradiative rate from the 19/2 and In/2 states of the Er + ion in LiNbOs. (b) If a fluorescence lifetime of 535 /us is measured from the excited state Fs/2 of the Yb + ion in this crystal, estimate the radiative lifetime from this state. 

The spectra Fo(v) and Ca(v) are represented on the wavenumber scale and the fluorescence spectrum (F(v)) of the donor is normalized on this scale n is the refractive index, e iv) is the molar decadic extinction coefficient of the acceptor and To is the radiative lifetime (s) and R(nm) is the D-A center to center distant. For very strong coupling the rate is given by... 

JABLONSKI DIAGRAM RADIATIONLESS TRANSITION FLUORESCENCE RADIATIVE LIFETIME RADICAL (or, FREE RADICAL)... 

The underlying reason for all these observations is that the growth of any product of reaction always reflects the lifetime of the precursor species, ferf-butoxyl radical in our examples. Interestingly, this is the same concept that applies when one measures properties, such as fluorescence that is, the observable fluorescence lifetime reflects the lifetime of the singlet state and not its radiative lifetime. 

Weller24 has estimated enthalpies of exciplex formation from the energy separation vg, — i>5 ax of the molecular 0"-0 and exciplex fluorescence maximum using the appropriate form of Eq. (27) with ER assumed to have the value found for pyrene despite the doubtful validity of this approximation the values listed for AHa in Table VI are sufficiently low to permit exciplex dissociation during its radiative lifetime and the total emission spectrum of these systems may be expected to vary with temperature in the manner described above for one-component systems. This has recently been confirmed by Knibbe, Rehm, and Weller30 who obtain the enthalpies and entropies of photoassociation of the donor-acceptor pairs listed in Table XI. From a detailed analysis of the fluorescence decay curves for the perylene-diethyl-aniline system in benzene, Ware and Richter34 find that... 

Table 2 Fluorescence lifetimes ti, natural radiative lifetimes tr, and calculated fluorescence lifetimes for compounds 3, 5, and 11 in different solvents... 

The spontaneous fluorescent decay time tf is connected with the radiative lifetime tfr and the quantum yield of fluorescence ijf by jjf =tf/tfr. Since the radiative lifetime is of the order of a few nanoseconds in most dyes, the spontaneous fluorescent decay time is about the same for quantum yields of fluorescence near unity (i.e., k Q ttksT 0) and decreases to a few picoseconds for quantum yields of the order of 10-3. 

The processes III and IV termed as E-type and P-type delayed emissions have emission spectra identical with that of the normal fluorescence but with longer radiative lifetime. The long life is due to the involvement of the triplet state as an intermediate. Hence the short-lived direct fluorescence emission from the Sx state is referred to as prompt fluorescence. E-type delayed fluorescence was called a-phosphorescence by Lewis in his early works. 

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