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Molecular Modeling of Surfactant-Covered Oil-Water Interfaces

Permanent Link: http://ufdc.ufl.edu/UFE0022610/00001

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Title: Molecular Modeling of Surfactant-Covered Oil-Water Interfaces
Physical Description: 1 online resource (96 p.)
Language: english
Creator: Gupta, Ashish
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

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Subjects / Keywords: Chemical Engineering -- Dissertations, Academic -- UF
Genre: Chemical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

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Abstract: Microemulsions are nanosized drops of oil floating in water stabilized by surfactants(surface active molecules) at the interface. These nanoparticles find numerous applications in drug delivery, drug detoxification, separations, oil-recovery and nano-particle synthesis. A computationally efficient coarse-grained model is used to model the surfactant-covered oil-water interface in these nanoparticles. The structure and dynamics of the interface is investigated to determine the mechanism of mass transport across the interface. The role of surfactants in creating a barrier to mass transport has been investigated. We demonstrate that the interface investigated at molecular level shows interesting phenomena which are difficult to capture from experiments. Some of the findings of this study are also applicable to mass transport across wide class of interfacial systems like oil-water interface and lipid bilayers.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Ashish Gupta.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Kopelevich, Dmitry I.
Local: Co-adviser: Chauhan, Anuj.

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Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022610:00001

Permanent Link: http://ufdc.ufl.edu/UFE0022610/00001

Material Information

Title: Molecular Modeling of Surfactant-Covered Oil-Water Interfaces
Physical Description: 1 online resource (96 p.)
Language: english
Creator: Gupta, Ashish
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: Chemical Engineering -- Dissertations, Academic -- UF
Genre: Chemical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Microemulsions are nanosized drops of oil floating in water stabilized by surfactants(surface active molecules) at the interface. These nanoparticles find numerous applications in drug delivery, drug detoxification, separations, oil-recovery and nano-particle synthesis. A computationally efficient coarse-grained model is used to model the surfactant-covered oil-water interface in these nanoparticles. The structure and dynamics of the interface is investigated to determine the mechanism of mass transport across the interface. The role of surfactants in creating a barrier to mass transport has been investigated. We demonstrate that the interface investigated at molecular level shows interesting phenomena which are difficult to capture from experiments. Some of the findings of this study are also applicable to mass transport across wide class of interfacial systems like oil-water interface and lipid bilayers.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Ashish Gupta.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Kopelevich, Dmitry I.
Local: Co-adviser: Chauhan, Anuj.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022610:00001


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mysisterandfriend,Anjulika;andmylovingwife,Saloni. 3

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Myrstandforemostthankgotomysupervisorycommitteechair,Dr.DmitryKopelevich.Iwasfortunatetobeoneoftherststudentstojoinhisresearchgroup.Withouthisconstantguidance,thisdissertationwouldnothavebeenpossible.Hispatienceandencouragementcarriedmethroughdiculttimes,andhisinsightsandsuggestionsthathelpedtoshapemyresearchskills.Hisvaluablefeedbackcontributedgreatlytothisdissertation.Iamgratefultomycochair,Dr.AnujChauhan,whoadvisedmeonvariousaspectsofmyresearch.Fromtheverybeginningofmygraduatestudies,hisfriendlyadviceonvariousmattersmadealotofdierencetome.ItakethisopportunitytothankDr.TonyLaddandDr.SusanSinnottfortheirvaluablesuggestionsregardingmyresearch.SpecialthanksgotoDr.Laddforhisexpertise,hardworkandinspiringenthusiasminmanagingthechemicalengineeringclusteronwhichmostofmycalculationsweredone.Ialsothankmyresearchgroupandfellowgraduatestudentsfortheirsupportandcamaraderie.IowemuchtomyfriendswhohavealwaysbeentherewhenIneededhelpandfriendship.IacknowledgethefacultyandstaintheDepartmentofChemicalEngineeringforcontinuouslysupportingmyeortsinmanyaspectsofmygraduateschoolcareer.ThisresearchwassupportedbyNationalScienceFoundation(AwardNo.CTS-0500090).ComputationalresourceswereinpartprovidedbytheUniversityofFloridaHigh-PerformanceComputingCenter. 4

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page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 7 LISTOFFIGURES .................................... 8 ABSTRACT ........................................ 11 CHAPTER 1INTRODUCTION .................................. 13 1.1Background ................................... 13 1.1.1Interfaces ................................. 13 1.1.2MolecularDynamics ........................... 14 1.1.3Overview ................................. 17 2DYNAMICSANDMICROSTRUCTUREOFSURFACTANTMONOLAYERSATOIL-WATERINTERFACE ........................... 19 2.1Introduction ................................... 19 2.2ModelandSimulationDetails ......................... 20 2.3InterfacialCoverageandInterfacialTension ................. 23 2.4Time-ScalesofSurfactantDegreesofFreedom ................ 27 2.5MicrostructureofSurfactantMonolayer .................... 31 2.5.1PoresinMonolayer ........................... 32 2.5.2ApplicationofthePercolationTheorytotheMonolayerMicrostructure 38 2.5.3PoreDynamics ............................. 45 2.6Conclusions ................................... 55 3ENERGYBARRIERSFORMASSTRANSPORTACROSSSURFACTANTMONOLAYERS ................................... 57 3.1Introduction ................................... 57 3.2ModelandSimulationDetails ......................... 57 3.3BarriertoSoluteTransportAcrossInterfaces ................. 59 3.3.1EectofSurfactantLength ....................... 59 3.3.2EectofNatureofParticle ....................... 66 3.3.3SynergisticEectofSoluteSizeandSurfactantLength ....... 69 3.4Discussion .................................... 70 4EFFECTOFHYDRODYNAMICANDELASTICFLUCTUATIONSONMOLECULARTRANSPORTACROSSFLUIDINTERFACESANDFLEXIBLEMEMBRANES 74 4.1Introduction ................................... 74 4.2ModelandSimulationDetails ......................... 76 5

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....... 79 4.4ModelforCoupledSolute-InterfaceDynamics. ................ 82 4.5Discussion .................................... 86 5CONCLUSIONS ................................... 88 REFERENCES ....................................... 90 BIOGRAPHICALSKETCH ................................ 96 6

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Table page 2-1Time-scalesofthesurfactantcenterofmassandorientation. ........... 30 3-1ComparisonofthefreeenergybarrierheightGwithparameterscharacterizingtheexcessdensity. .................................. 73 7

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Figure page 2-1Hexadecane-water-H3T3systemcontainingtwooil-waterinterfacescoveredbyself-assembledsurfactantmonolayers. ........................ 23 2-2Dependenceoftheinterfacialtensionatthehexadecane-water-H3T3interfacesontheinterfacialcoverage. ............................ 25 2-3Dependenceoftheinterfacialtensionatthehexadecane-water-HnTninterfacesonthesurfactantlength2natconstantinterfacialcoverage=1:51molecules/nm2;n=0correspondstothesurfactant-freehexadecane-waterinterface. ....... 26 2-4AutocorrelationfunctionsC?,Ctilt,Crot,andCT4ofuctuationsofmolecularmotion. ........................................ 29 2-5AveragedistancesofsurfactantbeadsfrommoleculardirectorsuforH3T3,H5T5,andH7T7surfactants. ................................ 31 2-6DecaytimesoftheautocorrelationfunctionsCj(t)ofindividualbeadswithinH3T3,H5T5,andH7T7surfactantmolecules. ................... 32 2-7PoresinH3T3monolayerobtainedwithproberadius(a)Rp=0:47nmand(b)Rp=0:6nm. ..................................... 33 2-8Examplesofcross-sectionsofporestructuresin(a)H3T3and(b)H7T7monolayers. 35 2-9DependenceofthemeanvolumeVofporesinH3T3andH7T7monolayersontheproberadiusRp. ................................. 36 2-10DependenceofthedensitypofporesinH3T3andH7T7monolayersontheproberadiusRp. ....................................... 37 2-11AverageprobabilitiespofpointsinsideH3T3andH7T7monolayerstobelongtoapore. ......................................... 42 2-12ConnectivityfunctionsCf(r;Rp)inH7T7monolayerfordierentproberadiiRp. 44 2-13Propertiesofinstantaneouspores:(a)correlationlength,(b)poredensityp,and(c)meanVand(d)standarddeviationV;fofvolumesofnitepores. ... 45 2-14EvolutionofvolumesofallporeswithinH3T3monolayer. ............. 47 2-15DetailsoftheporecoalescenceshowninFig. 2-14 b. ................ 48 2-16Dependenceofthedensityp(Rp;tav)ofaveragedporesinH3T3(solidsymbols)andH7T7(opensymbols)monolayersontheaveragingtimetavandtheproberadiusRpfordierentporetypes. .......................... 49 8

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................................. 52 2-18Frequencies!j(Rp;tav)(j=c,d,fus,ors)oftransitioneventsforporesinH3T3monolayerobtainedwithproberadiusRp=0:47nm. ............... 53 2-19Frequencies!j(Rp;tav)(j=c,d,fus,ors)oftransitioneventsinH3T3(solidsymbols)andH7T7(opensymbols)monolayerscorrespondingtothecross-overaveragingtimetav. .................................. 54 3-1Summaryofsurfactant-solutesystemsconsideredinthiswork. .......... 59 3-2Densityprolesofsurfactant-freeandsurfactant-coveredhexadecane-waterinterfaces. 60 3-3Averageshcosjiandstandarddeviations(cosj)oftheorientationscosjofthesurfactantbondswithrespecttothemonolayernormal. ........... 62 3-4ComparisonofdensityprolesofH3T3,H5T5,andH7T7monolayers. ...... 62 3-5Freeenergyprolesfortransportofsphericalhydrophobicsoluteacrossthesurfactant-freehexadecane-waterinterfaceandthehexadecane-waterinterfacescoveredbyH3T3,H5T5,H7T7,H3T7andH7T3surfactantmonolayers. ................ 64 3-6Freeenergyprolesfortransportofsphericalhydrophobicsolute(T),sphericalhydrophilicsolute(H),hydrophobicdimer(T2),hydrophilicdimer(H2)andamphiphilicdimer(HT)acrosshexadecane-waterinterfacescoveredbyH7T7surfactantmonolayers. ............................................. 68 3-7Distributionoforientationangleof(a)amphiphilicdimer(b)hydrophobicdimer(c)hydrophilicdimeratvedierentpositionsnearthedividingsurfaceofH7T7monolayer ....................................... 69 3-8FreeenergyprolesforTinH7T7monolayer,T0inH3T3andH7T7monolayersshowingsynergisticeect. .............................. 70 3-9FreeenergyprolesforTinH7T7andT5inH3T3andH7T7monolayersshowingsynergisticeect. ................................... 71 4-1Magnitudeofuctuationsofmodes^hkoftheoil-waterinterface. ........ 78 4-2AutocorrelationfunctionsC(t;z)oftherandomforce(t;z)actingonthesolutenearthesurfactant-freeoil-waterinterface. ..................... 80 4-3Correlationtimef(z)oftheslowestuctuationsoftherandomforce(z;t)actingonthesoluteconstrainedatdistancezawayfromthedividingsurfaces. 81 4-4Equilibriumdividingsurfacesheq(r;rs)correspondingtosoluteconstrainedatdierentpositionsrs. ................................. 83 9

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............................... 85 10

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Masstransportacrossoil-waterinterfaceandsurfactant-coveredoil-waterinterfacesplaysanimportantroleinnumerousapplications.Inthecurrentwork,weusecoarse-grainedmoleculardynamicssimulationstoinvestigatemodelsurfactant-freeoil-waterinterfaceandoil-waterinterfacescoveredbymonolayersofnon-ionicsurfactantsofvariouslength.Severalpropertiesofthesurfactantmonolayersrelevanttothemasstransportareconsidered,includingthemonolayermicrostructure,dynamicsandafreeenergybarriertothesolutetransport.Itisobservedthatthedominantcontributionofasurfactantmonolayertothefreeenergybarrierisastericrepulsioncausedbyalocaldensityincreaseinsidethemonolayer.Thelocaldensities,andhencethefreeenergybarriers,arelargerformonolayerscomposedoflongersurfactants.Sinceitislikelythatthesolutetransportmechanisminvolvesasequenceofjumpsbetweenshort-livedporeswithinamonolayer,weperformadetailedanalysisofstructure,size,andlife-timeofthesepores.Wedemonstratethattheporestatisticsisconsistentwithpredictionsofthepercolationtheoryandapplythistheorytoidentifycharacteristiclength-scaleofthemonolayermicrostructure.Theobtainedporestructuresaresensitivetominutechangesofsurfactantcongurationsoccurringonthepicosecondtime-scale.Toreducethissensitivity,theporesareaveragedovershorttimeintervals.Theoptimaldurationofthesetimeintervalsisestimatedfromanalysisofdynamicsofporeswithdiameterscomparabletoorexceedingthecharacteristicpercolationlength-scale.Thedevelopedapproachallowsonetolterouttransient 11

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Toobtainthesolutetransportrate,wedevelopaLangevinequationforthesolutetransport.Itisfrequentlyassumedthattheuctuationsofthethermalrandomforceareadequatelydescribedbythewhitenoise,i.e.thatthecorrelationtimeoftherandomforceismuchsmallerthanthecharacteristictimeofthesolutetransport.Wedemonstratethatalthoughthisassumptioniscorrectwhenthesoluteislocatedsucientlyfarfromtheinterface,thecorrelationtimeoftherandomforcebecomessignicantwithinaverynarrow(lessthan1nmwide)regionoftheinterface.Wedemonstratethattheslowuctuationsoftherandomforceinthisnarrowregionarecausedbyuctuationsoftheinterface.Unliketherandomcollisionsofthesolutewiththesolventmoleculesinhomogeneousuids,theinterfaceuctuationschangethecompositionofthesolvationshellofthesolute.Weproposeamulti-dimensionalLangevinequationwhichexplicitlyaccountsforthesoluteinterfacecouplingandvalidateitforsurfactant-freeandsurfactant-coveredinterfaces.Thestrengthofthesolute-interfacecouplingisdeterminedbythemagnitudeoftheprotrusionsoftheinterfaceformedwhensoluteisconstrainedinthevicinityoftheinterface.Similarphenomenaisexpectedtooccurinotherinterfacialsystemssuchaslipidbilayers. 12

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1.1.1Interfaces 2 ]usedtoretrievecomponentsfrommixtures. Anotherclassofinterfacialsystemsconsideredinthisworkisasurfactant-coveredoil-waterinterfacepresentinmicroemulsions.Microemulsionsarethermodynamicallystableisotropicdispersionsmadeoftwoimmisicibleliquidsconsistingofnanosizeddomainsofoneliquidinanother,stabilizedduetosignicantloweringofinterfacialtensionbyadsorptionofamphiphilesontheliquid-liquidinterface.Thedispersedphaseconsistsofmonodisperseddropletsinthesizerangeof100-1000A.Microemulsionsarefundamentallydierentfromemulsionsincetheformerarethermodynamicallystableonephasesystemswhilethelatterarekineticallystabilizeddispersions.Theexcellentlongtermstabilityofmicroemulsionmakesitamuchmoreattractivecandidateforsuchapplicationsasseparations,controlleddrugreleaseanddrugdetoxication.Inalltheseapplications,masstransportacrosssurfactant-coveredinterfaceplaysakeyrole. Ourfocuswasonoil-waterinterfacecoveredwithnon-ionicsurfactants.Interestinnonionicsurfactantsformicroemulsionformulationsfordrugdeliveryisincreasingbecauseoflowirritationcausedbythemandtheirhighchemicalstability.Theuseofnonionicsurfactant,suchasn-alkylpolyoxyethyleneether(CmEn)tostabilizeamicroemulsionisparticularlyattractivebecauseitisgenerallypossibletocreateamicroemulsion 13

