- Email: [email protected]
Brillouin scattering study of glass-forming propylene glycol
Materials Science and Engineering A 442 (2006) 379–382
Brillouin scattering study of glass-forming propylene glycol S. Tsukada ∗ , Y. Ike, J. Kano, S. Kojima Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan Received 30 July 2005; received in revised form 20 March 2006; accepted 27 March 2006
Abstract The elastic properties of propylene glycol (PG) were studied by Brillouin scattering between 100 K and 442 K using a high-resolution Fabry–Perot interferometer. The acoustic phonon velocity, phonon damping, and relaxation time were measured as functions of temperature. At high temperatures, the temperature dependence of the relaxation time obeyed the Arrhenius law, τ = τ 0 exp (E/kB T). We obtained E = 0.27 eV and τ 0 = 6.40 × 10−16 s. The dynamical properties between racemic PG and chiral isomer (S)-PG were compared and small differences, which were within the experimental uncertainty, were observed. These differences were attributed to the molecular interaction, which played an important role in relaxation. Neither material displayed an elastic anomaly at its melting point. © 2006 Published by Elsevier B.V. Keywords: Propylene glycol; Brillouin scattering; Liquid–glass transition; Chiral isomer; Lower alcohol
1. Introduction The liquid–glass transition has been known for thousands of years. However, the details of the transition are still unclear. Supercooled liquids are one of the most interesting phenomena related to liquid–glass transitions. The structures of lower alcohols are relatively simple. Thus, there should be few intramolecular effects. Liquid–glass transitions of lower alcohols are caused by the frustration between the hydrogen bonds and the close packing of the alkyl groups [1]. In the 1980s, Leutheusser applied the mode coupling theory (MCT) to a liquid–glass transition using the density fluctuation modes [2] and since then theoretical studies, which include molecular dynamical simulations (MD) on the liquid–glass transition, have been carried out. Although the original MCT assumed spherical molecules, today anisotropic molecules are used in the MCT. Hence, the validity of the MCT can be tested using lower alcohols. PG, (HO)CH2 –CH(OH)–CH3 , with two –OH groups in a molecule is a lower alcohol that undergoes a liquid–glass transition near 165 K [3]. The relaxation time of the ␣-relaxation obeys the Vogel–Fulcher law [4]. Numerous dynamical properties have been measured to test the validity of theoretical models [3,5]. Brillouin scattering is a powerful tool to measure the phase velocity and damping of a ∗
Corresponding author. Tel.: +81 29 853 5262; fax: +81 29 853 5262. E-mail address: [email protected] (S. Tsukada).
0921-5093/$ – see front matter © 2006 Published by Elsevier B.V. doi:10.1016/j.msea.2006.03.131
longitudinal acoustic (LA) wave in materials and the relaxation time in the gigahertz (GHz) frequency range. Glass-forming PG is a well-studied, prototype glass-forming liquid. The Brillouin scattering study of PG using a Sandercock-type 3 + 3-pass tandem Fabry–Perot interferometer has already been published [6]. In this report, Brillouin scattering of PG was measured by an angular dispersion Fabry–Perot interferometer (ADFPI) with a high resolution (finesse = over 100) and short acquisition time. Currently, chiral isomers receive attention due to physical, chemical, biological, and medicinal reasons [7]. The characteristics between PG and chiral isomer (S)-PG are also discussed. Because the chiral isomer has a simple arrangement compared to the racemic mixture, differences in the dynamical properties are expected. However, there is not a report that compares the chiral isomer to the racemic mixture. 2. Experimental As mentioned above, ADFPI is a very powerful tool for studying the Brillouin scattering of a liquid. The development of a charge-coupled-device (CCD) detector, a solid etalon, and the light source with a highly stable wavelength allows for much shorter acquisition times and provides a higher resolution than using a scanning FPI. Fig. 1 shows a schematic diagram of the ADFPI. The light source was a diode-pumped solid-state laser (DPSS, coherent) with a ring cavity operating at 532 nm and 100 mW. Lens L1
380
S. Tsukada et al. / Materials Science and Engineering A 442 (2006) 379–382
Fig. 2. Rayleigh and Brillouin spectra of PG at four different temperatures. Near 300 K, the Rayleigh-wing becomes large.
