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COMMENTARY

Closer look at the surface of iceDavid T. Limmera,b,c,1

aDepartment of Chemistry, University of California, Berkeley, CA 94720; bKavli Energy NanoScience Institute, Berkeley, CA 94720;and cMaterials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720Author contributions: D.T.L. analyzed data and wrote the paper.The author declares no conflict of interest.See companion article 10.1073/pnas.1608888113.1Email: dlimmer@berkeley.edu.

When hydrogen bonds are broken at an interface,water molecules are forced to adopt configurationsthat are not as energetically favorable as those deepwithin the bulk of the material. At the interfacebetween ice and its vapor, this can result in the top lay-ers of ice becoming disordered. Such disorder makesit possible for water at the surface to flow, much likea liquid, accounting for why ice is slippery. This liquid-like layer exists over a wide range of naturally occurringconditions—from the depths of glaciers to the cloudsof the upper atmosphere—and is responsible for manygeological processes—from the shapes of snowflakesto the sliding of ice sheets (1). Although experimen-tal and theoretical work has confirmed the existenceof a liquid-like layer atop ice surfaces, its molecular ori-gins and physical properties are still actively debated.In PNAS, using high-resolution optical interferometry,Murata et al. (2) propose that the liquid layer atop icecan adopt two different wetting states with a first-orderphase transition between them.

Premelting is the term most often used todescribe the thermodynamically stable disorder atthe interface between an otherwise ordered solid andits vapor. Near the triple point, the thermodynamicdriving force for premelting is given by the decreasein the surface free energy relative to an orderedsolid–vapor interface. In the case of water and ice,the thermodynamics can be easily rationalized froma microscopic perspective. Shown in Fig. 1A is arepresentative configuration of the surface of icetaken from a molecular dynamics simulation at condi-tions close to water’s triple point. Far away from thesurface, the water molecules form hydrogen bondswith four of their nearest neighbors, establishingthe open, locally tetrahedral environment that leadsto the lower density of ice relative to liquid water.Molecules at the surface are forced to break one ofthose hydrogen bonds on average, incurring an ener-getic penalty that is large relative to kBT, or typicalthermal energies. This large energetic loss is bal-anced by an entropic gain from melting the surface.

Since premelting was definitely established withlow energy X-ray scattering (3), advances in surface

selective experimental techniques such as atomicforce microscopy (4), and vibrational (5) and elec-tronic spectroscopy (6) have provided powerful toolsto probe the surface structure of ice. These experi-mental studies have been complemented by a num-ber of detailed atomistic simulations that also finda premelting layer on the surface of models of ice(7, 8). However, quantifying the properties of the liq-uid layer and their dependence on external param-eters, such as temperature and vapor pressure, hasresulted in large uncertainties and little consensus (9).This is, in part, due to the difficulty in preparing andisolating pristine surfaces experimentally, and in partdue to the different molecular features probed by dis-tinct experimental methods, which may be more (orless) correlated with molecular order. Theoretically,well-known difficulties in modeling water, as well asthe large length and time scales required to samplethe relevant interfacial fluctuations, have proved chal-lenging for simulation.

Murata et al. (2) succeed by making direct in situobservations of the surface of ice using an advancedoptical microscope. In doing so, they challenge theconventional understanding of premelting on ice as asimple uniform liquid layer. Their measurements com-bine laser confocal microscopy with differential inter-ference contrast microscopy to approach molecular-level resolution in the surface height direction, witha wide field of view along the surface. Direct visu-alization of the surface avoids the difficulty in relat-ing specific spectroscopic or physical features to inter-facial order. Their interferometry enables them toquantify subtle interfacial features as they evolve,across wide spatial and temporal windows. As withtheir previous observations (10), they observe thatthe liquid-like layer on the surface of ice exists in astate of spatiotemporal heterogeneity, where dropletssitting on top of a thin liquid layer come into andout of existence. Such droplets were visualized ear-lier by Elbaum et al. (11) over shorter time scaleswith poorer optical resolution. Murata et al. (2) com-bine their ability to quantify the contact angles ofthese droplets and manipulate them through changes

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A B C

Fig. 1. Molecular thermodynamics of ice premelting. (A) Snapshot taken from a molecular dynamics simulation of under conditions wherepremelting occurs. (B) Dependence of the premelting thickness on temperature, away from the triple point (Tp), as predicted from the modelfree energy discussed in the text. (C) Free energy as a function premelting thickness, near conditions of a first-order transition between twodifferent wetting states.

in the water vapor pressure, with simple physical modelingrooted in classical wetting theory, to propose a thermodynamicorigin for these observations.

