Structural relaxation and crystallization in supercooled water from 170 to 260 K

Abstract

The origin of water's anomalous properties has been debated for decades. Resolution of the problem is hindered by a lack of experimental data in a crucial region of temperatures, T, and pressures where supercooled water rapidly crystallizes-a region often referred to as "no man's land." A recently developed technique where water is heated and cooled at rates greater than 10⁹ K/s now enables experiments in this region. Here, it is used to investigate the structural relaxation and crystallization of deeply supercooled water for 170 K < T < 260 K. Water's relaxation toward a new equilibrium structure depends on its initial structure with hyperquenched glassy water (HQW) typically relaxing more quickly than low-density amorphous solid water (LDA). For HQW and T > 230 K, simple exponential relaxation kinetics is observed. For HQW at lower temperatures, increasingly nonexponential relaxation is observed, which is consistent with the dynamics expected on a rough potential energy landscape. For LDA, approximately exponential relaxation is observed for T > 230 K and T < 200 K, with nonexponential relaxation only at intermediate temperatures. At all temperatures, water's structure can be reproduced by a linear combination of two, local structural motifs, and we show that a simple model accounts for the complex kinetics within this context. The relaxation time, τ _rel , is always shorter than the crystallization time, τ _xtal For HQW, the ratio, τ _xtal /τ _rel , goes through a minimum at ∼198 K where the ratio is about 60.

Keywords: metastable states; nonexponentialkinetics; supercooled water.

Fig. 1.

Representative experimental relaxation data (symbols) and stretched exponential fits to the data (black lines). The data are shown in ∼5 K increments for f_CI ≤ 0.02. See text for details. (A) $f_{HQW}^H$ from 200 K (blue) to 236 K (red). (B) $f_{HQW}^H$ from 170 K (blue) to 195 K (red). (C) $f_{HQW}^L$ from 185 K (blue) to 251 K (red).

Fig. 2.

Relaxation and crystallization constants for the transiently heated water films. (A) $N_{rel}^H$ (red circles), $N_{rel}^L$ (blue squares), and N_xtal (black diamonds). (B) Ratio of the LDA_i to HQW_i relaxation constants, R_rel = $N_{rel}^L/N_{rel}^H$. The dashed line corresponds to R_rel = 1. (C) Ratio of the crystallization constant to the relaxation time for the different starting configurations (HQW_i, red circles; LDA_i, blue squares). For HQW_i, the minimum is at 196 K where the ratio is ∼60. For LDA_i, the minimum is at 216 K where the ratio is ∼20. The solid lines are smooth curves to guide the eye.

Fig. 3.

Fit parameters for the RDW kinetic model for experiments with HQW_i (A, C, and E) and LDA_i (B, D, and F). (A) $\mathrm{\Delta }{G}_f^H$ (red circles) and $\mathrm{\Delta }{G}_r^H$ (purple squares). (B) $\mathrm{\Delta }{G}_f^L$ (blue squares) and $\mathrm{\Delta }{G}_r^L$ (orange circles). The arrows in A and B indicate the temperatures for the schematics shown in E and F. The full width at half maxima for the distributions are shown in C and D for HQW_i and LDA_i, respectively. At high temperatures where there is little change in structure when starting with HQW, it is difficult to determine the FWHM leading to large uncertainties. Schematics of the barriers for (E) HQW_i and (F) LDA_i at 200 K (Left), 210 K (Middle), and 221 K (Right). The schematics show the mean heights and FWHM determined from fitting the data.

Fig. 4.

Relaxation, diffusion, and crystallization times versus temperature. ${\tau }_{rel}^H$ (red circles), τ_xtal (black diamonds), and τ_diff (purple line) (36) measured in transiently heated water films are compared to the corresponding times in bulk water (blue lines) (19, 20, 74) and in MD simulations using TIP4P/ICE (gray triangles and black line) (38). The blue square shows a relaxation time of 100 s at the glass transition temperature (136 K).