Quantum effects in the dynamics of deeply supercooled water

Despite its simple chemical structure, water remains one of the most puzzling liquids with many anomalies at low temperatures. Combining neutron scattering and dielectric relaxation spectroscopy, we show that quantum fluctuations are not negligible in deeply supercooled water. Our dielectric measurements reveal the anomalously weak temperature dependence of structural relaxation in vapor-deposited water close to the glass transition temperature $T_g\sim 136\mathrm{K}$. We demonstrate that this anomalous behavior can be explained well by quantum effects. These results have significant implications for our understanding of water dynamics.

Figure 1

(a) Dielectric loss spectra of amorphous water measured on initial cooling and subsequent heating cycles. Amorphous water is stable at temperature below 150 K. (b) Crystallization of deposited water film occurs at temperatures above 150 K, with the main relaxation peak irreversibly decreasing in amplitude and broadening in width. The order of temperatures corresponds to the order of lines.

Figure 2

Dielectric spectra of amorphous water (symbols) measured on an initial cooling cycle in terms of (a) storage and (b) loss permittivity. Solid lines present the simultaneous fit of the real and imaginary spectra by the sum of three Cole-Cole functions.

Figure 3

Time-temperature superposition plot of the dielectric loss. Here, solid lines represent contributions of the individual processes: black (upper curve), α-relaxation; blue (middle curve), β-relaxation; green (bottom curve), γ-relaxation.

Figure 4

Dynamical structure factor $S\left(Q,E\right)$ for an LDA sample obtained from the INS spectra measured at $T=15\mathrm{K}$: The experimental spectrum (red curve with squares), calculated multiphonon (black line), and single-phonon (blue curve with circles) contributions.

Figure 5

(a) Temperature dependence of the characteristic relaxation times of different processes observed in the spectra of amorphous vapor-deposited water. In addition, open stars are the data for cubic ice (from Refs. [68, 69]) and open pentagons present relaxation data of hexagonal ice (from Ref. [70] and references therein). (b) Temperature dependence of ${\tau }_{\alpha }$ vs inverse temperature (symbols) and its fit by the Arrhenius behavior (line). The latter provides estimates of the activation energy $E_a\approx 36\pm 1\mathrm{kJ}/\mathrm{mol}$ and $\mathrm{lo}{\mathrm{g}}_{10}\left[{\tau }_0\left(s\right)\right]=-10.9\pm 0.3$.

Figure 6

MSD in LDA water and in water that is vapor deposited at low temperatures (solid lines). The dashed line marks the expected $T_g\sim 136\mathrm{K}$ of water. Zero-point vibrations dominate MSD and contribute 55%–61% to the total MSD of amorphous water at $T_g$. The inset shows the generalized vibrational density of states $g\left(E\right)$ for intermolecular vibrations in LDA and deposited water obtained from INS spectra [59, 60, 61].

Figure 7

Temperature dependence of the isothermal dielectric relaxation time (symbols) in the vapor-deposited film of water measured on cooling (open symbols) and on heating (solid symbols) vs $T_g/T$. $T_g=135.6\mathrm{K}$ was chosen as the temperature at which ${\tau }_a=1000\mathrm{s}$. The slope of the temperature dependence indicates an unusually low value of fragility, $m=14$. The lines show the expected temperature dependence of ${\tau }_{\alpha }\left(T\right)$ estimated using Eq. (6) with the total MSD of the deposited unannealed sample (dashed line), with the total MSD of LDA water (solid line) and MSD with excluded zero-point vibrations for LDA water (dotted line). The total MSD of LDA reproduces well the temperature dependence of ${\tau }_{\alpha }\left(T\right)$ and emphasizes the importance of quantum fluctuations in the dynamics of deeply supercooled water.

Figure 8

Comparison of low- and high-temperature data for the structural relaxation time in water and in glycerol. Open squares: dielectric spectroscopy data in water [80]; solid circles: shifted viscosity data [25]; stars: dielectric spectroscopy data in glycerol [81]. The dashed line presents the approximation of the low-temperature behavior by an Arrhenius dependence, and the solid line is the approximation of the high-temperature behavior using the Vogel-Fulcher-Tammann function.

Figure 9

Schematic presentation of the potential well used to estimate the tunneling probability. Lines in the well correspond to different quantum levels.