Collective excitations in liquid and glassy 3-methylpentane

We present a detailed investigation of the terahertz vibrational dynamics of 3-methylpentane performed by means of high-resolution inelastic x-ray scattering (IXS). We probe the dynamics in a large temperature range, which includes the glass, the supercooled liquid, and the liquid phases. The characteristic frequency of the excitations follows a well-defined dispersion curve extending beyond $8{\mathrm{nm}}^{-1}$ at all the investigated temperatures, indicating the persistence of a solidlike behavior also in the liquid phase. This implies the existence of a pseudo-Brillouin zone whose size compares surprisingly well with the periodicity inferred from the first sharp diffraction peak in the static structure factor. We show that, in the investigated temperature range, both sizes undergo a variation of about 15%–20%, comparable to that of the average intermolecular distance. We finally show that the IXS sound velocity coincides with the infinite frequency sound velocity previously inferred from visible and ultraviolet Brillouin spectroscopy data. This analysis confirms the role of the shear relaxation processes in determining the variation with frequency of the apparent sound velocity.

Figure 1

Selection of IXS spectra (black dots) as measured at $T=120$ K in the liquid phase (bottom panel) and at $T=63$ K in the glassy phase (top panel). The spectra are vertically shifted by an amount proportional to the exchanged wave vector (from bottom to top, $q=2.5,4.0,5.5,7.0$, and $8.5{\mathrm{nm}}^{-1}$). The full line (blue) is the measured instrumental transfer function while the dashed line (red) is the linear dispersion obtained using the apparent sound velocity (see discussion).

Figure 2

Measured static structure factor $S\left(q\right)$ at selected temperatures (from left to right): $T=300$ K (magenta), $T=150$ K (gray), and $T=63$ K (green). The intensities of the data are arbitrarily normalized to their maxima. The inset shows the temperature behavior of the position $q_{\max }$ of the first sharp diffraction peak. These values have been obtained fitting $S\left(q\right)$ with a parabola around its maximum.

Figure 3

IXS spectra (black dots) measured in the glassy phase ($T=63$ K) for selected values of $q$. The logarithmic intensity scale allows one to appreciate the details of the instrumental transfer function (thin green solid line) and of the inelastic contribution of the fitting function (red dashed line). The reconstructed profile $I\left(\omega \right)$ is shown as a thick solid line (blue).

Figure 4

IXS spectra (black dots) measured in the liquid phase ($T=120$ K) for selected values of $q$. Symbols as in Fig. 3.

Figure 5

The fitting parameter ${\omega }_0$ versus $q$ (see text) at different temperatures as indicated in the legend. For each temperature, the line is the best fit of Eq. (1) to the data. The high-$q$ data, typically above $8.5{\mathrm{nm}}^{-1}$, have not been included in the fitting procedure.

Figure 6

Apparent sound velocity $\upsilon$ versus temperature as obtained from IXS measurements (blue dots) and from Brillouin scattering measurements at ${90}^{\circ }$ with 266-nm excitation (black triangles). The full thick line (blue) and the dashed line (red) represent, respectively, the infinite- and zero-frequency limits, as argued from [16]. Diamonds are the transverse velocities measured by Brillouin scattering at ${90}^{\circ }$ with 532-nm excitation together with the extrapolation of their high-temperature behavior (thin solid line, magenta) following Barlow [20].

Figure 7

Characteristic length $a$ versus temperature. The $a_0$ values (blue full dots) are obtained fitting the dispersion curves (see text) while $a_m$ values (red diamonds) are obtained from the maxima of $S\left(q\right)$. The full (black) line is obtained from density data (see text).