Structure and solvation forces in confined films: Linear and branched alkanes

Structure and solvation forces in confined films: Linear and branchedalkanesJianping Gao, W. D. Luedtke, and Uzi Landman Citation: J. Chem. Phys. 106, 4309 (1997); doi: 10.1063/1.473132 View online: http://dx.doi.org/10.1063/1.473132 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v106/i10 Published by the American Institute of Physics. Additional information on J. Chem. Phys.Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors

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Structure and solvation forces in confined films: Linearand branched alkanes

Jianping Gao, W. D. Luedtke, and Uzi LandmanSchool of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332

~Received 1 November 1996; accepted 4 December 1996!

Equilibrium structures, solvation forces, and conformational dynamics of thin confined films ofn-hexadecane and squalane are investigated using a new grand canonical ensemble moleculardynamics method for simulations of confined liquids. The method combines constant pressuresimulations with a computational cell containing solid surfaces and both bulk and confined liquidregions in equilibrium with each other. For both molecular liquids layered density oscillations in theconfined films are found for various widths of the confining gap. The solvation force oscillations asa function of the gap width for the straight chainn-hexadecane liquid are more pronouncedexhibiting attractive and repulsive regions, while for the branched alkane the solvation forces aremostly repulsive, with the development of shallow local attractive regions for small values of thegap width. Furthermore, the nature of the transitions between well-formed layered configurations isdifferent in the two systems, with then-hexadecane film exhibiting solid-like characteristicsportrayed by step-like variations in the number of confined segments occurring in response to asmall decrease in the gap width, starting from well-layered states of the film. On the other hand thebehavior of the squalane film is liquid-like, exhibiting a monotonic continuous decrease in thenumber of confined segments as the gap width is decreased. These characteristics are correlated withstructural properties of the confined films which, forn-hexadecane, exhibit enhanced layeredordering and in-plane ordered molecular arrangements, as well as with the relatively high tendencyfor interlayer molecular interdigitation in the squalane films. Reduced conformational~trans-guache! transition rates in the confined films, compared to their bulk values, are found, andtheir oscillatory dependence on the degree of confinement is analyzed, showing smaller transitionrates for the well-formed layered states of the films. ©1997 American Institute of Physics.@S0021-9606~97!50610-6#

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I. INTRODUCTION

Understanding the structure, dynamics, and rheologyultrathin films~of nanometer scale thickness! of low molecu-lar weight hydrocarbons adsorbed on solid surfaces, anparticular of such films confined between solids, is of fundmental interest as well as practical importance for many pcesses, such as lubrication, adhesion, coatings, chromatphy, and membrane separation. Indeed, the propertiesuch systems have been the subject of numerous investions ~for recent reviews, see Refs. 1–5! employing sensitivemicroscopies@the surface force apparatus~SFA!, atomicforce microscopy~AFM!, and friction force microscopy~FFM!#, computer simulations,1,6–9 and other theoreticaapproaches.10–15

Focusing here on confined films, certain key featupertinent to our current study, extracted from a large bodyavailable literature on the subject, may be summarizedfollows:

~i! Liquids confined between solid boundaries~as well asthose adsorbed on a solid surface! tend to organizeinto layered structures,1,10,11 that is strata parallel tothe solid surfaces, provided that the boundarysmooth compared to the molecular scale. In sustructures the mean local density of the liquid osc

J. Chem. Phys. 106 (10), 8 March 1997 0021-9606/97/106(10)/4

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lates with distance normal to the boundary, and tunderlies oscillations in the force between the confiing boundaries as the distance between them~i.e., theconfining gap width! is varied, with a period approxi-mately equal to the molecular width.

~ii ! Such oscillatory solvation forces between confinisurfaces11 were observed and calculated for simpliquids16 ~e.g., modeled as spheres!, nonpolar globularmolecules17–19 ~e.g., octamethylcyclotetrasiloxaneOMCTS!, straight chain alkanes6,20–25 ~e.g.,n-hexadecane,n-C16H34), and even for chain mol-ecules with a single pendant methyl group,18 such as3-methylundecane, C12H26, ~although in earliermeasurements26,27 of force-distance profiles o2-methyloctadecane and 2-methylundecane vanishof the oscillations and the observation of a singletractive minimum have been reported, the possibilof lack of equilibration in these measurements wsubsequently raised!.11,29On the other hand solvationforce measurements18,29for a longer and more heavilybranched molecule~i.e., 2,6,10,15,19,23-hexamethytetracosane, or squalane, a molecule with a C24 back-bone and six, symmetrically placed, methyl sigroups! confined between mica surfaces havevealed disappearance of the force oscillations, wit

