Why is Ice Slippery - R. Rosenberg

Why ls lce Slippery?In 1859 Michael Faraday postulated that a thin film of liquid covers the surlace ot ice---evenat temperatures well below freezing, Neglected {or nearly a century, the dynamics ot icesurfaces has now grown into an active research topic.

Robert Rosenbero

T l p f i " a z B o r $ a r c r a n d m " l r i n s o i i c ' a r " d m o r g r h "I no- d ism;. ic" \ "1 p l "s o p-"s" ra s i r ion. ' - narur" .

Melt;ng ice accounts for eveiyday phenomena as dive8eas the electrification ofthunderclouds, in which the liquidlayer on ice chunks facilitates the transfer of mass andcharge dunng collisions between themi liost heave pow-ertul enough to lift boulders ftom the ground lsec PHysIcsToDAY, April 2003, page 23)! and, of course, slippery sur-

Evelyday er"erience suggestB why ice sudaces shouldbe slip!el)': Water spilled on a kitchen floor or minwateron asphalt or conoete can c.eate the sane kinds ofhaz-ards foi rvalkers and ddvers ihai ice can. Presunably, iheliquid makes the surface slippery because liquids are no-bile, \rhereas solid surfaces are rclatively rigid. Askingwhy ice is slilpery is thu6 roughly equi\-alent to askinghow a liquid or liquid like layer can occur on the ice surface in the first place.

Pressure meltingThe common pereption, even among those with a moderate knowledge ofscience, is that skate$ slide morc easilyon ice than on other solids because ice nelts under theirskates'pressure to produce a film ofwater.lvater is denserthan ice and occupias about 107.less \-olume per mole. Sor , c o " d c r o L " c h a r , l i ' ; p l ' . : p l , . a n , ( r ' r q n p a . .surc results in melting the ice and decrcases the sampletvolune. That is, ifmelting had occuned by itsell it wouldhave rcsulted in a decrease in lressure.

The science of the obBervation o.isinated in 1850,when JameB Thomson developed an expression for the lin-ear dependence of the lieezing point delression on pres-sure. His brother William,lat€r LoId Kelvin, veified thatrcsult e:pedmentaltl Neithcr however, refened to iceskatins. That inference had to wait until 1886, when ayoung ensineer named John Joly wofked on ihe problemand rcferred to Thonson's fesults. Joly pointed out thatthe presBur€ ofa skater's blade edge is so great because ittouches the ice over so small anarea. He calculated a pres-sure of 466 atmospheres and a conesponding meltingpoini of 3.5 'C, a temperatue that creates af m ofwateron which the skaier slides (see freue 1).

Osborne Rel{1olds also invoked pressure neltins in1899 to exllain ice skating. Buthis inspiration came {iom

Bob Fosenberg s ar emer tLs prolessor of chem slry arLawf€nce Unversily in Applelon Wisconsin, and avstingscholar at Nodhweslem Unversty i. Evanston, lll.ors.

50 December 2005 Physics Today

watching solder nlelt when it was pressed asainst a sol'de ns ircn. Relnolds assumed that a similar pressure pro-duced a ]i{tuid fi1m on ice that made skating posBible.L

Joly never explained hov skating might be posBible attemperatures lowef than 3.5 'C. Ald iherc's the lroblem.The optimum temperahre for fisure skatins is 5.5 "Cand for hockey, -9 "C; figl]re skaters prcfer sloser, softerice for their landinss, irhereas hockey players exploit thehardef, faster ice. Indeed, skatins is lossible in climatesa6 cold as 30 'C and skiing waxes are connercially avail-able for srch low temperatues. In his 1910 account of hisI ast expedition to the SouthPole, Robed lalcon Scott tellsof skiing easily at 30 "C. But Scott's chief scientist, nd-rard Wilson, descdbed the snow surface as sandlike at

46'C. Bascd on his soldering-iron expedments,Reynolds mieht have anticipated that liictional fteltingmust play a role as well as prcssure melting, inasmuch asheai cauled the meltins of his solder. But surprisingly,even with litt1e ei,idence in its favor, pressure meltins rcmained the dominant explanation of the slipperiness oficefbr nearly a century.

