Experimental and theoretical evidence for bilayer-by-bilayer surface melting of crystalline ice

Abstract

On the surface of water ice, a quasi-liquid layer (QLL) has been extensively reported at temperatures below its bulk melting point at 273 K. Approaching the bulk melting temperature from below, the thickness of the QLL is known to increase. To elucidate the precise temperature variation of the QLL, and its nature, we investigate the surface melting of hexagonal ice by combining noncontact, surface-specific vibrational sum frequency generation (SFG) spectroscopy and spectra calculated from molecular dynamics simulations. Using SFG, we probe the outermost water layers of distinct single crystalline ice faces at different temperatures. For the basal face, a stepwise, sudden weakening of the hydrogen-bonded structure of the outermost water layers occurs at 257 K. The spectral calculations from the molecular dynamics simulations reproduce the experimental findings; this allows us to interpret our experimental findings in terms of a stepwise change from one to two molten bilayers at the transition temperature.

Keywords: crystalline ice; stepwise; sum frequency generation; surface melting; water.

Fig. 1.

High symmetry faces of ice Ih. Top view of the basal (Left), primary prism (Center), and secondary prism (Right) face of ice Ih. Circles represent oxygen atoms. The crystallographic unit cell is highlighted by solid black lines. Dashed lines and Insets indicate the hexagonal symmetry. For the basal and primary prism plane, dark and light red circles represent oxygen atoms in the upper and lower part, respectively, of the bilayer. For the secondary prism plane, the first (dark red) and second (gray) layers are shown. Shaded circles indicate the positions of oxygen atoms in underlying layers. At the surface, each “upper molecule” (either upper part of the bilayer or of the first layer) contributes exactly one dangling OH bond.

Fig. S1.

Single crystalline ice. (A) Picture of the experimental ice-growing machine showing the seed and supercooled melt. (B) Ice between two crossed polarizers; only one big domain is observed in the single crystalline sample. (C) Cross-section of the SFG measuring cell.

Fig. S2.

Images of the basal, primary prism, and secondary prism plane after Formvar etching. The red bar represents 50 μm.

Fig. S3.

Rocking curve of the (30.0) reflection measured at the primary prism surface (symbols). The red curve represents a fit of a pseudo Voigt function to the experimental data.

Fig. 2.

Ice−quasi-liquid−air interface studied with SFG. (A) SFG spectra under ssp polarization between 235 K and 273 K for the basal face of ice Ih. The black lines are the experimental results; the red lines are results of the two component fit (see Results and Discussion). The data are offset for clarity. (B) First moment of the spectral intensities shown at different temperatures for the basal and secondary prism face averaged over up to four different experiments. The lines are sigmoidal fits through the data points. (C) Contribution of the 235 K and 269 K spectra to the SFG spectra at intermediate temperatures, for the basal face. Typical error bars based on reproducibility from experiment to experiment are given in the graph.

Fig. S4.

Laser influence on ice sample. Shown are SFG spectra in the hydrogen-bonded OH stretch region of the basal face at 235 K at different irradiation conditions. The SFG signal is stable in time and has similar intensity and spectral shape at 250 and 164 Hz.

Fig. S5.

Ice−quasi-liquid−air interface study with SFG. (A) SFG spectra between 235 K and 273 K for the secondary prism plane. The black lines are the experimental result; the red lines are the results of the fit. (B) Contribution of the 235 K and 269 K spectra to the SFG spectra at intermediate temperatures.

Fig. 3.

SFG spectra of the basal face in the free OH region. (A) SFG spectra from 3,630 cm⁻¹ to 3,760 cm⁻¹ at different temperatures. Data are offset for clarity; the solid lines are to guide the eyes. Note that, due to different acquisition time and laser power, the intensity cannot be compared with the intensity in Fig. 2A. (B) Spectra area of the free OH vibration vs. temperature.

Fig. 4.

Density profiles. Density profiles obtained with the TIP4P/Ice model for (A) the basal and (B) the secondary prism plane of ice Ih, illustrating the bilayer and monolayer structure, respectively. For the basal plane at 250 K, only the outer bilayer has lost its characteristic density profile, whereas, at 270 K, the outer two bilayers are molten, as indicated by the orange color. The density profile for the secondary prism face, with equal distance between the layers, changes gradually, as indicated by a gradual transition of the envelope from a rectangular to an elliptical shape. Additional temperatures are depicted in Fig. S6. Molten (orange) vs. crystalline (black) layers are identified by (bi)layer by (bi)layer RDFs (Fig. S7).

Fig. S6.

Density profiles. Density profiles for the (A) basal and (B) secondary prism planes at temperatures between 230 K and 272 K.

Fig. S7.

RDFs. (A) Temperature-dependent RDFs of reference ice Ih systems and liquid water. The reference samples for ice Ih contain 1,536 water molecules. The reference systems for the liquid system contain 480 water molecules. (B and C) Temperature-dependent RDFs for the (B) first and (C) second bilayer of the basal plane of ice Ih.

Fig. 5.

Calculated SFG spectra. (A) Calculated ssp polarized SFG spectra of the basal face of ice at different temperatures. (B) Frequency at the maximum SFG intensity of the hydrogen-bonded peak as a function of temperature (squares) with a sigmoidal fit. (C) Spectral area under the free OH peak (∼3,700 cm⁻¹) vs. temperature.

Fig. 6.

O−H groups orientation. (A and B) Orientation distribution of the water OH groups for the first three bilayers at (A) 230 K and (B) 270 K. (C) Maxima of the orientation distribution of up- and down-pointing OH groups in the second bilayer around cos θ = 0.3 (red) and −0.3 (blue) as a function of temperature. (D) Definition of angle θ, so that OH groups are pointing up and down, for, respectively, positive and negative cos θ.

Fig. 7.

SFG spectra of ice and supercooled water. Normalized SFG spectra of supercooled liquid water (green/blue) and ice, both at 269 K (orange/red), and ice at 243 K (gray/black). The lines are to guide the eye.

Fig. S8.

Average tetrahedrality $\langle q\rangle$ of the bilayers B1 through B5 as a function of system temperature. (Inset) A sectional view of the ice slab.