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Heat-pulse propagation in polymers detected by selectively laser-excited dye molecules
Solid State Communications, Printed in Great Britain.
HEAT-PULSE
Vol. 69, NO. 1, pp. 73-77,
1989.
PROPAGATION IN POLYMERS DETECTED LASER-EXCITED DYE MOLECULES K. Beck, U. Bogner
0038-1098/89 $3.00 + .OO Pergamon Press plc
BY SELECTIVELY
and Max Maier
Naturwissenschaftliche Fakultat II - Physik, Universitlt Regensburg, D-8400 Regensburg, Federal Republic of Germany (Received 16 May 1988 by M. Balkanski) Anti-Stokes sideband spectroscopy and phonon-induced changes of a spectral hole in the strongly inhomogeneously broadened transition of dye molecules in polymers have been applied to the study of heat-pulse propagation in thin polymer films with high time resolution. The measurements indicate a diffusive propagation and a Planck frequency distribution of the phonons in the polymer.
ANTI-STOKES sideband phonon spectroscopy [l-3] in the literature usually termed vibronic [4] sideband phonon spectroscopy - is a versatile optical method for the investigation of high frequency acoustic phonons with high spatial, temporal and spectral resolution. This method, which is based on the electronphonon interaction of impurities like rare earth ions, has been applied to phonon spectroscopy in crystals with the detecting impurities inside the sample. In this letter we present an optical method for the detection of heat-pulse propagation in amorphous polymers. The method utilizes anti-Stokes sideband spectroscopy and in addition phonon-induced changes of a spectral hole of dye molecules. The dye molecules are embedded in low concentration only in that thin part below the surface of the polymer which operates as the phonon detector. A phonon detector which can be applied to disordered systems such as amorphous solids is of general interest. These systems show anomalous thermal properties at low temperatures [5], like the plateau in the thermal conductivity [6] or the excess specific heat capacity [7], which have been discussed using a variety of theoretical models [5, 81. In addition there is a growing demand of polymer materials and composites in cryogenic engineering [9]. Therefore, in situ measurements of thermal properties, e.g., of local temperatures, with high spatial and temporal resolution are of considerable interest for practical purposes. The optical transitions of the dye molecules used in our method of phonon detection in amorphous polymers are strongly inhomogeneously broadened. The required high spectral resolution of the antiStokes sideband spectroscopy is obtained by fluorescence line narrowing with monochromatic laser light. This type of excitation allows the observation of
narrow zero-phonon lines, Stokes sidebands and in particular phonon-induced anti-Stokes sidebands. The information on the spectral distribution of the phonons is extracted from the anti-Stokes sideband spectra. Because of the strong inhomogeneous broadening of the optical transition there are different contributions to the anti-Stokes sideband which are analysed. Additional information on phonon propagation in polymers is obtained from a method of broad-band phonon detection which is based on phonon-induced changes of a persistent spectral hole [lo-121. In this method the temporary filling of the spectral hole is a measure of the presence of phonons. The experimental setup was similar to that used for the measurement of ballistically propagating phonons in crystals [l 11.A sapphire crystal serves as a support of the sample which is shown schematically in the insert of Fig. 1. On top of a thin constantan heater a polyvinyl butyral (PVB) film was prepared. This polymer film consisted of a first layer without dye molecules, which was about 15pm thick, and a very thin second layer (2pm) in which perylene molecules were embedded in low concentration (5 x 10m5mol/l). Both layers have been prepared by successive dipping of the sapphire crystal into solutions of PVB in ethanol without and with perylene. The viscosity of both solutions was adjusted to obtain the different film thicknesses, which were measured by an a-step apparatus. After each dipping process the layers were carefully dried. In order to check the phonon detection properties of the thin doped layer in the polymer film, we prepared a second sample in which just a 2 pm thick doped layer was directly on top of the constantan heater film. A cavity-dumped dye laser (stilbene 3), pumped by a cw Ar+ laser, was used for selective excitation of 73
74
HEAT-PULSE
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IN POLYMERS (a)
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Vol. 69, No. 1