Frictional heatingFrankP Bolrden and T. P Hushes sussestedthe ftictionalheating altemative to pressure melting in a 1939 article.'Remarkably, no one before ihem had calculated that askier's pressure on snoris insuffici€nt to cause metting atlorv temperatures. BoNden and Huehes caded out an ex-tensive set ofexpedments in acave dug out ofthe ice abovethe rcsearch station in Jungfraujoch, Switze and, at analtitude of 33.16 metels. Oale temperatures never roseabove 3'C, and the team achieved lower temperatu.esbyusinssolid carbon dioxide and liquid al. Usins surfacesofwood and mctal. they measured boih static and kineticftiction. Because metal skis Bhowed higher friction thanwooden skis, ihe researchers concluded that frictionalheating was rcsponsible for nelting the ice i frictional heat-ing would be affected by the conductivity of the skis, butpressure meltine itould not. Pressure nelung seemed toplay a role only near the melting loint.

Geophysicist Samuel Colbeck made a sedes of contd-buuons to the debate in a sedes of papen published be-tween 1988 and 1997.r In the earliest, he arsued againBtthe pressure-mclting explanatjon on the basis of calculations ofthe prcssure rcquired to melt ice at los'tempera-tureB and on the basis of the phase diasram, which showsthe transition of ice ftom one solid phase to another at-22'C (see fisurc 2). The arsment confimed again how

Figure 1. An ice skatcrexenr prcss!res on i reofder o l r tew r lndrdarmorpheres on tre cc

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c€ .rs skJters nolc

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pressure meltingleales unexplained the abiliL! lo ski andskate at temp-atatures as lor as 35 "C. Colbeck alsopointed out that the prcssure rcquired to causc mclting atihc lower tempemtures would squeeze the liquid film to-quch an elte.i i,lat ihc friction genented, far liom facilitai.ing skating, roukl resist it.

He and corrorkers thcn lrovided etpedfleni.al cvidence Jbr liictional heatingLy fasie.ing a thennocoulle toaskatehladeiand lai.r to the bottoms ofskis). Thcincrca-cein temrcmture riith velocit!:, tleJ observcd, was consiste.lwith friciional, localized hearing of thc ice unde.fooL iocreate a thin waler laJer.ll'erc pressure melling an eDdo-thermic proccss the domi.anl contdbuiioD. dre re,sca.chers would ha\'e expe(led a dccrcase in tenlell1i,ure.

Melting below zeroNeithcr pressure nelting no. fiici.ional h€ating elplai.swhy ice can be so slipperJ ercn while one is standing ltillon ii. $'l1at evidenc. is there for the eristence ofliquid atihe surface-elcn at tenlentures below zem? Althoughhe {as allarenll! urconcer,led nith ice skaiing ard |ric-tional effecls on surJaces, Nlichael Fafada] Lo.k ihe Jirst

" t . 0 . " ' - d b n - . ' B . h r o p o , i l b d i . , , - 4 s r . F '

at the Royal insiltuilon on 7 Junc 1850, he deloled trostol his remarks io clcgant e:pedments le had conductedon regclation, the fteezing togeiher ol two icc cubes whenthey come inlo coniaci. Faradal* suggested ihat a lilm ofwaler on icc will f.eeze {'hen placed betwccD the twopicccs ofice. althoush the film remains liquid on the su.face of a single piece. Tlic liquid layer that coaLs i,le icccubes, he rrgned. must play aoiiicalrole in freezing themtogether ObseNalions ol wet snow freezing may have in-spired Faradat''s clains, bul his exlcriments were ney-"Ftheless ile liNt to iDvestigate the lhenohenon of premclting, the developnent .f a liquid laXcr that fonns onsolids at tcmp.ratures belo{ the bulk melling loint.