Building on previous work by Elbaum and Schick (12), Murataet al. (2) posit that droplets form due to long-ranged attractiveinteractions between ice and vapor. For thick liquid layers, long-ranged interactions in the form of dispersion forces dominateover molecular interactions and ultimately determine the wettingbehavior of the premelted layer. Provided the dielectric func-tions of ice and water, the strength of these interactions can beestimated using Lifshitz theory. This calculation adds a contri-bution to the free energy per area of the interface of the formW/`2, where ` is the thickness of the premelting layer and W isthe Hamaker constant for uniform slabs of ice, liquid water, andvapor. This constant is dominated by the relative static dielectricresponses of the pure phases. Because the static dielectric con-stant of ice is larger than those of liquid water and vapor at thetriple point, the Hamaker constant is negative (13). Its magnitudeis small, W ≈−0.01 kBT, because the difference in the dielectricconstant between water and ice at the triple point is only a fewpercent. This attraction pins the premelting layer thickness to afinite value, rendering surface melting incomplete as the triplepoint is approached. In the study by Murata et al. (2), incom-plete melting is clearly signaled by the protruding micrometer-sized droplets they are able to optically image. These dropletsfail to wet the surface of ice and consequently have finite contactangles. With their two-beam interferometer they are also able tomeasure the contact angle, which is as small as 0.6o, in reason-able agreement with that found previously (11).

The long-ranged attractive interactions that suppress pre-melting layers compete against short-ranged repulsive forcesthat enhance them. Short-ranged repulsions can arise withinLifshitz theory from the high-frequency contributions of the dielec-tric functions, or from molecular correlations. Effective short-ranged repulsions derived from molecular-scale interactionschange the temperature dependence of the premelting thicknessfrom a power law predicted for dispersion forces to a logarith-mic divergence. The logarithmic dependence is well understoodwithin the context of the Landau theory of surface melting (14),where the repulsive force takes the form Aexp[−`/`o ]. Here, thelength scale `o and coefficient A are determined by a competitionbetween bulk energetics favoring order and interfacial energeticsopposing it. An exponential form for the repulsive potential hasbeen found in molecular dynamics simulations of several models

of water (15). Using coarse-graining procedures, the constantsentering the repulsive potential can be extracted and mappedto available experimental data, which yields `o ≈ 5Å and A ≈0.1kBT/Å2 (16). At molecular length scales (` . 1nm) the short-ranged repulsion is more than an order of magnitude largerthan the long-ranged attraction. Shown in Fig. 1B is the resul-tant temperature dependence of the premelting layer thickness.Approaching the triple point from low temperatures, the thick-ness of the layer first increases logarithmically before eventuallyplateauing to an ultimate thickness less than 10 nm.

The evidence supporting incomplete melting on ice is animportant contribution by itself. However, by far the most intrigu-ing proposal put forward by Murata et al. (2) is the idea that thetwo different interactions, with their different scalings, strengths,and signs, can result in a first-order transition between differentwetting states. These states are characterized by either a dropletof liquid forming directly on the surface of ice, as would be favoredby the long-ranged forces, or a droplet of liquid forming on topof a thin liquid film, as would be favored by the short-rangedforces. Clear observations of both are provided in the study byMurata et al. (2), and, importantly, hysteresis is found in transi-tioning between these two states. This hysteresis is postulated tooccur due to the metastability afforded by a first-order phase tran-sition. It is triggered experimentally by moving between condi-tions of over- and undersaturation of water vapor pressure.