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Fig. 1. Fluorescence intensity I of the 0’-1 transition of perylene versus delay time At between the probing laser pulse and the voltage pulse applied to the constantan heater. The insert shows schematically the sample configuration. the perylene molecules. The laser wavelength was 441 nm, the pulse length 9ns, the repetition rate 40 kHz and the linewidth about 7 GHz. The laser light was focused with a cylindrical lens on the polymer film on top of the constantan heater (dimensions 0.2 x 1.5 mm). All measurements were made with the sample immersed in superfluid helium at 1.4 K. We treat first the broad-band detection of heat pulses by phonon-induced changes of a spectral hole [ 1 I]. The spectral hole is burned in the S,-S, transition of perylene in the detecting polymer layer using the dye laser with an average power of 2mW for about 40min. Changes of the population in the hole center in the presence of phonons were detected by measuring the fluorescence intensity Zof the zero-phonon line of the transition from the S, state of perylene to the first excited vibrational [4] level (355cm-‘) of the S, state. For brevity we term this transition 0’-1 transition. During the fluorescence measurements the average laser power was small (about 2pW). Temporal resolution was achieved by varying the delay time At between the probing laser pulse (9ns duration) and the short voltage pulse (50 ns duration) applied to the constantan heater, which generates a short heat pulse. Figure 1 shows the fluorescence intensity I (normalized to its maximum value) versus delay time At for the sample in which the heat pulse propagates through the 15pm thick PVB layer without perylene molecules before it is detected in the 2 pm doped layer. The strongly asymmetric fluorescence signal rises rapidly, reaches a broad maximum at about 250ns and decreases slowly in the ~LS range. The broad
-1 SO
-_ -
Fig. 2. Schematic energy level diagram of perylene in PVB. (a) Laser light absorption and phonon-assisted anti-Stokes emission. (b) Phonon-assisted anti-Stokes absorption and emission of zero-phonon lines and Stokes phonon sidebands. The vertical solid, wavy and dash-dotted lines represent photon transitions, phonon transitions and the relaxation of vibrational states. The insert shows a spectral hole at the energy E, in the inhomogeneous population distribution N(E).
asymmetric signal indicates diffusive propagation of the heat pulse in the polymer. It will be discussed below. In the second sample in which the perylene-doped detecting layer was prepared directly on top of the heater film, we observed a very short fluorescence signal. Its halfwidth of about 1OOns represents the time resolution of the detector with 2pm thickness. Sideband phonon spectroscopy provides the spectral resolution which was missing in the preceding method of phonon detection. The anti-Stokes sideband of the 0’-1 transition of perylene molecules embedded in low concentration in the polymer film is used for phonon spectroscopy. Since the S,-S,, transition is strongly inhomogeneously broadened, the required high spectral resolution is provided by excitation with a narrow laser line which gives rise to fluorescence line narrowing. There are two contributions to the anti-Stokes fluorescence which are shown in the energy level diagram of Fig. 2. Contribution (a) refers to the antiStokes phonon sideband emission [l, 21. The energy level EL is excited directly by the laser light. The emission of the anti-Stokes light involves the absorption of a phonon in the excited S, state via the electron
Vol. 69, No. 1
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phonon interaction for the 0’-1 transition. Contribution (b) is due to phonon-assisted anti-Stokes absorption [3]. It is based on the electron-phonon interaction for the pure electronic 0’-0 transition. The excitation of the higher lying energy level Ehis possible only when simultaneously a laser photon and a phonon are absorbed [see Fig. 2(b)]. The main contribution to the observed fluorescence from the higher level Ehis the 0’-1 zero-phonon line, which lies on the anti-Stokes side of the 0’-1 zero-phonon line of the lower energy level E,.The emission from the higher level E,, contains also the Stokes phonon sideband and a small anti-Stokes phonon sideband. The total observed anti-Stokes fluorescence is composed of contributions (a) and (b), i.e., of the true anti-Stokes phonon sideband from energy level E,and of the zero-phonon lines and the Stokes and antiStokes phonon sidebands from higher lying energy levels in the broad inhomogeneous population distribution