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80 60 .10 20 0 20 40 60 80 100 1:0TE]1IPEF,{TURE fCJ

Figure 2. Phase diagrarn of H.O. lce.\hibits ar ch v. r et l , o i . r \n i r l ine and ' t lassy nr ! . tL res na1 e. ! t r r d s t inct p, ; rses (7 r re sro\ rn hcrct atd iierenr pfe\sr fes a.d (enlpeartures. Thei . - . $ ,at - " ' ph.se l fars l ion s s inrp er . The ne t nEtenrpef.rt!re in.'ease\ neadi y w th presnrrc c\ceJrt.rt ow p'ess!rc!. where the iarn iar hcxa8ora ice lh n ! . t ! ie is le$ dcnsc as a sol i . l than.iqlicl. lD asranr .ourfcst oj Steven . Drt.h, L,ni

lers i ty o i Wisconsin at Creen Bav. l

December 2005 Physcs Today 51

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to have bccn fbryottcn, and Thomson's views prerailed.ThomtsoD'c lurely verbal argumeDts held sway lbr ncarlya ccnturr. Indeed, it $,asn't until 1949 that a nodcm sclcntist, C. Guniel, suggEsted thai an tut isic liquid filmplars a role in the slipperiness olice. Gur. ey hypoUr esizedthat molecules, inhercntly unstabie at the suface due tothc lack of othcr molcculcs abovc them, migrate into thebulk ofthe solid until ihe curfaccbccomcs unsiablc, s.hichprompts ihe formation ofa liquid lhase. T\!o Jeais laier,$I. A. Weyl accepted Fafaday's concept of a liquld filn o.the suface ofice and deleloped a nodel based on ihe dif-ferences bets'een the molecular arangement of water nol -ecules in the bulk and on the suface.t

In the mid 1950s, different rcsearch teams put theconcelt on a quanillailve tboiing ly peilbrtuing exleri-nenis rcminis.eni ofFaradav's own invesiigations oo ihefreezing together of ice cubes.In each case theymeasurcdthc force of adhcsion betiveen tNo sphcrcs oficc allowedto touch.' Charles Hosler'c group aL the Penns."'lvaniaState f,-nivcrBity achicvcd lalticularlx compclling rcsults(see fignrc 31. The group comliled data from a serics of c!-pedmentr, each conducted ai a dilterent temperature bc-tween -25 'C and 0 'C at the vapor pressure ofice, to con-struct a smooth cune of the forces required to pull icespheres alart. At valor prcssurcs bclowicc saturation, roadhesion occuned belo$ '!'C. Tlre researclrers ini'er.edihat the exlected rcushness of th-" sudaces \ras removedby the lresence ofa liquid filn whose thickness was sut:ficieni. to provlde a smooth surface ofcontaci.

ln the yean since \\teyl's and Gurneyt papers ap'peared. expednenialists and theo.eticians have donemuch to uDderstand the relative conidbutions of prcssueneliins, frictional hcatins, and thc prcscncc ofliquid-likcfiins.n su.faces ofice. Each mechanism llays a roLe thatdepends on ihe temperature (for arcvie!, see reference 8).Ofthose contdbutions, the precise nature of the liquid iikelayer has bccn thc nost clusilc.

Measuring thicknessIn 1963 J. \1'. Tcllbrd and J. S. Tudicr carded out a s.ricsofrgelationcrpc mcnts.cachatadiffcrcnttemperaturc,if $hicf a wire under prcssure slowlr fligrates l,hroughice.3 The expedment was a quantitative rersion ofan earlier one used to salport the hwoth.sis of prcasurc mclt-ing. Using a contact on the Fire as part ol a poteDtiome-ier circuit. lhe researchers preciselJ m-.asured the velocil.lard found ihat it increasedlinearly {'ith temperature from

