State lifetimes

At still shorter time scales other techniques can be used to detenuiue excited-state lifetimes, but perhaps not as precisely. Streak cameras can be used to measure faster changes in light intensity. Probably the most iisellil teclmiques are pump-probe methods where one intense laser pulse is used to excite a sample and a weaker pulse, delayed by a known amount of time, is used to probe changes in absorption or other properties caused by the excitation. At short time scales the delay is readily adjusted by varying the path length travelled by the beams, letting the speed of light set the delay. 

The interpretation of emission spectra is somewhat different but similar to that of absorption spectra. The intensity observed m a typical emission spectrum is a complicated fiinction of the excitation conditions which detennine the number of excited states produced, quenching processes which compete with emission, and the efficiency of the detection system. The quantities of theoretical interest which replace the integrated intensity of absorption spectroscopy are the rate constant for spontaneous emission and the related excited-state lifetime. 

Demas J N 1983 Excited State Lifetime Measurements (New York Aoademio)... 

Data on duorescence, phosphorescence, excited-state lifetimes, transient absorption spectra, and dye lasers are tabulated in Ref. 16. The main nonduorescent process in cyanine dyes is the radiationless deactivation Sj — Sg. Maximum singlet-triplet interconversion ( 52 ) methanol for carbocyanines is about 3% (maxLgrp > 0.03), and the sum [Lpj + st] I than 0.10. 

Quantum well interface roughness Carrier or doping density Electron temperature Rotational relaxation times Viscosity Relative quantity Molecular weight Polymer conformation Radiative efficiency Surface damage Excited state lifetime Impurity or defect concentration... 

Moderately slow exchange. The state lifetime is 2t we ask how the absorption band is affected as this becomes smaller. The uncertainty principle argument given earlier is applicable here lifetime broadening will occur as the state lifetime decreases. Thus, we expect resonance absorption at (or near) frequencies Va nnd Vb but the bands will be broader than in the very slow exchange limit. Equation (4-68) is applicable in this regime. 

Pulsed method. Using a pulsed or modulated excitation light source instead of constant illumination allows investigation of the time dependence of emission polarization. In the case of pulsed excitation, the measured quantity is the time decay of fluorescent emission polarized parallel and perpendicular to the excitation plane of polarization. Emitted light polarized parallel to the excitation plane decays faster than the excited state lifetime because the molecule is rotating its emission dipole away from the polarization plane of measurement. Emitted light polarized perpendicular to the excitation plane decays more slowly because the emission dipole moment is rotating towards the plane of measurement. 

The value of tan A depends upon the modulation frequency, the excited state lifetime, and the rate of rotation. The value decreases to zero when the rotation period is either longer or shorter than the excited state lifetime and is a maximum when the two times are comparable in magnitude. Tan A also increases as the modulation frequency increases. For spherical rotators, the measured value of tan A for a given modulation frequency and excited state lifetime allows the rotational rate to be calculated from... 

Demas, J.N. Excited State Lifetime Measurements Academic New York, 1983 ... 

Figure 11. Experimental He 12(8,v ) and Ne 12(8,v ) excited-state lifetimes, circles and squares, plotted as a function of vibrational quanta, v. The values taken from line width [72] and time-domain [73] measurements are shown as solid and open symbols, respectively.

In this and subsequent equations enters as a constant of integration such that [M-] = 0 at t = to. According to Eq. (45), 2kt[M-]s on the right-hand side of Eq. (48) may be replaced by the reciprocal of the steady state lifetime r. Making this substitution and rearranging, we obtain the compact relation... 

The description of states participating in a spin-state transition as electronic isomers with discrete nuclear configurations, in particular different metal-ligand distances, requires that separate electronic and vibrational spectra of the two spin states exist. Indeed, a superposition of the individual vibrational spectra of the two states is in general observed, the relative contribution of the states being a function of temperature [41, 139, 140, 141, 142]. This observation sets a lower limit for the spin-state lifetime longer than the nuclear vibrational period, i.e.,... 

On the other hand, NMR spectra appear in general as the average of the spectra of the two spin states [36, 153]. This observation determines an upper limit for the spin-state lifetime shorter than the nuclear spin relaxation time Tl = l/ktH < lO s. In general, therefore, either the superposition or the average of the particular spectroscopic properties of the two spin states is observed, subject to the relative magnitude of lifetime of the excited spectroscopic state and the rate of spin-state conversion. The rate /clh is thus estimated... 

A unique situation is encountered if Fe-M6ssbauer spectroscopy is applied for the study of spin-state transitions in iron complexes. The half-life of the excited state of the Fe nucleus involved in the Mossbauer experiment is tj/2 = 0.977 X 10 s which is related to the decay constant k by tj/2 = ln2/fe. The lifetime t = l//c is therefore = 1.410 x 10 s which value is just at the centre of the range estimated for the spin-state lifetime Tl = I/Zclh- Thus both the situations discussed above are expected to appear under suitable conditions in the Mossbauer spectra. The quantity of importance is here the nuclear Larmor precession frequency co . If the spin-state lifetime Tl = 1/feLH is long relative to the nuclear precession time l/co , i.e. Tl > l/o) , individual and sharp resonance lines for the two spin states are observed. On the other hand, if the spin-state lifetime is short and thus < l/o) , averaged spectra with intermediate values of quadrupole splitting A q and isomer shift 5 are found. For the intermediate case where Tl 1/cl , broadened and asymmetric resonance lines are obtained. These may be the subject of a lineshape analysis that will eventually produce values of rate constants for the dynamic spin-state inter-conversion process. The rate constants extracted from the spectra will be necessarily of the order of 10 -10 s"F... 

The nuclear y-resonance effect in ° Ni was first observed in 1960 by Obenshain and Wegener [2]. However, the practical application to the study of nickel compounds was hampered for several years by (1) the lack of a suitable single-line source, (2) the poor resolution of the overlapping broad hyperfine lines due to the short excited state lifetime, and (3) the difficulties in producing and handling the short-lived Mossbauer sources containing the Co and Cu parent nuclides, respectively. 

As seen in Eqs. (59)—(61), dephasing processes introduce two new time scales into the dynamics, in addition to the intermediate state lifetime that determines the structure of 8s in the isolated molecule case. One is the time scale of pure dephasing, and the other is the lifetime of the final state. Equation (64) illustrates that the Tff dependence of 8s is a condensed phase effect that vanishes in the limit of no dephasing. The more careful analysis later shows that the qualitative behavior of the channel phase is dominated by the rpd/rrr and Tpd / [ ratios, that is, by the rate of dephasing as compared to the system time scales. 

Concern for the physical and chemical integrity of topical systems is no different than for other dosage forms. However, there are some unique and germane dimensions to stability associated with semisolid systems. A short list of some of the factors to be evaluated for semisolids is given in Table 12. All factors must be acceptable initially (within prescribed specifications), and all must remain so over the stated lifetime for the product (the product s shelf life). 

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