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3 ]. InordertoincreasetheeciencyofMDsimulations,weuseacoarse-grained(CG)modelinthiswork.IntheCGmodel,agroupofatomsarerepresentedbyasingleparticle.Thisleadstoreductioninthenumberofdegreesoffreedomofthesystemwhichenablestheuseofshortrangepotentialsandlargertimestep.ThesefactorsmaketheCGmodelcomputationallyfourtoveordersofmagnitudemoreecientthanatomisticsimulations.AlthoughnechemicaldetailsareinaccessibleinanyCGapproach,themodelusedcapturestheimportantpropertiesofthesystem. WeuseamodicationofaCGmodelproposedbyMarrinketal[ 4 ]Withinthismodel,interactionsbetweenparticlesiandjnotconnectedbychemicalbondaredescribedbytheLennard-Jonespotential withijrepresentingtheeectiveminimumdistanceofapproachbetweenthetwoparticlesandijisthestrengthoftheirinteraction.Interactionsbetweenchemicallyconnectedparticlesaredescribedbyaweakharmonicpotentialforthebondlength 2Kbond(RRbond)2;(1{2) 14

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2Kangle[cos()cos(0)]2:(1{3) InEq. 1{2 and 1{3 ,Rbondand0aretheequlibriumbondlengthandangleandKbondandKanglearespringconstants.Thevaluesoftheparametersforindividualmoleculeswillbegiveninchapters2and3. Todeterminetheparticlepositionsandvelocities,Newtonsequation'sofmotionaresolved whereireferstotheparticlenumber,risthepositionvector,misthemassoftheparticleandFi=@V=@ri,istheforceactingontheparticleandVisthepotentialenergyofthesystem.EvolutionofthesystemisobtainedbysimulataneousofEq. 1{4 forallparticles.TheseequationsaresolvedusingVerletalgorithm[ 5 ],v(t+4t Eq. 1{5 updatesthevelocityattimet+4t 1{6 ,usingthevelocityattimet+4t ThesimulationsareperformedinNPTensemblei.e.thetemperatureandpressurearemaintainedatconstantvalues.TemperatureofanN-particlesystemisgivenbyitstotalkineticenergy, 2Ni=1miv2i:(1{7) FromthistheabsolutetemperatureTcanbecomputedusing: 1 2NdfkBT=Ekin(1{8) 15

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whereVisthevolumeofthecomputationalbox. Inthesimulations,thetemperatureismaintainedconstantbyusingtheBerendsenalgorithmwhichmimicsweakrst-orderkineticcouplingtoanexternalheatbathwithgiventemperatureT0.TheeectofthisalgorithmisthatadeviationofthesystemtemperaturefromT0isslowlycorrectedaccordingto dt=T0T ;(1{10) i.e.thetemperaturedeviationdecaysexponentiallywithatimeconstant.Theheatowintooroutofthesystemisaectedbyscalingthevelocitiesofeachparticleateverystepwithatime-dependentfactor.Thestrengthofthecouplingcanbevariedbyadjustingthetimeconstant. Similarly,thepressureismaintainedconstantbycouplingthesystemtoa\pressurebath"usingBerendsenalgorithmthatscalescoordinatesandboxvectorseverystepwithamatrix.TheBerendsenalgorithmrescalesthecoordinatesandboxvectorswhichhastheeectofarst-orderkineticrelaxationofthepressuretowardsagivenreferencepressureP0, dt=P0P p:(1{11) Thescalingmatrixisgivenby whereistheisothermalcompressibilityofthesystem,P0iandPiarethecomponentsofthereferencepressureandthesystempressureintheithdirection. 16

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4 ]ismodiedtomimicoil-water-surfactantsystems.Thestructureanddynamicsofthesurfactantmonolayerattheoil-waterinterfaceareanalyzedindetail.Thedynamicsofindividualsurfactantmoleculesatwithinthemonolayerisanalyzedindetailbysplittingtheirmotionintotranslational,tilt,rotationandbonductuationcomponents.Dynamicsoffastdegreesoffreedomofsurfactantsleadtofastchangesintheinternalmicrostructureofthesurfactantmonolayer.Theinternalmicrostructureofsurfactantmonolayerisanalyzedbyidentifyingporesbetweenthesurfactants.Scalingofporepropertiesisfoundtobeconsistentwithpercolationtheory.Usingtheresultsofpercolationtheoryamethodisdevelopedtolteroutfastinsignicantporevolumechangescausedbyfastuctuationsofsurfactantbeadpositions.Thisallowsonetofocusoneventsasfusionandssionofpores. Inthethirdchapter,wecomputeenergybarriertotransportofsoluteacrossthesurfactant-freeandsurfactant-coveredinterfaces.Surfactantsofdierentlengthsandsolutesofdierentsizesandhydrophobicityareconsidered.Weshowthatenergybarriersarecausedbythemaximainlocaldensitieswhichleadsstericrepulsion.Theenergybarrierisalsoaectedbyhydrophobicity/hydrophilicityofparticlesinlocalregionaroundthesolute.Theenergybarriers,densitymaxima,widthsofdensitymaximumregionsallincreasewithincreaseoftheirsurfactantlength. Inthefourthchapter,theroleofsurfaceuctuationsandcapillarywavesonsolutetransportacrosssurfactant-freeandsurfactant-coveredhexadecane-waterinterfacesis 17

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Thefthchapterconcludesthethesisandpresentsitspossiblebroaderimpacts. 18

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6 { 9 ].Itiswellknownthatathinsurfactantlayersuchasalipidlayeronthesurfaceofatearlmcanoersignicantmasstransferresistance,andthusretardtheevaporationofwater[ 10 ].Similarmasstransferresistancecanbeexpectedtooccuronthesurfaceofmicroemulsiondroplets,particularlyduetoveryhighpackingdensityofthesurfactantsonthedropletsurface.Infact,recentexperiments[ 11 12 ]onsolutereleasefrommicroemulsiondropletsloadedintoahydrogelsuggestthatthemicroemulsionscouldpresentbarrierstosolutetransport. Despitetheimportanceofthesolutetransportacrosssurfactant-coveredinterfacesofmicroemulsions,understandingofmolecularmechanismsofthistransportiscurrentlylimited.Mostmolecularmodelingstudies[ 13 { 18 ]ofsurfactant-coveredoil-waterinterfacesarefocusedonsuchpropertiesofthesurfactantmonolayerasinterfacialtension,lateraldiusionofsurfactantmoleculeswithinthemonolayer,andsurfactantconformationsanddensityproleswithinthemonolayer. Investigationsofmasstransferacrosssurfactantmonolayersatoil-waterinterfacesmaybenetfromextensivestudies[ 19 { 27 ]oftransportacrosslipidbilayers.Althoughadetailedmolecularstructureofalipidbilayerdiersfromthatofasurfactantmonolayerattheoil-waterinterface(especiallyforhighlycurvedmicroemulsiondropletsofsmallradius),bothofthesestructuresconsistoftightlypackedchainmolecules.Therefore,anticipatedtransportmechanismsacrosssurfactantmonolayerscanbededucedfromtheanalogywithlipidbilayers.Thefollowingtwocompetingmechanismsofsolute 19

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22 23 ]:transientchannelandsolubility-diusionmechanisms.Inthetransientchannelmechanism,theuctuationsinthebilayerleadtoformationofatransientchannelthroughtheentirebilayerfollowedbythesolutediusionthroughthiswaterchannel.Inthesolubility-diusionmechanism,thesoluteentersandleavesthebilayerthroughshort-livedcavitiesintheheadgroupregionsofthebilayer.Themovementofthesoluteinsidethebilayertakesplacebyhopsbetweensmallvoidsinthebilayer. Similarcooperativedynamicsbetweensoluteandamphiphilicmoleculesislikelytoplayacrucialroleinsolutetransportacrosssurfactant-coveredoil-waterinterfaces.Therefore,understandingthistransportrequiresdetailedknowledgeofthemonolayermicrostructureanddynamics,includingstructure,size,andlife-timeofporesinthemonolayer.Inthecurrentstudy,weinvestigatethesecharacteristicsforathexadecane-waterinterfacescoveredbymodelnon-ionicsurfactantsofvariouslength.Thesesystemaremodeledbycoarse-grainedmoleculardynamics(CGMD)simulations[ 4 ].Inadditiontoinvestigationoftheporeproperties,weanalyzedegreesoffreedomofindividualsurfactantsandcomparetheirtime-scaleswiththoseofporefusion,ssion,creation,anddestruction,i.e.ofprocessesinvolvingcollectivesurfactantdynamics. 4 28 { 31 ].Inthecurrentstudy,weusethemodelofMarrinketal.[ 4 ]whichhasbeenshowntoaccuratelyreproduceseveralphysicalpropertiesofwaterandalkanes,including 20

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Allmoleculesintheconsideredmicroemulsionsystemsaremodeledusingtwotypesofbeads:hydrophobictailbead(denotedhereasT)andhydrophilicheadbead(denotedasH).ThisnotationisdierentfromthatofRef.[ 4 ],wherefourbeadtypesareintroducedinordertomodelawiderangeofamphiphilicmolecules.ThebeadsdenotedinthisworkasHandTaredenotedinRef.[ 4 ]asP(polar)andC(apolar),respectively.Weusethisdierentnotationasitismorecommonintheliteratureonsurfactantsystemsandmicroemulsions. AhydrophobicTbeadapproximatesfourmethylormethylenegroupsinalkanechainsandahydrophilicHbeadapproximatesfourwatermolecules[ 4 ].MohanandKopelevich[ 32 ]recentlysuggestedtoapproximateachainoftwoethoxygroupsbyasingleHbeadandtomodelanethoxylatedsurfactantC4nH8n+1[OCH2CH2]2m-OH(C4nEO2m)byacoarse-grainedmodelHmTn.Althoughinthismodeltheterminal-OHgroupisnottakenintoaccountexplicitly,insection 2.3 wedemonstratethatthemodeladequatelyreproducesphysicalpropertiesofCiEOjmonolayersatthewater-hexadecaneinterface. Allcoarse-grainedbeadshaveequalmassof72atomicmassunits.Theinteractionbetweentwonon-bondedbeadsismodeledbytheLennard-Jones(LJ)potentialwiththesameeectivediameter,LJ=0:47nm,forallbeads.Thecharacterofinteractionsismodeledthroughthevaluesoftheenergyparameter.TheinteractionbetweentwoHbeadsishighlyattractive(HH=5kJ/mol),betweentwoTbeadsisslightlyattractive(TT=3.4kJ/mol),andbetweenHandTbeadisalmostpurelyrepulsive(HT=1:8kJ/mol).AllLJpotentialsaresmoothlyshiftedtozerofrom0.9nmtothecut-odistance1.2nm2:5LJ.Interactionsbetweenchemicallyconnectedbeadsaremodeledbyharmonicpotentialsforthebondlengthandanglevibrations.TheforceconstantforthebondlengthpotentialisKbond=1250kJmol1nm2andthecorrespondingequilibriumbondlengthisRbond=LJ=0:47nmforallbonds.The 21

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AllMDsimulationsareperformedusingGROMACSsimulationspackage[ 33 ].Thetemperatureandpressurearekeptconstantat300Kand1bar,respectively,usingBerendsentemperatureandpressurecouplingschemes[ 34 ]withtimeconstantsof1ps.Thecompressibilityvalueforthepressurecouplingschemeis105bar1. Thefollowinginterfacesareinvestigated:surfactant-freehexadecane-waterinterfaceandhexadecane-waterinterfacescoveredbyHnTnsurfactantswithn=1;:::;5and7.Tofacilitatecomparisonofmonolayerproperties,wenumberthebeadsinHnTnsurfactantssothatH1andT1correspondtohead-andtail-beadsclosesttothecenterofthemoleculeandHnandTncorrespondtobeadsattheendsofthemolecularchain.Forexample,H3T3surfactantcorrespondstochainH3-H2-H1-T1-T2-T3. Thesimulationofthesurfactant-freesystemandsystemscontainingrelativelyshortHnTnsurfactants(n3)areperformedincubic101010nm3simulationcells.SimulationcellsizesforsystemswithlongerHnTnsurfactantsare121212nm3forn=4and5and261010nm3forn=7.Thesurfactant-freeinterfaceandinterfacescoveredbyHnTnsurfactantswithn5arepreparedbysimulationsofself-assemblyofmixtureswithequalornearlyequalmassfractionsofoilandwater.Arandommoleculardispersionassemblesintoasystemcontainingtwointerfaceswithin100ns.Anexampleofsuchself-assembledsystemisshowninFig. 2-1 .InterfacescoveredbyH7T7surfactantsarepreparedusingadierentapproachsinceself-assemblysimulationsareinecientfortheselongsurfactants.Inthiscase,hexadecane,water,andsurfactantmoleculesareinitiallyplacedintothreedierentrectangularboxes.Afterminimizingenergyofeachofthesesystems,theyarestackednexttoeachotherinthefollowingsequence:water-surfactant-oil-surfactant-water.Theobtainedsystemisthenequilibratedfor100ns. 22

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Hexadecane-water-H3T3systemcontainingtwooil-waterinterfacescoveredbyself-assembledsurfactantmonolayers.Theblack,lightgray,andsmallblue(darkgray)spheresrepresentthesurfactant,hexadecane,andwaterbeads,respectively.Theunitcellsizeis101010nm3.ThisplotisgeneratedusingVMDpackage[ 1 ]. DuetoperiodicboundaryconditionsimposedinMDsimulations,allconsideredsystemscontaintwoidenticaloil-waterinterfaces.Inouranalysiswefocusononeoftheseinterfaces.Thesystemofcoordinatesisorientedsothatthexaxisisnormaltotheinterfaceandtheyzplanecoincideswiththedividingsurfaceoftheinterface.Forthesurfactant-freeinterface,thedividingsurfaceisdenedastheplaneinwhichthelocaloilandwaterbeaddensitiesareequal.Forthesurfactant-coveredinterfaces,thedividingsurfaceischosentocorrespondtothecenterofmassofsurfactantsinthemonolayer.Inwhatfollows,wewillrefertothedirectionofthex-axisasthenormaldirectionandthedirectionsofthey-andz-axesasthelateralorparalleldirections. 4 ]wasdevelopedandvalidatedforarangeofamphiphilicsystemsbutnotformicroemulsionscontainingethoxylatedsurfactants.Therefore,beforeproceedingwithdetailedinvestigationsofthemonolayer 23

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DetailedinvestigationoftheinterfacialcoveragewasperformedforH3T3monolayer.Themaximummonolayercoveragemwasestimatedbyasetofself-assemblysimulationswithvaryingsurfactantmassfractionss,whilekeepingtheoilandwatermassfractionsequaltoeachother.Forsucientlysmalls,thesystemformsbulkwaterandoilphasesseparatedbyatmonolayers.Increasingsabovecertaincriticalvalueleadstoinstabilityoftheatmonolayersandformationofcylindricalmicelles.Notethatinexperimentalsystems,increaseofsslightlyabovethiscriticalvaluedoesnotleadtothemonolayerinstability.Instead,micellesandreversemicellesformedinbulkwaterandoilphasesareinequilibriumwiththemonolayer.However,criticalmicelleconcentrationsofethoxylatedsurfactantsareverylow[ 35 ]andarenotaccessiblebydirectMDsimulationsduetolimitationsonthesimulationcellsize.Therefore,realizationofmicellesandamonolayerinequilibriumwitheachotherinMDsimulationisnotpossible,leadingtothemonolayerinstabilityabovethecriticalsurfactantmassfractions.Thecorrespondingmaximumcoverageofthehexadecane-waterinterfacebyH3T3surfactantsobservedinoursimulationsism=2:0molecules/nm2. ThemodelH3T3surfactantcorrespondstoC12EO6.TheclosestsystemsforwhichtheexperimentaldataareavailableareC12EO4andC12EO8monolayersathexadecane-waterinterfaces[ 36 ].Theexperimentallyobtainedmaximuminterfacialcoveragesofthesemonolayersarem(C12EO4)=1:90molecules/nm2andm(C12EO8)=1:59molecules/nm2.Sincem(C12EO6)isexpectedtobebetweenthesetwovalues,weconcludethatthecoarse-grainedmodelsomewhatoverestimatesthemaximuminterfacialcoverage.Nevertheless,theagreementisreasonablygoodconsideringapproximationsinvolvedinthemodel. 24