3.5 'C to 0.5 'C.Ffom 0.5 "C tothe mel t ingpoiDt . therelocity of the wire's passagc increascd sharpl-v For th.fbrcc alplied and the size of wire used. tfey calculared aftelting-poini. de.rease of 0.5 'C due to pessure melting.yet anothef indication that prcssurc melting was not re-slonsible for tlie passase ol the wire throush ice belorv thaitemperature. The quasi'slati. nalure ol the molion meanifrictional processes played no role either Nor {as crcepthe slow nechanical defomation of a solid rcsponsibl.o h " * " p . n r u , . u . , d ' , - t i u n l - b ' ' i ' " , u n - , F " L J

Ratler, lelfod and Turner interpreted theD resultsin terms ofthe floiv of a thin Ne$tonian shear lat€r of aliscous fluid around thc sirc. and calculated a layer thick-ness that satisfied a fun.iion (?' ?l ) 'xr. where Tris thetetuperalurc in kellin, and ?,,, is the melting point tempe.ature. h 1980, R. R. Gillin! e:tended Telford andTurne/s wo.k to the broader temperature range of 35 'C

io 0.005 "C. At 35 "C, the calculated \iscosity of thewatef ln the liquid layer is at most a feir times greaterthan that ofbulk rrater. Gilpin found both a sloe mode anda fast node for the wire's motion. n1 accord s'ith Tclford

20 10TEMPERAIURE I'C]

Figure 3. In a ser ies o i 1957 exper iments, Cr ; r e!Hosler and .o lea8res meas!red the iorce f€q! 'ed lopr I ap.r l a p. r o i ice spheres in eqr l ibr i lm and tou.h-ing ei.h olher. The lofce fcreased as the Lemper.nurei f . reased, an nd.at ion that warm-of thorsh st I s !b-zero tenrpefatLr-os iorm ncfeasi ig lv ih ick iq !k l - ike' . d b , h

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Not everyore at the time s'as convinced. Shori,ly afterFaraday's publishcd account app€arcd in 1859.1 JanesThornson took the lositionthatthe regelaiio. l-arada! ob-served Bas due 1,o lressure on i,he ice cubes. The resultingJ b . o r l r o o r . l . J o i n " r B . r - " d l p d i d d z - 8 . h 4argued. although he pmvided no addliional experinientalevidence. Later ihat year, laradar replicd to Thomson'sviews, argning for the presence of a liquid layer near themelting point mainly on the basis that ice camol be iu-perheated, $hereas liquid water can be sule/heated and

An 11360 article offered amore comllete rebuttal. wiihne$ erperimental rcsults. Famday prepared iwo pleces 01icc, cach atiachcd by a ihrcad to lcad Neights that submerged them in a rvater bath maintained at 0'C. \\thendisllaced laierall), the!,elui.ed lo lheir orieinal places"with coNid.rablc forcc." 'Ifbrought into the slightest contact, regelaiion en-qtred, the blocks adhered. and lhey re-h ained adheren L notwithslanding i.h e lbrce tending to pu11them apart."' Thomson, unconvinccd. rcplied r..ct asain.J. \Villad Gibbs, in a long, though little noticed, fool,nol,eio his lamous 18r-6 laper on thermodynamics. took accouni ofihe work and fou.d that his conclusions \yere mharmony {ith the opinion ofProfessor Famdar"

Remarkably. despjte the elesant a.d sinple expei-ments and published suplort from Gibbs. Famday seems

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Figur€ !r. A compilation of dala lronr dllterent experimcnrarpproachcs il !sirates ihe vari.rtion oi thicknc$cs oi rheiquid ikc ayer on .e obtained bv differenr mcrhods.