4309309/10/$10.00 © 1997 American Institute of Physics

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4310 Gao, Luedtke, and Landman: Structure and solvation forces in confined films

sole broad attractive minimum at a gap widthD518Å, and what appears as a hard wall repulsionD516 Å ~measurements for smaller gap width hanot been attempted!.18 From these observations it habeen concluded that branching~via pendant methylgroups! can disrupt oscillatory forces, though the dgree of branching must be moderately large.18

~iii ! Confined ultrathin films30 may exhibit two differentresponses~in shear,30 as well as in response to variation of the normal distance between the confinisurfaces!;19 a liquid-like response in which the liquidresponds to the deformation by flow,30 or spreading~as in drainage measurements!,31,32 and a solid-likeresponse characterized by observation of the devement of ‘‘yield stress’’ in the confined fluid,33 por-trayed by lack of deformation over macroscopic dtances unless a critical shear stress is attained~leadingto the development of ‘‘stick’’ and ‘‘slip’’patterns!.33–36 Additionally, recent SFAmeasurements19 on confined films of OMCTS~whosediameter is; 9 Å!, suggest the abrupt developmeof solid-like behavior in relatively thick films of 6layers. It should be emphasized that in these measments the transition from liquid-like behavior for7-layer film to a solid-like one for a 6-layer film habeen induced solely by the additional confineme~i.e., without an imposed lateral motion of the confiing surfaces!. In this context we remark that liquidlayering and force oscillations have also been pdicted recently37 in molecular dynamics simulationof n-hexadecane films sheared between solid surfacontaining structural nonuniformities~asperities!. Inthese studies the density oscillations occurred inliquid region between the approaching asperities leing to oscillatory variations in the lateral force. Futhermore, a transition from liquid-like responselarge interasperity distances to a soft solid-like owhen the two asperities approach each other, has bdescribed and analyzed using a rheological nonlinMaxwell model, extending elastohydrodynamicsthe nanoscale regime.7,37

~iv! Liquid dynamics at interfaces and particularly undconfinement is influenced in a marked way, becommore ‘‘sluggish’’ in nature with increased confinement of the fluid.30 Furthermore, molecular architecture and complexity appear to influence the dynamof confined liquids. Thus, for example, in a homolgous series of confined polymers, long chain mecules are found to be more sluggish than shochains.38 These effects on the molecular dynamicsinterfacial and confined complex liquids pertain boto intra and intermolecular relaxation times, and dpend also on the strength of interactions betweenconfined molecules and the solid surfaces.21,24

On the theoretical front interfacial and confined liquihave been investigated using both analytical methods10 andcomputer-based simulations.1,6–9,16,22–25,28,35–37In particular

J. Chem. Phys., Vol. 106,


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molecular dynamics~MD! and Monte Carlo~MC! simula-tions allow direct investigation of such complex systemwith atomic-scale spatial and temporal~using MD! resolu-tion. While early simulations employed model monoatomsimple liquids interacting via central-force pairwise additipotentials~i.e., Lennard-Jones interatomic potentials!, morerecent ones~see reviews in Refs. 1,5–8! focus on liquids ofa more complex molecular structure~e.g., alkanes! with vari-ous degrees of complexity~and realism! of the inter andintramolecular interactions. Such simulations have revealewealth of information pertaining to energetic, structural, dnamical, and rheological properties of interfacial and cofined molecular liquids under static and shear conditionsthese simulations the confining surfaces were modeledstructureless boundaries or as atomically structured solidfaces, and for various configurations. In most simulationsconfining surfaces and the confined liquids were extenindefinitely, or alternatively the liquid has been modeled aconfined droplet28 ~or semidroplet!.21 Extensive simulationshave also been performed for complex liquids adsorbedatomically structured solid surfaces, interacting with ti~modeling AFM and FFM experiments!; in this context, seeRefs. 6, 22 and 23 for simulations of the interactions btween tapered~blunt! tips and adsorbed liquid films using aad hoc grand canonical ensemble,22~b! where the layeredstructure and solvation force oscillations of a confinn-hexadecane liquid in AFM and FFM have been predictas well as investigations of cavitation phenomena associwith withdrawal of immersed tips.23

