Interfaces - Alosious et al. - 2021 - Unknown

《Interfaces - Alosious et al. - 2021 - Unknown》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

pubs.acs.org/LangmuirArticleNanoconfinementEffectsontheKapitzaResistanceatWater−CNTInterfacesSobinAlosious,SridharKumarKannam,SarithP.Sathian,andB.D.Todd*CiteThis:Langmuir2021,37,2355−2361ReadOnlineACCESSMetrics&MoreArticleRecommendations*sıSupportingInformationABSTRACT:TheKapitzaresistance(Rk)atthewater−carbonnanotube(CNT)interface,withwaterontheinsideofthenanotube,wasinvestigatedusingmoleculardynamicssimulations.Weproposeanewequilibriummoleculardynamics(EMD)method,alsovalidintheweakflowregime,todeterminetheKapitzaresistanceinacylindricalnanoconfinementsystemwherenonequilibriummoleculardynamics(NEMD)methodsarenotsuitable.TheproposedmethodisindependentofthecorrelationtimecomparedtoGreen−Kubo-basedmethods,whichonlyworkinshortcorrelationtimeintervals.RkbetweentheCNTandtheconfinedwaterstronglydependsonthediameterofthenanotubeandisfoundtodecreasewithanincreaseintheCNTdiameter,theoppositetowhatisreportedintheliteraturewhenwaterisontheoutsideofthenanotube.Rkisfurthermorefoundtoconvergetotheplanargraphenesurfacevalueasthenumberofwatermoleculesperunitsurfaceareaapproachesthevalueinthegraphenesurfaceandahigheroverlapofthevibrationalspectrum.AslightincreaseinRkwiththeadditionofthenumberofCNTwallswasobserved,whereasthechiralityandflowdonothaveanyimpact.■INTRODUCTIONwhichweintroducedanewmethodtocomputetheKapitza11,12resistanceataplanarsolid−fluidinterface.OurEMDInrecentyears,grapheneandcarbonnanotube(CNT)-basedmethodisfreefromtheplateauproblemintheEMDmethodmaterialshaveexhibitedvastpotentialforresolvingnanoscale13,14basedontheGreen−Kuboformalization.Usingournewdevices’thermalmanagementobstacles.Suspensionsofmethod,weexaminedvariousfactorsaffectingtheKapitzananoscalegrapheneflakesandCNTsinfluidsconsiderablyenhancethethermalcharacteristicsofthebasefluids.1Theresistance/lengthincylindricalnanoconfinementsystems,suchDownloadedviaCLARKUNIVonMay16,2021at06:18:13(UTC).transportofwaterthroughCNTshasdrawnsignificantasdiameter,chirality,thenumberofwalls,andflow.WefindthattheKapitzaresistancereduceswithanincreaseintheattentionduetotheirbroadrangeofapplicationssuchaswaterdesalination,drugdelivery,hydrogenstorage,etc.2−5Indiameterduetoanincreaseinthenumberofwatermoleculesperunitsurfaceareaadjacenttotheinterfaceandahigheradditiontothat,thehigherKapitzaresistancebetweenwateroverlapofthevibrationalspectrum.Otherparameters,suchasandCNTscanbeutilizedforeffectivelytransportingliquidsatSeehttps://pubs.acs.org/sharingguidelinesforoptionsonhowtolegitimatelysharepublishedarticles.thenumberofwalls,chirality,andflow,donotsignificantlytemperatureshigher/lowerthantheambienttemperaturesinaffecttheheattransferattheinterface.futurenanoscaledevicesforheating/coolingpurposesatspecificlocations.StudiesbasedonKapitzaresistanceinCNTsystemsweremostlyfocusedonnanocompositesand■THEORY6−10CNT-basedbulknanofluidsystems.However,studiesonThederivationforournewlyproposedmethodisgivenbelow.thenanoconfinementeffectonKapitzaresistanceinsystemsItisanimprovedversionfromourpreviouswork,inwhichwewithwaterfilledinsideaCNTandmoleculardynamicsnowformanautocorrelationfunctionwiththekineticvariablemethodstocomputetheKapitzaresistanceinsidesuch(temperature)insteadofheatflux,whichhasbothkineticandcylindricalnanoconfinementsystemsareseldomreportedto(strongly)configurationterms.11,12Themodifiedderivationthebestoftheauthors’knowledge.Inthispaper,weintroduceanovelwaytocomputetheKapitzaresistance/lengthattheCNT−waterinterfaceusingReceived:November15,2020bothequilibriummoleculardynamics(EMD)andnon-Revised:January29,2021equilibriummoleculardynamics(NEMD)simulationtechni-Published:February11,2021ques.WealsostudythevariousfactorsinfluencingtheKapitzaresistance/lengthincylindricalnanoconfinement.ThepresentEMDmethodisanimprovedversionofourformerwork,in©2021AmericanChemicalSocietyhttps://dx.doi.org/10.1021/acs.langmuir.0c032982355Langmuir2021,37,2355−2361