Fig. 1. Schematic diagram of the ADFPI experimental setup. Solid etalon is combined with a highly sensitive CCD area detector.
focused the laser beam into the sample cell. The scattered light was collected at a 90◦ angle. The scattered light passed through the collimator with L2a, L2b, and L2c. To reduce the stray light, a slit was used between L2b and L2c. The interference fringes were observed after passing through a Fabry–Perot Interferometer (FPI). Between these fringes, frequency shifted light was transmitted. ADFPI was composed of a solid etalon, which is mechanically stable. The solid etalon was made of a single fused silica plate. The mirror was made from a soft-coated dielectric material and the degree of flatness was better than λ/100 and 30 GHz of FSR with a reflectivity of 99.0%. An etalon with a very high reflectivity was used to obtain high contrast and high resolution. The transmitted light through an etalon was focused onto CCD2 by the L3 lens. The exposure time of CCD2 was 5 s, which is 1/10 shorter than that of the conventional scanning method. To reduce thermal noise, CCD2 was operated at 243 K by a thermoelectric cooler. CCD1 was used to monitor the samples and to easily align the optics. A helium refrigerator and heater were used to change the sample temperature. Measurements were performed from 100 K to 450 K. The temperature was monitored by a silicon diode sensor on the sample cell below room temperature and by a chromel–alumel thermocouple in the sample cell above room temperature. The samples, which had a purity of 99.0%, were filtered by a millipore filter with a pore size of 0.22 m to remove impurities. More details are available in previous works [7–10].
Fig. 3 shows the longitudinal sound velocity, V, and the full width at half-maximum (FWHM) of the Brillouin component, ν. The following equation is used to determine V, V =
λ0 νB , 2n sin(θ/2)
(1)
where νB is the Brillouin shift, n the refractive index of PG (1.436) measured by the minimum deviation method, λ0 the wavelength of the incident beam (532 nm), and θ is the scattering angle (90◦ ). The difference between the observed Brillouin component and the instrumental function are regarded as the true FWHM of the longitudinal acoustic phonon. In this analysis, the Lorentz function was assumed to be an instrumental function. The sound velocity and FWHM lead to an elastic constant, M, and sound attenuation, α, using the following equations: ν M = ρV 2 1 − 3 (2) 2V and α = 2π
ν V
,
(3)
where ρ is the density. The low frequency limit of the sound velocity, V0 , is necessary to determine the relaxation time. To
3. Results and discussion Fig. 2 shows the spectra at four temperatures obtained by ADFPI. The spectra are well fitted by the damped harmonic oscillator model. One spectrum has one elastic Rayleigh component and two inelastic Brillouin components. The small asymmetry in the Brillouin components around room temperature may be due to the Rayleigh-wing. Due to the high flatness and high reflectivity of the etalon, the finesse is above 100 in all the temperatures.
Fig. 3. Temperature dependence of sound velocity () and damping () measured by ADFPI. The low frequency limit of sound velocity, V0 , is measured by the ultrasonic pulse-echo method () and approximated as a second order polynomial function of temperature, T (lower broken line). Upper broken line is V∞ obtained by Eq. (5). Solid line represents V∞ * obtained by the conventional equation [5,7,9,12].