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37 ], Here,Lxisthelengthofthesimulationboxinthenormaldirection,Ns=2isthenumberofinterfacesinthesystem,andPxx;Pyy;Pzzarethediagonalcomponentsofthepressuretensorcomputedusingthevirialtheorem. EectsoftheinterfacialcoverageandthesurfactantlengthontheinterfacialtensionareexaminedinFigures 2-2 and 2-3 ,respectively.Fig. 2-2 showsthecalculatedatthewater-hexadecane-H3T3interfaceforsurfactantcoveragerangingfrom0to2molecules/nm2andFig. 2-3 showscomputedforoil-waterinterfacescoveredbysurfactantsHnTnforn=0;:::;5withinterfacialcoverage=1:51molecules/nm2.Increaseofthecoverageofaninterfacebythesamesurfactantandincreaseofthesurfactantlengthwhilekeepingtheinterfacialcoverageconstantbothleadtoloweringofinterfacialtension,inagreementwithexperimentallyobservedtrends[ 38 ]. Figure2-2. Dependenceoftheinterfacialtensionatthehexadecane-water-H3T3interfacesontheinterfacialcoverage. Moreover,thecomputednumericalvalueoftheinterfacialtensionatthesurfactant-freehexadecane-waterinterface(44.6mN/m)isingoodagreementwiththeexperimentally 25

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Dependenceoftheinterfacialtensionatthehexadecane-water-HnTninterfacesonthesurfactantlength2natconstantinterfacialcoverage=1:51molecules/nm2;n=0correspondstothesurfactant-freehexadecane-waterinterface. measured[ 39 ]value=49mN/m.Thisquantitativeagreementisremarkableconsideringthatthemodelhasnotbeenspecicallyoptimizedtoreproducetheinterfacialtensionatoil-waterinterfaces[ 4 ].Aquantitativecomparisonofthecomputedinterfacialtensionatthesurfactant-coveredinterfaceswithexperimentaldataismoredicultduetoanextremesensitivityoftheinterfacialtension()tosmallchangesoftheinterfacialcoveragewhenthelatterapproachesitsmaximumvalue,m.Consider,forexample,theinterfacialtensionatthehexadecane-water-H3T3interface.Atthelargestinterfacialcoverageachievedinoursimulation,=2molecules/nm2,theinterfacialtensionisMD(=2)=24:22mN/m.TheclosestsystemforwhichtheexperimentaldataareavailableisC12EO8monolayeratthehexadecane-waterinterface[ 36 ]forwhichtheinterfacialtensiondecreasesfrom13to7mN/masthesurfactantconcentrationinwater,Cw,changesfromCw=2:5105mol/LtoCw=7:9105mol/L.UsingLangmuiradsorptionisothermandtakingintoaccountthatthefreeenergyofadsorptionofC12EO8frombulkwatertothehexadecane-waterinterfaceisG0=51:1kJ/mol(seeRef.[ 36 ]),weestimatethecorrespondingsurfactantcoveragestobe0.9976mand0.9992m, 26

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TheexperimentallymeasuredinterfacialtensionisconsistentwithFrumkinequation[ 38 ] m;(2{2) whichallowsustoextrapolatetheexperimentaldatatoobtainthatMD=24:22mN/mwouldbeobservedexperimentallyattheinterfacialcoverage=0:98mandthecorrespondingsurfactantconcentrationinbulkwaterCw=3:0106mol/L.ThisvalueofCwislowerthantheconcentrationsconsideredintheexperimentsandthereforetheexperimentalresultscannotbecompareddirectlywiththecalculatedinterfacialtension.However,theobtainedestimateof=m,leadsustoconcludethat,inthemolecularmodel,m=2:04molecules/nm2,whichisveryclosetothemaximuminterfacialcoverage(m=2molecules/nm2)obtainedbyanindependentcalculationbasedonthemonolayerstability.ThegoodagreementbetweentheestimatesofmobtaineddirectlyfromMDsimulationsandthroughextrapolationoftheexperimentaldatatotthecomputedinterfacialtensionimpliesthattheinterfacialtensionpredictedbytheCGMDmodelisingoodagreementwiththeexperiments. Thesurfactantdynamicscanbedecomposedintodynamicsofthefollowingdegreesoffreedom: 1. Translationalmotionofthesurfactantcenterofmass. 27

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Tiltingofthesurfactantmoleculewithrespecttothemonolayernormaln. 3. Rotationofthesurfactantmoleculearoundn. 4. Fluctuationsofindividualsurfactantbeads. Translationalmotionofthesurfactantmoleculeconsistsofdiusioninthelateraldirectionanductuationsinthenormaldirection.ThelateralsurfactantdiusivityandthedisplacementofthesurfactantcenterofmassfromthemonolayerdividingsurfacewillbedenotedasDkandL?,respectively.Orientationofasurfactantmoleculeischaracterizedbyadirectorvectoru.Thereisnouniquewaytochoosethisvectorforaexiblemolecule.Inthecurrentwork,wedeneuasaunitvectorwhichspeciesdirectionofastraightlineclosest(intheleastsquaressense)tothebeadsofthemolecule.Thetiltingandrotationofasurfactantmoleculecorrespondtouctuationsoftheprojectionsu?andukofthemoleculardirectoruonthemonolayernormalnandthemonolayerplane,respectively.Inordertoseparatemotionofindividualsurfactantbeadsfrommotionoftheentiremolecule(i.e.,motionofitscenterofmassanddirector),weconsiderdisplacementsdjofbeadsfromthemoleculardirector.Hereandintheremainderofthissection,jdenotesabeadpositionintheHnTnsurfactantchain,j=HiorTi,i=1;:::;n: 2-4 .Forallconsideredsurfactants,theautocorrelationfunctionsCtilt()andCrot()closelyobeytheexponentialdecaylaw, withrelaxationtimeskquantifyingthetime-scalesoftiltingandrotation.Ontheotherhand,thesinglerelaxationtimeapproximation( 2{3 )isnotvalidforC?()andCj()duetopresenceoftwodistinctscalesintheuctuationsofthemolecularcenterofmassandofindividualsurfactantbeads.FunctionsC?()andCj()obeythedoubleexponential 28

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AutocorrelationfunctionsC?,Ctilt,Crot,andCT4ofuctuationsofmolecularcenterofmassinthenormaldirection,projectionsu?andukofthemoleculardirectorvector,anddisplacementsdT4ofsurfactantbeadT4fromthedirectorofH5T5surfactants.Thickdashedlinesshowtsbysingleexponetials( 2{3 )(forCtilt,Crot)anddoubleexponentials( 2{4 )(forC?,CT4).TheautocorrelationfunctionsarenormalizedsothatC(0)=1.Forclarity,thesymbolsareshownonlyforsomevaluesof. decaylaw, ThecontributionofthersttermofEq.( 2{4 )toC?()isrelativelysmallindicatingthatthedynamicsofthecenterofmassaredominatedbytheslowrelaxationcharacterizedby(2)?.Wenotethatthefastuctuationtimeisalsopresentinthedynamicsofthemoleculartiltandrotation,butitscontributiontothecorrespondingautocorrelationfunctionsisevensmallerthantoL?andthereforeweneglectthesefasttime-scalesindynamicsofu?anduk.Onthecontrary,forCj,contributionofthesecondtermofEq.( 2{4 )isrelativelysmall,i.e.thedynamicsofindividualbeadsisdominatedbyfastuctuationscharacterizedby(1)j.Thepresenceofthefasttime-scaleinthedynamicsofthemolecularcenterofmassandorientationandthepresenceoftheslowtime-scaleinthedynamicsofindividualbeadsareduetocorrelationsbetweenthesedegreesoffreedom. 29

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2-1 .ItisobservedthatuctuationsofL?anduoccuronsimilartime-scales.Characteristicdiusiontime-scalecorrespondstotheaveragetimeofdiusionofasurfactantoveracharacteristicdistancewhichistakentobetheaveragedistancebetweentwonearest-neighborsurfactantsinamonolayer(1nm).Therefore,thediusiontime-scaleisontheorderof1ns,i.e.itisslowerthantheuctuationsofL?andu.Forallconsideredsurfactants,theuctuationsoftiltandL?arefasterthanthemolecularrotation. Table2-1. Time-scalesofthesurfactantcenterofmassandorientation:diusivityDkinthelateraldirection,correlationtimes(1)?and(2)?ofuctuationsinthenormaldirection,andcorrelationtimestiltandrotoftiltandrotationaroundthemonolayernormaln. Surfactant H3T3 318 184 344 H5T5 374 421 655 H7T7 692 613 762 Increaseofthesurfactantlength,2n,slowsdownthedynamicsofcenterofmassandtheorientationofthemolecule.Itisinterestingtonotethatthelateraldiusivityisconsiderablydecreasedwhennincreasesfrom3to5,whileitsfurtherdecreaseisrelativelysmallwhennisincreasedfrom5to7.Onthecontrary,thetime-scales(i)?ofthecenterofmassuctuationsinthenormaldirectionareverycloseforH3T3andH5T5surfactants,whiletheseuctuationsaresignicantlyslowerinH7T7monolayers. Averagedeviationdjofanindividualsurfactantbeadfromthemoleculardirectorexhibitsdependenceonthepositionjofthebeadwithinthesurfactantchain,seeFig. 2-5 .Thisdependenceisqualitativelythesameforallconsideredsurfactants.Thelargestdisplacementisexhibitedbythebeadslocatedattheendsofthesurfactantswhereasthesmallestdjareexhibitedbythebeadslocatedinthecentersofthehead-andtail-groupsofsurfactantmolecules. 30

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AveragedistancesofsurfactantbeadsfrommoleculardirectorsuforH3T3,H5T5,andH7T7surfactants. Therelaxationtimes(i)jofthebeaductuationsaresummarizedinFig. 2-6 .Theslowrelaxationtimes(2)jstronglydependonthebeadpositionwithinthesurfactantchainandfollowthesametrendsasthemeanbeaddisplacementsdj.Theserelaxationtimescorrespondtothecorrelationoftheindividualbeaddynamicswiththedynamicsofanentiremoleculeandareverysimilar(albeitsomewhatsmaller)tothetime-scalesofuandL?.Onthecontrary,thefastrelaxationtime-scales(1)jintroduceanewtime-scale.Dependingonthebeadpositions,(1)jrangesfrom10psto30psforH3T3,from20psto45psforH5T5,andfrom25psto55psforH7T7monolayers. Insummary,thetime-scalesofindividualsurfactantmoleculesrangefromO(1ns)forlateraldiusiontoO(10ps)foructuationsofindividualbeads. 22 23 ]suggestsatleasttwopossibletransportmechanismsinvolvingactiveparticipationofthemicrostructureinthesolutetransport.Forexample,itispossiblethatthesolutetransporttakesplacethroughaseriesofactivatedjumpsbetweenvoidsformedbytheslowermovingsurfactants.Alternatively,thesolutemay 31

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DecaytimesoftheautocorrelationfunctionsCj(t)ofindividualbeadswithinH3T3,H5T5,andH7T7surfactantmolecules.Theopenandclosedsymbolsshowthefast((1)j)andslow((2)j)decaytimes,respectively. betransportedthroughatransientchannelconnectingtwobulkphases.Inordertoobtainbackgroundinformationforfutureinvestigationsofthepossiblecooperativeeectsbetweenthesolutetransportandthemonolayermicrostructure,inthissectionweexploresize,structure,anddynamicsofporeswithinamonolayer.Wedemonstratethatstatisticsoftheporestructureisconsistentwithpredictionsofthepercolationtheoryandusethistheorytogainadditionalinsightintotheporedynamics. 40 ]andlipidbilayers[ 41 ].Attimet,apore(t;Rp)isdenedasaconnectedvolumenotoccupiedbysurfactantmoleculesandaccessibletoasphericalprobeofradiusRp.ApointwithinamonolayerisconsideredaccessibletotheprobeifthedistancebetweenthecentersofmassofthisprobeandofallsurfactantbeadsislessthantheproberadiusRp.Thisdenitionallowstheporevolumetobeoccupiedbysolventmolecules,whichisadeparturefromtheearlierdenition[ 41 ]ofporesinlipidbilayers.Ourmotivationfortherequirementthatporewallsconsistonlyofsurfactantmoleculesisbasedontheexpectationthattherate-limitingstepinthesolute 32

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3.3 )and(2)thehighermobilityofthesolventmoleculesascomparedtothesurfactants. Wewillsometimesrefertotheporesk(t;Rp),k=1;2;:::;denedaboveastheinstantaneousporesinordertodistinguishthemfromaveragedporeswhichwillbediscussedinsection 2.5.3 .Theporestructureswereresolvedbymovingthesphericalprobeonacubicgridwithgridsize0.1nm.ExamplesofporesinH3T3surfactantmonolayerobtainedwithprobeofradiusRp=0:47nmareshowninFig. 2-7 a.TheseporescorrespondtospaceaccessibletosmallsolutemoleculesconsideredinSection 3.3 ifboththesoluteandthesurfactantbeadsareapproximatedbyhardsphereswithdiametersequaltotheirLJdiameterLJ=0:47nm.Fig. 2-7 ademonstratesthatsomeoftheporesformchannelsconnectingthebulkhexadecaneandwaterphases.Inordertoassessapossibilityofsolutepermeationthroughoneofthesechannels,itisnecessarytoinvestigatethechannelstabilityaswellasexistenceofchannelsaccessibletoprobesofvarioussizes.Thechannelstabilityisaddressedindetailinsection 2.5.3 andtheeectoftheprobesizeontheporestructureisdiscussedinthisandthenextsections. Figure2-7. PoresinH3T3monolayerobtainedwithproberadius(a)Rp=0:47nmand(b)Rp=0:6nm. 33

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2-7 bwhichshowsporesobtainedwithaprobeofradiusRp=0.6nmforthesameinstantaneousmonolayercongurationasthatshowninFig. 2-7 a.Note,inparticular,thatthenumberofchannelsconnectingthebulkphasesdecreasessignicantlywithincreaseofRp.TheeectoftheproberadiusontheporeconnectivityandvolumecanbeseenmoreclearlyinFig. 2-8 ,whichshowscross-sectionsoftheporesinH3T3andH7T7monolayersobtainedwithproberadiirangingfrom0.42to0.7nm.Forexample,Fig. 2-8 ashowsthatachannelinH3T3monolayerconnectingthebulkphasesatz8nmexistsforrelativelysmallprobesizesandbecomesdisconnectedasRpincreases.Eectsofsurfactantlengthontheporestructurescanbeassessedqualitativelyfromcomparisonofthecross-sectionsofporesinH3T3andH7T7monolayers.Thechannelsconnectingthebulkphasesaresignicantlylessfrequentinthemonolayerwithlongersurfactantsandacommonfeatureofthismonolayerisa\half-channel"protrudingfromoneofthebulkphasestowardsthemonolayercenter. Ingeneral,onecanidentifythefollowingfourporetypes: 1. 2(3). 4. WeperformedadetailedstatisticalanalysisofporestructuresinH3T3andH7T7monolayers.Thisanalysiswasconnedtoregionswithsubstantialsurfactantdensity.Theboundariesoftheseregionswerechosentobexmin=0:95nmandxmax=0:55nmforH3T3monolayerandxmin=2:06nmandxmax=1:74mmforH7T7monolayer.Thischoiceofxminandxmaxensuresthatthebulkphasesareexcludedfromtheporestructureanalysisandspuriousconnectionsbetweenchannelsandhalf-channelsthroughthebulkphasesareavoided.Theboundaryofthemonolayerxmaxinthehead-groupregionwas 34

