Deactivation, nonradiative rates

The lowest triplet states of porphyrins and metallopoiphyrins with typical metal atoms have generally long lifetimes from several hundreds of j.s to several ms even in fluid solution at ambient temperature (Table 2). Nonradiative deactivation from the triplet state of porphyrins was revealed to be well described [19,24,25] by the energy gap law [23]. As typical examples, OEP derivatives with Er larger than that of TPP are shown to have generally a longer triplet lifetime than TPP daivatives (Table 2). For magnesium porphyrins, the nonradiative rate constant of the lowest triplet state was expressed by Eq. (2) [25,26]... 

A third possible channel of S state deexcitation is the S) —> Ti transition -nonradiative intersystem crossing isc. In principle, this process is spin forbidden, however, there are different intra- and intermolecular factors (spin-orbital coupling, heavy atom effect, and some others), which favor this process. With the rates kisc = 107-109 s"1, it can compete with other channels of S) state deactivation. At normal conditions in solutions, the nonradiative deexcitation of the triplet state T , kTm, is predominant over phosphorescence, which is the radiative deactivation of the T state. This transition is also spin-forbidden and its rate, kj, is low. Therefore, normally, phosphorescence is observed at low temperatures or in rigid (polymers, crystals) matrices, and the lifetimes of triplet state xT at such conditions may be quite long, up to a few seconds. Obviously, the phosphorescence spectrum is located at wavelengths longer than the fluorescence spectrum (see the bottom of Fig. 1). 

As a preliminary test of equations 1-3, we calculated the values of required to explain the observed nonradiative deactivation rates for 0s(phen)3 " and 0s(bpy)3 at 4.2 K.1 The resulting values, respectively, 0.29 and 0.33 are in good agreement with the value of 0.29 calculated by Byrne et al. for skeletal stretching modes in large aromatic molecules. 

The pK of tyrosine explains the absence of measurable excited-state proton transfer in water. The pK is the negative logarithm of the ratio of the deprotonation and the bimolecular reprotonation rates. Since reprotonation is diffusion-controlled, this rate will be the same for tyrosine and 2-naphthol. The difference of nearly two in their respective pK values means that the excited-state deprotonation rate of tyrosine is nearly two orders of magnitude slower than that of 2-naphthol.(26) This means that the rate of excited-state proton transfer by tyrosine to water is on the order of 105s 1. With a fluorescence lifetime near 3 ns for tyrosine, the combined rates for radiative and nonradiative processes approach 109s-1. Thus, the proton transfer reaction is too slow to compete effectively with the other deactivation pathways. 

Marginal fluorescence quantum yields (1%) are generally observed though 25 and 33 fluorescence with 8% and 14% yields, respectively. Such low quantum yields are indicative of the effective competition of radiationless processes such as the Si —> Tj ISC and fast internal conversion (Si —> S0). The rate constants for radiative decay of Si (kF) range from 8 x 106 to 1.3 x 108 s-1, and the nonradiative decay rate constants (fcNR) range from 1.9 x 108 to 3.5 x 109 s / The nonradiative deactivation pathway is thus six times faster than the radiative one for 33 (anti) and about 110 times faster for 32 (syn). 

Although the existence of the M.I.R. may have appeared counter-intuitive to many chemists, photophysicists had a different point of view, since an inverted" relationship of the rate constant of nonradiative transitions and the energy difference between the states is well established [91]. This energy gap law results from the decreasing vibrational overlap of electronic states, the so-called Franck-Condon factor. It predicts an exponential relationship of the rate constant of nonradiative deactivation of excited states with the energy gap, of the form ... 

In addition to mastering the various processes leading to electronic excitation of the lanthanide ions, one has to prevent excited states to de-excite via nonradiative processes. The overall deactivation rate constant, which is inversely proportional to the observed lifetime r0bs, is given by ... 

Nonradiative deactivation of the Yb(2F5/2) excited state occurs through vibrational states of surrounding molecular groups. Since the contributions of these molecular groups to the overall nonradiative deactivation rate constant are known to be additive, the following equation can be written ... 

Fig. 49. Nonradiative deactivation rate constants of Ybnl ion intris or ternary (J-diketonate complexes for various...

Thus if one wants to improve the overall quantum yield of /3-diketonate complexes, removal of coordinated water molecules is absolutely necessary. By means of the estimated nonradiative deactivation rate constants, calculations showed that removal of these water molecules allows one to reach a maximum quantum yield of 2.6% in toluene for the Ybm-tta complex. However, water molecules are usually replaced with a coordinating secondary ligand, such as phenanthroline, which also contributes to the nonradiative deactivation ( Phen 3.6 x 104 s-1), but to a much lesser extent than water molecules. Further improvement can be reached by deuteration of the central C-H group in the /i-dikctonatc in Yb(ttax/i )3(phcn) for instance, deactivation due to C-H oscillators occurs eight times faster when compared to C-D oscillators. 

In competition to electron transfer processes is internal conversion (IC), in which deactivations of excited states occur via a nonradiative transition to the electronic ground state. Visualizing IC rates is practically impossible because of the lack of a direct probe mechanism for nonradiative transitions. A notable approach to overcome this lack of detectability implies fluorescence quantum yield measurements, which is, however, only indirect. 

The lack of the triplet-triplet absorption of carbocyanine dyes is due to low values of the intersystem crossing rate constants as compared with the rate constants of competing processes [5, 9]. The dye-DNA interactions lead to an increase in the quantum yield of the triplet state of the dye molecules, since the complexation impedes the processes of photoisomerization and vibrational relaxation (nonradiative deactivation), thus permitting the detection of T-T absorption spectra of the bound dyes upon direct photoexcitation. In the presence of DNA in the solutions, the triplet lifetimes of the dyes comprise himdreds of microseconds [10]. 

As described previously, nonradiative decay due to solvent interactions can severely reduce lanthanide luminescence through energy dissipation by vibronic modes, with the O—H oscillator being the most common and eflBcient quencher. However, if these O—H oscillators are replaced with lower-frequency O—D oscillators, the eflBciency of vibronic deactivation decreases substantially. Therefore, the rate constants for luminescence lifetimes (th o) of lanthanide excited states in water or alcoholic solvents are often much shorter than those in analogous deuterated solvents (td o)- This property can be utilized to determine the degree of solvation for luminescent lanthanides. 

This enhancement of intersystem crossing by combining heavy atom and paramagnetic effects explains the relative insensitivity of the Gd phosphorescence lifetime (Table IV) to any additional heavy atom effect (as in the chelate with iodo-BTFA), or to deuteration of solvent or ligand which, by inhibiting nonradiative deactivation, usually increases the lifetime of organic phosphorescence. This insensitivity of the lifetime of the Gd chelate permits us to assign the value of ca. 3 X sec." as the intrinsic radiative rate for the triplet state for Gd BTFA chelates, and a similar value should apply for the Eu compounds. 

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