S. Tsukada et al. / Materials Science and Engineering A 442 (2006) 379–382
381
obtain V0 , the ultrasonic velocity was measured at 10 MHz using the standard pulse-echo method. Thus, V0 can be approximated by the second order polynomial function of temperature, T. Although V0 is generally approximated by a linear function of T, the linear function is not sufficient to fit our data. In fact, Comez et al. measured the Brillouin scattering of glycerol and found that V0 was not approximated by a linear function [11]. Therefore, the approximation of a second order polynomial function of temperature can be reasonable. The liquid–glass transition temperature, Tg = 165 K, is determined at the point where the slope dV/dT changes. An anomalous broadening of the FWHM near Tg is not observed. To obtain the relaxation time, τ, a single relaxation time model (Debye model) is employed and τ is given by: τ=
V 2 {1 − 3(ν/2νB )2 } − V02 , 4πν{1 − 2(ν/2νB )2 }
(4)
which is more accurate than the conventional equation [5,7,9,12]. Compared to the conventional equation, Eq. (4) adds additional terms, including (ν/2νB ). Thus, the improved equation for V∞ is given by: 2 V∞
V 2 {1 − 3(ν/2νB )2 } − V02 = + V02 , ωB2 τ 2 /(1 + ωB2 τ 2 )
(5)
where ωB is the phonon angular frequency defined by ωB = 2πνB . Fig. 3 shows the temperature dependence of V∞ . ∗ obtained by the conventional equation is For comparison, V∞ also plotted. Fig. 3 also shows the difference between Eq. (5) and the conventional equation, which is due to the denominator in Eq. (5). The denominator in Eq. (5) approaches 0 at lower temperatures. To prevent the divergence of V∞ , a more accurate V0 is needed. However, as mentioned above, a method to more accurately determine V0 is in progress. Actually, V∞ does not diverge in the temperature region where V0 is obtained by ultrasonic measurements. Fig. 4 shows the temperature dependence of the relaxation rate, f = 1/τ of PG. It obeys the Arrhenius law τ = τ 0 exp (E/kB T) when E = 0.27 eV and τ 0 = 6.40 × 10−16 s. E is almost same and τ 0 is half of the previous value [3]. As mentioned above, the difference is due to the equation used to determine V0 . The activation energy is about three times larger than the internal rotational energy of an alkyl chain of PG at the room temperature. Thus, it is determined that the molecules interact with the surrounding molecules through hydrogen bonds and the potential barrier of the rotational motion of the alkyl chain is elevated. The potential barrier increases by associative and disassociative processes between the molecules through hydrogen bonds. Compared to the relaxation time obtained by dielectric measurements [4], τ is a few orders smaller than that of the ␣-relaxation. Hence, the relaxation process measured by Brillouin scattering is a fast process and not an ␣-relaxation process. The inset of Fig. 4 shows the difference in the relaxation rate between racemic PG and (S)-PG. As expected, the relaxation rate of racemic PG is slightly faster than that of the chiral isomer below 300 K because (S)-PG is associated differently
Fig. 4. Temperature dependences of relaxation rates of PG () and (S)-PG () determined by Brillouin scattering and dielectric measurements (, [4]). Solid triangles are fitted by Arrhenius law (dashed line), but open triangles are fitted by Vogel–Fulcher law (solid line). Inset shows the log f values for the comparison between PG and (S)-PG in the range from 1000/T = 3.0 to 4.0.
than the racemic one. It is likely that alkyl groups in the liquid can independently rotate at higher temperatures and the independency is suppressed as the temperature decreases. Thus, the different structures of associated clusters are more influential below room temperature. Ike et al. reported that (S)-1-amino-2propanol has a lower glass-forming tendency than the racemic one [7] and concluded that the configuration variation of the system is an important factor of the liquid–glass transition. Our interpretation is consistent with theirs. In addition, PG has a simple molecular structure, which makes it easier to observe the difference. Neither (S)-PG nor racemic PG has an elastic anomaly at its melting point. Therefore, crystallization does not occur, and both (S)-PG and racemic PG transform into a supercooled liquid phase, indicating that both liquids have a good tendency for glass forming. 4. Conclusion Propylene glycol, a lower alcohol, was investigated using an angular dispersion Fabry–Perot interferometer with a highly sensitive CCD detector. The Brillouin spectra of PG were obtained in a wide temperature range, 100–442 K, and Tg was determined to be 164 K using the point where the slope of the sound velocity curve as a function of temperature changed in the low temperature region. Our main purpose was to determine the temperature behavior of the relaxation process in the GHz region. The relaxation time obeyed the Arrhenius law. The values of the relaxation time from the Brillouin spectra were a few orders smaller than those obtained by dielectric measurement [4]. A detailed comparison with the mode coupling theory is currently underway. A small difference was obtained in the relaxation time of PG and (S)-PG, which is attributed to the variations in the system configurations and their simple structures. Neither PG nor (S)PG displayed a sound velocity anomaly at its melting point.