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Examplesofcross-sectionsofporestructuresin(a)H3T3and(b)H7T7monolayers.Theporesareobtainedusingsphericalprobeswithradiirangingfrom0.42to0.7nm.Darkercolorscorrespondtotheporesobtainedwithlargerproberadiiandwhiteregionscorrespondstoregionsnotbelongingtopores.Oilandwaterbulkphasesarelocated,respectively,ontheleftandontherightofthemonolayers,seealsoFig.??. chosentobeclosertothemonolayercenterthantheboundaryxmininthetailregionduetothedeeperpermeationofwatermoleculesintothemonolayer,seeFig. 3-4 ThemeanvolumeVanddensitypofporesofeachofthefourtypesareshowninFigures 2-9 and 2-10 ,respectively.Theporedensitypwithinamonolayerisdenedastheaveragenumberofporesperunitarea.DependenceofVandpontheproberadiusRpfollowsqualitativelysimilartrendsforbothshortandlongsurfactants.Themeanvolumeofporesofalltypesislargerinthemonolayercomposedoflongersurfactants.ThedensityofvoidsishigherinH7T7monolayerwhereasthedensityofchannelsishigherinH3T3monolayer,sinceitismorelikelythataporewouldpercolatethroughathinnermonolayer.Thedensityofhalf-channelsinbothofthesemonolayersisalmostthesame. ItseemsintuitivethatthemeanvolumesofallporesshoulddecreaseuponincreaseoftheproberadiusRp.Thisisindeedobservedforthemeanvolumeofchannelsandwater 35

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DependenceofthemeanvolumeVofporesinH3T3andH7T7monolayersontheproberadiusRpfordierentporetypes:(a)voids,(b)oilhalf-channels,(c)waterhalf-channels,and(d)channels. half-channels,seeFig. 2-9 c,d.However,themeanvolumeofvoidsinH3T3monolayerisessentiallyindependentofRp,seeFig. 2-9 a.ThisobservationisexplainedbyabalanceoftwoprocessestakingplaceasRpisincreased,namely 1. Decreaseofvolumesofindividualvoidsand 2. Transformationsofchannelsandhalf-channelsintovoidsduetoclosuresoftheirconnectionswiththebulkphases. Thevoidsappearinginprocess2haverelativelylargevolumesosettingthedecreaseinthevoidvolumesduetoprocess1,thusleadingtoarelativelyconstantmeanvoidvolume.Ontheotherhand,themeanvoidvolumeinH7T7monolayerdecreasesrelativelyfastuponincreaseofRpsinceinthismonolayertheratioofthedensitiesofvoidsand(half-) 36

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DependenceofthedensitypofporesinH3T3andH7T7monolayersontheproberadiusRpfordierentporetypes:(a)voids,(b)oilhalf-channels,(c)waterhalf-channels,and(d)channels. channelsismuchlargerthaninH3T3monolayer.Therefore,creationofnewlargevoidsinprocess2doesnotcompensatethevoidvolumedecreaseduetoprocess1. Asimilarmechanismisresponsibleforasignicantincreaseintheaveragevolumesofoilhalf-channelsuponincreaseofRpforsmallRp(Rp0:47nmforH7T7monolayerandRp0:5nmforH3T3monolayer),seeFig. 2-9 b.AsRpincreases,channelsclosetheirconnectiontothebulkwaterphase,whichleadstoatransitionfromchannelstooilhalf-channelsofrelativelylargevolumes. Theabsenceofasimilarmaximumofthemeanvolumeofthewaterhalf-channelsindicatesthat,uponincreaseofRp,channelsaremuchmorelikelytobeclosedonthe 37

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2-10 bandcshowthat,forsucientlylargeRp,thedensityofwaterhalf-channelsislowerbyalmostanorderofmagnitudethanthedensityoftheoilhalf-channelsduetoalargernumberoftransitionsfromwaterhalf-channelstovoidsinresponsetoincreaseofRp.Ontheotherhand,atsmallRp(Rp0:5nm),thedensityofthewaterhalf-channelsishigherthanthatoftheoilhalf-channelssincethereisasmallerbarrierforpenetrationofsmallerwatermoleculesintothemonolayerandhenceahigherprobabilityofformationofthewaterhalf-channels. DependenceoftheporedensitypontheproberadiusRpisqualitativelysimilarforallporetypes;p(Rp)reachesamaximumatarelativelysmallvalueofRp=Rmaxp,0.45nmRmaxp0:5nm.ThedensityincreasewithincreaseofRpforRp
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2.5.3 thepercolationtheoryisappliedtogainadditionalinsightsintothemonolayerdynamics. Beforeproceeding,webrieyreviewrelevantresultsofthepercolationtheory.FurtherdetailsmaybefoundinRef.[ 42 ].Theoreticalinvestigationsoftenconsideramodelsystemconsistingofaninnitegridwithallgridsiteshavingequalprobabilityptobelongtoacluster.Theclustersofthepercolationtheorycorrespondtoporesinamonolayerandinwhatfollowswewillrefertoclustersaspores.Theprobabilitypisanorderparameterofthesystemand,aspisincreasedfrom0to1,thesystemundergoesaphasetransitionatacriticalvalue(percolationthreshold)pcofp.Inthesupercriticalphase,i.e.forp>pc,thereexistsaninniteporepercolatingthroughthesystem,whereasinthesubcriticalphase(p
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Itcanbeshownusingrenormalizationtechniquesthat,aspapproachespc,multiplesystemcharacteristicsdivergeasanegativepowerofjppcj.Thesecharacteristicsincludethecorrelationlength(p),andthemeanVf(p)andstandardthedeviationV;f(p)ofvolumesofnitepores.Theporedensitypremainsniteandapproachesanextremumatthepercolationthreshold, where,A,andBaresomeconstants. Ournormalizationoftheporedensityisslightlydierentfromthestandardnormalizationusedinthepercolationtheory[ 42 ].Commonly,thedensityismeasuredintermsofnumberofporesperunitvolume.However,herewedenepasthenumberofporesperunitarea,whichismorenaturalfor(half-)channelsinamonolayer.Sincetheareaandthevolumeofthemonolayersegmentusedinourporeanalysisarekeptconstantforeachoftheconsideredmonolayers,thisdierentnormalizationdoesnotaectapplicationofthetheorytothemonolayersystems. Severalotherapproximationsinvolvedinapplicationofthepercolationtheorytomonolayermicrostructuremeritadditionaldiscussion.Thetheoreticalanalysisisoftenconcernedwithmodelsystemsunboundedinalldirections.Amodelmoreappropriateforasurfactantmonolayerwouldbeaslabboundedinthenormaldirectionandunboundedinthelateraldirection.Thepercolationpropertiesoftheslabmaydierfromthoseofthefullspace.However,asthicknessoftheslabgrows,theslabpercolationpropertiesapproachthoseofthefullspace.Forexample,itisknownthatpercolationinthefullspaceimpliespercolationinsomesucientlythickslab[ 43 ].Moreover,someoftheresultsforfullspacescanbereadilyappliedtoslabsofanarbitrarythickness.Forexample, 40

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2{5 ))isvalidforthesubcriticalphaseinaslabofanarbitrarythickness[ 42 ].Wethereforeassumethatallscalingrelationshipsobtainedforinnitespacesalsoholdforslabsofnitethickness. Anotherdierencebetweenthemonolayermicrostructureandthemodelsystemofthepercolationtheoryarisesduetonon-uniformdensityofthesurfactantmoleculesinthenormaldirection,whichimpliespositiondependenceoftheprobabilitypandmakesitdiculttousepasanorderparameter.Inthiscase,itisnaturaltoassociatethepercolationorderparameterwiththeprobesizeRp.WeexpectthatdependenceofthekeymonolayercharacteristicsonRpisqualitativelysimilartotheirdependenceonp.Inparticular,whenRpisclosetoitscriticalvalueRcp,thecorrelationlength(Rp)andthemeanVf(Rp)andthestandarddeviationV;f(Rp)ofporesofnitevolumedivergeasanegativepowerofjRpRcpj,whiletheporedensityisapproximatedas ThisiscertainlytrueiftheorderparameterpisreplacedbyRpinahomogeneoussystem.Inthiscase,bothpandRpareposition-independentandthereexistsasmoothandmonotonouslydecreasingfunctionp(Rp)connectingthesetwoquantities.WecangeneralizethisfunctionforthecaseofinhomogeneoussystemsandconsiderdependenceofthespatialaveragepofprobabilityponRp.Thefunctionsp(Rp)forH3T3andH7T7monolayersaresmoothandmonotonouslydecreasing,asevidentfromFig. 2-11 .Therefore,itisconceivablethattheporepropertiesinaninhomogeneousmonolayernearitscriticalpointRcparequalitativelysimilartotheporepropertiesinahomogeneoussystemand,inparticular,that(Rp),Vf(Rp),andV;f(Rp)divergeasanegativepowerofjRpRcpjandp(Rp)isapproximatedbyEq.( 2{7 ).NotethatthesubcriticalandsupercriticalphasescorrespondtoRp>RcpandRp
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AverageprobabilitiespofpointsinsideH3T3andH7T7monolayerstobelongtoapore.TheuppertwocurvesshowdependenceofpontheproberadiusRpforinstantaneousporesandthelowertwocurvesshowdependenceofpontheaveragingtimetavforaveragedporesatRp=0:47nm.ThecorrespondingvaluesofRp(tav)forinstantaneous(averaged)poresareshownatthetop(bottom). Itisexpectedthatporesinamonolayerhaveagreateranitytoextendinthedirectionnormaltothemonolayersurface,i.e.,unlikethemodelsystem,themonolayerporesareanisotropic.Theanisotropyismostnaturallyrepresentedwithintheframeworkofthebondpercolationmodel.Inthismodel,twositesbelongtothesameporeiftheyareconnectedbyabondandtheprobabilityofthebondformationdependsonitsdirection.Foramonolayer,theprobabilityp?ofabondformationinthenormaldirectionishigherthantheprobabilitypkofabondformationinthelateraldirection.Inthiscase,thecriticalpointisreplacedbyacriticalsurface[ 42 ],i.e.thereexistsafunction(p?;pk)suchthatthesub-andsupercriticalphasescorrespondto(p?;pk)<0and(p?;pk)>0,respectively.Foramonolayermicrostructure,bothp?andpkaremonotonouslydecreasingfunctionsofasingleparameter,Rp,andtheaboveconditionsforthesub-andsupercriticalphasescanbereplacedby(Rp)<0and(Rp)>0.Therefore,despiteitsanisotropy,themonolayermicrostructurecanbecharacterizedbyasingleorderparameter,Rp. 42

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Withthesepreliminaries,weturntotheresultsofourcalculations.ExamplesoftheconnectivityfunctionsobtainedfromoursimulationsareshowninFig. 2-12 .Afteraninitialtransient,whichcorrespondstothepowerlawdependence,Cf(r)decaysexponentially,inagreementwithEq.( 2{5 ).Forlarger,theexponentialscalingbecomesinvalidduetothenitesizeofthemonolayerinthelateraldirection.Thecorrelationlengths(Rp)showninFig. 2-13 aareobtainedbyttingtheexponentiallydecreasingsegmentsofCf(r;Rp)toconster=.Theobtainedcorrelationlengthsareconsistentwiththecross-overlengthsbetweenthepowerlawdecayandtheexponentialdecayoftheconnectivityfunctions,whichprovidesanadditionalconrmationofvalidityofEq.( 2{5 ).AtRp=0:45nm,(Rp)reachesitsmaximumanditisexpectedthatinthelimitofaninnitelylargesimulationcell,(Rp)willdivergeintheneighborhoodofthisRp. Theporedensityp(Rp)andthemeanVf(Rp)andthestandarddeviationV;f(Rp)ofthevolumesofniteporesareplottedinFig. 2-13 b,c,andd,respectively.ThemaximaofVf(Rp)andV;f(Rp)correspondtothedivergenceofthesequantities.Thereisa 43

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ConnectivityfunctionsCf(r;Rp)inH7T7monolayerfordierentproberadiiRp. smalldiscrepancybetweentheexpectedlocationsofthesingularitiesof(Rp),Vf(Rp),andV;f(Rp)andthemaximumofp(Rp).pattainsitsmaximumatRp=0:47nm,whereasthesingularitiesof,Vf,andV;fareexpectedtotakeplaceneartheirmaximainthenitesystem,i.e.nearRp0:45nm.Thisdiscrepancyappearstocontradictthepercolationtheorypredictionthattheextremumofpandthesingularitiesof,Vf,andV;fshouldtakeplaceatthesamevalueoftheorderparametrer,Rp=Rcp.However,inanitesystem,asinglecriticalvalueRcpmaybereplacedbyapercolationwindow,i.e.arangeofcriticalvaluesoftheorderparameter.Inthiscasethetransitionbetweenthesub-andsupercriticalphasestakesplacecontinuouslyastheorderparameterpassesthroughthisrange.Theexistenceofacriticalwindowhasbeenrigorouslyproven[ 44 ]forcertainclassesofniteperiodicsystems.TheMDmodelofthemonolayerisperiodiconlyintwooutofthreedirectionsandthisrigorousresultcannotbedirectlyappliedtothissystem.Nevertheless,itislikelythatasimilarcriticalpercolationwindowexistsforthenitemonolayermodel. Insummary,weobservethat,despitetheintroducedapproximations,thepercolationtheoryforasimplemodelsystemcorrectlycapturesthebehaviorofthekeypropertiesofthemonolayermicrostructure.Figure 2-13 suggeststhatthepercolationthresholdin 44

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Propertiesofinstantaneouspores:(a)correlationlength,(b)poredensityp,and(c)meanVand(d)standarddeviationV;fofvolumesofnitepores. bothH3T3andH7T7monolayersisRp0:47nm,i.e.thecriticalprobesizeisclosetotheLennard-Jonesdiametersofthebeadsinthecoarse-grainedmodel.Thisguaranteesexistenceofapercolatingpaththroughamonolayerforabeadofdiameterlessthan0.47nm.However,asresultsofthenextsectionindicate,thispathislikelytobeunstableonthetime-scaleofthesolutetransport. 2-14 a.Atypicaltime-dependenceV(t)ofvolumesofallporeswithinamonolayershowninthisgurepossessesmultiplediscontinuitiesduetoconstantformation, 45

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2.4 .Inordertoclarifytheoriginofthisextremelyfastporedynamics,considereventsleadingtoadiscontinuityofV(t)inanexamplecircledinFig. 2-14 a.ThecorrespondingsegmentofthetrajectoryismagniedingureFig. 2-14 b.Thediscontinuityofthevolumesofpore1andpore2showninthisgureisduetoacoalescenceofthesetwoporestoformalargerpore3.DetailsofthiscoalescenceprocessareexploredinFig. 2-15 .Figures 2-15 aandbshowthatattimet1=0:56ps,pores1and2correspondtotwoalmostparallelchannels.Attimet2=0:60ps,thesechannelsbecomeconnectedbyanarrowpassage,whichimpliesfusionofthesetwochannelsandhenceadiscontinuityintheporevolume.Suchafusionprocessisnotexpectedtoplayanysignicantroleinthesolutetransport.Asonemightexpect,thenarrowpassageisveryshort-livedandindeedFig. 2-14 ashowsthatpore3splitswithin1ps.Thelateralcross-sectionsoftheporestructuresshowninFig. 2-15 c,dfurtherrevealthatthesurfactantcongurationremainsessentiallyunchangedbetweentimest1andt2andformationofachannelbetweenpore1andpore2iscausedbyaslightmovementofthesurfactants.Thisexampledemonstratesthatevenminutechangesinthesurfactantcongurationoccurringonthetime-scaleof1psorlesshaveatremendouseectontheapparentporestructureandveryfewoftheapparentporecoalescenceandbreak-upprocessescorrespondtoasubstantialchangeinthemonolayermicrostructure. Inordertolteroutthefastandinsignicantporefusion/ssionevents,weproposeamorerobustporedenitionbasedontimeaveragingoftheporestructures.WedenoteanaveragedporeobtainedwiththeprobeofradiusRpandtheaveragingtimeintervaloflengthtavcenteredaroundtimet0ask(t0;Rp;tav),k=1;2;:::,anddeneitasaconnectedvolumesuchthateachpointwithinthisvolumebelongstosomeinstantaneousporem(t;Rp)ateachmomentoftimewithintheinterval[t0tav=2;t0+tav=2].Thisdenitionimplies,inparticular,thatk(t;Rp)=k(t;Rp;0). 46