N(E). Therefore, the determination of the spectral distribution of the phonons from the measured anti-Stokes emission spectrum in amorphous solids is more complicated than in crystals. It requires a detailed quantitative analysis of the different contributions similar to that presented for the Stokes sideband in amorphous solids [13]. In our case this analysis could be avoided by comparing the antiStokes spectrum caused by a heat pulse in the polymer film with anti-Stokes spectra at elevated temperatures. In practice, it is convenient for our system perylene in PVB to burn first a spectral hole, because otherwise hole burning can occur during the antiStokes fluorescence measurements. The insert in Fig. 2 shows schematically the spectral hole at the energy E, in the inhomogeneous population distribution N(E).Since the population density in the hole center at EL is small, contribution (a) to the anti-Stokes spectrum is strongly reduced compared to contribution (b). Figure 3 shows fluorescence spectra in the spectral range of the 0’-1 transition of perylene. They consist of a narrow zero-phonon line, a broad Stokes sideband, which is shown partly, and an anti-Stokes sideband [only in Fig. 3(a) and (c)l. The spectra of Fig. 3(a) and (b) have been measured with the sample in which the detecting layer was directly on top of the heater film. They were recorded during and before the heat pulse, respectively. In Fig. 3(a) there is a strong anti-Stokes signal due to the presence of the heat pulse which is absent in Fig. 3b. We measured also the anti-Stokes spectra of the sample in which the heat pulse propagates through a 15pm thick polymer layer before it is detected in the 2pm doped layer. The results obtained in the maximum of the heat pulse
15
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Fig. 3. Fluorescence spectra of the 0’-1 transition of perylene in PVB. (a) Sample with the detecting layer directly on top of the constantan heater; spectrum recorded at the end of the voltage pulse applied to the heater. (b) Same sample as in (a); detection before the voltage pulse. (c) Sample in which the heat pulse propagates through a 15pm thick undoped PVB layer; delay time At = 250ns between the probing laser pulse and the voltage pulse applied to the heater. (d) Same sample as in (c); At = - 100 ns. signal (see Fig. I) and before the heat pulse are shown in Fig. 3(c) and (d), respectively, which correspond to delay times At = 250ns and - 100 ns between the laser pulse and the voltage pulse of the heater. The time resolution of these experiments is determined mainly by the duration of the dye laser pulses (9ns). The anti-Stokes signal in Fig. 3(c) caused by the heat pulse which propagated through the undoped polymer film is smaller than that of Fig. 3(a) where the detecting layer was directly on top of the heater. It should be mentioned that different intensity scales have been used in the upper and lower parts of Fig. 3. The intensity of the 0’-1 zero-phonon line in Fig. 3(b) is about two times larger than that of
76
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Fig. 3(d). This difference is due to the phonon memory effect [lo, 141. The phonon memory effect denotes the phonon-induced filling of the center of the spectral hole which remains after the irradiation of the sample with phonon pulses. The difference in the zero-phonon line intensities of Figs 3(a) and (b) [or Figs 3(c) and (d)] is caused by the real-time effect of the phonons on the spectral hole. The dependence of this difference on the delay time At between the laser pulse and the voltage pulse was used in the measurements of Fig. 1. We return to the anti-Stokes spectra. For a determination of the phonon frequency distribution from the anti-Stokes spectra usually a quantitative analysis is necessary. In order to avoid this, we compared the anti-Stokes spectra caused by the heat pulses with those measured at various elevated temperatures between 5 K and 25 K without heat pulses. Within the experimental accuracy the heat-pulse induced spectral shapes of the anti-Stokes fluorescence for the samples with the detecting layer directly on the heater [Fig. 3(a)] and with the intermediate undoped polymer layer [Fig. 3(c)] agreed with those measured without heat pulses at the elevated temperatures 15 K and 7 K, respectively. Similar comparisons were also made for the anti-Stokes spectra recorded at different delay times At between the laser pulse and the voltage pulse applied to the heater. All the results indicate that the phonons propagating in the polymer films have a Planck frequency distribution both in the immediate neighbourhood of the heater film and in a