The configuration of both SFA and tip-based expements is that of a confined liquid in thermodynamic equilrium with a surrounding bulk fluid~or unconfined film!.Consequently, the measured force~or pressure! is more ap-propriately described as a disjoining force~or pressure!which is the difference between the force~pressure! in theconfinement and that of the bulk fluid with which the cofined film is in equilibrium.10,11 Therefore it is desirable toconduct simulations of such systems under grand canon~GC! ensemble conditions~i.e., constant chemical potentiam, pressureP, and temperatureT). An early formulation ofgrand canonical ensemble MC simulations39,40 ~GCEMC,wherem,T, and the volume were held constant! has beenused in studies of confined simple liquids. In this methfluid molecules are inserted or eliminated from the systaccording to the grand canonical ensemble distribution fution with the value ofm determined separately from bulfluid simulations.

In this paper we describe a grand canonical (mPT) mo-lecular dynamics~GCMD! method for simulations of confined lubricants of complex molecular structure~in our case,n-hexadecane and squalane!. The method which we developed combines constant pressure MD with a computatiocell containing both bulk and confined fluid regions, allowing systematic GCMD investigations of confined liquids, aalleviating the difficulties associated with insertion of mo

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4311Gao, Luedtke, and Landman: Structure and solvation forces in confined films

ecules as in the GCEMC method39,40 which at the densitiesof interest to us and for the complex molecules which wewould pose significant practical difficulties.

In Sec. II, we describe the formulation and implemention of our GCMD method. Results of comparative simutions of confinedn-hexadecane and squalane films are psented in Sec. III, followed by a summary given in Sec. I

II. GRAND CANONICAL MD FOR CONFINED LIQUIDS

In this section we describe the formulation and impmentation of a grand canonical molecular dynam~GCMD! method for simulations of confined liquid systemand discuss pertinent details of our simulations. An overvof the simulated system is shown in Fig. 1. The simulatcell contains both liquid~alkane! molecules and solid blockswith periodic boundary conditions extending the systemall three directions. The solid blocks are of finite size in tx andz directions, with the distance between the two sosurfaces in thez direction defining the width of the ga(D) confining the fluid~in our simulations the solid surfaceforming the gap in the middle of the cell are modeled as g~111! planes!. In the y direction, the solid blocks are extended through the whole cell. The rest of the space in3-dimensional cell is filled with alkane molecules; in thpaper, we have studied two different alkane liquids: linen-hexadecane (n2C16H34) and a branched alkane, i.esqualane~C30H62).

To facilitate studies of the properties of the confinalkane thin films, which are in equilibrium with a surrouning bulk liquid, the solid blocks as shown in Fig. 1 are aranged to create two regions of the alkane fluid. Insidegap, between the two solid surfaces, the alkanes are con

FIG. 1. View of the three-dimensional~3D! computational cell for grandcanonical molecular dynamics simulations of confined liquids. The cerepeated using 3D periodic boundary conditions. It contains solid subst~small spheres! of finite extent in thex direction and extending through thcell in they direction. The dimension of the cell inx direction (Hx) variesdynamically in response to the applied external pressure in that directaking different values depending on the gap width between the opposolid surfaces. The cell is filled with liquid molecules, part of them are inconfinement and the rest outside it.Hx is taken to be large enough such thbulk liquid behavior can be established in the regions outside the conment.



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as a thin film with a thicknessD ranging between 10 and 3Å. The size of the cell in thex direction is taken to besufficiently large so that the alkanes in the regions outsthe confined one can exhibit bulk liquid alkane behavior. Tsize of the computational cell in thez direction is varied togive the desired film thickness in the gap. In our simulatiothe extent of the solid blocks in thex direction is 49 Å andthe height of each block isds513 Å; the size of the cell inthez directionHz is thus given byHz52ds1D, and the sizeof the cell in they direction is kept constant,Hy540 Å. Thesize of the cell in thex direction Hx is allowed to varydynamically, using constant pressure MD,41 from ; 120 Åto ; 165 Å, depending on the gap widthD. The hydrostaticpressure, determining the magnitude ofHx , is taken to beone atmosphere; on the scale of all other stresses in thetem this represents a vanishingly low pressure.

In this study, the alkane molecules are treated dynacally while the gold atoms of the solid substrates are st~treating the solids dynamically does not affect our resul!;the solid gold blocks contain a total of 3520 atoms whichimmersed in 206 to 234 squalane or 242 to 4n-hexadecane molecules~for sufficiently thin films bulk be-havior in the regions outside the confinement canachieved for a smaller number of molecules in the computional cell!. The equations of motion of the alkane segmeare solved by the Verlet algorithm with an integration timstep of 3 femtoseconds. The temperature of the systemcontrolled via scaling of the atomic velocities at infrequeintervals ~when equilibrium is reached no temperature cotrol is necessary!; the temperature for these simulations350 K which allows the systems to equilibrate in a reasable amount of computing time.