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(a)EvolutionofvolumesofallporeswithinH3T3monolayer.PoresareobtainedwiththeprobeofradiusRp=0:47nm.(b)Magnicationoftheareacircledinplot(a)whichshowscoalescenceofpore1andpore2toformpore3(thicklines).Volumesofallotherporesareshownbythinlines. TheporeaveragingwasperformedforRp=0:47,0.5,0.6,and0.7nmandtavrangingfrom0psto100ps.Theaveragingtime-step(i.e.,thetime-stepwithwhichtheinstantaneousporesweresampledduringtheaveragingprocess)wastakentobe1ps.Thedensitiesp(Rp;tav)ofaveragedvoids,oilandwaterhalf-channels,andchannelsinH3T3andH7T7monolayersareplottedinFig. 2-16 .Itisclearthatevenaveragingoverrelativelyshorttimeintervalsleadstoasignicantreductionofthedensityofporesofalltypes.ThisdensityreductionisespeciallydramaticforchannelswhichessentiallydonotexistinH7T7monolayerwhentav10ps.EvenfortheshorterH3T3surfactants,averagingovertav=10psleadstomorethananorderofmagnitudedecreaseofthechanneldensity.Thisimpliesthatthechannelsconnectingthebulkoilandwaterphasesareextremelyunstableandtheirlife-timeiscomparabletoorislessthan10ps.Therefore,itisextremelyunlikelythatasolutewouldbetransportedthroughatransientchannelacrosstheentiremonolayer. Thehighsensitivityofthedensitiesoftheaveragedporestotheaveragingtimetavcallsforselectionofanappropriatetav,whichwouldbesucientlylargetoremovethefastandinsignicantfusionandssioneventsandsucientlysmalltoavoiddestruction 47

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DetailsoftheporecoalescenceshowninFig. 2-14 b.Pores1and2att1=0:56psshownin(a)coalesceintoasinglepore3att2=0:60psshownin(b)byforminganarrowchannelbetweenthesepores.Figures(c)and(d)showthecorrespondingcross-sectionsofthemonolayerbyplanex=0:8nmatt1=0:56psandt2=0:60ps.Circlesrepresentcross-sectionsofsurfactantbeads.ThebeaddiameterisassumedtocoincidewithitsLJdiameterLJ=0:47nm.Cross-sectionofpore1isshownbythegreyshadedareain(c)andcross-sectionsofpores2and3areshownbytheblackshadedareasin(c)and(d),respectively. 48

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Dependenceofthedensityp(Rp;tav)ofaveragedporesinH3T3(solidsymbols)andH7T7(opensymbols)monolayersontheaveragingtimetavandtheproberadiusRpfordierentporetypes:(a)voids,(b)oilhalf-channels,(c)waterhalf-channels,and(d)channels.Forclarity,thesymbolsareshownonlyforsomevaluesoftav. ofrelevantporestructuresintheaveragingprocess.Inordertoestimateanoptimalaveragingtime,weconsiderdynamicsofaveragedporesandmeasurefrequenciesofeventschangingthenumberofporesinthesystem.Therearefourtypesofsuchevents:porecreation,destruction,fusion,andssion.Forbrevity,wecallthemtransitionevents.Wewilldemonstrateexistenceofacross-overvaluetavoftheaveragingtimetavsuchthatfortavtavtheaveragingalsoremoveseventsthatleadtosubstantialchangesofthemonolayermicrostructure. 49

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2.5.2 ,themonolayermicrostructureonthescalemuchsmallerthanthecorrelationlengthisqualitativelysimilartothatatthepercolationthreshold.Therefore,inordertoinvestigatetheporedynamicspertinenttoaspecicvalueoftav,itisnecessarytoconneourattentiontoeventsinvolvingonlyporeswithdiametercomparabletoorlargerthanthecorrelationlength.ThecorrelationlengthisdeterminedusingtheconnectivityfunctionCf(r)denedinsection 2.5.2 .Intheanalysisoftheaveragedpores,weinvestigatethechangeoftheirpropertiesinresponsetoachangeoftheaveragingtimetav,whilekeepingtheprobesizeRpxed.Inthiscase,thepercolationorderparametercorrespondstotheaveragingtimetav.Followingargumentssimilartothosepresentedinsection 2.5.2 fortheinstantaneouspores,weconcludethatwhentavisclosetoitscriticalvaluetcav,thecorrelationlengthdivergesasanegativepowerofjtavtcavj,whiletheporedensitypcanbeapproximatedaspA00+B00jtavtcavj00;00>0. Aswiththeinstantaneouspores,theprobabilitypthatapointwithinamonolayerbelongstoanaveragedporeisposition-dependent.Thespatialaveragesp(Rp;tav)ofpcomputedforRp=0:47nmandtavrangingfrom0psto100psareshowninFig. 2-11 .Thebehaviorofp(Rp;tav)forotherconsideredproberadiiRpisqualitativelysimilar.Asexpected,p(Rp;tav)isamonotonouslydecreasingfunctionoftav,sincethetimeaveragingoverthesurfactantuctuationsreducestheavailablespacebetweenthesurfactants.ThisinparticularimpliesthattheaveragedporesobtainedwithRp0:47nmcorrespondtothesubcriticalphase(seeFig. 2-13 ). Weobserveseveralqualitativedierencesbetweenthedependenceofp(Rp;tav)ontavfortheaveragedporesandthedependenceofp(Rp;0)onRpfortheinstantaneouspores.Inthelattercase,lnp(Rp;0)decreasesatanalmostconstantrate.Moreover,p(Rp;0)inH7T7monolayerissmallerthanp(Rp;0)inH3T3monolayerforallRpduetoahighersurfactantdensityinH7T7monolayer.Incontrast,foraveragedpores,weobserveasharpdeclineofp(Rp;tav)atsmalltav(tav20ps),followedbyamoregradualdecreaseatlargertav.Theinitialfastdeclineofp(Rp;tav)isduetoremovalofthefastand 50

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2-1 andFig. 2-6 ).Therefore,averagingoverlongertimeintervalsdestroysporesinH3T3monolayermoreeectively,causingp(Rp;tav)tobesmallerinH3T3thaninH7T7monolayerforsucientlylargetavdespiteahighersurfactantdensityinthelattermonolayer. Bothofthesetrends{fastdeclineofp(Rp;tav)atsmalltavandmoreecientporedestructioninH3T3monolayeratlargetav{areconsistentwiththeobserveddependenceofp(Rp;tav)ontav,showninFig. 2-16 .Atsmalltav,thedecreaseinp(Rp;tav)ismuchfasterthanatlargertavandthedensityofvoidsandhalf-channelshasafasterdecreaserateinH3T3monolayerthaninH7T7monolayerforsucientlylargetav.TheratesofchangesofthechanneldensitiescannotbecomparedduetoanegligibledensityofaveragedchannelsinH7T7fortav10ps. Thecorrelationlengths(Rp;tav)obtainedfromtheconnectivityfunctionsCf(r;Rp;tav)areshowninFig. 2-17 .Asevidentfromexamplesoftheconnectivityfunctionsfortheaveragedpores(shownintheinsertofFig. 2-17 ),thesefunctionsarequalitativelysimilartotheconnectivityfunctionsfortheinstantaneouspores(seeFig. 2-12 )andareconsistentwiththepredictionsofthepercolationtheory.Dependenceofthecorrelationlength(Rp;tav)ontheaveragingtimetavisqualitativelysimilartothetav-dependenceofp(Rp;tav)andp(Rp;tav)discussedabove.Atsmalltav,(Rp;tav)exhibitsafastdeclinewithincreaseoftavfollowedbyamoregradualdecreaseatlargertav.ThedeclineofthecorrelationlengthatsmalltavisespeciallysteepfortheprobesizeRp=0:47nm.Aswasshowninsection 2.5.2 ,Rp=0:47nmisveryclosetothepercolationthresholdoftheinstantaneouspores.Therefore,thecorrelationlengthoftheaveragedporeswithRp=0:47nmapproachesadivergentbehaviorastav!0ps. 51

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Dependenceofthecorrelationlength(Rp;tav)ofaveragedporesinH3T3(solidsymbols)andH7T7(opensymbols)monolayersontheaveragingtimetavandtheproberadiusRp.Forclarity,thesymbolsareshownonlyforsomevaluesoftav.Insert:ExamplesofconnectivityfunctionsCf(r;tav;Rp)foraveragedporesinH3T3monolayerobtainedwithproberadiusRp=0:47nm. Theobtainedcorrelationlengthsallowustoidentifysucientlylargepores(i.e.,poreswithdiametercomparabletoorexceedingthecorrelationlength)foranalysisofthetransitionevents.Theporetransitioneventsbetweentwoconsecutivetimesteps,t1andt2=t1+tareidentiedusingthefollowingalgorithm.First,wecountthenumberNdm(t1)ofdescendantporesofeachporem(t1)atstept1andthenumberNpm(t2)ofparentporesofeachporem(t2)atstept2,m=1;2;::::Aporek(t1)issaidtobeaparentofaporem(t2)(and,correspondingly,m(t2)isadescendantofk(t1))iftheseporessharesomecommonvolume,i.e.k(t1)\m(t2)6=;.Thus,Npm(t2)=0impliescreationofanewpore,Ndk(t1)=0impliesaporedestruction,Npm(t2)>1impliesthatporem(t2)isaresultofaporefusion,andNdk(t1)>1impliesthatporek(t1)hassplitintoseveralpores. Weidentifythetransitioneventswithtimestept=1psandmeasuretheeventfrequency(i.e.numberofeventsperporeperunittime).Thefrequenciesofporecreations,destructions,fusions,andssionsaredenotedas!c,!d,!fus,and!s,respectively.ThefrequenciesofthetransitioneventsinH3T3monolayerobtainedat 52

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2-18 .TheobservedtrendsaresimilarforallconsideredprobesizesforbothH3T3andH7T7monolayers.Inallconsideredsystems,therateoftheporedensityincreaseduetoacombinedeectoftheporecreationandssioncoincideswiththerateoftheporedensitydecreaseduetoacombinedeectoftheporedestructionandfusion,asexpectedatequilibrium. Figure2-18. Frequencies!j(Rp;tav)(j=c,d,fus,ors)oftransitioneventsforporesinH3T3monolayerobtainedwithproberadiusRp=0:47nm. Atsmalltav,frequencies!j(Rp;tav)(j=c,d,fus,ors)ofthetransitioneventsdecreasesharplyduetoremovalofthefastandinsignicantevents,similarlytop(Rp;tav),p(Rp;tav),and(Rp;tav).Fortavexceedingsomecross-overvalue,tav,thefrequencies!fusand!soffusionsandssionsdecreasemoregraduallyastavincreases.Thisslowerdecaycanbeapproximatedbyanexponentiallaw, Inmostconsideredsystems,thefrequencies!cand!dofporecreationsanddestructionsincreasewithincreaseoftavabovethecross-overvaluetav.TheonlyexceptionofthistrendisobservedforRp=0.7nminH3T3monolayerwherethefastdecayof!cand!disfollowedbyaslowerdecayfortav>tav.Inthelattercase,therateofdecreaseof!cand!dfortav>tavisslowerthanthatof!fusand!s. Theobservedtav-dependenceofthefrequenciesoftransitionevents,aswellasothercharacteristics(p,p,and)oftheaveragedporessuggeststhattheoptimalaveragingtimeininvestigationsofporedynamicsisthecross-overtimetav.Inourcalculations,wedenetavasthevaluesoftavsuchthatthefusionandssionfrequenciesobeythe 53

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2{8 )fortavtav.Thusestimatedvaluestavareingoodagreementwiththecross-overvaluesoftavforotherconsideredporecharacteristics,!d,!c,p,p,and.Thevaluesoftavrangefromfromtav20psforsmallerRptotav10psforlargerRp. Thefrequencies!j(Rp;tav)oftransitionevents,aswellasdensitiesp(Rp;tav)ofporeswithdiameterscomparabletoorexceedingthecorrelationlength(Rp;tav),areshowninFig. 2-19 .Forallconsideredsystems,!j(Rp;tav)0:1events/(poreps).Therefore,aporeonaverageexperiencesanon-negligibletransitioneventatmostevery10ps.ThefrequenciesoffusionsandssionsdonotchangebymorethanafactoroftwoasRpisvariedbetween0.47and0.7nm.Incontrast,thefrequencies!cand!dofporecreationanddestructioneventsincreasebyanorderofmagnitudeastheprobesizeRpincreasesfrom0.47to0.7nm.Moreover,thesefrequenciesarehigherinH3T3monolayerwhichcontainsmoredynamicsurfactants. Figure2-19. Frequencies!j(Rp;tav)(j=c,d,fus,ors)oftransitioneventsinH3T3(solidsymbols)andH7T7(opensymbols)monolayerscorrespondingtothecross-overaveragingtimetav.Theinsetshowsdensitiesp(Rp;tav)ofporeswithdiameterscomparabletoorexceedingthecorrelationlength(Rp;tav).Thelinesareshowntoguidetheeye. 54

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TheporestatisticsisobservedtobeconsistentwithpredictionsofthepercolationtheorywiththepercolationorderparametergivenbytheproberadiusRp.Thepercolationthreshold,Rcp0:47nm,isfoundtobeveryclosetotheLJdiameterofthemodelcoarse-grainedbeadswhichimpliesthatthemonolayeralwayscontainsapercolatinginstantaneousporeaccessibletosoluteswithdiameterlessthanRcp.However,thisporeisverydynamicsince,asFig. 2-17 indicates,thecorrelationlength(Rp;tav)ofthemonolayermicrostructuresignicantlydecreasesuponaveragingoverrelativelyshorttimeintervals(tav20ps).Theporeaveragingalsopredictsthatmostchannelsconnectingthebulkoilandwaterphasesareveryunstable(seeFig. 2-16 )andthelifetimeofmostchannelsiscomparabletoorlessthan10ps.Thisimpliesthatthetransientchannelmechanismisunlikelyevenforarelativelyfasttransportofahydrophobicsolutefromwatertooilphase.Therefore,thesolutetransportmechanismisexpectedtoconsistofhopsbetweensmallervoidsandhalf-channels. Theporedynamicsisfurtherexploredforporeswithdiameterscomparabletoorlargerthanthecharacteristiclength-scaleofthemonolayermicrostructure.We 55

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56

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Inarecentstudy[ 45 ]describedinthepreviouschapter,weinvestigatedpropertiesofmodelnon-ionicsurfactantmonolayersatoil-waterinterfaces,andinparticularweinvestigatedtheinternalmicrostructureofsurfactantmonolayer.Inthischapter,weprobethefreeenergybarrierfortransportofasmallhydrophobicsoluteacrossamonolayeranddemonstratethat,inadditiontohydrophobic/hydrophilicinteractions,thebarrierheightiscontrolledbystericeectsduetoalocaldensityincreasenearthedividingsurfaceofamonolayer.Weinvestigateawiderangeofnon-ionicsolutesandsurfactantsandassestheconnectionbetweentheirphysicalproperties(suchassize,shape,hydrophobicity)andthefreeenergybarriertosolutetransportacrosstheinterface.Wealsodemonstrateexistenceofasynergisticeectofsoluteandsurfactantpropertiesonfreeenergybarriertosolutetransport. 4 ]describedinthepreviouschapter.Recallthatinthismodelinteractionsbetweentwonon-bondedbeadsaremodeledbyLennard-Jones(LJ)potentialwitheectiveLJdiameterforbothHandTbeadsLJ=0.47nm.Inordertoinvestigateeectsofsolutesizeonitstransportacrosssurfactantmonolayers,in 57