distance of about 15 pm. We have calculated the temperature of the constantan heater film and compared it with the temperature of the 2pm polymer layer on top of the heater film. For the calculation of the heater temperature we used the acoustic mismatch model of Weis [I 51. We assumed that the main part of the heat pulse phonons is radiated into and propagates ballistically through the sapphire crystal which supports the heater film (see insert of Fig. I). The effect of the phonons, which are transferred from the heater film to the polymer film, on the heater temperature is neglected in first approximation. From the relation T, = (6733~~ + Tl)“4 we calculated a heater temperature TH = 15 K. We used a heater power density of pH = 8 W/mm* and a value of T, = 1.4 K. pH is multiplied by a factor 6733 which is characteristic for the acoustic mismatch of constantan and sapphire [15]. Our results show that the calculated heater temperature T, agrees within the experimental accuracy with the temperature of the 2pm polymer layer on top of the heater film. This fact indicates that the thin polymer layer acquires the temperature of the heater film in the temporal course of the heat pulse on a very short time scale, so that the
IN POLYMERS
Vol. 69, No. 1
radiation of the heater film into the polymer becomes negligible compared to that into the sapphire crystal. Therefore, the above approximation is justified. The results on the thermal equilibrium in the polymer film obtained from anti-Stokes sideband spectroscopy and the strongly asymmetric signal with ps duration which was found using phonon-induced filling of a spectral hole show that diffusive heat pulse propagation is dominant in the amorphous polymer. A treatment of this diffusive propagation with the usual diffusion equation (see, e.g., [16]) should be considered with caution for the following reasons. The mean free path of phonons in disordered solids is strongly frequency dependent. Anharmonic decay of high frequency phonons may be important. Strong inelastic phonon scattering was found in glass [ 171and is expected to occur also in polymers. Raman scattering or relaxation scattering of phonons from two-level tunneling states were discussed as inelastic scattering mechanisms [17]. We would like to suggest that phonon-induced crossing of the barriers of asymmetric double-well potentials of amorphous solids [lo, 141 provides a contribution to inelastic phonon scattering. In addition this mechanism could result in a delayed release of energy [18] stored in the doublewell potentials and therefore also in a delay of phonon propagation. In conclusion, we have presented an optical method of phonon detection in amorphous polymers, which includes anti-Stokes sideband spectroscopy and phonon-induced filling of a spectral hole. This method is also applicable to other disordered solids, e.g., to inorganic glasses where rare earth ions or even dye molecules [ 191 could be used as detecting impurities. It could be used also for phonon detection on solid surfaces with adsorbed molecules [20] as detection elements. Acknowledgements We would like to thank Hoechst for providing polyvinyl butyral. One of the authors (U.B.) is indebted to Prof. R. 0. Pohl for helpful discussions. Financial support from the Deutsche Forschungsgemeinschaft is gratefully acknowledged. REFERENCES 1.
2.
J. Shah, R.F. Leheny & A.H. Dayem, Phys. Rev. Lett. 33, 8 18 (1974); M.J. Colles & J.A. Giordmaine, Phys. Rev. Lett. 27, 670 (1971); W.E. Bron & W. Grill, Phys. Rev. B16,5303 and 53 15 (1977). K.F. Renk, in Nonequilibrium Phonons in Nonmetallic Crystals, (Edited by W. Eisenmenger & A.A. Kaplyanskii), p. 277. North-Holland, Amsterdam (1986).
HEAT-PULSE
Vol. 69, No. 1 3.
R.S. Meltzer,
PROPAGATION
J.E. Rives & G.S. Dixon,
Phys.
12.
Rev. B28, 4786 (1983).
4.
5.
6. 7. 8.
9.
We avoid the term “vibronic” in this letter because it is used in the literature in two different meanings. The term “vibronic” sideband spectroscopy has been used in connection with phonons in crystals, detected in particular by the fluorescence of rare earth ions. In the low temperature spectroscopy of molecules in matrices “vibronic” refers to the internal vibrations of the molecules. Scattering in Condensed See, e.g., Phonon & J.P. Matter J (Edited by A.C. Anderson Wolfe). Springer Series in Solid State Sciences 68. Springer-Verlag, Berlin (1986)) J.J. Freeman & A.C. Anderson, Phys. Rev. B34, 5684 (1986). R.O. Pohl & E.T. Swartz, J. Non-Crystalline Solids 76, 117 (1985). See, e.g., Amorphous Solids: Properties (Edited by W.A.
Phillips), Topics Berlin (1981).
Curr. Phys. Vol. 24. Springer, See, e.g., G. Bogner in Nonmetallic and Composites
10. 11.
