Brillouin and Umklapp scattering in polybutadiene: Comparison of neutron and x-ray scattering

Abstract

We report a comparison of high resolution inelastic x-ray Brillouin scattering to coherent inelastic neutron scattering for amorphous deuterated polybutadiene, done for one temperature in the glass phase and another one in the melt. The x-ray scattering proves to be by far the better technique for such a polymer within its present resolution bounds. The neutron scattering allows one to extend these measurements to a much better resolution, showing an additional quasielastic signal in the melt. The results suggest x-ray measurements at higher momentum transfer, to see whether they are complementary to neutrons. ͓S1063-651X͑99͒50109-8͔ PACS number͑s͒: 63.50.ϩx, 64.70.Pf The most pronounced difference between the vibrational properties of crystals and glasses appears at low energies E Ϸ2 -5 meV. In ordered crystals, this region is usually dominated by acoustic vibrations which show a Debye-like density of states g(E)ϳE 2 . However, the vibrational spectra in all disordered systems have a g(E) which significantly exceeds the one expected in the Debye model ͓1͔. The excess g(E) appears as a peak, the so-called boson peak, in the dynamic structure factor S(Q,E) in neutron and Raman scattering spectra of glasses ͓2͔. The nature of these excess vibrations is at present a subject of intense discussion.Significant information about the nature of the atomic motion at the boson peak can be obtained from an analysis of S(Q,E), accessible by neutron and x-ray scattering. However, each technique has its characteristic limitations. Inelastic neutron scattering ͑INS͒ spectroscopy has a kinematic limitation at small Q which is related to the velocity of neutrons: if the latter is lower than the longitudinal sound velocity, then one cannot reach Brillouin conditions. Due to that reason INS is mainly used for an analysis of S(Q,E) at higher Q ranges, the so-called Umklapp scattering around the first and the second diffraction peak, i.e., at 0.5-5 Å Ϫ1 . The recent developement of high-resolution inelastic x-ray scattering ͑IXS͒ allows to measure the Brillouin spectra of glasses without any kinematic limitation. However, up to now these measurements were restricted to the Brillouin Q range, i.e., to QϽ1 Å Ϫ1 , and still have only a resolution of about 1.5 meV, which does not allow one to analyze S(Q,E) below this frequency. Nevertheless, these data clearly demonstrate the presence of a strong soundlike contribution to S(Q,E) at energies around and above the boson peak ͓3͔.In the present Rapid Communication we report combined IXS and INS measurements on deuterated 1,4-polybutadiene ͑PB͒ in the liquid and in the glassy state. This combination enabled the measurement of the dynamic structure factor for both Brillouin and Umklapp scattering. In our experiment, the former is significantly weaker than the latter. We present a quantitative analysis, which gives an estimate of the soundlike contribution and demonstrates the way one can check different model approaches using both IXS and INS.PB, a well-known glass forming polymer, was cho...

Relaxation in glassforming liquids and amorphous solids

“…The occurrence of the related umklapp processes ͑momentum conserving͒ in glasses and liquids 255 is only now being recognized as a physical reality. 256 Another accomplishment of the inelastic x-ray scattering technique is to observe the viscoelastic behavior of liquids on the picosecond time scale and to determine the structural relaxation from the ϭ1 condition in this highly fluid regime. This extends the study of viscoelasticity orders of magnitude beyond the previous limit attained by the related Brillouin light scattering technique and into a regime previously only studied by computer simulations.…”

Intensity sharing between Brillouin and Umklapp scattering in glasses

“…Figure 1 shows a first comparison of the result (equation (22)), to measured data in amorphous polybutadiene (Sokolov et al 1999). Since these data stem from a relatively hot melt (324 K, while the glass transition is at 186 K), it is not an ideal case.…”

“…With these assumptions, Q, and r, were fitted to the data, giving Qo = 0.6A I and rs = 5 A . (Sokolov et al 1999)) inelastic neutron scattering data from amorphous polybutadiene at 323K. The continuous line is the full scattering from localized modes and sound waves as described in the text; the dashed line is only the contribution from the elastic dipole field around the localized mode.…”

X-ray and neutron scattering studies in vitreous silica: acoustic nature of vibrational dynamics in the mesoscopic range

“…In this energy range between 2 and 10 meV, an excess exists in the vibrational density of states with respect to the predictions of the Debye theory . Experimentally these extra modes are responsible for the occurrence of the so-called boson peak (BP) observed in inelastic scattering experiments (Buchenau et al 1986, 1988, Sokolov et al 1993, Brodin et al 1994) not only on v-SiO 2 but also on all glassy systems (Carini et al 1995). The occurrence of the BP is in fact one of the well-known universal anomalies of glasses with respect to crystals, together with the anomalous heat capacity and heat conductibility at low temperatures (Zeller and Pohl 1971, Phillips 1972, 1981.…”