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Thesummaryoftheconsideredsolute-interfacesystemsisgiveninFig. 3-1 .Wecomparefreeenergyproleshydrophilic(H,H2),hydrophobic(T,T2)andamphiphilic(HT)solutestodeterminetheeectofsolutehydrophobicity.Eectsofsolutesizeandstructurearedeterminedbycomparisonoftransportpropertiesoftwosphericalhydrophobicsoluteswithdierentdiameters(T,T0),aswellasabranchedsolute(T5)whosestructureisshowninFig. 3-1 Solutetransportacrossthefollowinginterfacesisinvestigated:surfactant-freehexadecane-waterinterfaceandhexadecane-waterinterfacescoveredbyH3T3,H5T5,H7T7,H3T7andH7T3surfactants.H3T7andH7T3areconsideredtostudytheeectofasymmetryofsurfactants. AllMDsimulationsareperformedusingGROMACSsimulationspackage[ 33 ].Thetemperatureandpressurearekeptconstantat300Kand1bar,respectively,usingBerendsentemperatureandpressurecouplingschemes[ 34 ]withtimeconstantsof1ps.Thecompressibilityvalueforthepressurecouplingschemeis105bar1. Preparationofsurfactant-freeinterfacesandinterfacescoveredbyH3T3,H5T5andH7T7surfactantsisdescribedinthepreviouschapter.H3T7andH7T3monolayersarepreparedinamannersimilartoH7T7monolayer. Solutetransportisinvestigatedacrosssurfactantmonolayerswithasurfacecoverageof2.0molecules/nm2.Althoughthemaximumsurfacecoveragevariesfortheconsideredsurfactants,wefocusourattentionontheeectofsoluteandsurfactantpropertiesonthebarrierand,therefore,considerthesamesurfacecoverageforallmonolayers.Asasidenote,weobservethatthecoarse-grainedmodelslightlyoverestimatesthesurfacecoverage.TheclosestsystemsforwhichtheexperimentaldataareavailableareC12EO2, 58

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Summaryofsurfactant-solutesystemsconsideredinthiswork.Therowsofthetablecorrespondtodierenttypesofsurfactantscoveringhexadecane-waterinterfaceandthecolumnscorrespondtosolutes.Theconsideredinterface-solutesystemscorrespondtoshadedareas C12EO3,C12EO4,C12EO8andC16EO8monolayersathexadecane-waterinterfaces[ 36 ].Theexperimentallyobtainedmaximuminterfacialcoveragesofthesemonolayersrangefrom1.59molecules/nm2forC12EO8to2.0molecules/nm2forC12EO3. 3.3.1EectofSurfactantLength Densityproleofthesurfactant-freehexadecane-waterinterfaceisshowninFig. 3-2 aandindicatesthatthedividingsurfacecorrespondstoaminimumofthetotaldensitycausedbydewettingduetohydrophobicrepulsionofoilandwater.Similardensityminimumatthewater/decaneinterfacewasobservedinatomisticMDsimulationsperformedbyPateletal.[ 46 ].Densityproleatthehexadecane-waterinterfacecoveredbyH3T3surfactantsisshowninFig. 3-2 bandisqualitativelysimilartodensityprolesofotherconsideredsurfactantmonolayersshowninFig. 3-2 c,d,e,andf. 59

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DensityprolesofA)surfactant-freehexadecane-waterinterfaceandhexadecane-waterinterfacecoveredbyB)H3T3,C)H5T5,D)H7T7,E)H3T7,andF)H7T3monolayer. 60

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3-3 .Thebondsclosesttothedividingsurfacetendtoorientthemselvesinthenormaldirectioninordertoreducetheinteractionbetweenthehydrophilicandhydrophobicbeads.Asthedistancebetweenabondandthedividingsurfaceincreases,contactbetweenthebeadsconnectedbythisbondandthebeadsontheoppositesideofthedividingsurfacebecomesnegligible.Thissignicantlyrelaxestheenthalpicconstraintsonthebondorientationandthustheentropiccontributiontothefreeenergybecomesmoresignicant.Theentropicforcecausesthesurfactantstocoilupevenatexpenseofalocaldensityincrease.Forlongersurfactants,theentropicforceislargerandiscapableofovercominglargerenthalpicrepulsionsbetweenthebeadscausinghigherlocalsurfactantdensity.Theseargumentsareconrmedbythesurfactantdensityprolessurf(x)inH3T3,H5T5,andH7T7monolayersshowninFig. 3-4 a.Asthesurfactantlengthincreases,boththesurfactantdensityatthemaximumofsurfandthewidthofthehighdensityregionincrease. Thetotaldensitywithinthemonolayerisfurtherincreasedduetopenetrationofsolventmoleculesintothemonolayer.ThesolventdensityprolessolvforthethreeconsideredmonolayersareshowninFig. 3-4 b.Thedensityofwaterinthehead-groupregionishigherthanthedensityofhexadecaneinthetail-groupregion,sincethesmallerwatermoleculesareabletopenetratethespacebetweensurfactantmoleculesmore 61

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(a)Averageshcosjiand(b)standarddeviations(cosj)oftheorientationscosjofthesurfactantbondswithrespecttothemonolayernormalforH3T3,H5T5,andH7T7monolayers. eectivelythanthebulkierhexadecanemolecules.Thisleadstoalargertotaldensitymaximuminthehead-groupregionthaninthetail-groupregion,seeFig. 3-4 c.Thedensityofthesolventinsidethemonolayerdecreaseswithincreaseofthesurfactantlengthsincethelargerdensityoflongersurfactantsprovidesalargerbarrierforthesolventpenetrationintothemonolayer.However,themaximaofthetotaldensityofmonolayers,=surf+solv,stillincreasewiththesurfactantlengthsincetheincreaseinthesurfactantdensitysurfismoresubstantialthanthedecreaseinthesolventdensitysolv. Figure3-4. ComparisonofdensityprolesofH3T3,H5T5,andH7T7monolayersfor(a)surfactantdensitysurf,(b)solventdensitysolv,and(c)totaldensity. 62

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Theinhomogeneityoftheinterfacialdensityplaysasignicantroleinprovidingafreeenergybarrierformasstransferacrosstheinterfaces.Toillustratethis,considerthetransportofasmallhydrophobicsolutemodeledbyasinglehydrophobicbeadT.Thismodelcorrespondstoacoarse-grainedrepresentationofbutane. ThefreeenergyG(x0)ofthesystemwhenthesoluteislocatedatdistancex=x0correspondstothepotentialofmeanforceactingonthesoluteandisobtainedbyaseriesofconstrainedsimulations[ 19 47 ].ThemeanforcehFxirequiredtoconstrainthesoluteintheplanex=x0is Theinitialconditionsforsimulationswiththesoluteconstrainedatvariouspositionsxjaregeneratedbyintroducingthesoluteintothewaterphaseandthenpullingitacrossthemonolayerbyapplyinganarticialforceontheparticle.Foreachxj,thesoluteisconstrainedatx=xjusingtheSHAKEalgorithm[ 48 ]andthesystemisequilibratedfor10nsbeforea390nsproductionrun. Thefreeenergyprolesobtainedforthesoluteatthesurfactant-freehexadecane-waterinterfaceandattheinterfacescoveredbytheH3T3,H5T5,H7T7,H3T7andH7T3surfactantsareshowninFig. 3-5 .Thefreeenergyofthesolutepartitioningbetweenthehexadecaneandwaterphasesiscomputedtobe22kJ/mol.Thisenergyisexpectedtobe 63

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49 ]ofthelatterfreeenergyis21.0kJ/molandthevaluecomputedusingthesamecoarse-grainedmolecularmodelandadierentcomputationalapproach[ 4 ]is22:52kJ/mol. (a)Freeenergyprolesfortransportofsphericalhydrophobicsoluteacrossthesurfactant-freehexadecane-waterinterfaceandthehexadecane-waterinterfacescoveredbyH3T3,H5T5,H7T7,H3T7andH7T3surfactantmonolayers.Forclaritytheerrorbarshavebeenomitted(b)Totallocaldensitiesofthecorrespondinginterfaces. Forthesurfactant-freeinterface,theresistancetothesolutetransportfromhexadecanetowaterismostlyduetothedierencebetweenthesolutefreeenergiesinthesesolvents.Thereisasmalladditionalincrease(1kJ/mol)ofthefreeenergybarrier,whicharisesduetoaminimumoffreeenergyattheinterfacecenter.Thelattercorrespondstotheminimumofthetotaldensitycausedbydewettingattheoil-waterinterface(seeFig. 3-2 a). 64

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3-4 c)and(ii)interactionsofthehydrophobicsolutewiththehydrophobicbeadsinthetailregionaremorefavorablethantherepulsiveinteractionswiththehydrophilicbeadsinthehead-groupregion,whichleadstoanalmostnegligibleresistancetothesolutetransportthroughthedenserpartofthetail-groupregion.Similarlytothesurfactant-freeinterface,thesurfactantmonolayercontainsasmallfreeenergyminimumatthedividingsurfaceand,sincethedensitydropatthemonolayerdividingsurfaceissmallerthanatthesurfactant-freeinterface,thefreeenergyminimumisalsomoreshallowatthesurfactantmonolayer. WenotethatthefreeenergybarrierinheadgroupregionofasymmetricsurfactantH3T7andH7T3closelymatchesthebarrierinheadgroupregionofH3T3andH7T7respectivelyduetosimilaritiesdensityprolesintheheadgroupregionsofthesesurfactants.DuetosimilarreasontheenergybarrierintailregionsofH3T7andH7T3matchesthebarrierintailregionofH7T7andH3T3. Insummary,locationsoftheminimaandmaximaofthefreeenergyG(x)correlatewellwiththoseofthetotaldensity(x),whichsuggeststhatasignicantcontributiontothefreeenergybarrierisduetostericinteractionsbetweenthesoluteononehandandthesolventsandthesurfactantsontheother.Forcomparison,recentcomputationalstudies[ 50 ]ofsolubilizationofoilymoleculesinmicellesdemonstratedabsenceofalocalfreeenergymaximuminthemicellarhead-groupregion.Thisndingisconsistentwithasmallerlocaldensityinthemicellarhead-groupregionthaninthehead-groupregionofa 65

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Sincethedensitymaximumisrelativelyclosetotheinterface,thesolutelocatedatthismaximumwouldbewithintheinteractionrangeofoneormorehydrophobicbeads.Thisattractiveinteractionsomewhatreducestheenergypenaltyimposedbythestericrepulsion.Asthesolutemovesfurtherintothehydrophilicphase,itbecomessurroundedexclusivelybyhydrophilicbeadsand,eventhoughthedensityaroundthesolutedecreases,therepulsivehydrophobicinteractionsaddanenergypenalty.Themaximumofthefreeenergycorrespondstothemaximumofthetotalofthestericandhydrophobicrepulsionforcesandisthereforesomewhatshiftedtowardsthewaterphase.Sincethehydrophobicrepulsionisnearlyindependentofthesurfactantlength2n,thetotalfreeenergybarrierGdoesnotgrowasfastwithincreaseofnasitsstericcomponentcapturedbythetotaldensity. Similareectsleadstoashiftinthelocationofthefreeenergyminimumtowardstheoilphase,ascomparedtothelocationofthecorrespondingdensityminimum,seeFigures 3-4 cand 3-5 .Thestericrepulsionpushesthesolutetowardsthedensityminimumandawayfromthedensitymaximumintheoilphase.Ontheotherhand,thesolutelocatedatthemonolayerdividingsurface(whichcoincideswiththedensityminimum)willexperienceastrongrepulsionfromthehydrophilicbeadswhichwillpushthesolutetowardstheoilphase.Therefore,theminimumofthefreeenergyisshiftedtowardstheoilphaseandcorrespondstoabalancebetweenthesetwocompetingforces. Finally,stericrepulsionatthedensitymaximuminthehydrophobicphaseisnearlycounterbalancedbyhydrophobicattractionbetweenthesoluteandthetailandoilbeadsleadingtoarelativelysmalllocalfreeenergymaximumintheoilphase. 3-6 comparesthefreeenergyproleforhydrophilicsolutes(H,H2),hydrophobicsolutes(T,T2)andamphiphilicdimer(HT)acrossH7T7monolayer.Thetotalfreeenergy 66

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Forhydrophilicsolutes,afreeenergybarrierisobservedinthetailregion(1kJ/mol)whichissmallerthanthecorrespondingfreeenergybarrierforTintheheadgroupregion(6kJ/mol).Thisisconsistentwiththefactthatdensitymaximumislessprominentinthetailregionthanintheheadgroupregion.Forthesamereason,thefreeenergybarrierforH2inthetailregion(2kJ/mol)issmallerthanfreeenergybarrierforT2intheheadgroupregion(10kJ/mol). Intheheadgroupregion,agradualdecreaseinthefreeenergyisobservedforhydrophilicsolutes.Thegradualchangeintheheadgroupregioniscausedbytheunfavorablestericrepulsionduetodensitymaximumintheheadgroupregion.Thedensitymaximumintheheadgroupregionincreasesthefreeenergyofsolutewithrespecttowaterphase.Asimilarbutsmallergradualchangeinfreeenergyisobservedforhydrophobicsoluteinthetailregion. Next,weconsiderorientationofdimersnearthecenterofmonolayerandmeasuretheanglebetweenthedimerbondandthemonolayernormal.Foramphiphilicdimer,is00withsoluteorientedindirectionofmonolayernormalwithhydrophilicbeadtowardswaterphaseandhydrophobicbeadtowardshexadecanephaseandis1800forbeadsorientedinoppositedirection.Forhydrophilicandhydrophobicdimers=00and=1800areequivalentduetosymmetricnatureofthesolutes. Fig. 3-7 showsthedistributionoftheseanglesatvedierentpositionsneartheinterfaceforamphiphilic,hydrophobicandhydrophilicdimer.Fig. 3-7 ashowsthatneartheinterfacetheamphiphilepreferstoorientwithhydrophilicbeadtowardswaterphaseandhydrophobicbeadtowardshexadecanephase.Thisleadstoloweringoffreeenergy 67

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(a)Freeenergyprolesfortransportofsphericalhydrophobicsolute(T),sphericalhydrophilicsolute(H),hydrophobicdimer(T2),hydrophilicdimer(H2)andamphiphilicdimer(HT)acrosshexadecane-waterinterfacescoveredbyH7T7surfactantmonolayers.(b)Totallocaldensityofthecorrespondinginterface. attheinterface(seeFig. 3-6 ).Theamphiphileisorientedrandomlyinthebulkphases.Similarly,thehydrophobicandhydrophilicdimersareorientedrandomlyinthebulkphases(Fig. 3-7 bandc).Whenthecenterofmassofthesedimersliesonthedividingsurfacethesedimersprefertoorientindirectionperpendiculartomonolayernormalwhileclosetotheinterfacedimersaremorelikelytoorientindirectionofthemonolayernormal.Atthedividingsurfacethesoluteisabletomaximizeitsinteractionwithlikephaseparticlesbylyingonthedividingsurface.Ontheotherhand,closetothedividingsurfaceitisfavorableforthedimertoorientindirectionnormaltointerfaceduetoinuenceofsurroundingsurfactant. 68

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Distributionoforientationangleof(a)amphiphilicdimer(b)hydrophobicdimer(c)hydrophilicdimeratvedierentpositionsnearthedividingsurfaceofH7T7monolayer 3-8 ashowsthefreeenergyproleforsoluteT0inH3T3,H7T7monolayerandforsoluteTinH7T7monolayer.ThefreeenergybarrierinheadgroupregionforT0inH3T3monolayerandTinH7T7monolayeris3kJ/moland6kJ/molrespectively.ThefreeenergybarrierinheadgroupregionforT0inH7T7monolayeris20kJ/molwhichisgreaterthanthesumoffreeenergybarriersobservedinprevioustwocases.Thisillustratesthatlargesoluteandlongersurfactantssynergisticallyincreasefreeenergy 69