382
S. Tsukada et al. / Materials Science and Engineering A 442 (2006) 379–382
Acknowledgments This work was supported in part by Grant-in-Aid Nos. 137400232 and 15654057 from the Ministry of Education, Culture, Sports, Science, and Technology, Japan. References [1] H. Tanaka, Phys. Rev. Lett. 80 (1998) 5750–5753. [2] E. Leutheusser, Phys. Rev. A 29 (1984) 2765–2772. [3] A. Yoshihara, H. Sato, S. Kojima, Jpn. J. Appl. Phys. 35 (1996) 2925–2929.
[4] I.S. Park, S. Kojima, J. Phys. Soc. Jpn. 67 (1998) 4131–4138. [5] S. Itoh, T. Yamana, S. Kojima, Jpn. J. Appl. Phys. 35 (1996) 2879– 2881. [6] S. Kojima, H. Sato, A. Yoshihara, J. Phys. Condens. Matter 9 (1997) 10079–10085. [7] Y. Ike, S. Kojima, J. Mol. Struct. 744 (2005) 521–524. [8] J.H. Ko, S. Kojima, Rev. Sci. Inst. 73 (2002) 4390–4392. [9] G. Matsui, S. Kojima, S. Itoh, Jpn. J. Appl. Phys. 37 (1998) 2812–2814. [10] J.H. Ko, S. Kojima, Phys. Lett. A 321 (2004) 141–146. [11] L. Comez, D. Fioretto, F. Scarponi, J. Chem. Phys. 119 (2003) 6032–6043. [12] K. Lapsa, M. Trybus, T. Runka, W. Proszak, M. Drozdowski, J. Mol. Struct. 704 (2004) 215–218.
Brillouin scattering study of glass-forming propylene glycol S. Tsukada ∗ , Y. Ike, J. Kano, S. Kojima Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan Received 30 July 2005; received in revised form 20 March 2006; accepted 27 March 2006
Abstract The elastic properties of propylene glycol (PG) were studied by Brillouin scattering between 100 K and 442 K using a high-resolution Fabry–Perot interferometer. The acoustic phonon velocity, phonon damping, and relaxation time were measured as functions of temperature. At high temperatures, the temperature dependence of the relaxation time obeyed the Arrhenius law, τ = τ 0 exp (E/kB T). We obtained E = 0.27 eV and τ 0 = 6.40 × 10−16 s. The dynamical properties between racemic PG and chiral isomer (S)-PG were compared and small differences, which were within the experimental uncertainty, were observed. These differences were attributed to the molecular interaction, which played an important role in relaxation. Neither material displayed an elastic anomaly at its melting point. © 2006 Published by Elsevier B.V. Keywords: Propylene glycol; Brillouin scattering; Liquid–glass transition; Chiral isomer; Lower alcohol
1. Introduction The liquid–glass transition has been known for thousands of years. However, the details of the transition are still unclear. Supercooled liquids are one of the most interesting phenomena related to liquid–glass transitions. The structures of lower alcohols are relatively simple. Thus, there should be few intramolecular effects. Liquid–glass transitions of lower alcohols are caused by the frustration between the hydrogen bonds and the close packing of the alkyl groups [1]. In the 1980s, Leutheusser applied the mode coupling theory (MCT) to a liquid–glass transition using the density fluctuation modes [2] and since then theoretical studies, which include molecular dynamical simulations (MD) on the liquid–glass transition, have been carried out. Although the original MCT assumed spherical molecules, today anisotropic molecules are used in the MCT. Hence, the validity of the MCT can be tested using lower alcohols. PG, (HO)CH2 –CH(OH)–CH3 , with two –OH groups in a molecule is a lower alcohol that undergoes a liquid–glass transition near 165 K [3]. The relaxation time of the ␣-relaxation obeys the Vogel–Fulcher law [4]. Numerous dynamical properties have been measured to test the validity of theoretical models [3,5]. Brillouin scattering is a powerful tool to measure the phase velocity and damping of a ∗
Corresponding author. Tel.: +81 29 853 5262; fax: +81 29 853 5262. E-mail address: [email protected] (S. Tsukada).
