Rounded Layering Transitions on the Surface of Ice

Understanding the wetting properties of premelting films requires knowledge of the film’s equation of state, which is not usually available. Here we calculate the disjoining pressure curve of premelting films and perform a detailed thermodynamic characterization of premelting behavior on ice. Analysis of the density profiles reveals the signature of weak layering phenomena, from one to two and from two to three water molecular layers. However, disjoining pressure curves, which closely follow expectations from a renormalized mean field liquid state theory, show that there are no layering phase transitions in the thermodynamic sense along the sublimation line. Instead, we find that transitions at mean field level are rounded due to capillary wave fluctuations. We see signatures that true first order layering transitions could arise at low temperatures, for pressures between the metastable line of water-vapor coexistence and the sublimation line. The extrapolation of the disjoining pressure curve above water-vapor saturation displays a true first order phase transition from a thin to a thick film consistent with experimental observations.

Figure 1

Density profiles of liquidlike molecules for the basal interface as measured relative to (a) the laboratory reference frame, (b) the $f\text{−}v$ surface, and (c) the $i\text{−}f$ surface. Since the liquidlike layer has finite thickness, the profiles vanish at the solid phase to the left and the vapor phase to the right of the $z$ axis.

Figure 2

Film thickness (a), disjoining pressure (b), and interface potential (c) for the basal facet. Results are shown for two system sizes with $n_x\times n_y=5120$ (blue filled circles) and $n_x\times n_y=1280$ (green hollow circles) molecules. (a) The dashed lines indicate discrete film heights in units of the molecular diameter. (b) The lines are a fit of Eq. (2) to the blue symbols for $h>4.0\AA$. The insets show inverse surface susceptibilities as obtained from numerical derivatives (symbols) and from analytical derivatives of the fits (lines). Error bars are shown here only for the system fitted to Eq. (2). Panel (c) shows the decay of the interface potential at intermediate distances as extrapolated from the fit to Eq. (2). Arrows indicate states that can transition at supersaturation, i.e., to frustrated complete wetting states.

Figure 3

System size analysis of thickness distributions at the basal plane. (a) Probability distribution of the global film thickness $h$. (b) Probability distribution of the partial film thickness $h_{1/4}$. (c) Probability distribution of the local order parameter $h(\mathbf{x})$. Dashed vertical lines show the film thickness in units of the molecular diameter. Results are shown for temperatures in the range from $T=210\mathrm{K}$ to $T=271\mathrm{K}$, with color code as indicated in each panel.