Nonradiative relaxation rates

There is another question with respect to the lifetime behavior of lanthanides in nanocrystals. Will the lifetime of all excited states be lengthened The answer is obviously no since the observed lifetime depends on both the radiative and nonradiative relaxation rates. Although the correction of effective refractive index (eq. (9)) may be applicable to all excited states, it affects only the radiative lifetime. 

Luminescence lifetime depends upon radiative and nonradiative decay rates. In nanoscale systems, there are many factors that may affect the luminescence lifetime. Usually the luminescence lifetime of lanthanide ions in nanocrystals is shortened because of the increase in nonradiative relaxation rate due to surface defects or quenching centers. On the other hand, a longer radiative lifetime of lanthanide states (such as Dq of Eu " ) in nanocrystals can be observed due to (1) the non-solid medium surrounding the nanoparticles that changes the effective index of refraction thus modifies the radiative lifetime (Meltzer et al., 1999 Schniepp and Sandoghdar, 2002) (2) size-dependent spontaneous emission rate increases up to 3 folds (Schniepp and Sandoghdar, 2002) (3) an increased lattice constant which reduces the odd crystal field component (Schmechel et al., 2001). 

Wong, K. S., Bradley, D. D. C., Hayes, W., Ryan, J. F., Friend, R. H., Lindenberger, H., and Roth, S., Correlation between conjugation length and nonradiative relaxation rate in poly(p-phenylenevinylene) a picosecond photoluminescence study, J. Phys. C Solid State Phys., 20, L187-Ll94 (1987). 

The occurrence of nonradiative losses is classically illustrated in Figure 3. At sufficiently high temperature the emitting state relaxes to the ground state by the crossover at B of the two curves. In fact, for many broad-band emitting phosphors the temperature dependence of the nonradiative decay rate P is given bv equation 1 ... 

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]

The rate of a nonradiative relaxation such as the km process of equation (7) can be estimated from t° values measured at a sufficiently low temperature such that ka and kbisc are likely to be unimportant because of their higher activation energy. Under such a condition, 1/t° = (kr + knT), and kT can be estimated from the low temperature limit to t°, or from equation (25). For coordination compounds, knT is usually not very temperature dependent, act typically being 8-12 kJ mol-1. 

Kim et al. observed a very fast ion pair formation (below their detection limit of about 1 ps) from transient absorption spectra of fullerenes in the presence of aromatic amines such as /V,/V-dimcthyl- or /V,/V-dicthyl-anilinc, corresponding to a rate > 1 X 1012 M-1 s-1. An explanation for such extremly fast electron transfer is most likely a ground-state complex of fullerene and amine. Excitation leads to the neutral aminc/ C 0 contact pair followed by electron transfer. The decay of the both transient absorption from Cfo and Qo/amine occurs with the same rate suggesting that charge recombination is the major nonradiative relaxation channel [138],... 

Previous studies on paraffins, rhodamine dyes, and l,3-bis(N-carbozoyl) propane excimers have concluded that there is a relationship between km and polymer viscosity and free volume [103-105], Indeed, this dependence has been investigated in the context of decreasing free volume during methyl methacrylate polymerization [83,84], It has been shown that the nonradiative decay processes follow an exponential relationship with polymer free volume (vf), in which kra reduces as free volume is decreased [see Eq. (5)]. Here, k. represents the intrinsic rate of molecular nonradiative relaxation, v0 is the van der Waals volume of the probe molecule, and b is a constant that is particular to the probe species. Clearly, the experimentally observed changes in both emission intensity and lifetime for/ac-ClRe(CO)3(4,7-Ph2-phen) in the TMPTA/PMMA thin film are entirely consistent with this rationale. 

Q. Shi and E. Geva. Nonradiative electronic relaxation rate constants from approximations based on linearizing the path-integral forward-backward action. J. Phys. Chem. A, 108 6109, 2004. 

Concerning the relaxation processes of Ru(II) tris(diimine) complexes whose lowest excited state is the MLCT state, a good linear relationship between the logarithm of the nonradiative decay rate ( a) and the energy gap ( )oo( MLCT)), the energy difference from the ground state to the MLCT state, is observed. This is termed as the Energy Gap Law (5,27). In a series of rhe-nium(I) bipyridine tricarbonyl complexes, such a linear correlation was also observed (Fig. 4) (26,27), where the net... 

Excitation and the relaxation (radiative and non radiative) processes of the Tryptophan solution and the colloids are represented in figure 18.7. The new relaxation pathways introduced by the metal nanoparticles (nonradiative decay rate, K p) are shown in figure 18.7(b). Although, one photon at 270nm and two-photons at 532nm are resonant with the excited states of the molecule, these wavelengths are not in resonance with the Plasmon energy level. 

They neglected the reverse rate governed by b (assuming an exothermic initial step) and assumed rapid nonradiative relaxation of nascent D BA (governed by rate constant e). The steady-state result once again identifies the charge injection process as the rate-determining step (i.e., k -t = a) under the conditions d e. 

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