- Email: [email protected]
Looking below the Brillouin line in a polymer melt
Physica B 276}278 (2000) 394}395
Looking below the Brillouin line in a polymer melt W. Schmidt *, U. Buchenau Forschungszentrum Ju( lich, IFF, D-52425 Ju( lich, Germany Institut Laue Langevin, 6, rue Jules Horowitz, BP 156, F-38042 Grenoble, Cedex 9, France
Abstract We report on high-resolution inelastic neutron-scattering studies in amorphous deuterated polybutadiene at low momentum transfer, taken on the cold neutron triple-axis spectrometer IN12 at the ILL in Grenoble. The measurements show a clearly non-zero contribution down to the lowest accessible Q-vectors. The results are interpreted in terms of an elastic distortion around low-frequency localized modes. 2000 Elsevier Science B.V. All rights reserved. Keywords: Amorphous materials; Brillouin scattering; Polymers; Triple-axis spectrometers
In glasses, it seems that both tunneling and lowfrequency vibrational modes exist which strongly distort the elastic medium in which they move. The elastic distortion around such localized modes is one of the possible explanations [1] for the unexpected inelastic scattering at low momentum transfer Q in deuterated polybutadiene [2]. In terms of that explanation, the onephonon inelastic scattering S(Q, x) from the elastic distortion cloud is written as
k ¹e\5 4(1!f ) S (Q, x)" d (x ) Q S # D 6NMx 3f
(1!f ) ;S S # S #Qf , D \D \D / f
(1)
3sin Qr !3Qr cos Qr Q Q Q, S " D (Qr ) Q
(2)
12sin Qr !3Qr cos Qr !9Si Qr Q Q Q Q, S " \D (Qr ) Q
(3)
v 3" . . f" , Q " v 5Mv
(4)
* Corresponding author. Present address: Institut Laue Langevin, 6, rue Jules Horowitz, BP 156, F-38042 Grenoble, Cedex 9, France, Tel.: #33-47620-7427; fax: #33-47648-3906. E-mail address: [email protected] (W. Schmidt)
Here N is the number of atoms with mass M in the sample, T is the temperature, v and v are the longitudi nal and transverse sound velocities, respectively. " is the . dipole strength of the localized mode and r its e!ective Q diameter. f represents the structure factor of the localiz/ ed mode at higher Q, a function which is supposed to oscillate around 1 (1 corresponds to incoherent scattering). The experimental data have been obtained by means of inelastic neutron scattering on the cold triple-axis spectrometer IN12 which is operated by the Forschungszentrum JuK lich as a CRG-instrument at the ILL. The challenge in this experiment was to test and to prove the ability to compete with time-of-#ight spectrometers [2] in the low-Q range. Due to the very low background at IN12 we already were able to get valuable results in a standard set-up. Another experiment will be done shortly with optimized conditions for the incident wavelength, collimation and sample environment. Fig. 1 demonstrates the di$culties for low scattering angles in showing the high count-rates both for the sample and the empty container. This requires longer counting times to get acceptable statistics for the di!erence signal. In Fig. 2 we have plotted the net signal, also taken at an energy transfer of 0.5 meV with an energy resolution of about 0.1 meV. Despite the relative high temperature of 300 K (the glass transition is at 186 K), there is a significant contribution at low Q. For a "t we have made several assumptions: f from Eq. (1) was set equal to 1. / Estimates for multiple scattering processes are used in
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 5 9 1 - 4
W. Schmidt, U. Buchenau / Physica B 276}278 (2000) 394}395
Fig. 1. Data taken from deuterated polybutadiene (open squares) on IN12 at room temperature with an energy transfer of 0.5 meV. The lower values (solid diamonds) show the scattering of the empty container. Both measurements are normalized to a counting time of 400 s.
395
the "t. For low Q this is essentially a linear background. Since the data will consist of a mixture of localized modes and sound waves both contributions must be considered. For the latter the structure factor is taken as Q S (Q) where S (Q) is obtained from the elastic data [3]. The "t gives about 40% for that contribution. Concerning the parameters for the localized modes according to Eq. (1) we get Q "0.33$0.13 As \, r "8.4$0.6 As and f" Q 0.135$0.05. From soft potential data [4], Q "0.46 As \ has been calculated. Also r is a rea Q sonable value in the order of the distance of neighboring polymer chains. Further, the value for f is consistent with optical Brillouin measurements in the glass phase [5]. Thus, the model can su$ciently explain the low-Q contributions in the scattering signal with reasonable assumptions and "tting parameters. Instrumentally, we believe that a triple-axis spectrometer like IN12 can achieve valuable data for this kind of physics. Further experiments will be done to con"rm both the model predictions and technical aspects. This work has been funded by the German Research Ministry BMBF under contract number 05-300-CJB-6.
References
Fig. 2. Scattering signal of deuterated polybutadiene at room temperature with an energy transfer of 0.5 meV. The solid line shows the "t for the total structure factor while the dashed line indicates the contribution of the localized modes as calculated in the model.
[1] U. Buchenau, A. Wischnewski, M. Monkenbusch, W. Schmidt, Philos. Mag. B 79 (1999) 2021. [2] A. P. Sokolov, U. Buchenau, D. Richter, C. Masciovecchio, F. Sette, A. Mermet, D. Fioretto, G. Ruocco, L. Willner, B. Frick, Phys. Rev. E 60 (1999) 2464. [3] J.M. Carpenter, C.A. Pelizzari, Phys. Rev. B 12 (1975) 2391. [4] M.A. Ramos, U. Buchenau, Phys. Rev. B 55 (1997) 5749. [5] B. Strube, private communication.