1Langmuirpubs.acs.org/LangmuirArticleFigure1.Schematicdepictionofthesimulationsetup.(a)WaterfilledinsidetheannularregionbetweentwoconcentricCNTsfortheNEMDsimulation.(b)WaterfilledinsideaCNTfortheEMDsimulation.givesbetterstatisticsandacorrelationtime-independentresultThetime-correlationfunctionscanbedefinedasCTJ(t)≡qandisalsorecommendedforplanarinterfaces.⟨ΔT(0)Jq(t)⟩andCTT(t)≡⟨ΔT(0)ΔT(t)⟩,soeq5canbeTheKapitzaresistanceortheinterfacialthermalresistance,expressedasRk,isdefinedastΔTCtTJq()=−∫0GttCttkT(′)T()d′′(6)Rk=Jq(1)TheLaplacetransformofsomearbitraryfunctionf(t)isdefinedbyTheinterfacialthermalconductance,Gk,canbedefinedasthe∞inverseofRkLft(())≡≡∫ft()ed−sttfs̃()0(7)1JqNotethatasaconsequence,wehaveGk==RkΔT(2)∞f̃(0sf==)∫(t)dt0(8)whereJqistheheatfluxatthewater−CNTinterfaceandΔT=Tf−TwisthedifferencebetweenthetemperatureoftheCNT,whichisthesteady-statetime-independentvalueoff.Hence,Tw,andawaterslabofsomesmallthicknessimmediatelytakingtheLaplacetransformofeq6providesadjacenttotheCNT,Tf.CsGsCs̃()=̃()̃()TheinstantaneousgoverningconstitutiveequationcanbeTJkTTq(9)formulatedwithregardstothetimedependenceoftheKapitzaTheKaptizaresistancecannowbedirectlyevaluatedusingeqkernelatequilibriumas9,i.e.,tCs̃()Jtq()=−∫GttTttk(′)Δ()d′′+JtR()(3)TJq0Gs̃()=kCs̃()TT(10)whereJR(t)isarandomheatfluxnoiseterm,whichisuncorrelatedwithΔTwithazeromean,givenbyfromwhichGk≡G̃k(s=0)canbeextracted.However,thisprocedureisaninefficientwaytoextractGksincewearenot⟨JtRR()⟩=0and⟨ΔTJt(0)()⟩=0(4)usingthewholedataavailable.So,toobtainastatisticallymoreprecisevalue,wecanusealloftheavailabledataanddeduceSimilartotheassumptionofHansenetal.,15here,weareG̃k(s)byfittingtheright-handsideofeq9totheleft-handsideassumingthatwecanneglectnonlocaleffectsgeneratedbyofthesameequationandthendirectlycalculatethevalueats=fluidstructuralinhomogeneity.Multiplyingeq3byΔT(t=0)0.andcalculatingtheensembleaveragegivesMoreover,ifweassumethatGkhasaMaxwelliantime15distribution,asrecognizedbyHansenetal.,thetime16⟨ΔTJt(0)()⟩dependenceofGkcanbeexpressedasqn=−μttGtk()=∑kieiΔ−TG(0)∫k(tt′)ΔT()dt′t′i=1(11)0=wherekiandμiarecoefficients.TakingtheLaplacetransformtofthisgives∫GttTk(−′Δ)(0)Δ′′Ttt()d0nkGs̃()=∑i=kti=1s+μi(12)∫Gttk()(−′⟨ΔT0)(Δ′⟩′Ttt)d0(5)Substitutingeq12intoeq9gives2356https://dx.doi.org/10.1021/acs.langmuir.0c03298Langmuir2021,37,2355−2361

2Langmuirpubs.acs.org/LangmuirArticleFigure2.(a)ComparisonoftheKapitzaresistanceobtainedfromtheNEMDandthepresentEMDmethods.(b)ComparisonoftheKapitza13,14resistanceasafunctionofcorrelationtimecalculatedusingthepresentmethodandtheGreen−Kubo-likemethodofBarratandChiaruttini.nkinsidetheCNTwasvariedbyprovidingexternalaccelerationsCs̃()=∑iCs̃()2TJTTrangingfrom0to5m/s.Themodelingaspectsaregiveninqs+μi=1i(13)theSupportingInformation.Thewatermoleculeswere19,20Thus,forsteady-stateconditions(s=0),wehavemodeledusingthesimplepointcharge(SPC/E)water21model.TheSHAKEalgorithmwasusedtokeepthewaternkimoleculesrigid,andtheparticle−particleparticle−meshGGkk≡̃(0)=∑22μ(PPPM)solverwasusedtocomputethelong-rangei=1i(14)electrostaticforces.PeriodicboundaryconditionswereFinally,theKapitzaresistanceisobtainedasemployedinallthreedirections.Toeliminatetheerrorsduetoelectrostaticinteractionsbetweenperiodicimageswhile1Rk=implementingthePPPMmethod,a5nmvoidspacingGk(15)betweenperiodicimageswasintroducedinthexandy23directions.TheintralayercarboninteractionsweremodeledWecanextractCTJq(t)andCTT(t)fromEMDsimulations.usingtheadaptiveintermolecularreactiveempiricalbond-AftertakingtheLaplacetransforms,wecanfittheright-handorder(AIREBO)24potential.Also,theinterlayercarbonsideofeq13totheC̃TJq(s)datawiththehelpoffittinginteractionsforthemultiwallCNTweremodeledusingapairwiseLennard−Jones(L−J)potential,ϕ(r)=4ϵ[(σ/r)12−parameterskiandμi.Finally,wecalculatetheKapitzaij(σ/r)6]withtheparametersσ=3.414Åandϵ=0.2323kJ/resistancefromeqs14and15withtheinclusionofthese25fittingparameters.Theinstantaneousheatfluxatthewater−mol.Thecarbon−waterinteractionsweremodeledbyL−JCNTinterface,Jq,canbecalculatedusingthefollowingpotentialswithparametersσ=3.190Åandϵ=0.3920kJ/17,18mol.26Acutoffdistanceof10Åwassetfortheshort-rangeequationCoulombicforcesandtheL−Jpotential.TheLarge-scaleJt()=+JtK()Jtϕ()27qqq(16)Atomic/MolecularMassivelyParallelSimulator(LAMMPS)packagewithatimestepof1.0fswasemployedtoperformallwhereJK(t)isthekinetictermandJϕ(t)isthepotentialtermofqqoftheMDsimulationsandvisualmoleculardynamicstheheatflux.(VMD)28wasutilizedforvisualization.Thesimulationprocedureinvolvesenergyminimizationof■METHODOLOGYtheentiresystem,followedbya2.0nsequilibrationintheThesimulationdomainfortheNEMDmethodisshownincanonical(NVT)ensemble.Afterthat,thesystemstabilitywasFigure1a,whichconsistsofwaterfilledinsideanannularverifiedforanother2.0nsbysimulatingunderamicro-portionoftwoconcentricCNTswithdiametersD=5.41nmcanonical(NVE)ensemble.FortheNEMDsimulation,aandd=1.62nm(correspondingtochiralities(40,40)andtemperaturegradientinwateralongtheradialdirectionwas(12,12)).TheselectionoftheseparticulardiametersisgeneratedbytheadditionandsubtractionofheatfromthedescribedintheSupportingInformation.RigidconcentricinnerandtheouterCNTs,respectively.TheheatadditionandCNTswereimmersedinalargewaterbathandequilibratedatsubtractionprocesswasachievedbythermostattingtheinner300Ktemperatureand1atmpressure.Subsequently,theandtheouterCNTsatdifferenttemperatures(350and250K)29watermoleculesexceptfortheannularregionwereremoved.withthehelpofaLangevinthermostat.TheprocessofheatThesimulationdomainfortheEMDmethodisshowninadditionandremovalcontinuedfor6.0nsuntilasteady-stateFigure1b,whichwaspreparedbyimmersingarigidCNTofheatfluxandalineartemperatureprofilealongtheradialdiameter5.41nminalargewaterbathandequilibratedat300directionwereobtained.ThetemperatureprofileandheatfluxKtemperatureand1atmpressure.Thewatermoleculesdatawereextractedfromanother5.0nsproductionrun.TheoutsidetheCNTwereremovedaftertheequilibration.Kapitzaresistance,Rk,wascomputedwiththeequationRk=Differentparameters,suchasthenumberofwalls,diameter,ΔT/Jq,whereΔTisthetemperaturedifferenceatthewater−chirality,andflow,werevariedtostudythedifferentCNTinterfaceandJqistheheatfluxacrosstheinterface,whichconfinementvariablesthataffecttheKapitzaresistance.Theisobtainedbycomputingtheenergyadded/subtractedfromnumberofCNTwallsvariedfrom1to5,andthediameteroftheinnerandouterCNTperunittimeperunitsurfacearea.theCNTvariedfrom1.36to6.78nm.CNTsoffivedifferentFortheEMDsimulations,aftercheckingthesystemstability,chiralitieswithsimilardiameterswerechosen.Also,theflowsimulationswerecarriedoutatanequilibriumtemperatureof2357https://dx.doi.org/10.1021/acs.langmuir.0c03298Langmuir2021,37,2355−2361