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SimilarsynergisticeectisseenfortransportofT5.ThefreeenergybarrierfortransportofT5inH7T7monolayeris20kJ/mol(seeFig. 3-9 )whichisgreaterthanthesumoffreeenergybarriersfortransportofabranchedhydrophobicsoluteinH3T3monolayer(3kJ/mol)andsphericalsoluteinH7T7monolayer(6kJ/mol).Simultaneousincreaseofsurfactantlengthandsolutesizeleadstohigherincreaseinfreeenergybarrier. (a)FreeenergyprolesforTinH7T7monolayer,T0inH3T3andH7T7monolayersshowingsynergisticeect;(b)Totallocaldensityofthecorrespondinginterface. 70

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(a)FreeenergyprolesforTinH7T7andT5inH3T3andH7T7monolayersshowingsynergisticeect;(b)Totallocaldensityofthecorrespondinginterface. alocalincreaseofthedensityinsidethemonolayer.Thelocaldensityincreaseislargerformonolayerscomposedoflongersurfactantsduetoentropicforcesnearthemonolayerdividingsurface.Tomaketheseobservationsmorequantitative,considerrelationshipbetweenthefreeenergybarrierGandtheexcessdensityinthemonolayerhead-groupregion.Boththeexcessdensityandtheheightofthefreeenergybarrieraremeasuredwithrespecttothecorrespondingquantitiesinbulkwater,i.e.(x)=(x)wandG=GmaxGw,whereGmaxisthemaximumvalueofthefreeenergyandsubscriptwreferstoquantitiescorrespondingtobulkwater.Denetheexcessdensityregionasaninterval[xe1;xe2]withinwhichthetotaldensity(x)atleast2%higherthanthebulkwaterdensityw.Theexcessdensitycanbecharacterizedbythewidthoftheexcessdensityregion, themaximumoftheexcessdensity, maxmaxx2[xe1;xe2](x);(3{3) 71

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TZxe2xe1(x)dx:(3{4) Thesequantities,aswellasthefreeenergybarrierheightsarelistedinTable 3-1 forHnTnsurfactants(n=3;5;7).Itisclearthatallofthesequantitiesincreaseasthesurfactantlengthincreases.However,theratesofchangeofW(n),max(n),T(n),andG(n)withnaredierentfromeachother. Tocomparetheserates,weassumealineardependencebetweenrelativechangesofthesequantitiesonn, andestimatethegrowthratesk.Thelineardependence( 3{5 )isassumedforconvenienceofcomparisonoftheratesandmostlikelythedependenceofY(n)onnismorecomplex.Despitethis,theresultsoftheratecomparisondiscussedbelowaresucientlyrobustandonewouldreachthesameconclusionsiftheratecomparisonwasbasedonadierentassumptionregardingthefunctionalform(e.g.,apowerlaw)ofdependenceofY(n)onn. TheestimatedgrowthrateskarelistedinthelastrowofTable 3-1 .TheheightofthefreeenergybarrierGgrowsfasterthanboththeheightmaxandwidthWoftheexcessdensityregion,reectingthecumulativeeectofWandmaxincreatingthestericbarrier.ContributionsofbothWandmaxtothestericeectsarecapturedbythetotalexcessdensityT.WeobservethatthefreeenergybarrierGdoesnotincreaseasfastasTduetoareductionofthestericbarrierbythehydrophobic/hydrophilicinteractions. ComparisonofFig. 3-4 candFig. 3-5 ,showsthatthemaximumoffreeenergyisshiftedfurtherintothewaterphasethanthemaximumofthetotaldensity.Thisshiftoccursduetocompetitionbetweenthestericandhydrophobiceects. Thefreeenergyproleofamphiphilicdimerhasaminimumneartheinterfacesinceneartheinterfaceitorientswithitslikebeadsinlikephases.Thefreeenergy 72

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ComparisonofthefreeenergybarrierheightGwithparameterscharacterizingtheexcessdensity:widthWoftheexcessdensityregion,maximummaxoftheexcessdensity,andthetotalexcessdensity,T.Thelastrowshowsthegrowthratesk,seeEq.( 3{5 ). Surfactant max,bead/nm3 H3T3 0.80 0.53 2.56 H5T5 1.09 1.24 4.36 H7T7 1.41 2.26 7.75 0.19 0.82 0.51 barrierforamphiphilicsoluteislargerinheadgroupregionthanintailregionsincethedensitymaximuminheadgroupregionismoreprominent.Similarly,thehydrophilicandhydrophobicdimersexperiencegreaterstericrepulsionintheheadgroupregionthanintailregion.Increaseinsolutesize,leadstolargerbarrierduetoincreasedstericrepulsion.Simultaneousincreaseofsolutesizeandsurfactantlengthleadstogreaterincreaseinfreeenergybarrierthanthesumoffreeenergybarrierduetothesefactorsalone. 73

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6 { 9 ].Moleculartransportacrossaninterfaceoftwoimmiscibleuidsisasubjectofactiveexperimental[ 51 { 54 ],computational[ 46 55 { 63 ],andtheoretical[ 64 { 66 ]studies. Itmayseemintuitivethattransportofasimplesolute,suchasasphericalmoleculeoranion,canbereducedtodynamicsofasingledegreeoffreedom,namelythedistancezbetweenthesoluteandtheinterface.Inthiscase,theroleofthesolventsinthesolutetransportwouldreducetothatof(i)meanforceF(z)whichdependsonlyonzandactsonthesoluteasittraversestheinterfaceand(ii)thermalcollisionsbetweenthesoluteandsolventmoleculesresultinginaMarkovianrandomforceactingonthesolute.However,startingwiththepioneeringworkofBenjaminandco-workers[ 55 57 ],ithasbecomeapparentthat,atleastinthecaseofaniontransportacrossauid-uidinterface,solventsactivelyparticipateinthetransportprocessandtheirrolecannotbereducedtothatofthemeanforceF(z)andthethermalnoise.Moleculardynamics(MD)simulations[ 55 57 ]ofaniontransferacrossawater/1,2-dichloroethaneinterfacedemonstratedformationofshort-lived(withlife-timeontheorderoftensofpicoseconds)capillaryngersofsolventprotrudingtowardsthesolutewhenthelatterislocatedclosetothedividingsurface.TheformationofsuchprotrusionsduringtransportofanionacrossaninterfacebetweenwaterandanotherliquidhasbeenconrmedbyMDsimulationsformultipleion-solventsystems[ 61 { 63 67 { 69 ].Evidenceofimportanceofcapillarywavesinthetransportacrossaninterfacehasalsobeenobservedexperimentally[ 52 ]. 74

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64 ],theiontransportacrossaninterfaceisassumedtobeinitiatedbyasolutecapturebyaninterfaceprotrusionandproceedthoughasequenceofactivatedexchangesofmoleculesinsidethesolutesolvationshell.Kornyshevetal.[ 65 ]extendedthisideaandproposedamodelwhich,inadditiontoeectsoftheuctuation-inducedinterfaceprotrusiononthesolutetransport,capturesthefeedbackeectofthesoluteintheprotrusionformation.Inthismodelthecoupledsolute-surfacedynamicsfortheinterfaceisdescribedbyadegreeoffreedom,namelyheightofprotrusionandotherdegreesoffreedomareneglected.Despitethisapproximation,itallowsonetoqualitativelyassesseectsofthecoupledsurface-solutedynamicsonthesolutetransport.Itisdemonstratedthat,inthecaseofarelativelysmallenergybarrierfortransportacrosstheinterface,thecapillaryuctuationsslowdownthesolutetransport.AfurtherextensionofthismodelwhichexplicitlyaccountsforallmodesoftheinterfaceuctuationswasproposedbyDaikhinetal.[ 66 ].Sincethemainfocusofthelatterworkwastoassesstheinterfaceuctuationsinthepresenceofions,theauthorsdidnotpresentestimatesoftheiontransportratebasedonthisimprovedmodel. Theaboveobservationsandmodelsforthecoupledsolute-interfacedynamicsweremadeforachargedsoluteinasystemcontainingatleastonepolarorelectrolytesolvent.Inthecurrentchapter,wedemonstratethatthesolutetransportmaybecoupledtotheinterfaceuctuationsevenintheabsenceoflong-rangeelectrostaticinteractions.Weusecoarse-grainedMDsimulationstoinvestigatetransportofasmallnon-ionicsoluteacross(i)anoil-waterinterfaceand(ii)amonolayerofnon-ionicsurfactantsadsorbedatanoil-waterinterface.Inbothconsideredsystems,thesolute-interfacecouplingleadstolocallynon-Markovianstochasticforceactingonthesolute.Thecorrelationtimeofthestochasticforcesignicantlyincreases(byasmuchastwoordersofmagnitude)whenthesoluteislocatednearafreeenergybarrierorintheregioncorrespondingtoalargefreeenergygradient.Therefore,detailedunderstandingoftheoriginoftheposition 75

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66 ].Finally,wediscusseectsofthiscouplingonthesolutetransportrateanddiscussimplicationsoftheslowuctuationsontheanalysisofMDsimulationsofinterfacialsystems. 4 ]discussedinchapter2.TheMDsimulationsareperformedusingtheGROMACSpackage[ 33 ].Verletintegrationschemeisusedwithatimestepof0.04ps.Thetemperatureandpressurearekeptconstantat300Kand1bar.Unlessstatedotherwise,weuseBerendsentemperatureandisotropicpressurecouplingschemes[ 34 ]withtimeconstant1psandcompressibility105bar1inthepressurecouplingscheme. Thesimulationsareperformedinacubiccellwithasideof10nm.Weconsiderasurfactant-freehexadecane-waterandahexadecane-waterinterfacecoveredbyH3T3monolayer.Theinterfacesarepreparedbysimulationsofself-assemblyofmixturesofoil,water,andifapplicable,surfactantmoleculeswithnearlyequalmassfractionsofoilandwater,asdescribedinchapter2.Inwhatfollows,wewillfocusononeoftheseinterfaces.Thesystemofcoordinatesisorientedsothatthezaxisisnormaltotheinterface,thepositivedirectionofthez-axispointstothewaterphase,andz=0nmcorrespondstothedividingsurfaceoftheinterface. Thedenitionofthedividingsurfaceusedinthischapterisdierentfromthatusedinchapters2and3.Themodicationofthedenitionisnecessarytoanalyzethesurface 76

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70 ].Foreachwaterbead,wedeneapivotpointasalocationofanoilbeadclosesttoit.Thesurfacedenedbythesepointsisreferedtoastheoilsurface.Similarly,wedenepivotpointsofthewatersurfaceasacollectionofwaterbeadsclosesttooilbeads.Propertiesoftheoilandwatersurfacesrelevantinthecurrentstudyarethesame.Therefore,inwhatfollowswereportresultsobtainedforthewatersurface.Forthesurfactant-coveredinterfaces,thepivotpointscorrespondtomid-pointsofbondsconnectingthetail-andhead-groupsofsurfactantmolecules. Inwhatfollows,wewillneedtoanalyzecontinuousapproximationstoandFouriertransformsoftheinstantaneousdividingsurfaces.TheinstantaneousFourierharmonics^hk(t)correspondingtothewavevectorkareobtainedbyaleastsquarestoftheinstantaneousdividingsurfacetotruncatedFourierseries, where isthecontinuousinstantaneousdividingsurfacecongurationdenedbythepivotpoints.InEq.( 4{2 ),Aistheareaofanunperturbedinterfaceandkcut=2nm1isthecut-owavelengthwhichapproximatelycorrespondstotwodiametersofthecoarse-grainedbeads. Despitearelativelysmallsimulationcellsize,theinstantaneousdividingsurfacez=h(x;y)canbeadequatelymodeledbyamacroscopicmodel.Todemonstratethis,weconsideraveragemagnitudeofthermaluctuationsoftheoil-waterinterface.Assumingthattheinterfacialuctuationsaresucientlysmall,thecontributionofsurfacetensionto 77

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whereistheinterfacialtensioncoecient.Fromtheequipartitiontheorem,themagnitudeofuctuationsofeachmodeis[ 71 ] k2;(4{4) wherekBisBoltzmann'sconstantandTisthetemperatureofthesystem. Themagnitudeoftheuctuationsofthesurfacemodes(Fig. 4-1 )showsthatforkupto3nm1,thevarianceof^hkscalesask1:8whichisingoodagreementwiththetheoreticalscalingEq. 4{4 .TheinterfacialtensionobtainedfromEq.( 4{4 )is46.3mN/m.Forcomparison,theinterfacialtensionobtainedfromthedierencebetweenthelateralandnormalcomponentsofthestresstensoris44.6mN/m(seechapter2)andtheexperimentallymeasuredinterfacialtensionforthissystemis49mN/m[ 39 ].Hence,theMDsimulationsareabletocorrectlycapturethehydrodynamicuctuationsinthesystem. Figure4-1. Magnitudeofuctuationsofmodes^hkoftheoil-waterinterface. 78

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Inthisequation,zisthedistanceofthesolutefromtheinterface,misthemassofthesolute,G(z)isthefreeenergyorthepotentialofmeanforce,(t;z)isthememoryfrictionkernel,(t;z)istherandomforcewithGaussiandistributionandzeromean.TheautocorrelationC(t;z)of(t;z)isrelatedtothefrictionkernel(t;z)bytheuctuation-dissipationtheorem[ 19 47 72 ], ThegradientofthefreeenergyG0(z)andthefrictionkernelcanbeobtainedusingconstrainedsimulations[ 19 47 ].ThecalculationsofG0(z)aredescribedinchapter3.Inthischapter,wefocusonanalysisoftherandomforceactingonthesolute,whichcorrespondstodeviationsoftheconstrainingforceFzfromitsmean, (t;z)=Fz(t;z)hFz(z)i:(4{7) Time-scaleofuctuationsof(t;z)isextremelysensitivetothedistancezbetweenthesoluteandthedividingsurface,ascanbeseenfromexamplesoftheforceautocorrelationfunctionsC(t;z)showninFig. 4-2 .Theforceuctuationshavelongcorrelationtimeatz=0:59nmwhileattheothertwopositionsthecorrelationtimeisveryshort.InordertoconrmthattheobservedlargecorrelationtimesoftherandomforcerepresentarealphysicalphenomenonandarenotduetoanartifactoftheMDconstrainingmethodsforthetemperature,pressure,orsolute,weperformadditionalsimulationswith(1)weakBerendsentemperatureandpressurecoupling(timeconstant100ps)and(2)Nose-Hooverthermostat[ 73 74 ]withtimeconstant1psandParrinello-Rahmanbarostat[ 75 76 ]withtimeconstant5ps,and(3)constraintonthesolutepositionimplementedviaassignment 79

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Figure4-2. AutocorrelationfunctionsC(t;z)oftherandomforce(t;z)actingonthesolutenearthesurfactant-freeoil-waterinterface.Thedistancebetweenthesoluteandthedividingsurfaceisconstrainedat(a)z=1:06nm(solidline),(b)z=0:59nm(dashedline),and(c)z=1:75nm(dash-dottedline).TheinsetshowsamagniedplotofC(t;z)forsmallt. Fig. 4-2 indicatesthat,afterfastinitialoscillations(fort2ps),thedecayoftheforceautocorrelationfunctionsfollowseitherasingleexponentialoradoubleexponentiallaw, dependingonthesolutelocation.Thefastdecaytime,1,isalwayssmall(15ps),whereastheslowdecaytime,2,isextremelysensitivetothesolutelocation,ascanbeseenfromFig. 4-3 a.Inthisgureweplotf(z)whichisdenedas1(z)ifEq. 4{8 holdsand2(z)ifEq. 4{9 holds.Thedecaytimefvariesbytwoordersofmagnitudeinanarrowregionneartheinterface.ThecorrespondingfreeenergyprolesareshowninFig. 4-3 b.Itisclearthattheslowdecaytimescorrespondstoafreeenergybarrierregion 80

