**1. Introduction**

2022 is declared a United Nations International Year of Glass (IYOG), which celebrates the heritage and importance of this material in our lives [1]. Glass is technologically very important in industry, and it is clear that modern life would not be possible without glass. Glass is also very interesting in fundamental sciences related to random structure and non-equilibrium state. When a viscous liquid is cooled from a high temperature, it changes into a supercooled liquid state, and upon further cooling, it undergoes a liquid–glass transition into a nonequilibrium glassy state at a glass transition temperature *T*g. However, a simple liquid is solidified into an equilibrium crystalline state at its melting temperature,*T*m. The temperature dependence of enthalpy is shown in **Figure 1** for a liquid (AB), supercooled liquid (BD), glassy (DE), and crystalline (CG) states. The enthalpy of a liquid crosses to that of a crystal at the point, F, which is the Kauzmann temperature,*T*<sup>K</sup> [1]. It is a static ideal glass transition temperature and close to the Vogel–Fulcher temperature, the dynamic ideal glass transition temperature,*T*VF [3, 4], which is lower than the calorimetric *T*g.

#### **Figure 1.**

*Temperature dependence of the enthalpy for the liquid (AB), supercooled liquid (BD), glass (DE), and crystalline (CG) states, where* T*m,* T*g, and* T*<sup>K</sup> are the melting, glass transition, and Kauzmann temperatures, respectively [2].*

The temperature dependence of the relaxation time, τα, of α-structural relaxation process obeys the following Vogel-Fulcher law and the relaxation time diverges at *T*VF.

$$\pi\_a = \pi\_0 \exp\left(\frac{B}{T - T\_{\rm VF}}\right) \text{ for } T > T\_{\rm VF} \tag{1}$$

Here, τ<sup>0</sup> and B are material-dependent constants, and *T*<sup>g</sup> > *T*VF. The fragility index *m* is defined by Eq. (2) using the parameters of Eq. (1). When the intermolecular interactions are weak, *m* is large and materials are fragile. While the interactions are strong, Eq. (1) goes to the Arrhenius law and materials are strong.

$$m = \left[\frac{d\log\tau\_a}{d\left(\frac{T\_\xi}{T}\right)}\right]\_{T=T\_\xi} = \frac{B}{T\_\xi \ln\mathbf{1} \mathbf{0} \left(\mathbf{1} - T\_{VF}/T\_\mathbf{g}\right)^2} \tag{2}$$

In a liquid-glass transition, main three dynamical processes are the α-structural relaxation, fast β-relaxation, and boson peak. These three dynamics are interrelated with each other. According to the mode-coupling theory, the α-relaxation is related to the creation and annihiration of a molecular cage, the fast β-relaxation is related to a relaxation of molecules trapped in their cages. A boson peak is related to a damped librational motion of molecules trapped in their cages [5].

Glycerol (propane-1,2,3-triol, C3H8O3) undergoes a liquid–glass transition at about *T*<sup>g</sup> = 187 K. Glycerol is intermediate with *m* = 53. The melting temperature is *T*<sup>m</sup> = 291 K, while it does not crystalize even in very slow cooling. It is one of the typical glassforming materials and well-known cryoprotectants due to its strong glass-forming tendency [6]. The dominant interaction among molecules is the intermolecular hydrogen bond, and the related O-H stretching band showed a remarkable temperature dependence in the vicinity of *T*<sup>g</sup> [7]. By the broadband dielectric spectroscopy, the slowing down of the α- relaxation time towards *T*g, which obeys the Vogel-Fulcher law of Eq. (1), was clearly observed in the milli hertz to gigahertz range [8]. For the dynamical properties in the terahertz range, the temperature dependence of lowfrequency Raman scattering spectra is shown in **Figure 2** [9]. The remarkable changes in Raman spectra were observed in the low-frequency range. In a liquid phase at 328

#### **Figure 2.**

*Temperature dependence of low-frequency Raman scattering spectra of a liquid-glass transition of glycerol [9].*

K, the broad Rayleigh wing appears, and the main contribution of this wing is the αstructural relaxation and fast β-relaxation. In supercooled liquid states at 271 and 228 K, the α-relaxation time becomes slow and the contribution to the Rayleigh wing becomes small. While the fast β-relaxation time does not depend on temperature, and its intensity gradually changes into a boson peak at about 40 cm<sup>1</sup> (=1.2 THz). In a glass state at 96 K, only a boson peak appears. The liquid-phase transition also occurs by the application of hydrostatic pressure at room temperature at *P*<sup>g</sup> = 5 GPa. The boson peak was also observed in the pressure-induced glass state [10]. These dynamical properties on the boson peak, α- and fast β-relaxation processes in **Figure 1** are common in liquid-glass transitions of organic and inorganic glass-forming materials.
