Supercooled Water and the Kinetic Glass Transition

arXiv:cond-mat/9706039v1[cond-mat.soft]5Jun1997SupercooledWaterandtheKineticGlassTransitionII:CollectiveDynamicsFrancescoSciortino†,LindaFabbian†,Sow-HsinChen††andPieroTartaglia††DipartimentodiFisicaandIstitutoNazionaleperlaFisicadellaMateria,Universit´adiRomaLaSapienza,P.leAldoMoro2,I-00185,Roma,Italy††DepartmentofNuclearEngineering,MassachusettsInstituteofTechnology,Cambridge,MA02139(February1,2008)AbstractInthisarticlewestudyindetailtheQ-vectordependenceofthecollectivedynamicsinsimulateddeeplysupercooledSPC/Ewater.Theevolutionofthesystemhasbeenfollowedfor250nsatlowT,allowingaclearidentificationofatwosteprelaxationprocess.Wepresentevidenceinfavoroftheuseofthemodecouplingtheoryforsupercooledliquidasframeworkforthedescriptionoftheslowα-relaxationdynamicsinSPC/Ewater,notwithstandingthefactthatthecageformationinthissystemiscontrolledbytheformationofanopennetworkofhydrogenbondsasopposedtopackingconstraints,asinthecaseofsimpleliquids.PACSnumbers:61.20.Ja,64.70.PfTypesetusingREVTEX1I.INTRODUCTIONTheslowdynamics(α-relaxation)insupercooledmolecularliquidsandtheglass-transitionaretworelatedtopicswhichhavereceivedparticularattentionfromthescien-tificcommunityinthelastyears[1,2].Significantprogresshavebeenmadebyasinergeticapproachbasedontheoretical,experimentalandmorerecentlyonnumericalwork.Nowa-days,numericalsimulationswithrealisticpotentialsdescribingtheevolutionofmolecularsystemcomposedbythousandatoms,fortimeintervallongerthan100ns,arebecomingfeasible,allowingaclosercheckofthetheoreticalpredictionsandbridgingthegapbetweenexperimentsandtheory.Suchlongsimulations,althougharesufferingonthedeficiencyofthepotentialusedcomparedtotherealsystemswhichtheyaimtosimulate,offeraidealreferenceforcomparingwiththenoveltheoreticalpredictionsconcerningtheslowdynamicsabovetheglasstransition.Inthecasewherethestudiedsystemiswater,theinterestininterpretingthemolecu-lardynamicsintermofglass-transitionconceptsgoesbeyondthecomparisonbetweenthesimulatedsystemandthetheoreticalpredictions.Indeed,iftheexperimentallyobservednon-Arrheniusincreaseofthetransportcoefficientsonsupercooling[3,4]canbeexplainedwithinthesameframeworkofsimplesupercooledliquids[5,6],thepresenceofhiddenther-modynamicsanomaliesatambientpressure[7,8]doesnothavetobeinvoked[9,10].Inthefirstpaperofthisseries[11]wehavetestedModeCouplingTheory(MCT)[12]predictionsforthecorrelationfunctionsofsingleparticledynamicsinwaterwithcorrespondingquanti-tiescalculatedfromMolecularDynamics(MD)simulations,carriedoutforsufficientlylongtime(20to50ns)astoallowtheslowdynamicstobeobserved.WetriedtoassesstowhatextenttheMCT,whichhasbeenshowntodescribesimpleliquids[13,14],isapplicablealsotothedescriptionofthesingleparticledynamicsof(simulated)supercooledwater,anhydrogenbondedliquidwithstrongnon-isotropicinteractionsamongmolecules.AsaresultwefoundthatthecenterofmasstaggedparticledynamicscanbequalitativelyinterpretedintermsofMCT.Thisresultstimulatedustomakethecomparisonmorestringentandto2extendittothecollectivecenterofmassdynamics.Withonefurtheryearofcomputertimeonthreeworkstationsworkingfull-time,thelimitof250nsofcontinuoussimulationtimehasbeenreached,allowingthecalculationofthecollectiveproperties,forwhichthenoiselevelcannotbereducedaveragingoverdifferentmoleculesinthesimulatedsystem.TheoreticalworkbasedontheMCThasmainlyfocusedonsimpleatomicliquidsandonmolecularliquidswithspherical-symmetricinteractions.Onlyrecentlythetheoryhasbeenextendedtotreatthecaseofmolecularsystemswithnon-isotropicinteractionpotentialsopeningthewayforafullanddetailedquantitativecomparisonbetweentheoryandsimula-tion/experimentsformolecularsystems[15].Unfortunately,preliminaryresultsattheidealMCTlevelareonlyavailablefordipolarhardspheres[16,17],i.e.moleculeswithasimplergeometrythanthewatermoleculegeometry.Suchresults[16]stronglysupportsthevalidityofgeneralpredictionsbasedontheMCTforsimpleliquids.InthisarticlewestudyindetailtheQ-vectordependenceofthecollectivedynamicsinSPC/EwaterandpresentevidenceinfavorofaMCTdescriptionoftheslowα-relaxationdynamics.Thecomparisonisperformedonatwolevelscale:(i)Atqualitativelevel,wecom-paretheMCTpredictionforsimpleliquids(exemplifiedbythehard-sphereliquidwithinthePercus-Yevickapproximation)withthecenterofmassdynamicsinthecaseofsupercooledSPC/Ewater.Althoughthecomparisonisbydefaultqualitative,wethinkthattheanalogyintheQdependenceofallrelevantparametersisparticularlysignificant.(ii)Atquantitativelevel,wecomparetheSPC/EslowdynamicswiththedynamicspredictedbyMCTinthelateβ-region;moreoverweevaluatethevonSchweidlerexponentsbandγgoverningtherelaxationprocess(Sec.II)andweverifythattheyarerelatedasMCTpredicts.InbothcasestheagreementisstrikingandstronglysupportsthevalidityofMCTasthecorrectframeworkforinterpretingtheslowcollectivedynamicsinsimulatedsupercooledwater.3II.MCTSeveralreviewpaperspresentindetailthetheoryofmodecouplingforsupercooledliquids,inparticularinitsidealformulation.AreviewonthepredictionsofthetheorycanbefoundinRef.[11].Inthissectionwebrieflyreportthemainresultswhicharerelevantforthereadingofthearticle.MCTaim