The physics of premelted ice and its geophysical consequences

The surface of ice exhibits the swath of phase-transition phenomena common to all materials and as such it acts as an ideal test bed of both theory and experiment. It is readily available, transparent, optically birefringent, and probing it in the laboratory does not require cryogenics or ultrahigh vacuum apparatus. Systematic study reveals the range of critical phenomena, equilibrium and nonequilibrium phase-transitions, and, most relevant to this review, premelting, that are traditionally studied in more simply bound solids. While this makes investigation of ice as a material appealing from the perspective of the physicist, its ubiquity and importance in the natural environment also make ice compelling to a broad range of disciplines in the Earth and planetary sciences. In this review we describe the physics of the premelting of ice and its relationship with the behavior of other materials more familiar to the condensed-matter community. A number of the many tendrils of the basic phenomena as they play out on land, in the oceans, and throughout the atmosphere and biosphere are developed.

Figure 1

Calculations of the film thickness vs $T-T_t$, with $T_t$ the triple point temperature referred to in this paper as $T_m$. The dashed line is drawn to show the ${(T-T_t)}^{-1∕3}$ power law expected when retardation is unimportant. The upper curve corresponds to use of the data of 118, and the lower to data of 395. From 152.

Figure 2

(Color) Top image: A photograph of a tricrystal of ice in contact, at $T_m$, with the bulk liquid (the dark band above the crystal). Under polarized light the birefringence of ice delineates different crystallographic orientations by color. Bottom image: The bicrystal coarsened from the tricrystal after approximately $7\mathrm{h}$. The scene is $3\mathrm{mm}$ in width. Ice can be held near its melting temperature for a host of experimental studies. From 435.

Figure 3

Measurements of surface melting of ice, film thickness (nm) vs undercooling (K). From 359. Solid triangles, ice in air, ellipsometry from 188; circles, optical reflectometry from Elbaum and co-workers (154; 151); open circles are measurements in water vapor, and filled circles are in air; open squares are for glancing angle x-ray scattering from 139, 140. The solid line describes the wire regelation experiments (195), shown in Fig. 8, the dashed line derives from experiments on ice/glass interfaces using NMR (231) and the dot-dashed line is from experiment on interfacially melted ice/PVC interfaces (482). The substantial variation illustrates the great sensitivity of ice premelting to impurities and small perturbations of surface structure.

Figure 4

Film thickness (nm) vs undercooling (K) at the interface between ice and water vapor. $N_i=6\times {10}^{-4}$ (long dashed line), $6\times {10}^{-3}$ (dash-dotted line), 0.06 (solid line), 0.18 (small dashed line), and $6\mu M$ NaCl (dotted line) per square meter. See the text for discussion. Adapted from 473.

Figure 5

Film thickness (nm) vs undercooling (K) for various monovalent electrolyte (NaCl) concentrations at an ice grain-boundary with a solid/film surface charge density $q_s$ of $0.01\mathrm{C}{\mathrm{m}}^{-2}$. $N_i=6\times {10}^{-5}$ (solid line), $6\times {10}^{-4}$ (long dashed line), $6\times {10}^{-3}$ (medium dashed line), $1.8\times {10}^{-2}$ (small dashed line), and $6\mu M{\mathrm{m}}^{-2}$ (dotted line). See the text for discussion. Adapted from 38.

Figure 6

(Color) Molecular-dynamics computer simulations from 187 show sections of ice structure during surface melting at a simulation temperature of $265\mathrm{K}$. The upper arrows indicate the liquid layer and lower arrows the bulk crystal. The basal plane is on the left and the prism plane on the right. Adapted from 184.

Figure 7

Optical reflectivity measurements of the surface melting of the basal plane of ice in air. Replotted from the thesis research of 154. See also 151.

Figure 8

The calculated thickness of water film around wires, deduced from the rate of passage of a weighted wire through ice; “wire regelation” (195). Gilpin’s data are compared with the theoretical power-law temperature dependence of thickness of interfacial melting under dispersion forces (121). The more rapid decrease of the apparent film thickness at lower temperatures may be due to the effects of proximity, effectively enhancing the viscosity.

Figure 9

Comparison between measured and calculated liquid fraction of ${\mathrm{H}}_2\mathrm{O}$ in close-packed powders. The fraction of unfrozen water is the ratio of the melted volume to the interstitial volume in the powder. The top panel shows the comparison for a powder of graphitized carbon black of average particle diameter observed in the range of $0.19–0.24\mu \mathrm{m}$. The two curves have been recalculated using the theory of 76 and are for an assumed simple cubic (sc) and face-centered-cubic (fcc) packing of spheres using a particle radius of $0.1\mu \mathrm{m}$, which has been used as a fitting parameter. The lower panel displays the recalculated comparison in a close-packed powder of polystyrene spheres, again for assumed simple cubic and face-centered-cubic packing of spheres, using a particle radius of $1.5\mu \mathrm{m}$. Note that the original paper (76) states in the text that the typical dimension of polystyrene spheres under electron microscopy is $\sim 5\mu \mathrm{m}$ and in the associated figure caption (Fig. 3) that the average particle diameter is $10\mu \mathrm{m}$ and that the theoretical curves are obtained with no fitting factors. We correct this here and note that the agreement shown requires the choice of the particle radius noted above.

Figure 10

(Color) Examples of frost heaving phenomena. (a) Needle ice growing out of dead wood (N. Page photo). (b) Ice lenses (dark) formed during solidification of water-saturated clay (modified from 424, and reprinted with permission from the University of Chicago Press). (c) Stone circles in Spitspergen (B. Hallet photo, circles are $1–2\mathrm{m}$ across).

Figure 11

(a) The intersection of four liquid veins in polycrystalline ice (H. M. Mader photo, published originally in 289). (b) Schematic diagram of the interconnected vein-node system (from 330, where it was modified from 408). Reprinted from the Journal of Glaciology with permission of the International Glaciological Society.

Figure 12

The underside of the laboratory-grown sea ice showing the cellular solid/liquid structure of the interface and two clear brine-drainage channels. The $c$ axes of the ice crystals are oriented principally horizontally, parallel to the plane of the page, displaying the columnar structure and permeability of natural sea ice. The large-scale is in cm. Adapted from 479.

Figure 13

Charge transfer versus growth rate; theory and experimental data are shown as a solid line and solid circles. The collisional area is ${10}^{-8}{\mathrm{m}}^2$, the value of $\xi =4$, and the other experimental parameters as in 300. Adapted from 127.