Looking below the Brillouin line in a polymer melt W. Schmidt *, U. Buchenau Forschungszentrum Ju( lich, IFF, D-52425 Ju( lich, Germany Institut Laue Langevin, 6, rue Jules Horowitz, BP 156, F-38042 Grenoble, Cedex 9, France
Abstract We report on high-resolution inelastic neutron-scattering studies in amorphous deuterated polybutadiene at low momentum transfer, taken on the cold neutron triple-axis spectrometer IN12 at the ILL in Grenoble. The measurements show a clearly non-zero contribution down to the lowest accessible Q-vectors. The results are interpreted in terms of an elastic distortion around low-frequency localized modes. 2000 Elsevier Science B.V. All rights reserved. Keywords: Amorphous materials; Brillouin scattering; Polymers; Triple-axis spectrometers
In glasses, it seems that both tunneling and lowfrequency vibrational modes exist which strongly distort the elastic medium in which they move. The elastic distortion around such localized modes is one of the possible explanations [1] for the unexpected inelastic scattering at low momentum transfer Q in deuterated polybutadiene [2]. In terms of that explanation, the onephonon inelastic scattering S(Q, x) from the elastic distortion cloud is written as
k ¹e\5 4(1!f ) S (Q, x)" d (x ) Q S # D 6NMx 3f
(1!f ) ;S S # S #Qf , D \D \D / f
(1)
3sin Qr !3Qr cos Qr Q Q Q, S " D (Qr ) Q
(2)
12sin Qr !3Qr cos Qr !9Si Qr Q Q Q Q, S " \D (Qr ) Q
(3)
v 3" . . f" , Q " v 5Mv
(4)
* Corresponding author. Present address: Institut Laue Langevin, 6, rue Jules Horowitz, BP 156, F-38042 Grenoble, Cedex 9, France, Tel.: #33-47620-7427; fax: #33-47648-3906. E-mail address: [email protected] (W. Schmidt)
Here N is the number of atoms with mass M in the sample, T is the temperature, v and v are the longitudi nal and transverse sound velocities, respectively. " is the . dipole strength of the localized mode and r its e!ective Q diameter. f represents the structure factor of the localiz/ ed mode at higher Q, a function which is supposed to oscillate around 1 (1 corresponds to incoherent scattering). The experimental data have been obtained by means of inelastic neutron scattering on the cold triple-axis spectrometer IN12 which is operated by the Forschungszentrum JuK lich as a CRG-instrument at the ILL. The challenge in this experiment was to test and to prove the ability to compete with time-of-#ight spectrometers [2] in the low-Q range. Due to the very low background at IN12 we already were able to get valuable results in a standard set-up. Another experiment will be done shortly with optimized conditions for the incident wavelength, collimation and sample environment. Fig. 1 demonstrates the di$culties for low scattering angles in showing the high count-rates both for the sample and the empty container. This requires longer counting times to get acceptable statistics for the di!erence signal. In Fig. 2 we have plotted the net signal, also taken at an energy transfer of 0.5 meV with an energy resolution of about 0.1 meV. Despite the relative high temperature of 300 K (the glass transition is at 186 K), there is a significant contribution at low Q. For a "t we have made several assumptions: f from Eq. (1) was set equal to 1. / Estimates for multiple scattering processes are used in
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 5 9 1 - 4
W. Schmidt, U. Buchenau / Physica B 276}278 (2000) 394}395
Fig. 1. Data taken from deuterated polybutadiene (open squares) on IN12 at room temperature with an energy transfer of 0.5 meV. The lower values (solid diamonds) show the scattering of the empty container. Both measurements are normalized to a counting time of 400 s.
395
the "t. For low Q this is essentially a linear background. Since the data will consist of a mixture of localized modes and sound waves both contributions must be considered. For the latter the structure factor is taken as Q S (Q) where S (Q) is obtained from the elastic data [3]. The "t gives about 40% for that contribution. Concerning the parameters for the localized modes according to Eq. (1) we get Q "0.33$0.13 As \, r "8.4$0.6 As and f" Q 0.135$0.05. From soft potential data [4], Q "0.46 As \ has been calculated. Also r is a rea Q sonable value in the order of the distance of neighboring polymer chains. Further, the value for f is consistent with optical Brillouin measurements in the glass phase [5]. Thus, the model can su$ciently explain the low-Q contributions in the scattering signal with reasonable assumptions and "tting parameters. Instrumentally, we believe that a triple-axis spectrometer like IN12 can achieve valuable data for this kind of physics. Further experiments will be done to con"rm both the model predictions and technical aspects. This work has been funded by the German Research Ministry BMBF under contract number 05-300-CJB-6.
References
Fig. 2. Scattering signal of deuterated polybutadiene at room temperature with an energy transfer of 0.5 meV. The solid line shows the "t for the total structure factor while the dashed line indicates the contribution of the localized modes as calculated in the model.
[1] U. Buchenau, A. Wischnewski, M. Monkenbusch, W. Schmidt, Philos. Mag. B 79 (1999) 2021. [2] A. P. Sokolov, U. Buchenau, D. Richter, C. Masciovecchio, F. Sette, A. Mermet, D. Fioretto, G. Ruocco, L. Willner, B. Frick, Phys. Rev. E 60 (1999) 2464. [3] J.M. Carpenter, C.A. Pelizzari, Phys. Rev. B 12 (1975) 2391. [4] M.A. Ramos, U. Buchenau, Phys. Rev. B 55 (1997) 5749. [5] B. Strube, private communication.