Low-Temperature
at Low Temperatures
Materials 3 (Edited
by G. Hartwig & D. Evans), p. 209. Plenum Press, New York (1986). U. Bogner, Phys. Rev. Lett. 37, 909 (1976). K. Beck, G. Roska, U. Bogner & M. Maier, Solid State Commun.
57, 703 (1986).
13.
77
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U. Bogner & G. Riiska, in Phonon Scattering in Condensed Matter (Edited by W. Eisenmenger, K. Labmann & S. Dottinger), p. 395, Springer Series in Solid-State Sciences 51. SpringerVerlag, Berlin (1984). U. Bogner & R. Schwarz, Phys. Rev. B24, 2846 (1981); U. Bogner, K. Beck, P. Schltz & M. Maier, Chem. Phys. Lett. 110, 528 (1984); R.I. Personov, in Spectroscopy and Excitation Dynamics
of
Condensed
Molecular
Systems
17.
(Edited by V.M. Agranovich and R.M. Hochstrasser), p. 555. North-Holland, Amsterdam (1983). K. Beck & U. Bogner, to be published. 0. Weis, Z. f angew. Physik 26, 325 (1969); P. Herth & 0. Weis, ibid. 29, 101 (1970). Y. Kogure, T. Mugishima & Y. Hiki, in [5], p. 40; J. Madsen, J. Trefny & R. Yandfofski, ibid. p. 67. W. Dietsche & H. Kinder, Phys. Rev. Lett. 43,
18.
J. Zimmermann
14. 1.5. 16.
1413 (1979).
& G. Weber,
Phys. Rev. Lett.
46, 661 (1981).
19. 20.
T. Tani, H. Namikawa, K. Arai & A. Makishima, J. Appl. Phys. 58, 3559 (1985). U. Bogner, P. Schatz & M. Maier, Chem. Phys. Lett. 119, 335 (1985).
HEAT-PULSE
Vol. 69, NO. 1, pp. 73-77,
1989.
PROPAGATION IN POLYMERS DETECTED LASER-EXCITED DYE MOLECULES K. Beck, U. Bogner
0038-1098/89 $3.00 + .OO Pergamon Press plc
BY SELECTIVELY
and Max Maier
Naturwissenschaftliche Fakultat II - Physik, Universitlt Regensburg, D-8400 Regensburg, Federal Republic of Germany (Received 16 May 1988 by M. Balkanski) Anti-Stokes sideband spectroscopy and phonon-induced changes of a spectral hole in the strongly inhomogeneously broadened transition of dye molecules in polymers have been applied to the study of heat-pulse propagation in thin polymer films with high time resolution. The measurements indicate a diffusive propagation and a Planck frequency distribution of the phonons in the polymer.
ANTI-STOKES sideband phonon spectroscopy [l-3] in the literature usually termed vibronic [4] sideband phonon spectroscopy - is a versatile optical method for the investigation of high frequency acoustic phonons with high spatial, temporal and spectral resolution. This method, which is based on the electronphonon interaction of impurities like rare earth ions, has been applied to phonon spectroscopy in crystals with the detecting impurities inside the sample. In this letter we present an optical method for the detection of heat-pulse propagation in amorphous polymers. The method utilizes anti-Stokes sideband spectroscopy and in addition phonon-induced changes of a spectral hole of dye molecules. The dye molecules are embedded in low concentration only in that thin part below the surface of the polymer which operates as the phonon detector. A phonon detector which can be applied to disordered systems such as amorphous solids is of general interest. These systems show anomalous thermal properties at low temperatures [5], like the plateau in the thermal conductivity [6] or the excess specific heat capacity [7], which have been discussed using a variety of theoretical models [5, 81. In addition there is a growing demand of polymer materials and composites in cryogenic engineering [9]. Therefore, in situ measurements of thermal properties, e.g., of local temperatures, with high spatial and temporal resolution are of considerable interest for practical purposes. The optical transitions of the dye molecules used in our method of phonon detection in amorphous polymers are strongly inhomogeneously broadened. The required high spectral resolution of the antiStokes sideband spectroscopy is obtained by fluorescence line narrowing with monochromatic laser light. This type of excitation allows the observation of