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Figure4-3. (a)Correlationtimef(z)oftheslowestuctuationsoftherandomforce(z;t)actingonthesoluteconstrainedatdistancezawayfromthedividingsurfacesofthesurfactant-freeinterfaceandtheH3T3monolayer;(b)Correspondingfreeenergyproles. Theuctuationsoftheforceactingonthesolutearedirectlyrelatedtouctuationsofthesolventand,ifapplicable,surfactantdensitynearthesolute.Thefastdensityuctuationscorrespondtodiusivemotionofindividualparticles,whereastheslowdensityuctuationscorrespondtocapillarywavesattheinterface.Wenotethattheslow 81

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Inpart,thisasymmetryoftheforceuctuationtime-scalesisexplainedbyanattractiveinteractionbetweenthesoluteandthehydrophobicphase.EectsofthisattractiveforceareillustratedinFig. 4-4 whichshowsaverageddividingsurfacesinsystemswiththesoluteconstrainedneartheinterface.Forthepurposesofthisaveraging,thesolutewasconstrainedinalldirections,notonlyinz-directionasbefore,thesolutecoordinatesaredenotedasrs.Aswillbediscussedbelow,thedataobtainedfromMDsimulationswithsoluteconstrainedinalldirectionsarenecessarytocorrectlymodelthesolute-interfaceinteractions. Whenthesoluteislocatedonthewater-richsideoftheinterfaceandissucientlyclosetothedividingsurface,theattractionbetweenthesoluteandhydrophobicbeadslocatedontheoppositesideoftheinterfaceleadstoformationofaprotrusionoftheinterfacetowardsthesolute.Fig. 4-4 indicatesthattheprotrusionmaybecreatedbyoneofthefollowingtwomechanisms: 1. Presenceofthesoluteinthewater-richregioncausestheinterfacetocurvetowardsthesoluteduetoattractionofthesolutetowardshydrophobicbeads. 2. Amonolayerofhydrophobicbeads\wets"thesolutelocatedwithinafractionofitsLJdiameterfromthedividingsurface. Adetailedexplanationoftheroleoftheprotrusionsintheasymmetryoftheforcecorrelationtimesispresentedinthenextsection. 82

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Equilibriumdividingsurfacesheq(r;rs)correspondingtosoluteconstrainedatdierentpositionsrs.DividingsurfacesofH3T3monolayerandthesurfactant-freeoil-waterinterfaceareshownbysolidanddashedlines,respectively.Surfacesstronglyperturbedduetothepresenceofthesoluteareshownbygraylines.Linelabeled1correspondstothehydrophobicprotrusion\pulled"bythesolutelocatedinthehydrophilicphase.Line2correspondstoprotrusionformedduetowettingofthesolutebyamonolayerofhydrophobicmolecules. actingonthesoluteandtheinterface.TheusualcalculationbasedontheconstrainedMDsimulationsyieldstheforceactingonthesoluteaveragedoverallpossibleinterfacecongurations, anddoesnotprovideanyinformationregardingdependenceofG(rs;f^hkg)ontheinterfacemodesorthestochasticforcesactingontheinterfacemodes. Nevertheless,mostofthismissinginformationcanbeobtainedfromanadditionalanalysisoftheconstrainedsimulations.Considerthesurfacemodedynamicswhenthesoluteisconstrainedatrs.Weobservethat,whenthesoluteisconstrained,theautocorrelationfunctionsoftheinterfaceFouriermodescanbeapproximatedby 83

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Hereandbelow denotesadeviationofaninterfacemodes^hkfromitsequilibriumvalue^h(eq)k(rs).Inaddition,wewillalwaysconsiderinterfacemodescorrespondingtonon-zerowavevectorkandfromnowonwillnotwriteexplicitlythatk6=0. Eq.( 4{11 )impliesthatallk(t)correspondtoindependentOrnstein-Uhlenbeckprocesses[ 77 ],i.e. where Dk>0;k=kk>0:(4{14) Thefrictioncoecientkandthestochasticforcek(t)satisfytheuctuation-dissipationtheorem, Thedeterministiccomponentintheright-handsideofEq.( 4{13 )correspondstothenegativederivativeofG(rs;f^hkg)withrespectto^hk,whichimpliesthat 2Xk6=0k(rs)^hk^h(eq)k(rs)2;(4{16) whereG0(rs)isindependentoftheinterfaceshape.ItfollowsthattheinterfacedynamicsisdescribedbyEq.( 4{13 )evenwhenthesoluteisnotconstrained. ThesolutedynamicsisthendescribedbythefollowingLangevinequation: 2r"Xk6=0k(rs)^hk^h(eq)k(rs)2#+s(t);(4{17) 84

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whereIisa33identitymatrix. Thesecondtermoftheright-handsideofEq.( 4{17 )representscontributionoftheinterfaceuctuationstotheforceactingonthesolute.Thiscontributionwillbesignicantifk(rs)or^h(eq)k(rs)exhibitstrongdependenceonrsforsomek.Thetime-scaleoftheforceuctuationswillthenbedeterminedbythetime-scalesk(rs)ofthecorrespondinginterfacemodes.Atypicaldependenceof^h(eq)k,k,andkonzisshowninFig. 4-5 .Ascanbeseen,kandkareessentiallyindependentofthesolutepositionsinceadominantcontributiontotheinterfaceuctuationsisduetothesurfacetensionandbendingmodulusofamembraneandthesolutecontributionisrathersmall.Ontheotherhand,^h(eq)kexhibitsstrongdependenceonthesolutepositionduetoprotrusionsformedattheinterfaceinthepresenceofthesolute. B C Dependenceof(a)^h(eq)k,(b)k,and(c)konthedistancezbetweenthesoluteandthedividingsurface.Thesoluteisconstrainedinalldirectionsandthemagnitudeofwavevectorkis0.64nm1. Therefore,theprotrusionsplayakeyroleinthesolute-surfacecoupling.Moreover,Fig. 4-5 ademonstratesthatthegradientof^h(eq)kismuchlargeronthewatersideofthe 85

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4{17 )thenimpliesthatthecontributionsoftheinterfaceuctuationstothesolutedynamicsissignicantonlyonthewatersideoftheinterface,whichisconsistentwiththeobservationthattherandomforceuctuationsareslowonlyononesideoftheinterface(seeprevioussection). 4{13 ),( 4{17 )forthecoupledsolute-interfacedynamicsaresimilartothemodelproposedbyDaikhinetal.[ 65 ]forcouplingbetweenanionandanelectrolyteinterface.Inthecurrentwork,wedemonstratedthatthismodelcanbeappliedtonon-ionicuid-uidandsurfactantinterfaces.Moreover,thismodelisdirectlyveriedbyanditsparametersareobtainedfromMDsimulations,whichenablesquantitativepredictionsofthesolutetransportrates. Inconclusion,wediscussanimpactofthesolute-interfacecouplingonanalysisofconstrainedsimulationsandpredictionofthesolutetransportrate.First,notethatevenifthiscouplingisneglectedintheanalysisoftheconstrainedsimulations,onecanstillcorrectlyinfertheenergeticsofthesystem.ThisfollowsfromEqs.( 4{10 )and( 4{17 )whichimplythatthemeanforceF(rs)actingonthesoluteinconstrainedsimulationsis Inthederivationofthisequationweusedthefollowingequalities: k;rk Sincek(rs)areindependentofthesolutelocationrs,weconcludethattheconstrainedsimulationsyieldcorrect(uptoanadditiveconstant)potentialofmeanforceG(rs)actingonthesolute.Theadditiveconstantisproportionaltothesumintheright-handsideofEq.( 4{19 ).Thissumisnitebecauseofnaturalcut-ovaluesfor 86

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Ontheotherhand,onehastobecarefulininterpretationofthedynamicalpropertiesobtainedfromconstrainedMDsimulations.Intheanalysisoftherandomforceactingonthesolute,itisnecessarytoidentifyindividualcontributionsoftheMarkovianthermalforceandtheinterfaceuctuationstothesolutedynamicsinordertocorrectlypredictthesolutetransportratesfromsolutionofEqs.( 4{13 )and( 4{17 ).Moreover,todeterminecorrectenergeticsanddynamicalparametersofthesystem,itisnecessarytoconstrainallsolutedegreesoffreedominMDsimulations.Otherwise,ifthesoluteisconstrainedonlyinz-direction,then^h(eq)kcouldbeincorrectlyestimated.Theerrorofthisestimateisexpectedtoincreaseasthemembranestiness(andhence,itsrelaxationtime)increases. Theobservedphenomenonisexpectedtobequitegeneralandapplicabletotransportacrossotherexiblemembranes,suchaslipidbilayers. 87

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Inthisstudy,weveriedthatacoarse-grainedmodelcanmimicoil-watersurfactantsystemsfoundinmicroemulsions.MDsimulationsallowedustolookintothedetailedmicrostructureofsurfactantmonolayercoveringanoil-waterinterfacewhichisnotpossiblewiththecurrentlyavailableexperimentaltechniquessuchastransmissionelectronmicroscopy.Theinternalmicrostructureofsurfactantmonolayercontainsnumerousvoids,half-channelsandchannels.Withtheapplicationofpercolationtheorytotheporestructures,wedevelopedamethodtolteroutfastinsignicantmolecularmovementsfromtheporedynamicsandfocusonsucheventsasfusionandssionofpores.Thefastporedynamicsleadtotheconclusionthattransientchannelmechanismforsolutetransportislessfavorableandthedominantmechanismissolubility-diusionmechanisminwhichthesolutetransportoccursviajumpsbetweenvoidsandchannels. Itisobservedthatsolutetransportacrosssurfactant-freeandsurfactant-coveredoil-waterinterfaceinvolvesadynamiccouplingbetweenthesoluteandtheinterfaceuctuationsisanalyzedatmolecularlevel.Protrusionsformattheinterfacewiththelikephasebeingattractedtothesolutewhenthesoluteisclosetotheinterface.WedemonstratethatformationoftheseprotrusionsplaysakeyroleincouplingthesoluteandinterfacedynamicsALangevinequationwasdevelopedforsolutetransportwhichtakesintoaccountformationofprotrusionduetopresenceofsoluteandthecouplingbetweenhydrodynamicuctuationsandsolutetransport. Inthiswork,weinvestigatedvariousfactorswhichcanaecttransportacrosssurfactant-coveredoil-waterinterface:theinterfacemicrostructure,thefree-energybarriertotransportandtheuctuationsoftheinterface.Possibleextensionofthisworkwouldinvolvecomputingthesolutediusivitiesandobtainingthecorrelationbetweensolutediusivitiesandphysicalpropertiesofthesystemsuchaslocalfreevolume,solutesize, 88

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Thetoolsdevelopedinthisworkmightbeusefulforinvestigatingmasstransportinoil-water-blockcopolymersystemsusedtopreparemicroemulsions.BlockcopolymercanberepresentedbyEOxPOyEOxwhereEOisethyleneoxideandPOispropyleneoxide.Modelingoil-water-blockcopolymersystemsischallengingbecauseoftworeasons:(1)blockcopolymersare4-20timeslongerthannon-ionicsurfactantsconsideredinthisworkand(2)thehydrophobicsegment(POchain)oftheblockcopolymerdiersformthehydrophilicsegment(EOchain)inhavinganadditionalmethylgroup.Hence,itislikelythatthehydrophobicsegmentofthepolymerchaingetsadsorbedattheoil-watersurfaceanddoesnotextendtobulkoilphase.Tomodelthesystem,anecientCGmodelneedstobedevelopedwhichtakesintoaccountthesmalldierencebetweenthehydrophilicandhydrophobicsegmentsofthepolymerchain.TheparametersfortheCGmodelmaybeobtainedfromatomisticsimulations. Thegoalofthisworkisbetterunderstandingofinterfacialsystemsandmasstransportacrossthem.Themethodsdevelopedinthisworktoanalyzetheporestructureinsurfactantmonolayercanbeappliedtosimilarsystemswithporesbetweentightlypackedmoleculessuchaslipidbilayersandblockcopolymers.Understandingoffactorswhicheectbarriertomasstransportacrosssurfactant-coveredoil-waterinterfacewillprovideguidelinesforchoosingappropriatesurfactantandsolutepropertiestoobtaindesiredtransportrate.Theanalysisofinterfacialuctuationsandtherelationofinterfacialuctuationswithsolutetransportwillenhanceourunderstandingoftransportatmolecularlevel. 89

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D.J.Barsky,G.R.Grimmett,andC.M.Newman,\Percolationinhalf-spaces:Equalityofcriticaldensitiesandcontinuityofthepercolationprobability,"Prob.Th.Rel.Fields,vol.90,pp.111{148,1991. [44] C.Borgs,J.T.Chayes,R.vanderHofstad,G.Slade,andJ.Spencer,\Randomsubgraphsofnitegraphs:I.Thescalingwindowunderthetrianglecondition,"RandomStruct.Alg.,vol.27,pp.137{184,2005. [45] A.Gupta,A.Chauhan,andD.I.Kopelevich,\Molecularmodelingofsurfactantcoveredoil-waterinterfaces:Dynamics,microstructure,andbarrierformasstransport,"J.Chem.Phys.,vol.128,pp.234709,2008. [46] H.A.Patel,E.B.Nauman,andS.Garde,\Molecularstructureandhydrophobicsolvationthermodynamicsatanoctane-waterinterface,"J.Chem.Phys.,vol.119,pp.9199{9206,2003. [47] B.RouxandM.Karplus,\Iontransportinagramicidin-likechannel:Dynamicsandmobility,"J.Phys.Chem,vol.95,pp.4856{4868,1991. [48] J.P.Ryckaert,G.Ciccotti,andH.J.C.Berendsen,\Numericalintegrationofthecartesianequationsofmotionofasystemwithconstraints:Moleculardynamicsofn-alkanes,"J.Comp.Phys.,vol.23,pp.327{341,1977. [49] A.Ben-Naim,SolvationThermodynamics,PlenumPress,NewYork,1987. [50] N.Matubayasi,K.K.Liang,andM.Nakahara,\Free-energyanalysisofsolubilizationinmicelle,"J.Chem.Phys.,vol.124,pp.154908,2006. [51] C.J.Slevin,J.A.Umbers,J.H.Atherton,andP.R.Unwin,\Anewapproachtothemeasurementoftransferratesacrossimmiscibleliquid/liquidinterfaces,"J.Chem.Soc.,FaradayTrans.,vol.92,pp.5177{5180,1996. [52] K.Nakatani,M.Sudo,andN.Kitamura,\Intrinsicdroplet-sizeeectonmasstransferrateacrossasingle-microdroplet/waterinterface:Roleofadsorptiononasphericalliquid/liquidboundary,"J.Phys.Chem.B,vol.102,pp.2908{2913,1998. [53] T.Osakai,A.Ogata,andK.Ebina,\HydrationofionsinorganicsolventanditssignicanceintheGibbsenergyofiontransferbetweentwoimmiscibleliquids,"J.Phys.Chem.B,vol.101,pp.8341{8348,1997. [54] T.Sakai,Y.Takeda,F.Mafune,M.Abe,andT.Kondow,\Dyetransferbetweensurfactant-freenanodropletsdispersedinwater,"J.Phys.Chem.B,vol.106,pp.5017{5021,2002. [55] I.Benjamin,\Mechanismanddynamicsofiontransferacrossaliquid-liquidinterface,"Science,vol.261,pp.1558{1560,1993. 93

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AshishGuptareceivedhisBachelorofTechnologyinchemicalengineeringfromIndianInstituteofTechnology,Kanpur,Indiain2003.InAugust2003,hecametotheUnitedStatesinpursuitofgraduateeducationandwasadmittedtotheDepartmentofChemicalEngineeringattheUniversityofFlorida.Duringhisgraduatestudies,heworkedunderthesupervisionofDr.DmitryKopelevichandDr.AnujChauhan.HeexpectstoobtainhisDoctorofPhilosophydegreeinAugust2008.HeplanstojoinKBRatHouston,Texas. 96