Pfoloi brckscatterifg data (fed dashed line) .rre adaptcclhoD rei. ll, x{ay scattering data us rg a glass interfacelb.ck dashed l inc l and a s i l i .o f ln ter i .ce (b ack bo d l inc) ,i rom fe i . l .+ , H. Dosch. t a l . and S. Engenr. rnn et a l . ;alomic-iorce microscopl mcas!r-omeits (stars).o!rtesy oJHans- l ! rgen B! t t ; and regelat ion d. t , (b ue sol ld , , r r ( , ,nfer .9/ R. R. C p in.

been brought to bear on tlie premelting prcblen io deter-minc the temperature ra.ge and thickness of any posiu-lai,ed lnycr (Ior relieit ofthe literaiure on thc topic up tothat limc, scc reference 11.) Unforiunateh those different expe mental conditions, ransins fron high vacuun. L L p F o . : l i b i . n . o o o r p r p q s u , F 4 f c a n " l u n p J r l

son between experimcntal results difrcuh rsee figxre,1).Nuclear magnetic rcsonance (NMRI p&vided e!i-

dencc for a liquid layer on the surfacc of ice: Below themeliing point thcrc is a nanow absorpiion line, not thebmad line one would expcct ftom a periodic solid.l'Mole-clrles at the surface between -20'C and 0 "C toule aL aftequency five orders ofmasnitude greater then those inblrlk ice and about 1/25 as fhst as those in liquid llatei.Thc self diffusion coefficieni is tiro ordcrs of masnitudelargd than that in bulk ice.

Using proton backscatte ng, researchcrs in 1978found surlirce vibrationB ofthc oxygen atoos roughly 3.3timcs the amplitude of their value in thc bulk, and anamorphous layer 10 times thicker than enat \rtr]IR measurenents had cBtimated.r: But. unlike NMR, the protonbackscatieing fr easurements wcre Dade mderhigh vac-uum, a condition narkedlJ dilfcrcnt from the finite vaporpressurcs at which surface melling typically occun.

45 35 -25 15 5 5TEMPERAIURE fC)

and Tuner, and fit the velocity as a function oftempera-Lure jn thc slow mode to the same lilnction. The phenon-enon occurred at temperatures \rell below 22 "C.

In 1969, Michacl Orem and Arthff -Adanson foundyet more surprising eyidcnce for the presence ofa liquidlike layer on ihe su#hcc of ice \rhen ihey comparcd thep l ' s r c a a d . n r p r o o . . m p l ' h ) o . o . r r b o n . s ! . r . . u . i . .with thctu adsorytion on a liquid-watcr suface. Above

35 'C lhe adsorption isotherm of, hexane on the suface ofice lracks lhat ofthc same vapor on the sufac€ ofliquid water, but not at lenpemturcs belos' 35 oC. Theenhopy and enthalpy ofadsoryiion al$ track the pattenol liquid watcr abole 35'C, but not beloq Orem andAdamson lnterpreted thcir reslrlts as indicating that theonset ofice's surface premcltine is at 35 'C.

That liquid lat'ers persist to such lorv temperaturcscaD have stdking enrironmental consequenccs. In the1990s, chemisLry Nobel iaureate Mario Moli.a atrdcoworke$, for instance, attributcd the adsorltion of hy-drochlodc acid on polar shatospheric clouds to the eestence ofa llquid-likc layer on ice. The adsorpiion plays arole in the deiiruciion ofozone.ro

Since the nid-1960s, a varict"v of experimental ap-proaches, performed under a larietl' of conditions, have

rigure 5. Mol€culaFdynami.s simulations crlcu ate |r.v.rirtion fionr the per odi. larti.e lhaL s!rtace mole.ulcs. . f i " r r . r o ^ . , r p r ' , 0 . 6 r - 1 , | , 6 , 8 " ) i ,clcs repLos€nt oxyeen atoms nDd the smal bla.k c rcles,hydrogen aionN, lhe thi. lines represcnt coval-.nt bordsthai coine.t th€rn. ( d.rpted from rcf. I7.)

