Reorientation lifetime

In conclusion, we stress that the complementary NLO characterization techniques of pump-probe, Z-scan, and 2PF allow for the unambiguous determination of nonlinear optical processes in organic materials. The important molecular parameters of 2PA cross section, fluorescence efficiency, reorientation lifetimes, excited state cross sections, etc. can be determined. 

The transverse-vibration lifetime t is commensurable with the reorientation lifetime Tor (Fig. 12c). This lifetime strongly increases with decrease of temperature (see the dash-dotted curve in Fig. 12c). 

The high lability of cP [Cu(H20)6]2+ is coincident with the operation of a dynamic Jahn-Teller effect which causes its tetragonal distortion to randomly reorientate, or invert, about the x, y, and z axes very rapidly (Fig. 8) so that the lifetime of a given distortion, r, is much less than the lifetime of a given coordinated H20 molecule, THa0 (99,... 

In (8), the solvent-independent constants kr, kQnr, and Ax can be combined into a common dye-dependent constant C, which leads directly to (5). The radiative decay rate xr can be determined when rotational reorientation is almost completely inhibited, that is, by embedding the molecular rotor molecules in a glass-like polymer and performing time-resolved spectroscopy measurements at 77 K. In one study [33], the radiative decay rate was found to be kr = 2.78 x 108 s-1, which leads to the natural lifetime t0 = 3.6 ns. Two related studies where similar fluorophores were examined yielded values of t0 = 3.3 ns [25] and t0 = 3.6 ns [29]. It is likely that values between 3 and 4 ns for t0 are typical for molecular rotors. 

Observation of reorientational dynamics of dipolar groups surrounding the fluorophore in response to changes in the dipole moment of the fluorophore occurring upon electronic excitation. Such dynamics result in the appearance of spectral shifts with time,(1 ) in changes of fluorescence lifetime across the fluorescence spectrum,(7,32) and in a decrease in the observable effects of selective red-edge excitation.(1,24 33 34) The studies of these processes yield a very important parameter which characterizes dynamics in proteins— the reorientational dipolar relaxation time, xR. 

A species can be considered as an INC if its lifetime is long enough to allow for other chemical reactions than the mere dissociation of the incipient particles. This is the minimum criterion that has to be fulfilled to term a reactive intermediate an ion-neutral complex, because otherwise any transition state would also represent an INC. [171,178] In addition, the reorientation criterion [29,169] should be met,... 

Chromium(III) has a ground state in pseudo-octahedral symmetry. The absence of low-lying excited states excludes fast electron relaxation, which is in fact of the order of 10 -10 ° s. The main electron relaxation mechanism is ascribed to the modulation of transient ZFS. Figure 18 shows the NMRD profiles of hexaaqua chromium(III) at different temperatures (62). The position of the first dispersion, in the 333 K profile, indicates a correlation time of 5 X 10 ° s. Since it is too long to be the reorientational time and too fast to be the water proton lifetime, it must correspond to the electron relaxation time, and such a dispersion must be due to contact relaxation. The high field dispersion is the oos dispersion due to dipolar relaxation, modulated by the reorientational correlation time = 3 x 10 s. According to the Stokes-Einstein law, increases with decreasing temperature, and... 

The presence of second-sphere water molecules could be considered also for other metal aqua ions, like iron(III) and oxovanadium(IV) aqua ions, where the reorientational time is found to be longer than expected. However, in the other cases increases much less than for the chromium(III) aqua ion, thus suggesting that second-sphere water molecules are more labile, their lifetime being of the order of the reorientational time. 

In the reaction the implicit assumption is made that the step E P E-P removes 0, whereas it is conceivable that during the lifetime of E-Pi there might be a reorientation that would enable the removal of other oxygen atoms. Thus the k2 used here might be smaller, perhaps by a factor of four, than the value of k2 used in the other part of the reaction and in other reactions. 

As previously noted (see Section II.B.l), the A emission exhibits an important solvatochromic effect due to the appearance of a large dipole moment in the TICT state. The polar interactions between the solute molecule and the polar environment lead to the reorientation of the solvent molecules and to a relaxation of the electronic energy of the TICT state whose manifestation is a spectral shift during the lifetime of the excited state. The competition between the energy relaxation, whose dynamics is strongly viscosity dependent, and the deactivation of the TICT state has been made evident for DMABN78,89 ... 

Furthermore, let S(v, t>0 - n Avs/n0) denote the emission spectrum whose center of gravity is v0 - n A vs/n0 and corresponding to the reorientation of n solvent molecules. Then it follows that the time-resolved fluorescence spectrum I(t, v) is given by the expected value of S(v, v0 -N(t) A vs/n0)e "T, where t is the excited state lifetime, that is,... 

The time-resolved emission spectra were reconstructed from the fluorescence decay kinetics at a series of emission wavelengths, and the steady-state emission spectrum as described in the Theory section (37). Figure 4 shows a typical set of time-resolved emission spectra for PRODAN in a binary supercritical fluid composed of CO2 and 1.57 mol% CH3OH (T = 45 °C P = 81.4 bar). Clearly, the emission spectrum red shifts following excitation indicating that the local solvent environment is becoming more polar during the excited-state lifetime. We attribute this red shift to the reorientation of cosolvent molecules about excited-state PRODAN. 

Employing the additivity approximation, we find dielectric response of a reorienting single dipole (of a water molecule) in an intermolecular potential well. The corresponding complex permittivity jip is found in terms of the hybrid model described in Section IV. The ionic complex permittivity A on is calculated for the above-mentioned types of one-dimensional and spatial motions of the charged particles. The effect of ions is found for low concentrated NaCl and KC1 aqueous solutions in terms of the resulting complex permittivity e p + Ae on. The calculations are made for long (Tjon x) and rather short (xion = x) ionic lifetimes. 

The spectral function L(z) involved in Eq. (142) is determined by the profile of the model potential well (in this section it is the rectangular well). It follows from Eq. (148) that if we fix the dimensional quantities, such as frequency v and temperature, then the spectral function L(z) depends also on the lifetime x and the moment of inertia of a molecule I. We consider a gas-like reorientation of a polar molecule determined by a dipole moment p of a molecule in a liquid. Calculation of the moment of inertia I deserves special discussion. 

A) Reorientation of a single polar molecule during the mean lifetime ror in a rather narrow intermolecular potential well considered in Section V in terms of the hat-curved (HC) model. 

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