narrow zero-phonon lines, Stokes sidebands and in particular phonon-induced anti-Stokes sidebands. The information on the spectral distribution of the phonons is extracted from the anti-Stokes sideband spectra. Because of the strong inhomogeneous broadening of the optical transition there are different contributions to the anti-Stokes sideband which are analysed. Additional information on phonon propagation in polymers is obtained from a method of broad-band phonon detection which is based on phonon-induced changes of a persistent spectral hole [lo-121. In this method the temporary filling of the spectral hole is a measure of the presence of phonons. The experimental setup was similar to that used for the measurement of ballistically propagating phonons in crystals [l 11.A sapphire crystal serves as a support of the sample which is shown schematically in the insert of Fig. 1. On top of a thin constantan heater a polyvinyl butyral (PVB) film was prepared. This polymer film consisted of a first layer without dye molecules, which was about 15pm thick, and a very thin second layer (2pm) in which perylene molecules were embedded in low concentration (5 x 10m5mol/l). Both layers have been prepared by successive dipping of the sapphire crystal into solutions of PVB in ethanol without and with perylene. The viscosity of both solutions was adjusted to obtain the different film thicknesses, which were measured by an a-step apparatus. After each dipping process the layers were carefully dried. In order to check the phonon detection properties of the thin doped layer in the polymer film, we prepared a second sample in which just a 2 pm thick doped layer was directly on top of the constantan heater film. A cavity-dumped dye laser (stilbene 3), pumped by a cw Ar+ laser, was used for selective excitation of 73
74
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IN POLYMERS (a)
l-
Vol. 69, No. 1
(b) ‘-
Et,.
0’
I
I
0
I
I
time
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2
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Fig. 1. Fluorescence intensity I of the 0’-1 transition of perylene versus delay time At between the probing laser pulse and the voltage pulse applied to the constantan heater. The insert shows schematically the sample configuration. the perylene molecules. The laser wavelength was 441 nm, the pulse length 9ns, the repetition rate 40 kHz and the linewidth about 7 GHz. The laser light was focused with a cylindrical lens on the polymer film on top of the constantan heater (dimensions 0.2 x 1.5 mm). All measurements were made with the sample immersed in superfluid helium at 1.4 K. We treat first the broad-band detection of heat pulses by phonon-induced changes of a spectral hole [ 1 I]. The spectral hole is burned in the S,-S, transition of perylene in the detecting polymer layer using the dye laser with an average power of 2mW for about 40min. Changes of the population in the hole center in the presence of phonons were detected by measuring the fluorescence intensity Zof the zero-phonon line of the transition from the S, state of perylene to the first excited vibrational [4] level (355cm-‘) of the S, state. For brevity we term this transition 0’-1 transition. During the fluorescence measurements the average laser power was small (about 2pW). Temporal resolution was achieved by varying the delay time At between the probing laser pulse (9ns duration) and the short voltage pulse (50 ns duration) applied to the constantan heater, which generates a short heat pulse. Figure 1 shows the fluorescence intensity I (normalized to its maximum value) versus delay time At for the sample in which the heat pulse propagates through the 15pm thick PVB layer without perylene molecules before it is detected in the 2 pm doped layer. The strongly asymmetric fluorescence signal rises rapidly, reaches a broad maximum at about 250ns and decreases slowly in the ~LS range. The broad
-1 SO
-_ -
Fig. 2. Schematic energy level diagram of perylene in PVB. (a) Laser light absorption and phonon-assisted anti-Stokes emission. (b) Phonon-assisted anti-Stokes absorption and emission of zero-phonon lines and Stokes phonon sidebands. The vertical solid, wavy and dash-dotted lines represent photon transitions, phonon transitions and the relaxation of vibrational states. The insert shows a spectral hole at the energy E, in the inhomogeneous population distribution N(E).
