Cusp-like temperature behavior of the nonergodicity factor in polybutadiene revealed by a joint light and x-ray Brillouin scattering investigation

The dynamic structure factor of supercooled and glassy polybutadiene has been studied by Brillouin light and inelastic x-ray scattering in the momentum (q) region between 0.04 and $4 {\mathrm{nm}}^{\ensuremath{-}1}.$ The joint analysis of the spectra allows one to access a very large frequency range $(\ensuremath{\approx}0.2\char21{}2000 \mathrm{GHz}),$ and poses severe constraints on the value of the parameters, thus overcoming the arbitrariness encountered in modeling a single-q spectrum. The nonergodicity factor\char22{}derived from the amplitude of the $\ensuremath{\alpha}$ relaxation\char22{}shows the square-root cusp predicted by the mode-coupling theory.