The proposed first-order transition is rationalized by Murataet al. (2) from a premelting thickness-dependent surface free en-ergy, F (`). Collecting both long- and short-ranged interactions(16), it takes the form

F (`)= ∆µ`+Ae−`/`o +W /`2 .

For ice, A > 0 and W < 0, so the function is nonmonotonicin `. This is precisely the form of the free energy described byBrochard-Wyart et al. (17) when such exotic surface transitionswere first proposed. The addition of a chemical potential differ-ence between the liquid, ice, and vapor phases, ∆µ`, is includedin the free energy away from the triple point. By modulating thischemical potential, coexistence conditions between distinct sur-face states can be found, with a free energy barrier between them,as illustrated in Fig. 1C. Apart from observing hysteresis, Murata etal. (2) map the limits of metastability in the temperature–pressureplane and visualize the dewetting process that transitions onestate to the other. Within the limits of metastability, this processoccurs with what they characterize as facile nucleation, initiated

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via capillary fluctuations. Outside the limits of metastability, theyreport behavior akin to spinodal dewetting.

Because of its ubiquity and importance, water often servesas a testing ground for proposing and validating new physicalphenomena. This was true with Michael Faraday’s initial proposal

of premelting on the surface of ice (18), which in the proceedingcentury was found to occur quite generally in metals, semiconduc-tors, and even rare gases. Whether or not the behavior illuminatedby Murata et al. (2) proves to occur in other materials or is uniqueto ice, it undoubtedly provides motivation for future studies.

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10.1073/pnas.1608888113.3 Kouchi A, Furukawa Y, Kuroda T (1987) X-ray diffraction pattern of quasi-liquid layer on ice crystal surface. J Phys Colloq 48(C1):C1-675.4 Döppenschmidt A, Butt HJ (2000) Measuring the thickness of the liquid-like layer on ice surfaces with atomic force microscopy. Langmuir 16(16):6709–6714.5 Wei X, Miranda PB, Shen Y (2001) Surface vibrational spectroscopic study of surface melting of ice. Phys Rev Lett 86(8):1554–1557.6 Bluhm H, Ogletree DF, Fadley CS, Hussain Z, Salmeron M (2002) The premelting of ice studied with photoelectron spectroscopy. J Phys Condens Matter

14(8):L227.7 Kroes GJ (1992) Surface melting of the (0001) face of TIP4P ice. Surf Sci 275(3):365–382.8 Vega C, Martin-Conde M, Patrykiejew A (2006) Absence of superheating for ice Ih with a free surface: A new method of determining the melting point of

different water models. Mol Phys 104(22–24):3583–3592.9 Li Y, Somorjai GA (2007) Surface premelting of ice. J Phys Chem C 111(27):9631–9637.

10 Sazaki G, Zepeda S, Nakatsubo S, Yokomine M, Furukawa Y (2012) Quasi-liquid layers on ice crystal surfaces are made up of two different phases.Proc Natl Acad Sci USA 109(4):1052–1055.

11 Elbaum M, Lipson S, Dash J (1993) Optical study of surface melting on ice. J Cryst Growth 129(3):491–505.12 Elbaum M, Schick M (1991) Application of the theory of dispersion forces to the surface melting of ice. Phys Rev Lett 66(13):1713–1716.13 Eisenberg D, Kauzmann W (2005) The Structure and Properties of Water (Oxford Univ Press, Oxford).14 Lipowsky R (1982) Critical surface phenomena at first-order bulk transitions. Phys Rev Lett 49(21):1575.15 Conde M, Vega C, Patrykiejew A (2008) The thickness of a liquid layer on the free surface of ice as obtained from computer simulation. J Chem Phys

129(1):014702.16 Limmer DT, Chandler D (2014) Premelting, fluctuations, and coarse-graining of water-ice interfaces. J Chem Phys 141(18):18C505.17 Brochard-Wyart F, Di Meglio JM, Quére D, De Gennes PG (1991) Spreading of nonvolatile liquids in a continuum picture. Langmuir 7(2):335–338.18 Faraday M (1859) Note on regelation. Proc R Soc Lond 10:440–450.

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