asymmetric signal indicates diffusive propagation of the heat pulse in the polymer. It will be discussed below. In the second sample in which the perylene-doped detecting layer was prepared directly on top of the heater film, we observed a very short fluorescence signal. Its halfwidth of about 1OOns represents the time resolution of the detector with 2pm thickness. Sideband phonon spectroscopy provides the spectral resolution which was missing in the preceding method of phonon detection. The anti-Stokes sideband of the 0’-1 transition of perylene molecules embedded in low concentration in the polymer film is used for phonon spectroscopy. Since the S,-S,, transition is strongly inhomogeneously broadened, the required high spectral resolution is provided by excitation with a narrow laser line which gives rise to fluorescence line narrowing. There are two contributions to the anti-Stokes fluorescence which are shown in the energy level diagram of Fig. 2. Contribution (a) refers to the antiStokes phonon sideband emission [l, 21. The energy level EL is excited directly by the laser light. The emission of the anti-Stokes light involves the absorption of a phonon in the excited S, state via the electron
Vol. 69, No. 1
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phonon interaction for the 0’-1 transition. Contribution (b) is due to phonon-assisted anti-Stokes absorption [3]. It is based on the electron-phonon interaction for the pure electronic 0’-0 transition. The excitation of the higher lying energy level Ehis possible only when simultaneously a laser photon and a phonon are absorbed [see Fig. 2(b)]. The main contribution to the observed fluorescence from the higher level Ehis the 0’-1 zero-phonon line, which lies on the anti-Stokes side of the 0’-1 zero-phonon line of the lower energy level E,.The emission from the higher level E,, contains also the Stokes phonon sideband and a small anti-Stokes phonon sideband. The total observed anti-Stokes fluorescence is composed of contributions (a) and (b), i.e., of the true anti-Stokes phonon sideband from energy level E,and of the zero-phonon lines and the Stokes and antiStokes phonon sidebands from higher lying energy levels in the broad inhomogeneous population distribution N(E). Therefore, the determination of the spectral distribution of the phonons from the measured anti-Stokes emission spectrum in amorphous solids is more complicated than in crystals. It requires a detailed quantitative analysis of the different contributions similar to that presented for the Stokes sideband in amorphous solids [13]. In our case this analysis could be avoided by comparing the antiStokes spectrum caused by a heat pulse in the polymer film with anti-Stokes spectra at elevated temperatures. In practice, it is convenient for our system perylene in PVB to burn first a spectral hole, because otherwise hole burning can occur during the antiStokes fluorescence measurements. The insert in Fig. 2 shows schematically the spectral hole at the energy E, in the inhomogeneous population distribution N(E).Since the population density in the hole center at EL is small, contribution (a) to the anti-Stokes spectrum is strongly reduced compared to contribution (b). Figure 3 shows fluorescence spectra in the spectral range of the 0’-1 transition of perylene. They consist of a narrow zero-phonon line, a broad Stokes sideband, which is shown partly, and an anti-Stokes sideband [only in Fig. 3(a) and (c)l. The spectra of Fig. 3(a) and (b) have been measured with the sample in which the detecting layer was directly on top of the heater film. They were recorded during and before the heat pulse, respectively. In Fig. 3(a) there is a strong anti-Stokes signal due to the presence of the heat pulse which is absent in Fig. 3b. We measured also the anti-Stokes spectra of the sample in which the heat pulse propagates through a 15pm thick polymer layer before it is detected in the 2pm doped layer. The results obtained in the maximum of the heat pulse
15
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Fig. 3. Fluorescence spectra of the 0’-1 transition of perylene in PVB. (a) Sample with the detecting layer directly on top of the constantan heater; spectrum recorded at the end of the voltage pulse applied to the heater. (b) Same sample as in (a); detection before the voltage pulse. (c) Sample in which the heat pulse propagates through a 15pm thick undoped PVB layer; delay time At = 250ns between the probing laser pulse and the voltage pulse applied to the heater. (d) Same sample as in (c); At = - 100 ns. signal (see Fig. I) and before the heat pulse are shown in Fig. 3(c) and (d), respectively, which correspond to delay times At = 250ns and - 100 ns between the laser pulse and the voltage pulse of the heater. The time resolution of these experiments is determined mainly by the duration of the dye laser pulses (9ns). The anti-Stokes signal in Fig. 3(c) caused by the heat pulse which propagated through the undoped polymer film is smaller than that of Fig. 3(a) where the detecting layer was directly on top of the heater. It should be mentioned that different intensity scales have been used in the upper and lower parts of Fig. 3. The intensity of the 0’-1 zero-phonon line in Fig. 3(b) is about two times larger than that of