The alkane molecules are represented by the united amodel, without rigid constraints. The intramolecular potetials include bond stretching, bond angle bending, torsioangle, and Lennard-Jones~LJ! interactions between all atompairs separated by more than three bonds. The bond streing is represented by a stiff linear spring, with the bond forconstant reduced by a factor of 4 from its realistic valuefacilitate computations with an increased time step~this hasno effect on our results!. The angle bending, torsional potentials, and LJ potentials describing intra- and inter-alkaneteractions are the same as those used by MondelloGrest42 in their recent study ofn-alkanes and squalane. A Lpotential is used to describe the interactions between thekane segments and the gold atoms of the solid substrawith parameters fitted to experimental desorption data,described by us previously.21,43

The initial configuration of the system is set up withlarge value of the gap width (; 28 Å!. A random walk withfixed bond lengths and bond angles is employed to placealkane molecules into the computational cell. The nobonded interactions are not considered during the randwalk, but the molecular segments are not allowed to beclose to the solid blocks. After all molecules have beplaced into the computational cell, a molecular dynamsimulation with an upper-bound set on the nonbonded foris carried out to eliminate segmental overlaps which m

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have been generated in the initial random walk stage; inprocedure, the maximum LJ force allowed between a paiinteracting segments is limited tof LJ(r50.85s), wheres isthe LJ length parameters. We have found this procedurbe very effective in generating initial configurations of akane liquids. Subsequently, the upper limit on the forceremoved and a MD run of several hundred picosecondperformed to allow the system to fully equilibrate.

For a given value of alkane film thicknessD, which isthe distance between the two solid surfaces confiningalkanes, the squalane systems are equilibrated for 300–ps followed by a simulation period of 120–300 ps, duriwhich the computed properties are time averaged; forn-hexadecane systems, the equilibration periods are usu60–480 ps and the data acquisition periods are typicallyps ~the longer equilibrium periods were used for the thinnfilms!. The time histories of several energetic and structuproperties were monitored to assure that equilibrationbeen achieved after each adjustment of the gap width; sadjustments involve squeezing of the film to the next gwidth through a slow decrease ofD, followed by a pro-longed equilibration period at the required gap width asscribed above. During the squeezing process and thepart of the equilibration, the number of molecules in tconfined region decreases as some molecules are pushethe bulk region where the pressure remains constant vianamical variation ofHx . For the squalane film, reversal othe process at several values of the gap width~i.e., decreas-ing the confinement! resulted in only slight hysteresis in caculated properties~e.g., solvation force!, confirming ad-equate equilibration.

III. RESULTS

Using the new simulation method described in Sec. IIhave investigated the structures and properties of interfan-hexadecane (n-C16H32) and squalane~2,6,10,15,19,23-hexamethyl-tetracosane! films confined between two opposing surfaces modeled to represent Au~111! surfaces. As de-scribed in Sec. II the confined films are in equilibrium withe surrounding liquid in which the confining solids are immersed.

A. Layering transitions and solvation forces

We begin by presenting our results for the segmendensity profilesr(z) for the two systems, recorded versdistance in the direction normal to the surfaces, for aquence of separations~gaps! between the confining surfaceSuch profiles are shown forn-hexadecane in Fig. 2 and fosqualane in Fig. 3. The solvation forces~i.e., the total forceexerted by the interfacial film on the confining surfacewhich is the same as the force which would be requiredorder to hold the two surfaces at the corresponding seption! recorded for the two systems during the approach oftwo surfaces, are shown forn-hexadecane and squalaneFig. 4. Additionally, we display in Fig. 5 records of the num



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ber of molecular segments confined in the gap betweentwo surfaces,nc fn , as a function of the width of the gapD, as well as ofnc fn /D plotted versusD.

