Relaxation Time of High-Density Amorphous Ice

Amorphous water plays a fundamental role in astrophysics, cryoelectron microscopy, hydration of matter, and our understanding of anomalous liquid water properties. Yet, the characteristics of the relaxation processes taking place in high-density amorphous ice (HDA) are unknown. We here reveal that the relaxation processes in HDA at 110–135 K at 0.1–0.2 GPa are of collective and global nature, resembling the alpha relaxation in glassy material. Measured relaxation times suggest liquid-like relaxation characteristics in the vicinity of the crystallization temperature at 145 K. By carefully relaxing pressurized HDA for several hours at 135 K, we produce a state that is closer to the ideal glass state than all HDA states discussed so far in literature.

Figure 1

Difference in the thermal stability of uHDA (produced along Mishima’s path [11]) and eHDA (produced along Winkel’s path [17]). Part (a) shows the volumetric detection of the isobaric ($p=4\mathrm{MPa}$) transitions from 500 mg of uHDA (black solid line) and 500 mg of eHDA (red dotted line) to LDA, with a heating rate of $3\mathrm{K}{\min }^{-1}$. In this case, $T_e$ represents the volumetric extrapolated onset transition temperature. The blue dashed line is the thermal expansion curve of ice II. Part (b) shows thermograms of uHDA (black solid line) and eHDA (red dotted line) recorded at $10\mathrm{K}{\min }^{-1}$ heating rate. The first peak in the thermograms marks the exothermic $\mathrm{HDA}\to \mathrm{LDA}$, and the second peak marks the exothermic $\mathrm{LDA}\to I_c$ transition. Here, $T_e$ represents the calorimetric extrapolated onset transition temperature.

Figure 2

Ex situ characterization of the state of relaxation of HDA samples after having kept them at 0.1 GPa and 130 K for the indicated times. Note that $T_e$ shifts progressively to higher temperature (dotted black line).

Figure 3

Collection of all calorimetric $\mathrm{HDA}\to \mathrm{LDA}$ transition temperatures $T_e$ for (a) 0.1 GPa and (b) 0.2 GPa. In each panel, the temperatures $T_e$ are represented as (•) for samples annealed at 110 K, (▾) for samples annealed at 125 K, (▪) for samples annealed at 130 K, and (▴) for samples annealed at 135 K. The dashed curves are the fits according to Eq. (1). In both (a) and (b) all transition values of $T_e$ have an error of $\pm 1\mathrm{K}$.

Figure 4

Parts (a) and (b) show Arrhenius plots of relaxation times $\tau$ of uHDA (represented by ▴), as calculated from Eq. (1) and the data shown in Fig. 3. Relaxation times for 0.1 GPa in part (a) and for 0.2 GPa in part (b). The red dashed line is the Arrhenius fit, the blue dotted lines are the prediction bands (67%), and the black dashed line ($\tau =100\mathrm{s}$) marks the transition from a glass (above the line) to a liquid (beneath the line). Part (c) shows the glass transition temperatures $T_g$ obtained in this study (★) in comparison with data from literature: Seidl et al. [6], calorimetry (▴); Seidl et al. [6], volumetry (▾); Andersson, transient hot-wire method [5] ($▿$); Mishima, temperature change in emulsified water [3] (•) and gray area (Mishima’s extrapolation); Andersson and Inaba, dielectric spectroscopy [4] (□) and dotted line (Andersson’s extrapolation).