76
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Fig. 3(d). This difference is due to the phonon memory effect [lo, 141. The phonon memory effect denotes the phonon-induced filling of the center of the spectral hole which remains after the irradiation of the sample with phonon pulses. The difference in the zero-phonon line intensities of Figs 3(a) and (b) [or Figs 3(c) and (d)] is caused by the real-time effect of the phonons on the spectral hole. The dependence of this difference on the delay time At between the laser pulse and the voltage pulse was used in the measurements of Fig. 1. We return to the anti-Stokes spectra. For a determination of the phonon frequency distribution from the anti-Stokes spectra usually a quantitative analysis is necessary. In order to avoid this, we compared the anti-Stokes spectra caused by the heat pulses with those measured at various elevated temperatures between 5 K and 25 K without heat pulses. Within the experimental accuracy the heat-pulse induced spectral shapes of the anti-Stokes fluorescence for the samples with the detecting layer directly on the heater [Fig. 3(a)] and with the intermediate undoped polymer layer [Fig. 3(c)] agreed with those measured without heat pulses at the elevated temperatures 15 K and 7 K, respectively. Similar comparisons were also made for the anti-Stokes spectra recorded at different delay times At between the laser pulse and the voltage pulse applied to the heater. All the results indicate that the phonons propagating in the polymer films have a Planck frequency distribution both in the immediate neighbourhood of the heater film and in a distance of about 15 pm. We have calculated the temperature of the constantan heater film and compared it with the temperature of the 2pm polymer layer on top of the heater film. For the calculation of the heater temperature we used the acoustic mismatch model of Weis [I 51. We assumed that the main part of the heat pulse phonons is radiated into and propagates ballistically through the sapphire crystal which supports the heater film (see insert of Fig. I). The effect of the phonons, which are transferred from the heater film to the polymer film, on the heater temperature is neglected in first approximation. From the relation T, = (6733~~ + Tl)“4 we calculated a heater temperature TH = 15 K. We used a heater power density of pH = 8 W/mm* and a value of T, = 1.4 K. pH is multiplied by a factor 6733 which is characteristic for the acoustic mismatch of constantan and sapphire [15]. Our results show that the calculated heater temperature T, agrees within the experimental accuracy with the temperature of the 2pm polymer layer on top of the heater film. This fact indicates that the thin polymer layer acquires the temperature of the heater film in the temporal course of the heat pulse on a very short time scale, so that the
IN POLYMERS
Vol. 69, No. 1
radiation of the heater film into the polymer becomes negligible compared to that into the sapphire crystal. Therefore, the above approximation is justified. The results on the thermal equilibrium in the polymer film obtained from anti-Stokes sideband spectroscopy and the strongly asymmetric signal with ps duration which was found using phonon-induced filling of a spectral hole show that diffusive heat pulse propagation is dominant in the amorphous polymer. A treatment of this diffusive propagation with the usual diffusion equation (see, e.g., [16]) should be considered with caution for the following reasons. The mean free path of phonons in disordered solids is strongly frequency dependent. Anharmonic decay of high frequency phonons may be important. Strong inelastic phonon scattering was found in glass [ 171and is expected to occur also in polymers. Raman scattering or relaxation scattering of phonons from two-level tunneling states were discussed as inelastic scattering mechanisms [17]. We would like to suggest that phonon-induced crossing of the barriers of asymmetric double-well potentials of amorphous solids [lo, 141 provides a contribution to inelastic phonon scattering. In addition this mechanism could result in a delayed release of energy [18] stored in the doublewell potentials and therefore also in a delay of phonon propagation. In conclusion, we have presented an optical method of phonon detection in amorphous polymers, which includes anti-Stokes sideband spectroscopy and phonon-induced filling of a spectral hole. This method is also applicable to other disordered solids, e.g., to inorganic glasses where rare earth ions or even dye molecules [ 191 could be used as detecting impurities. It could be used also for phonon detection on solid surfaces with adsorbed molecules [20] as detection elements. Acknowledgements We would like to thank Hoechst for providing polyvinyl butyral. One of the authors (U.B.) is indebted to Prof. R. 0. Pohl for helpful discussions. Financial support from the Deutsche Forschungsgemeinschaft is gratefully acknowledged. REFERENCES 1.
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PROPAGATION
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