0921-5093/$ – see front matter © 2006 Published by Elsevier B.V. doi:10.1016/j.msea.2006.03.131
longitudinal acoustic (LA) wave in materials and the relaxation time in the gigahertz (GHz) frequency range. Glass-forming PG is a well-studied, prototype glass-forming liquid. The Brillouin scattering study of PG using a Sandercock-type 3 + 3-pass tandem Fabry–Perot interferometer has already been published [6]. In this report, Brillouin scattering of PG was measured by an angular dispersion Fabry–Perot interferometer (ADFPI) with a high resolution (finesse = over 100) and short acquisition time. Currently, chiral isomers receive attention due to physical, chemical, biological, and medicinal reasons [7]. The characteristics between PG and chiral isomer (S)-PG are also discussed. Because the chiral isomer has a simple arrangement compared to the racemic mixture, differences in the dynamical properties are expected. However, there is not a report that compares the chiral isomer to the racemic mixture. 2. Experimental As mentioned above, ADFPI is a very powerful tool for studying the Brillouin scattering of a liquid. The development of a charge-coupled-device (CCD) detector, a solid etalon, and the light source with a highly stable wavelength allows for much shorter acquisition times and provides a higher resolution than using a scanning FPI. Fig. 1 shows a schematic diagram of the ADFPI. The light source was a diode-pumped solid-state laser (DPSS, coherent) with a ring cavity operating at 532 nm and 100 mW. Lens L1
380
S. Tsukada et al. / Materials Science and Engineering A 442 (2006) 379–382
Fig. 2. Rayleigh and Brillouin spectra of PG at four different temperatures. Near 300 K, the Rayleigh-wing becomes large.
Fig. 1. Schematic diagram of the ADFPI experimental setup. Solid etalon is combined with a highly sensitive CCD area detector.
focused the laser beam into the sample cell. The scattered light was collected at a 90◦ angle. The scattered light passed through the collimator with L2a, L2b, and L2c. To reduce the stray light, a slit was used between L2b and L2c. The interference fringes were observed after passing through a Fabry–Perot Interferometer (FPI). Between these fringes, frequency shifted light was transmitted. ADFPI was composed of a solid etalon, which is mechanically stable. The solid etalon was made of a single fused silica plate. The mirror was made from a soft-coated dielectric material and the degree of flatness was better than λ/100 and 30 GHz of FSR with a reflectivity of 99.0%. An etalon with a very high reflectivity was used to obtain high contrast and high resolution. The transmitted light through an etalon was focused onto CCD2 by the L3 lens. The exposure time of CCD2 was 5 s, which is 1/10 shorter than that of the conventional scanning method. To reduce thermal noise, CCD2 was operated at 243 K by a thermoelectric cooler. CCD1 was used to monitor the samples and to easily align the optics. A helium refrigerator and heater were used to change the sample temperature. Measurements were performed from 100 K to 450 K. The temperature was monitored by a silicon diode sensor on the sample cell below room temperature and by a chromel–alumel thermocouple in the sample cell above room temperature. The samples, which had a purity of 99.0%, were filtered by a millipore filter with a pore size of 0.22 m to remove impurities. More details are available in previous works [7–10].