3Langmuirpubs.acs.org/LangmuirArticleFigure3.(a)Kapitzaresistance/lengthasafunctionoftheCNTdiameter.ThehorizontaldashedlinescorrespondtotheKapitzaresistance/length12attheinterfaceofwaterconfinedwithinagraphenenanochannelandtheinsetshowsthevariationoftheareadensityfactor,FNA,withthediameteroftheCNT.(b)VDOS(arbitraryunits)andtheoverlap,S,oftheCNTandthewaterslabfordifferentdiameterCNTs.300Kfor5.0nsbythermostattingonlytheCNT,andthedataFurthermore,sincethecorrelationfunctionsarerestrictedtowereextracted.Usingtheproposedmethodasdescribedintheaninterfaceregionoffluidthickness,Δ=3.165Å,wecanbeTheorysection,theKapitzaresistancewascalculatedwithacertainthattheKapitzaresistancethatwecalculateisnota11Maxwellianoneterm(n=1)memoryfunctionandafluidslabpropertyofthebulkfluid,ratheralocalinterfacialproperty.thicknessofΔ=3.165Å(thedistancemeasuredfromtheFigure3ashowstheinfluenceoftheCNTdiameteronthe30CNTtothefirstwaterdensitypeak).Finally,theKapitzaKapitzaresistance/length.ThehorizontaldashedlineslengthLkwascalculatedusingtheequationLk=Rkκ,whereκiscorrespondtotheKapitzaresistance/lengthattheinterface12ofwaterconfinedwithinagraphenenanochannel.Withthethethermalconductivityofwaterat300K.increaseintheCNTdiameter,theKapitzaresistancemonotonicallydecreasesasymptoticallytothegraphene−■RESULTSANDDISCUSSIONwaterinterfacevalue.11Therewasabouta56%reductioninComputationoftheKapitzaresistanceincylindricalgeometryKapitzaresistancewhentheCNTdiametervariedfrom1.36tousingtheNEMDmethodislimitedtoarangeofCNT6.78nm,correspondingtochiralitiesof(10,10)and(50,50),diameters,andthesimulationsystemismorecomplicatedthanrespectively.Alexeevetal.32reportedthattheKapitzatheEMDmethod.Sincetheheattransfertakesplacebetweenresistanceataplanargraphene−waterinterfaceisinverselytheconcentricCNTswithdifferentdiameters,theheatfluxisproportionaltothefirstwaterdensitypeakneartheinterface.notsymmetricatboththeinterfaces.Thus,twoseparateThefirstwaterdensitypeakinaCNTisfoundtobesimulationsarerequiredtoobtainthemeanKapitzaresistancedecreasingwithanincreaseinthediameter(seetheataparticularreferencetemperature.TheradialtemperatureSupportingInformationforthedensityprofile).However,inprofileandtheNEMDsimulationdetailsareprovidedintheaCNT,theKapitzaresistancereduceswithanincreaseintheSupportingInformation.diameterinsteadofincreasing,whichisexactlyoppositetotheAcomparisonoftheKapitzaresistancecalculatedusingbothfindingsofAlexeevetal.32Ifwelookclosely,ahighervalueoftheNEMDandEMDmethodsisshowninFigure2a.ThethefirstdensitypeakindicatesahighernumberofwaterNEMDresultsarethemeanoftheKapitzaresistanceatthemoleculesneartheinterface,andthusmoreheattransfertakesouterwater−CNTinterfacecorrespondingtotemperaturesofplaceattheinterfaceleadingtoalowKapitzaresistance.Thus,250and350K.TheresultsobtainedfromourEMDmethodthenumberofmoleculesperunitsurfaceareaoftheinterfaceareinexcellentagreementwiththeNEMDmethodresults.isthedecidingfactor,andforplanargraphenesurfaces,theAftervalidatingourEMDmethodwiththeresultsofthesurfacearearemainsthesame;therefore,thefirstdensitypeakNEMDmethod,allothersimulationsinthisstudywereisdirectlyproportionaltoit.However,foracylindricalperformedusingourEMDmethod.Thecorrelationfunctionsgeometry,thesurfaceareachangeswiththediameter,soweandthesimulationdetailsofourEMDmethodaregiveninthecannotpurelydependonthefirstdensitypeak.ToquantifySupportingInformation.BarratandChiaruttinidevelopedanthis,weintroducedanewtermcalledtheareadensityfactor,EMDmethodbasedontheGreen−KuboformulatocalculateFNA:theratioofthenumberofmoleculesinaslaboffluidtheKapitzaresistanceatplanargeometry.Wecompareouradjacenttotheinterface(walltothefirstdensitypeak),N,toEMDmethodwiththeirmethodandfindthatourmethodis33theCNT’ssurfacearea,A(FNA=N/πDL).Theinsetoffreefromthewell-knownplateauprobleminGreen−KuboFigure3ashowsthevariationofFNAwiththeCNTdiameter31formalismsforconfinedfluids.Thecomparisonoftheandisfoundtobeincreasingwithanincreaseinthediameter.KapitzaresistanceasafunctionofcorrelationtimewithourThisclearlyjustifiesthereductioninKapitzaresistancewithanEMDmethodandtheGreen−Kubo-likemethodofBarratandincreaseinthediameterasthenumberofwatermolecules13,14ChiaruttiniisshowninFigure2b.BoththemethodsmatchavailableneartheCNTperunitsurfaceareaincreases.Itisalsoatshortcorrelationtime;however,theGreen−Kubo-likeapplicableforplanarsurfacessincethearearemainsconstant;methoddivergeswithanincreaseinthecorrelationtime,hence,FNAonlydependsonthenumberofmoleculesinthewhereasourEMDmethodremainsnearlyindependentoftheslab,whichisproportionaltothefirstdensitypeak,asreported32correlationtime.Ourmethodmakesuseofthetemperature-byAlexeevetal.Inadditiontothat,theKapitzaresistanceisdifferencefluctuationandtheheatfluxattheinterface,thusfoundtobeincreasingwithanincreaseinthehydrophobicityusingmoreofthedataavailableinthesimulation.intheplanarinterfaceduetothedecreaseintheareadensity2358https://dx.doi.org/10.1021/acs.langmuir.0c03298Langmuir2021,37,2355−2361

4Langmuirpubs.acs.org/LangmuirArticleFigure4.(a)Kapitzaresistance/lengthasafunctionofCNTchiralityforsimilardiameters.(b)Kapitzaresistance/lengthasafunctionofthenumberofCNTwalls.32,34factorortheheightofthefirstdensitypeak.Forthecaseofonboth.However,theimpactofchiralityonthesliplengthcylindricalgeometry,ifweconsideraCNTwithaparticularandKapitzalengthisnotidentical.Thechangeinthepotentialdiameter,FNAwilldecreasewithanincreaseinthehydro-energylandscapeduetothechiralityisobservedonlyinthephobicity.Sincethediameterisconstant,FNAandtheheightofaxialflowdirection,whereastheheattransferhappensinthethefirstdensitypeakareproportionaltoeachother.radialdirection.Thus,theKapitzaresistanceandheattransferWehavealsoassessedthevibrationaldensityofstatesbetweenCNTandwaterareessentiallyindependentofthe(VDOS)oftheCNTandawaterslabadjacenttothewall.TheCNT’schirality.Figure4bshowsthechangeinKapitzaVDOSoverlap,S,ofthewaterandtheCNTwascalculatedresistanceasafunctionofthenumberofCNTwalls.Theinset35usingtheequationshowstheschematicdiagramofamultiwalledCNTwithfivelayers.ItisfoundthatthenumberofCNTwallsdoesnothave∞∫Pf()CNTPf()waterdfasignificantimpactontheKapitzaresistance.Onlyaslight0S=∞∞increaseinthevaluewasobservedwiththeadditionofthe∫∫Pf()CNTd.fPf()waterdf(17)numberofwalls.Liangetal.37pointedoutthatthe00transmissioncoefficientintheacousticmismatchmodeliswhereP(f)CNTandP(f)wateraretheVDOSoftheCNTanddecreasedwhenthethicknessofthesolidisshorterthanthewaterslab,respectively.ThecalculationoftheVDOSisphononmeanfreepathowingtothespecularreflectionatthedescribedintheSupportingInformation.Figure3bshowsthesurface.Also,thephononmeanfreepathofgrapheneintheVDOS(arbitraryunits)oftheCNTandthewaterslabforcross-planedirectionismuchhigherthanthehighestthicknessdifferentdiameterCNTsandtheiroverlap,S.Thevibrational38usedinthisstudy.Thus,theslightincreaseintheKapitzaspectrumoverlapincreaseswithanincreaseinthediameter.ItresistancewiththenumberofCNTwallscanbeassociatedshowsthatabettervibrationalcouplingbetweenwaterandwiththehighphononmeanfreepathofgraphenecomparedtoCNTathigherdiameters,whichincreasestheinterfaceheatthepresentmodel’swallthickness.Asimilarresultwas9transfer,leadstoareducedKapitzaresistance.Jabbarietal.observedforthegraphene−watersysteminwhichtheKapitzareportedanincreaseintheKapitzaresistancewithanincreaseresistanceisnearlyindependentofthenumberofgrapheneintheCNTdiameterinawater−CNTnanofluidsystem,11layers.wherethewaterisoutsidetheCNT.ThiscanalsobeexplainedFigure5showstheeffectofwaterflowthroughanarmchairintermsoftheareadensityfactor.Ifthewaterisoutsidethe(10,10)CNTontheKapitzaresistance/length.TheinsetCNT,FNAwillbehigherforsmallerdiameters(thetrendwillshowstheaveragevelocitiesasafunctionofappliedexternalbereversedifthewaterisinsidetheCNT),leadingtoabetteraccelerations.Theaccelerationvariedfrom0to5×1011m/s2,heattransferandreducedKapitzaresistance.Thus,byandtheobtainedaveragevelocitiesareinthelinearresponsecombiningthesefindings,wecaninferthattheKapitzaregime.ItisfoundthattheflowofwaterdoesnotinfluencetheresistanceisafunctionoftheCNTdiametersothatitKapitzaresistance.ThewaterdensitypeakandtheareadensitydecreaseswithanincreaseinthediameterifthewaterisinsidetheCNTandviceversaifthewaterisoutsidetheCNT.TheeffectoftheCNTchiralityontheKapitzaresistanceisshowninFigure4a.Fivedifferentchiralitiesof(10,10),(8,12),(7,13),(4,15),and(0,17)withsimilardiameters(<5%differencewithameandiameterof1.36nm)wereusedinthisanalysis.ThereisnonoticeablechangeinKapitzaresistancewiththechiralityofCNTs.Incontrast,Samet36al.reportedavariationinthefrictioncoefficientandsliplengthwithrespecttochangeinchirality.Theyobservedthehighestsliplengthforarmchair(10,10)CNTandlowestinthezigzag(0,17)CNT.ThisvariationintheflowrateisattributedtothedifferenceinpotentialenergylandscapeexperiencedbythewatermoleculesduetochangeintheCNTstructure,leadingtoachangeinthefrictioncoefficient.AnanalogyFigure5.Kapitzaresistance/lengthasafunctionofdifferentexternalbetweentheKapitzalengthandsliplengthcanbevisibledueforcefields.TheinsetshowstheaveragevelocityofwateralongthetothesimilarityintheeffectofdifferentinfluencingparametersaxialdirectionoftheCNTasafunctionofexternalforcefield.2359https://dx.doi.org/10.1021/acs.langmuir.0c03298Langmuir2021,37,2355−2361

5Langmuirpubs.acs.org/LangmuirArticlefactor,FNA(bothareproportionalsincethediameteristhe■ASSOCIATEDCONTENTsame),remainunchangedevenafterapplyingtheexternal*sıSupportingInformation39acceleration.Also,thereisnonoticeablechangeintheTheSupportingInformationisavailablefreeofchargeataveragewatertemperatureduetoviscousheatingwithinthishttps://pubs.acs.org/doi/10.1021/acs.langmuir.0c03298.rangeofappliedaccelerations(seetheSupportingInforma-tion).Thus,theKapitzaresistancealsoremainsunchangedModelingdetailsandthemethodology,thesimulationwithinthelinearresponseflowregime.EventhoughwenotedetailsandradialtemperatureprofilesoftheNEMDthatourmethodisstrictlytrueonlyatequilibrium,itappearsmethod,thecorrelationfunctionsandthesimulationtoworkquitewellinthelinearresponseflowregime.ThedetailsofourEMDmethod,thedensityprofilesofwatersystemisinanonequilibriumstateduetotheflow;however,insidetheCNTfordifferentdiameters,thecalculationwefoundthatthegoverningparametersofheatfluxandofVDOS,thenormalizedinstantaneousheatfluxandtemperaturedifferencefluctuateaboutzeroevenunderthethenormalizedinstantaneoustemperaturedifferenceforappliedexternalaccelerations(seetheSupportingInforma-differentaccelerations,thevariationofareadensitytion).Thus,aslongasthegoverningparametersarenotfarfactor,FNA,andtheaveragetemperatureofwaterforfromequilibrium,ourmethodcanbeusedinflowconditionsdifferentaccelerations(PDF)aswell.Thestatisticsoftheresultsobtainedforsystemswithflowconditionsusingthepresentmethodisshowntobehighly■AUTHORINFORMATIONreliable.However,wenotethattheNEMDmethodcannotbeCorrespondingAuthorusedtocalculatetheKapitzaresistanceforconfinedfluidsB.D.Todd−DepartmentofMathematics,SchoolofScience,underflowconditions,eveninplanarsystems.ThisisbecauseSwinburneUniversityofTechnology,Melbourne,VictoriatheNEMDmethodrequiresasteady-statelineartemperature3122,Australia;orcid.org/0000-0003-4683-5719;profileacrosstheinterface,whichisimpossibletoattainwhenEmail:btodd@swin.edu.authereisflowinthesystem.Authors■CONCLUSIONSSobinAlosious−DepartmentofAppliedMechanics,IndianInstituteofTechnologyMadras,Chennai600036,India;Insummary,wehaveinvestigatedthenanoconfinementeffectsDepartmentofMathematics,SchoolofScience,SwinburneonKapitzaresistanceataCNT−waterinterfaceusingEMDUniversityofTechnology,Melbourne,Victoria3122,andNEMDmethods.WeproposedanewEMDmethodtoAustralia;orcid.org/0000-0003-3579-4747computetheKapitzaresistanceincylindricalnanoconfinementSridharKumarKannam−DepartmentofMathematics,systems.WefindthattheNEMDmethodisnotsuitableforSchoolofScience,SwinburneUniversityofTechnology,cylindricalconfinementsystemsunderflowconditions(eveninMelbourne,Victoria3122,Australiaplanargeometry).WealsofindthatduetotheplateauproblemSarithP.Sathian−DepartmentofAppliedMechanics,IndianthatexistsintheGreen−Kubo-basedEMDmethods,theInstituteofTechnologyMadras,Chennai600036,India;Kapitzaresistancecalculatedishighlyuncertainandnotorcid.org/0000-0003-2756-7210reliableathighercorrelationtimes.Incontrast,ournewEMDmethodisindependentofthecorrelationtime,whichCompletecontactinformationisavailableat:eliminatestheneedforselectinganyparticularandarbitraryhttps://pubs.acs.org/10.1021/acs.langmuir.0c03298correlationtime.Aftervalidatingourmethod,westudieddifferentfactorsinfluencingtheKapitzaresistanceinaCNT−Noteswatersystemsuchasdiameter,chirality,numberofwalls,andTheauthorsdeclarenocompetingfinancialinterest.flow.TheCNTdiameterisasignificantdeterminingfactoroftheKapitzaresistance.Itisfoundthatwithanincreaseinthe■ACKNOWLEDGMENTSdiameter,theKapitzaresistancedecreasesandreachesTheauthorsacknowledgetheSwinburnesupercomputingasymptoticallynearthevalueoftheplanargraphene−waterOzSTARfacilityforprovidingcomputationalresourcesforthisinterface.Nearlya56%reductionisobtainedwhenthework.diameterincreasedfrom1.36to6.78nm.EventhoughthefirstdensitypeakofwaterishigherinthehighestdiameterCNT,■REFERENCESthenumberofmoleculespersurfaceareaislowestduetothe(1)Das,S.K.;Choi,S.U.;Yu,W.;Pradeep,T.Nanofluids:Sciencecylindricalgeometry,whichleadstolessheattransferandhighandTechnology;JohnWiley&Sons,2007.Kapitzaresistance.Also,theVDOSoverlapoftheCNTand(2)Chen,X.;Cao,G.;Han,A.;Punyamurtula,V.K.;Liu,L.;thewaterslabadjacenttotheinterfaceincreaseswithanCulligan,P.J.;Kim,T.;Qiao,Y.Nanoscalefluidtransport:sizeandincreaseintheCNTdiameter.Theareadensityfactorandtherateeffects.NanoLett.2008,8,2988−2992.VDOSoverlapexplainsthereasonforthereductionofthe(3)Thomas,J.A.;McGaughey,A.J.ReassessingfastwatertransportKapitzaresistancewithanincreaseintheCNTdiameter.Thethroughcarbonnanotubes.NanoLett.2008,8,2788−2793.Kapitzaresistancehasonlyaslightinfluenceonthenumberof(4)Majumder,M.;Chopra,N.;Hinds,B.J.MasstransportthroughwallsandisnearlyindependentoftheCNT’schirality.Wealsocarbonnanotubemembranesinthreedifferentregimes:ionicdiffusionandgasandliquidflow.ACSNano2011,5,3867−3877.findthattheflowofwaterinsidetheCNTdoesnothavea(5)Kannam,S.K.;Todd,B.;Hansen,J.S.;Daivis,P.J.HowfastsignificanteffectontheheattransferbetweentheCNTanddoeswaterflowincarbonnanotubes?J.Chem.Phys.2013,138,waterinthelinearflowregime.UnliketheNEMDmethod,ourNo.094701.EMDmethodissuitablefordeterminingtheKapitzaresistance(6)Li,Q.;Liu,C.;Fan,S.Thermalboundaryresistancesofcarboninsystemswithflowconditionswithinthelinearresponsenanotubesincontactwithmetalsandpolymers.NanoLett.2009,9,regime.3805−3809.2360https://dx.doi.org/10.1021/acs.langmuir.0c03298Langmuir2021,37,2355−2361

6Langmuirpubs.acs.org/LangmuirArticle(7)Gulotty,R.;Castellino,M.;Jagdale,P.;Tagliaferro,A.;Balandin,(31)Español,P.;delaTorre,J.;Duque-Zumajo,D.SolutiontotheA.A.Effectsoffunctionalizationonthermalpropertiesofsingle-wallplateauproblemintheGreen-Kuboformula.Phys.Rev.E2019,99,andmulti-wallcarbonnanotube-polymernanocomposites.ACSNanoNo.022126.2013,7,5114−5121.(32)Alexeev,D.;Chen,J.;Walther,J.H.;Giapis,K.P.;(8)Bui,K.;Duong4,H.M.;Striolo,A.;Papavassiliou,D.V.EffectiveAngelikopoulos,P.;Koumoutsakos,P.Kapitzaresistancebetweenheattransferpropertiesofgraphenesheetnanocompositesandfew-layergrapheneandwater:liquidlayeringeffects.NanoLett.2015,comparisontocarbonnanotubenanocomposites.J.Phys.Chem.C15,5744−5749.2011,115,3872−3880.