Induced spectral diffusion

The experimental results of this Section show that optically generated phonons can be used to study the transient broadening of the optical line shape of a single absorber. In principle, the dependence on the phonon frequency can be studied in such an experiment. In the same experiment the time-resolved dynamics of phonon diffusion and phonon decay in polymeric systems can be investigated via the dephasing mechanism of the optical probe. 

In analogy to the tiumeling model, which is based on the assumption of two potential minima, we assume two stable sites for each water molecule (Fig. 6.6). Since the experimental results indicate that a permanent change in the matrix occurs transitions between the two sites are only allowed via the first excited vibrational states. Using such a simple four-level model for the underlying kinetics, we are able to explain the temporal behaviour of the induced spectral diffrision in a quantitative fashion. 

The two ground states are labelled 1 and 2, the first vibrationally excited states 3 and 4, respectively. The IR induced and the spontaneous transition rate for each site are denoted by the Einstein coefficients B and, respectively. In our notation, B is proportional to the irradiated IR intensity. Transitions between the two sites are denoted by the conversion rate k. 

The transitions shown in Fig. 6.6 lead to a system of 4 coupled linear rate equations. Since we used in our experiments very low intensities of the IR light, we consider only the limit B A where the population of the excited levels 3 and 4 is negligible at all times. The result is a time-dependent number of flips between the two ground states n/= n 2 + 

Only those flips are taken into accoimt which contribute to a change in the total configuration of all water molecules with respect to the time / = 0 of the hole burning process. 

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Fig. 14. Thermally induced spectral diffusion broadening in mesoporphyrin IX-substi-tuted horseradish peroxidase ( ) as compared to mesoporphyrin IX in a glass (A). Inset shows the long-wavelength range of the protein absorption. The arrow indicates the hole burning frequency [From J. Zollfrank, J. Friedrich, J. Fidy, and J. M. Vanderkooi, Biophys. J. 59, 305 (1991)].

Optically Induced Spectral Diffusion in Polymers Containing Water Molecules... 

Figure 6.5 Transmission spectra of PMMA without (curve A) and with (curve B) natural water content. The quotient C = B/A shows the H2O absorption lines. Dependence of the hole broadening on the IR wavelength after tg = 35 min (curve D) due to induced spectral diffusion.

The high quantum yield of 18% for the flip of a single water molecule becomes obvious by a comparison of the number of absorbed IR photons (typically lO s ) with the total number of water molecules (about 10 ) in the sample volume. Since a strong induced spectral diffusion is observed within several minutes, a local reorientation process with a high quantum yield must be involved. 

The temperature dependence of hole formation and hole profile is affected by four factors decrease in the Debye-Waller factor, broadening of the hole width, spectral diffusion, and laser-induced hole filling. The first two effects are reversible phenomena and recover at low temperatures. The latter two are irreversible and their influence cannot be eliminated by cooling the sample again. The temperature dependence of the Debye-Waller factor (DiV(T) — S0(T)/S 4)) for TPP/PMMA and TPP/phenoxy resin systems, shown in Table 2.13 by a dotted line, agrees well with the slope of 0 at 4-20 K. The temperature dependence of the Debye-Waller factor is smaller in poly(vinyl alcohol), which shows a higher Es value (23 cm4). Thus, hole formation efficiency is controlled by the temperature dependence of Debye-Waller factor for temperatures below T and, for temperatures above T it is affected mainly by the simultaneous occurrence of spectral diffusion and laser-induced hole filling due to structural relaxation. 

In fact, single molecule spectroscopy (SMS) experiments have recently become a reality. The first experiments were performed on pentacene (the chromophore) in a p-terphenyl crystal [8-10]. I will focus here on the experiments of Ambrose, Basche, and Moemer [9, 10], which involved repeated fluorescence excitation spectrum scans of the same chromophore. For each chromophore molecule they found an identical (except for its center frequency) Lorentzian line shape whose line width is determined by fast phonon-induced fluctuations (and by the excited state lifetime), as discussed above. However, for each of a number of different chromophore molecules Moemer and coworkers found that the chromophore s center frequency changed from scan to scan, reflecting spectral dynamics on the time scale of many seconds The transition frequencies of each of the chromophores seemed to sample a nearly infinite number of possible values. Plotting the transition frequency as a function of time produces what has been called a spectral diffusion trajectory (although the frequency fluctuations are not necessarily diffusive ). These fascinating and totally... 

Spectral diffusion trajectories due to spontaneous (rather than light-induced) fluctuations have been measured for Tr in PE [14] and for TBT in PIB [15,16]. As in the crystalline case these trajectories reflect dynamics of the slow TLSs. The three published trajectories show that in two cases the chromophore visits a large number of frequencies, and in one case, only four. In this latter case the chromophore is presumably strongly coupled to two TLSs. A correlation function analysis was applied to the PIB system, but for neither the PIB nor the PE system was a temperature-dependent study reported. 

Another effect commonly observed in far-field low-temperature single molecule spectroscopy is spectral shifting due to effects other than macroscopically applied fields. Some shifts, termed spectral diffusion, are spontaneous and others, such as those responsible for hole burning, are photo-induced. At liquid He temperatures, spectral diffusion due to local physical perturbations has been observed to occiu in narrow frequency intervals (room temperature, the rate of diffusion and the spectral linewidth increase dramatically, which tends to wash out these effects on time scales accessible to measurement. So it was somewhat of a surprise when spectral shifts in emission spectra were observed at room temperature. 

To measure the longitudinal relaxation time Ti, an inversion or saturation pulse is applied, followed, after a variable time T, by a two-pulse echo experiment for detection (Fig. 5b). The inversion or saturation pulse induces a large change of the echo amplitude for T < T. With increasing T, the echo amphtude recovers to its equilibriiun value with time constant Ti. The echo amphtude of the stimulated echo (Fig. 5c) decays with time constant T2 when the interpulse delay T is incremented, and with the stimulated-echo decay time constant Tse < T1 when the interpulse delay T is incremented. A faster decay, compared to inversion or saturation recovery experiments, can arise from spectral diffusion, because of a change of the resonance frequency for the observed spins, of the order of Av = 1/t on the time scale of T. Quantitative analysis of spectral diffusion can provide information on the reorientation dynamics of the paramagnetic centers. 

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