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J Phys. Chem 1990, 94, 5642-5643
Investigatlon of 'She Effects" in Spectral Diffusion B r a a m of Optical tides In
Glasses P. Schellenberg, J. Zollfrank, and J. Friedrich* Institut f u r Physikalische Chemie, Johannes-Gutenberg-Universitat,Welder Weg 11, D4500 Mainz, West Germanv (Received: March 22, 1990)
There is no 'site effect" for the thermally induced spectral diffusion broadening in glasses under temperature cycling conditions. This suggests a hierarchical pattern of inhomogeneous line broadening.
Introduction Inhomogeneous line broadening and spectral diffusion effects are direct evidence for structural disorder. Hence, investigation of these phenomena promises insight into the details of how a probe molecule interacts with structurally disordered solvent molecules. Recently, Laird and Skinner' came up with a microscopic theory on inhomogeneous line broadening and pressure effects on spectral holes in glassy materials. They could show, by employing a modified Lennard-Jones potential, that short- and long-range interactions act quite differently on the probe molecule, as pressure is applied: The first ones cause a pressure-induced broadening of the hole whereas the latter ones cause a pressure-induced shift of its center frequency. Laird and Skinner's theory is based on elastic interactions only and hence does not include spectral diffusion effects. In this Letter, we report on our investigation of site effects in thermally induced spectral diffusion broadening of optical holes. We will show that these kinds of experiments give a deep insight into the details of inhomogeneous line broadening and the nature of solute-solvent interaction in structurally disordered materials. The major outcome of our study is in a way similar to the result of Laird and Skinner, namely, that short- and long-range interactions play a very different role in inhomogeneous line broadening phenomena. We stress, however, that the interactions which dominate the spectral diffusion effects are very different from those which dominate the pressure effects. Hence, the terms "short range" and "long range" refer to different length scales. What we mean exactly by these terms is specified below. Spectral diffusion effects in optical holes occur as a consequence of small structural rearrangements of the glass forming molecules. These rearrangement processes even occur at extremely low temperatures because the glass is far from equilibrium. They may as well be thermally induced.* Basic Features of Inhomogeneous Line Broadening in Glasses The present investigation is based on a recent temperature cycling hole burning study on tetracene doped alcohol glass, where we measured with a high level of precision the center frequency of a hole, burnt into the red edge of the inhomogeneous band, as it broadened under temperature cycling condition^.^ The result was clear-cut: Though there was strong irreversible line broadening, there was no measurable line shift. This result is contrary to what one would expect from a straightforward model of inhomogeneous line broadening: The line should wander in the center of the inhomogeneous band as it broadens, simply because the density of states increases toward this direction. The fact that it did not move at all was interpreted in terms of a hierarchical pattern of inhomogeneous line broadening. This hierarchical pattern of inhomogeneous line broadening seems to be a characteristic feature of glasses. The present study was undertaken ( I ) Laird, B. B.; Skinner, J. L. J . Chem. Phys. 1989, 90, 3274. (2) KBhler, W.; Zollfrank, J.; Friedrich, J. Phys. Rev. 1989, 839, 5414. (3) Hirschmann, R.; Friedrich. J. Chem. Phys. Left.,submitted for pub-
lication.
in order to check the consequences of this model. Before discussing the experiments, let us briefly go over the basic features of the model: The total inhomogeneous band is built from (at least) two independent distributions (Figure 1). We call the more important distribution the "site distribution". Basically, this distribution reflects the statistics of the solvent cages. The solvent cage around a probe molecule is formed by nearby solvent molecules. Hence, we argue that the site distribution results from short-range interactions. Since the coupling to the nearby solvent molecules is strong, the site distribution is responsible for almost all the inhomogeneous line broadening. Consider now a molecule in a specific site. Of course, the energy of this site changes a little bit, when the configurational state of the whole bulk changes. We describe the configurational state of the bulk in terms of TLS. A TLS can be viewed as a rather local metastable region in the bulk, where structural changes can occur.4 These regions are modeled in terms of double-minimum potentials, where only the two lowest states are taken into account. The molecule in the special site considered will fluctuate around its mean energy, as the bulk fluctuates between its configurational states. The associated width is the spectral diffusion width. We call the associated distribution the "bulk distribution". It reflects the density of configurational states of the bulk TLS (Figure 1). Compared to the width of the site distribution, the width of the bulk distribution is rather small because the concentration of TLS is smallS and, hence, their interaction with the probe molecule is weak. At sufficiently low temperatures, this width is purely inhomogeneous because the TLS will be frozen in either one of their two states. If the concentration of TLS is low enough, the probability of finding a TLS within the solvent cage molecules is rather small and, hence, the two distributions will be independent. Suppose we have just one site, whose energy is distributed because of the TLS configurations. Then, burning a hole into the edge of the bulk distribution of this special site, the hole will move to the maximum of the bulk distribution as it undergoes spectral diffusion broadening. In a real hole burning experiment, however, neighboring sites will also be burnt and, hence, the shift of the hole will be largely compensated as has been demonstrated by the experiment^.^
Results and Discussion We investigated the thermally induced spectral diffusion broadening under temperature cycling conditions as a function of the site energy. In case the line is indeed built from a convolution of two independent distributions, which originate from short- and long-range interactions, one would expect that the spectral diffusion broadening is independent of the site energy provided that the coupling between the probe molecule and the TLS i s independent of it. In a temperature cycling hole burning experiment, the hole is burnt at a low temperature. In the experiments discussed here, (4) Anderson, P. W.; Halperin, B. I.; Varma, C. M. Philos. Mug. 1972. 25. 1 ( 5 ) Hunklinger, S.; Raychauduri, A. K. In Progress in Low Temperature
Physics; Brewer, D . F., Ed.; Elsevier: Amsterdam, 1986; Vol. 9, p 265.