(33)Wang,G.J.;Hadjiconstantinou,N.G.Molecularmechanics(9)Jabbari,F.;Rajabpour,A.;Saedodin,S.;Wongwises,S.Effectofandstructureofthefluid-solidinterfaceinsimplefluids.Phys.Rev.water/carboninteractionstrengthoninterfacialthermalresistanceFluids2017,2,No.094201.andthesurroundingmolecularnanolayerofCNTandgrapheneflake.(34)Ge,Z.;Cahill,D.G.;Braun,P.V.ThermalconductanceofJ.Mol.Liq.2019,282,197−204.hydrophilicandhydrophobicinterfaces.Phys.Rev.Lett.2006,96,(10)Unnikrishnan,V.;Banerjee,D.;Reddy,J.Atomistic-mesoscaleNo.186101.interfacialresistancebasedthermalanalysisofcarbonnanotube(35)Chen,J.;Zhang,G.;Li,B.Tunablethermalconductivityofsystems.Int.J.Therm.Sci.2008,47,1602−1609.Si1‑xGexnanowires.Appl.Phys.Lett.2009,95,No.073117.(11)Alosious,S.;Kannam,S.K.;Sathian,S.P.;Todd,B.Prediction(36)Sam,A.;Prasad,V.;Sathian,S.P.WaterflowincarbonofKapitzaresistanceatfluid-solidinterfaces.J.Chem.Phys.2019,151,nanotubes:theroleoftubechirality.Phys.Chem.Chem.Phys.2019,No.194502.21,6566−6573.(12)Alosious,S.;Kannam,S.K.;Sathian,S.P.;Todd,B.Kapitza(37)Liang,Z.;Sasikumar,K.;Keblinski,P.Thermaltransportacrossresistanceatwater-grapheneinterfaces.J.Chem.Phys.2020,152,asubstrate-thin-filminterface:effectsoffilmthicknessandsurfaceNo.224703.roughness.Phys.Rev.Lett.2014,113,No.065901.(13)Puech,L.;Bonfait,G.;Castaing,B.Mobilityofthe3HeSolid-(38)Wei,Z.;Ni,Z.;Bi,K.;Chen,M.;Chen,Y.InterfacialthermalLiquidInterface:ExperimentandTheory.J.LowTemp.Phys.1986,resistanceinmultilayergraphenestructures.Phys.Lett.A2011,375,62,315.1195−1199.(14)Barrat,J.-L.;Chiaruttini,F.Kapitzaresistanceattheliquid-solid(39)Hanasaki,I.;Nakatani,A.Flowstructureofwaterincarboninterface.Mol.Phys.2003,101,1605−1610.nanotubes:Poiseuilletypeorplug-like.J.Chem.Phys.2006,124,(15)Hansen,J.S.;Todd,B.;Daivis,P.J.PredictionoffluidvelocityNo.144708.slipatsolidsurfaces.Phys.Rev.E2011,84,No.016313.(16)Evans,D.J.;Morriss,G.StatisticalMechanicsofNonequilibriumLiquids;CambridgeUniversityPress,2008.(17)Todd,B.D.;Daivis,P.J.NonequilibriumMolecularDynamics:Theory,AlgorithmsandApplications;CambridgeUniversityPress,2017.(18)Todd,B.D.;Daivis,P.J.;Evans,D.J.Heatfluxvectorinhighlyinhomogeneousnonequilibriumfluids.Phys.Rev.E1995,51,No.4362.(19)Berendsen,H.;Grigera,J.;Straatsma,T.Themissingtermineffectivepairpotentials.J.Phys.Chem.1987,91,6269−6271.(20)Wu,Y.;Tepper,H.L.;Voth,G.A.Flexiblesimplepoint-chargewatermodelwithimprovedliquid-stateproperties.J.Chem.Phys.A2006,124,No.024503.(21)Ryckaert,J.-P.;Ciccotti,G.;Berendsen,H.J.Numericalintegrationofthecartesianequationsofmotionofasystemwithconstraints:moleculardynamicsofn-alkanes.J.Comput.Phys.1977,23,327−341.(22)Hockney,R.W.;Eastwood,J.W.ComputerSimulationUsingParticles;CRCPress,1988.(23)Ostler,D.;Kannam,S.K.;Daivis,P.J.;Frascoli,F.;Todd,B.Electropumpingofwaterinfunctionalizedcarbonnanotubesusingrotatingelectricfields.J.Phys.Chem.C2017,121,28158−28165.(24)Stuart,S.J.;Tutein,A.B.;Harrison,J.A.Areactivepotentialforhydrocarbonswithintermolecularinteractions.J.Chem.Phys.2000,112,6472−6486.(25)Girifalco,L.;Hodak,M.;Lee,R.S.Carbonnanotubes,buckyballs,ropes,andauniversalgraphiticpotential.Phys.Rev.B2000,62,No.13104.(26)Werder,T.;Walther,J.H.;Jaffe,R.;Halicioglu,T.;Koumoutsakos,P.Onthewater-carboninteractionforuseinmoleculardynamicssimulationsofgraphiteandcarbonnanotubes.J.Phys.Chem.B2003,107,1345−1352.(27)Plimpton,S.Fastparallelalgorithmsforshort-rangemoleculardynamics.J.Comput.Phys.1995,117,1−19.(28)Humphrey,W.;Dalke,A.;Schulten,K.VMDVisualMolecularDynamics.J.Mol.Graphics1996,14,33−38.(29)Grest,G.S.;Kremer,K.Moleculardynamicssimulationforpolymersinthepresenceofaheatbath.Phys.Rev.A1986,33,No.3628.(30)Wang,G.J.;Hadjiconstantinou,N.G.Whyarefluiddensitiessolowincarbonnanotubes.Phys.Fluids2015,27,No.052006.2361https://dx.doi.org/10.1021/acs.langmuir.0c03298Langmuir2021,37,2355−2361