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December 2005 Plrysics Today 53

X-ray diffraction ofibrs lerhaps the most conlincinsevidence 1br the liquid-like layer on the suface of ice.raWork done in 1981- found ihat the intermol€cular distanceon the ice surface is slishtly smallcr than it is in liquid\rater. \rhose intermolecular disiances are, of cou6e,smaller than ice'B are. In the mid 1990s Helmut Dosch(I{ax Planck Institut€ for Metal Research and the LTniv-"rsity of Stuttcart) and coworkers publiBhed a sedes ofmore detailed papeN on their studt' ofice surfaces usingglancing-angte x-rax scattedng. This sroup found a liquid-like layer on the different crystallosiaphic ice surfaces be-trecn 13.5 'C and 0 'C. Their model describes a surfacelayer that enibits rotational disorder vith intact lone'range posi Li on ai order $ ell below the surface melttug temperaturc. At the suface melting iemperature, a com-plctcly disordered layer exists on the sudace above therotationally disordered layer.

In 200,! Harald Reichert, Dosch, and colleagueB stud-ied the inteface betrveen ice and solid silicon dloxide using: ray rcflectivity and calculated ihe ihickness and densityofthat liquid like layer bet\reen 25 "C and 0 'C. The den-sity ofth€ suface phase tumed out to vary fron ihe typ-ical valuc ofliquid {ater at the melting point to 1.17 g/cmrat -17 'C-c lose to that ofthe high density form ofamoryhous ice, and remi-niscent of Yoshinori Iu-rukawa's resulls on theintermolecular distanccneasured between oxygenatoms in the surface layer.

ln 1998, using atoflicforce microscoly. AstridDdppenschmidt and Hans-Jurgen Butt, both ai iheGutenberg University inNlainz, Germany. measuredthc thickness of the liquidlikc layer onicc.r! Capillarlibrces on the liquid su hc€prompted the AFM'S can-iilevei lip tojun! into con-tact with the solid ice onceit reached ihe much softcrlayer's level. The upperlimit in thickness ofthe liq-uid like layer varied ftom12 nm at 24 'C to 70 nmat 0.7'C. Their rcsultsindicated that a i about

33 "C surfa.e meltins

Doppenschfr id t andtsuil. al-qo found thal lhesuface layer is thickerwhen Balt is preBent. In-deed, Yale Unilersity'sJohn Wettlaufer argtres

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0.0-273 -225 -115 ,125 -15 -25

TENIPER,{ALTRE fC)

rigLrre 6. With fewer chemical bonds to hold them inplace, sLrlace mo ecules vibrate with Ereater anrp tudelhan those locaLed ir the b! k c.ystal. The mean squaredisplircenrent (MSD) oi oxysen and hydrogen atonrs onthe oLrtermost sud.rce oi ice ref ects that thernral v bration aid increnses as n iunction of temperature. Thesq!ar€s, trb.8 es. ,nd circ e! represent the nverir6.MSD oi the outermost or lgen b i laver o i the .Nsta s! riac. along ihe a , ]>, and . ax€s, resp€ctivelvr the doltcd, c lashed. a id so id I ne5 ndicale the MSD of b l lk(e n on8 thosc axcs. (Adapted tom ref. I7 )

The nature of ihe liquid like layer is not clear from ex-pe mental measurements, so theodsts have tried to clar-ifu the situation.In 2004 ftmoko Ikeda lukazawa (JapanScience and Technolosy Asency) and Katsuyuki Kawa-mura (Tob! Institute of Technolosx) peformed moleclrlardynamics simulalions ol ihe ice-Ih sur'1:1ce as a function oftemperaturc.rr Figue 5 illushates the melted or liquid-like surface layer calculated in a simulation of the sufacea t 2 0 ' c .