Fig. 3 shows the longitudinal sound velocity, V, and the full width at half-maximum (FWHM) of the Brillouin component, ν. The following equation is used to determine V, V =
λ0 νB , 2n sin(θ/2)
(1)
where νB is the Brillouin shift, n the refractive index of PG (1.436) measured by the minimum deviation method, λ0 the wavelength of the incident beam (532 nm), and θ is the scattering angle (90◦ ). The difference between the observed Brillouin component and the instrumental function are regarded as the true FWHM of the longitudinal acoustic phonon. In this analysis, the Lorentz function was assumed to be an instrumental function. The sound velocity and FWHM lead to an elastic constant, M, and sound attenuation, α, using the following equations: ν M = ρV 2 1 − 3 (2) 2V and α = 2π
ν V
,
(3)
where ρ is the density. The low frequency limit of the sound velocity, V0 , is necessary to determine the relaxation time. To
3. Results and discussion Fig. 2 shows the spectra at four temperatures obtained by ADFPI. The spectra are well fitted by the damped harmonic oscillator model. One spectrum has one elastic Rayleigh component and two inelastic Brillouin components. The small asymmetry in the Brillouin components around room temperature may be due to the Rayleigh-wing. Due to the high flatness and high reflectivity of the etalon, the finesse is above 100 in all the temperatures.
Fig. 3. Temperature dependence of sound velocity () and damping () measured by ADFPI. The low frequency limit of sound velocity, V0 , is measured by the ultrasonic pulse-echo method () and approximated as a second order polynomial function of temperature, T (lower broken line). Upper broken line is V∞ obtained by Eq. (5). Solid line represents V∞ * obtained by the conventional equation [5,7,9,12].
S. Tsukada et al. / Materials Science and Engineering A 442 (2006) 379–382
381
obtain V0 , the ultrasonic velocity was measured at 10 MHz using the standard pulse-echo method. Thus, V0 can be approximated by the second order polynomial function of temperature, T. Although V0 is generally approximated by a linear function of T, the linear function is not sufficient to fit our data. In fact, Comez et al. measured the Brillouin scattering of glycerol and found that V0 was not approximated by a linear function [11]. Therefore, the approximation of a second order polynomial function of temperature can be reasonable. The liquid–glass transition temperature, Tg = 165 K, is determined at the point where the slope dV/dT changes. An anomalous broadening of the FWHM near Tg is not observed. To obtain the relaxation time, τ, a single relaxation time model (Debye model) is employed and τ is given by: τ=
V 2 {1 − 3(ν/2νB )2 } − V02 , 4πν{1 − 2(ν/2νB )2 }
(4)
which is more accurate than the conventional equation [5,7,9,12]. Compared to the conventional equation, Eq. (4) adds additional terms, including (ν/2νB ). Thus, the improved equation for V∞ is given by: 2 V∞
V 2 {1 − 3(ν/2νB )2 } − V02 = + V02 , ωB2 τ 2 /(1 + ωB2 τ 2 )
(5)
where ωB is the phonon angular frequency defined by ωB = 2πνB . Fig. 3 shows the temperature dependence of V∞ . ∗ obtained by the conventional equation is For comparison, V∞ also plotted. Fig. 3 also shows the difference between Eq. (5) and the conventional equation, which is due to the denominator in Eq. (5). The denominator in Eq. (5) approaches 0 at lower temperatures. To prevent the divergence of V∞ , a more accurate V0 is needed. However, as mentioned above, a method to more accurately determine V0 is in progress. Actually, V∞ does not diverge in the temperature region where V0 is obtained by ultrasonic measurements. Fig. 4 shows the temperature dependence of the relaxation rate, f = 1/τ of PG. It obeys the Arrhenius law τ = τ 0 exp (E/kB T) when E = 0.27 eV and τ 0 = 6.40 × 10−16 s. E is almost same and τ 0 is half of the previous value [3]. As mentioned above, the difference is due to the equation used to determine V0 . The activation energy is about three times larger than the internal rotational energy of an alkyl chain of PG at the room temperature. Thus, it is determined that the molecules interact with the surrounding molecules through hydrogen bonds and the potential barrier of the rotational motion of the alkyl chain is elevated. The potential barrier increases by associative and disassociative processes between the molecules through hydrogen bonds. Compared to the relaxation time obtained by dielectric measurements [4], τ is a few orders smaller than that of the ␣-relaxation. Hence, the relaxation process measured by Brillouin scattering is a fast process and not an ␣-relaxation process. The inset of Fig. 4 shows the difference in the relaxation rate between racemic PG and (S)-PG. As expected, the relaxation rate of racemic PG is slightly faster than that of the chiral isomer below 300 K because (S)-PG is associated differently
Fig. 4. Temperature dependences of relaxation rates of PG () and (S)-PG () determined by Brillouin scattering and dielectric measurements (, [4]). Solid triangles are fitted by Arrhenius law (dashed line), but open triangles are fitted by Vogel–Fulcher law (solid line). Inset shows the log f values for the comparison between PG and (S)-PG in the range from 1000/T = 3.0 to 4.0.