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0 1990 American Chemical Society
The Journal of Physical Chemistry, Vol. 94, No. 15, 1990 5643
Letters
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Figure 1. Sketch of inhomogeneous line broadening in glasses. The line is built from a convolution of two independent distributions, namely, the ‘site distribution” and the “bulk distribution”. The first one represents the distribution of solvent cages, whereas the latter represents the distribution of glass configurations.
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Figure 2. Various burnt ‘sites”, for which the thermally induced spectral diffusion broadening was investigated. Sample: PC* in PMMA.
this temperature was 4.6 K. Then, the temperature is cycled between the burning temperature and a so-called excursion temperature. The excursion temperature is varied. The measured quantity is A q r , the thermally induced irreversible change of the hole width during a cycle. This type of experiment is exclusively sensitive to spectral diffusion effects.* We investigated a series of rather different materials: Two alcohol glass samples (EtOH/MeOH), a polymer glass (PMMA), and a pure hydrocarbon glass (3-methylpentane). We also used very different probe molecules with photochemical as well as photophysical hole burning reactions: tetracene, a phthalocyanine derivative (H2PC*, see Figure 3), and an aromatic boron complex. As an example, the data of the phthalocyanine doped PMMA sample are shown in Figures 2 and 3. Figure 2 shows the various positions in the inhomogeneous band where hole burning was performed. Figure 3 demonstrates impressively that the broadening patterns in the various sites can be mapped onto each other. The same result was obtained from the other samples. Hence, the overall result of our study is unambiguous: Though the irreversible line broadening as a function of excursion temperature is rather different for the various samples, there is no site effect
excursion temperature
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Figure 3. Line broadening pattern for the various holes shown in Figure 2. There is no site effect.
at all. This result strongly supports the idea of an hierarchical inhomogeneous line broadening as outlined above and as sketched in Figure 1. But how can we understand the fact that the coupling between probe and TLS is independent of the site energy. Would not we rather expect this coupling to be stronger for the red sites than for the blue sites? The answer is no. It is based on the following argument: We presume that the concentration of TLS is sufficiently low. This assumption is an essential ingredient of the model. Hence, the average distance between probe and TLS will be large. On this rather large length scale of the p r o b T L S interaction, the glass will be perfectly homogeneous. Hence, the coupling between probe and TLS will depend on the distance between probe and TLS, only. All the local variations around the probe molecule which lead to the solvent cage statistics will not show up in this coupling and, as a consequence, there will be no site effect. We conclude this Letter by coming back again to the paper by Laird and Skinner. They argued that the pressure broadening of the holes (as has been measured by Haarer’s group6) is a local effect, whereas the hole shift is caused by distant field effects. As stressed above, our argumentation for the interpretation of the temperature cycling experiments is just the other way around: The observed broadening is a distant field effect whereas the site shift is rather a local effect. The two argumentations are reconciled, however, by considering the different potentials which enter the two models: The spectral diffusion broadening is based on a dipole-dipole interaction’ which falls off as l / r 3 . In our argumentation “short-range” or “long-range” interaction is related to the length scale of the dipole-dipole interaction. Compared to this scale, the dispersion forces appearing in the Lennard-Jones potential are short-range interactions. Hence, there is no obvious discrepancy between the two argumentations.
Acknowledgment. We acknowledge support from the Deutsche Forschungsgemeinschaft (SFB 262, D12 and Fr 456/12-1). ( 6 ) Sesslemann, Th.; Richter, W.;Haarer, D.; Morawitz, H. Phys. Reo. 1987,836, 7601. ( 7 ) Black, J. L.; Halperin, B. 1. Phys. Reu. 1977, 816, 2879.
