Boson peak dynamics of glassy glucose studied by integrated terahertz-band spectroscopy

We performed terahertz time-domain spectroscopy, low-frequency Raman scattering, and Brillouin light scattering on vitreous glucose to investigate the boson peak (BP) dynamics. In the spectra of $\alpha \left(\nu \right)/{\nu }^2$ $\mathrm{[}\alpha \left(\nu \right)$ is the absorption coefficient], the BP is clearly observed around 1.1 THz. Correspondingly, the complex dielectric constant spectra show a universal resonancelike behavior only below the BP frequency. As an analytical scheme, we propose the relative light-vibration coupling coefficient (RCC), which is obtainable from the combination of the far-infrared and Raman spectra. The RCC reveals that the infrared light-vibration coupling coefficient $C_{\mathrm{IR}}\left(\nu \right)$ of the vitreous glucose behaves linearly on frequency which deviates from Taraskin's model of $C_{\mathrm{IR}}\left(\nu \right)=A+B{\nu }^2$ [S. N. Taraskin et al., Phys. Rev. Lett. 97, 055504 (2006)]. The linearity of $C_{\mathrm{IR}}\left(\nu \right)$ might require modification of the second term of the model. The measured transverse sound velocity shows an apparent discontinuity with the flattened mode observed in the inelastic neutron scattering study [N. Violini et al., Phys. Rev. B 85, 134204 (2012)] and suggests a coupling between the transverse acoustic and flattened modes.

Figure 1

Temperature dependence of (a) the real and (b) imaginary parts of the complex dielectric constants of the vitreous glucose during the heating process at 14, 20, $\cdots$, 320 K. The data are plotted every 10 K above 20 K. For convenience, $1\text{THz}=33.3{\mathrm{cm}}^{-1}=48\text{K}=4.14\text{meV}$.

Figure 2

Temperature dependence of the boson peak plot $\alpha \left(\nu \right)/{\nu }^2$ of the vitreous glucose during the heating process, at 14, 20, $\cdots$, 320 K. The data are plotted every 10 K above 20 K. For convenience, $\alpha \left(\nu \right)=\nu {\varepsilon }^{\prime \prime }\left(\nu \right)2\pi /\left[c{n}^{\prime }\left(\nu \right)\right]$, where $c$ and $n^{\prime }\left(\nu \right)$ are the speed of light and the refractive index, respectively.

Figure 3

(a) Raman intensity spectra of the vitreous glucose during the heating process. (b) The imaginary part of the Raman susceptibility ${\chi }^{\prime \prime }\left(\nu \right)$. (c) The reduced Raman intensity $I_{\mathrm{red}}\left(\nu \right)\propto {\chi }^{\prime \prime }\left(\nu \right)/\nu$.

Figure 4

(a) The IR and Raman light-vibrational coupling coefficients $\mathrm{[}{C}_{\mathrm{IR}}\left(\nu \right)$ and $C_{\mathrm{Raman}}\left(\nu \right)]$ of the vitreous glucose at 290 K. (b) Relative light-vibrational coupling coefficient $C_{\mathrm{IR}}\left(\nu \right)/C_{\mathrm{Raman}}\left(\nu \right)=\alpha \left(\nu \right)/\left(\nu {\chi }^{\prime \prime }\left(\nu \right)\right)$ at 290 and 215 K. (c) Calculated $C_{\mathrm{IR}}\left(\nu \right)$ of vitreous glucose at 215 K, assuming $C_{\mathrm{Raman}}\left(\nu \right)$ is $A^{\prime }(\nu +0.5{\nu }_{\mathrm{BP}-\mathrm{VDOS}})$. The solid line is the fitting result (see text).

Figure 5

Brillouin scattering spectrum of the vitreous glucose with ${90}^{\circ }$ scattering geometry at room temperature. LA denotes the longitudinal-acoustic mode. The solid line shows the fitting curve which consists of superposition of Voigt functions.

Figure 6

(a) Dispersion relations of $L$ and $H$ modes of the deuterated vitreous glucose [15]. Data depicted are from Ref. [15]. The vertical dashed line indicates the position of the first peak of the static structure factor $S\left(Q\right)$ [15]. (b) Vibrational density of states $g\left(\nu \right)$ and $g\left(\nu \right)/{\nu }^2$ of the hydrogenated vitreous glucose [15]. Data depicted are from Ref. [15]. (c) Imaginary part of the complex dielectric constant ${\varepsilon }^{\prime \prime }\left(\nu \right)$ and $\alpha \left(\nu \right)/{\nu }^2$ of vitreous glucose at room temperature. (d) Imaginary part of the Raman susceptibility ${\chi }^{\prime \prime }\left(\nu \right)$ and ${\chi }^{\prime \prime }\left(\nu \right)/\nu$ of vitreous glucose at room temperature.