The pedodic structure breaks down and thc molecu-lar lalefs adopt a more amoryhous reconstmctron n re-spo.se to ihe reduced nunber ofchenical bonds holdingthe surfac-" molecules in place.Atoms in the outermost sur-face vibrate with greater amplitude as a function oftetr-lerature ihan atoms in the intedor latticc (scc fisure 6)-Surface rnelung is atidbutable to the interaction ofthe \i-brationalmotion ofthe surface molecuies \rith the iniefior

Beyond iceThe phenonenon of srrface melting is not limited to ice.In 1985 Joost W- M. Frenken and J. F. van der Veen oftheInstitute for Atomic and Nlolecular Physics in Amsterdam

fircd a bcam ofions asainsta lead fiystal and noni-tored the scat tedng. ' rBased oD how the ionsbackscattered into theirenerg] detecton, the researche$ deduc€d thatlead haB a melting tran-sition far Bhort of itsbulk melting iempemlure(327 'C) and found a phasein which the sudacc b€-came complete ly d isor-dered at 30? "C. The sr-face film's thickness dseslosa.ithmically Rith temperature. Since then. experiments have verified liqujdlike surface layeft oDDetals, semiconductoB,molecllar soli&. aDd rare

The s l i lpe l iness ofothef solids is another mat-ter. Althoush diamond doesnot e:hibit suface meltingat room temperature- itdoes ha!e. belo$ its Delt.ins point, a kinctic coefft-cieni ol liiciion evensmallel ihai ice the fric'tion coefftcient, measuredin air can be as low as 0.11br diamondlike carbonfilms sliding on each other

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that the presence ofimpurities in the sulface films can ex- Fflction coefficrents rre hrehesL (about 0.6) on diamondplain the wide thickness vadation in the liqurd hke film mersured n vduun, with successivety loi'er vatueson ice and the temperature d.pendcnce ofthe thickness mcasurcd in hydrogen, oxygen, and wai,er-yapoi atnos-that rcsearcher have fornd usi.g larious techniques.'i pheres the lresence of gases serves to tie up reactiveWettlaufer describes the tnnsition $ith incfeasing tem- danelins bonds on a suface. The ftiction coefficient oficeperature from a disodered solid to a partly structured slidi;g ;n ice. in compariBoD. 'adcs bcts,een 0.1 and t.5,q u a - - l r q u o o d l L o : p , . p h " d r T . J l r l o I n d r e c a n o " o " ' o i n o o " o i n s ' . t u , r , .sistent iescriptions with different tech;iques. r;rrer

*'l;-J;;;i.id;;e, lccd, zinc, tin, and cadniun

prosress tos'ard understandins the suface of ice nay be Doederc an e*ibit lo;cr friction ftom 10 to 100 .C bclowdependent on pe brming several liinds ofmea6urements ihu mfttine DUints \vhen used as lubrican rs for sreel rub-on the samc surface undd comparable conditions. bins asain.r strtl. Indted. researchers have nodeled rhe

, Lo"P'

54 December 2005 Physics Today htlp://www phys csloday. org

lubrication bctveen two metal sufaces in which one hasa low meltins tempenture and found evidence that fric-tional nelting provides lubication by a liquid film.Whether these obsenations or the nodel support the notion that a ftictionally melted laye. would pemit skatingona metal sudace near or below il.s nelting point is surely

I an srutefirl to urian Hofftuan and Richa yan Dulne lblth. initial impetls to urite this a.ticle, to Sdnuel Colb.ch farmanr t)aluablc discussions, and to Franz Geiser and LauisALtrcLt lot a carcfut rcddne af an ed ! .l.tuft.

References1. J. Jol-r in .Sci. P.o.. d. Soc tzbl;n N,D,Se/tcs 5,453 (1886):

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\!11h x stxle of thc at nra0ufaclurjng facilil_! $hicl is c€rnffed toIS0 900112000 \rc cm delilcl n qna.fih magn€i. ,Lss€nbh or sub.r5sctnbl'lxrt. MC! cnn Nlso tull €ngin€er nnd d€sigr r so]ulio.for yonr nagnet r€qulr€ rerl. Call or ti\X us $ilh )oul|€qnneol,enr krr ̂ a lrnmedlate qrot^li(,r.

See M.pi.ims,cal6089-36 See M.pl.ims.ca/6039.37