than the racemic one. It is likely that alkyl groups in the liquid can independently rotate at higher temperatures and the independency is suppressed as the temperature decreases. Thus, the different structures of associated clusters are more influential below room temperature. Ike et al. reported that (S)-1-amino-2propanol has a lower glass-forming tendency than the racemic one [7] and concluded that the configuration variation of the system is an important factor of the liquid–glass transition. Our interpretation is consistent with theirs. In addition, PG has a simple molecular structure, which makes it easier to observe the difference. Neither (S)-PG nor racemic PG has an elastic anomaly at its melting point. Therefore, crystallization does not occur, and both (S)-PG and racemic PG transform into a supercooled liquid phase, indicating that both liquids have a good tendency for glass forming. 4. Conclusion Propylene glycol, a lower alcohol, was investigated using an angular dispersion Fabry–Perot interferometer with a highly sensitive CCD detector. The Brillouin spectra of PG were obtained in a wide temperature range, 100–442 K, and Tg was determined to be 164 K using the point where the slope of the sound velocity curve as a function of temperature changed in the low temperature region. Our main purpose was to determine the temperature behavior of the relaxation process in the GHz region. The relaxation time obeyed the Arrhenius law. The values of the relaxation time from the Brillouin spectra were a few orders smaller than those obtained by dielectric measurement [4]. A detailed comparison with the mode coupling theory is currently underway. A small difference was obtained in the relaxation time of PG and (S)-PG, which is attributed to the variations in the system configurations and their simple structures. Neither PG nor (S)PG displayed a sound velocity anomaly at its melting point.
382
S. Tsukada et al. / Materials Science and Engineering A 442 (2006) 379–382
Acknowledgments This work was supported in part by Grant-in-Aid Nos. 137400232 and 15654057 from the Ministry of Education, Culture, Sports, Science, and Technology, Japan. References [1] H. Tanaka, Phys. Rev. Lett. 80 (1998) 5750–5753. [2] E. Leutheusser, Phys. Rev. A 29 (1984) 2765–2772. [3] A. Yoshihara, H. Sato, S. Kojima, Jpn. J. Appl. Phys. 35 (1996) 2925–2929.
[4] I.S. Park, S. Kojima, J. Phys. Soc. Jpn. 67 (1998) 4131–4138. [5] S. Itoh, T. Yamana, S. Kojima, Jpn. J. Appl. Phys. 35 (1996) 2879– 2881. [6] S. Kojima, H. Sato, A. Yoshihara, J. Phys. Condens. Matter 9 (1997) 10079–10085. [7] Y. Ike, S. Kojima, J. Mol. Struct. 744 (2005) 521–524. [8] J.H. Ko, S. Kojima, Rev. Sci. Inst. 73 (2002) 4390–4392. [9] G. Matsui, S. Kojima, S. Itoh, Jpn. J. Appl. Phys. 37 (1998) 2812–2814. [10] J.H. Ko, S. Kojima, Phys. Lett. A 321 (2004) 141–146. [11] L. Comez, D. Fioretto, F. Scarponi, J. Chem. Phys. 119 (2003) 6032–6043. [12] K. Lapsa, M. Trybus, T. Runka, W. Proszak, M. Drozdowski, J. Mol. Struct. 704 (2004) 215–218.