High-frequency dynamics of glass-forming polybutadiene

Inelastic x-ray measurements of polybutadiene are reported, performed over a wide temperature range covering both the glass and the liquid phase. At each temperature, the frequency position $\Omega$ and the width $\Gamma$ of the inelastic peaks of the spectra have been obtained for different values of the scattering vector $Q$. A linear behavior of $\Omega \mathrm{}\left(Q\right)\mathrm{}$ for $Q<\mathrm{}4\mathrm{}{\mathrm{nm}}^{-1}$ has been revealed, allowing the determination of the unrelaxed sound velocity $v_{\infty }.$ Consistently with the results obtained in different glass-forming systems, the Q dependence of $\Gamma$ is well represented by a $Q^2$ law. For $Q>\mathrm{}5\mathrm{}{\mathrm{nm}}^{-1}$ the values of $\Gamma$ overtake those of $\Omega$ and the acousticlike excitations progressively loose their propagative nature. In the glass, $v_{\infty }\mathrm{}\left(T\right)\mathrm{}$ compares well with previous Brillouin Light Scattering (BLS) determinations, while in the liquid the BLS sound velocity shows a steeper temperature dependence related to the structural relaxation. The temperature behavior of the nonergodicity factor has been derived both from $v_o$ and $v_{\infty }$ (in the liquid phase) and from the ratio between elastic and inelastic intensities of inelastic x-ray scattering spectra (in the whole investigated temperature range). Both temperature and Q behavior of this quantity might be consistently interpreted in the framework of the mode coupling theory.