While the density profiles~Figs. 2 and 3! for both mate-rials exhibit oscillatory patterns, a closer inspection revedifferences between the two cases. Already for large septions between the surfaces~a wide gap,D528 Å! then-hexadecane film appears to be well layered throughwith 6 well-formed layers~Fig. 2, top left!, while for the

FIG. 2. Equilibrium segmental density profiles forn-hexadecane along thez direction~normal to the confining solid surfaces!; solid lines correspond tothe film in the confined region and the dashed lines calculated for the reoutside the gap. The gap widths (D) for which the profiles were calculatedare indicated. The well-formed layered configurations@see maxima in thesolvation force curve in Fig. 5~a!# correspond toD510, 14, 19, and 24 Å.The other equilibrium profiles were calculated for intermediate valuesD. Note that the liquid density outside the confinement~dashed line! isuniform and remains constant for all values ofD, while the layered densityfeatures in the confined film~particularly in the middle region of the film!vary in sharpness depending on the degree of confinement, becominsharpest for the values ofD corresponding to well-formed layers. Distancein unit of angstroms.

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same gap width the squalane film exhibits only 4 weformed layers and in the middle region of the gap the denis close to that in the bulk~Fig. 3, top left!. We also note forthe squalane case the appearance of distinct features betthe first interfacial layer on each side of the film and tsecond layer in, which are absent in then-hexadecane profile. These features, which may also be seen~though lesspronounced! between the second and third layer of tsqualane film are caused by the methyl branches whichpreferentially between the layers~a similar behavior has beeobserved in previous simulations of a single-branched hedecane film!.28

Decreasing the width of the gap is accompanied by

FIG. 3. Same as Fig. 2, but for squalane. The well-formed layer configtions correspond to the maxima in the solvation force shown in Fig. 5~b!.Note that small local density maxima on each side of the confined filocated between the interfacial layer and the next layer in; such local mmum between the interfacial layers is seen even for the 2-layer film cfigurations. The local density minima between layers are not as deethose found for then-hexadecane film~compare to corresponding configurations in Fig. 2!. Distances in units of angstroms.



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duction of the number of layers in the film~see Figs. 2 and 3for D524 Å, where 5 well formed layers are observed fboth films!. We also remark that the density minima betwethe layers are deeper for hexadecane. Moreover, for hexcane these density minima are always below the bulk dsity, while for squalane they may become larger than thathe bulk liquid density~see e.g., Fig. 3, correspondingD518 Å!.

In both cases narrowing of the gap results in expulsof molecules from the confined region~‘‘squeezing-out’’ ofthe film! and transition to a film with a smaller number olayers~which remain throughout to be of similar density, i.econtaining approximately the same number of molecular sments!, occurring with a periodicity of about 4.5–5 Å. Thlayering transitions in the confined films are portrayedsolvation force oscillations~Fig. 4!. However, while forhexadecane the force oscillates between positive and ntive values, with the local positive force maxima corresponing to configurations with well-formed layers, in thsqualane case at wider gaps the force does not take negvalues, and the amplitudes of the oscillations are smathan in the hexadecane case. For narrow gaps (D&15 Å! theforce maximum associated with a transition from a 3-layera 2-layer film is significantly larger in the squalane film ththat in the hexadecane one.

Further insights into the layering transition processesobtained from records of the number of segments in the cfined region,nc fn , plotted versus the distance between tconfining surfaces (D), shown in Figs. 5~a! and 5~b!. In thehexadecane film, forD<20 Å, ~i.e., a 4-layer film! nc fn var-ies in a step-like manner with sharp drops in the numbeconfined molecules occurring for the transition from4-layer film to a 3-layer one, and subsequently from a 3- t2-layer film @a weak step-like signature is seen also for ttransition from a 5- to a 4-layer film, see Fig. 5~a! for

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FIG. 4. Equilibrium solvation forces,f z in nN, plotted versus the width ofthe confining gap,D in Å, calculated for the confinedn-hexadecane~solidline! and squalane~dashed line! films. Note that forn-hexadecaneFz

(D.20 Å! is negative~attractive! while for the squalane film the force isoverall repulsive with small local attractive minima nearD; 17 Å and;12 Å. Well-formed layers occur forD;10 Å ~nL52!, 14 Å ~nL53!, 19Å ~nL54!, 24 Å ~nL55!. The repulsive forces in the squalane film astronger than in then-hexadecane one.

No. 10, 8 March 1997



FIG. 5. Solvation force,f z in nN ~upper panel!, number of segments in the confining gap,nc fn ~middle panel!, andnc fn /D ~bottom panel!, plotted versus thegap width,D, in Å, for then-hexadecane film~a!, and the squalane film~b!.

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D<25 Å#. For each of these transitions the drop innc fn iscaused by a relatively small reduction (;1 Å! of the gapwidth from that corresponding to an initial well layered cofiguration of the film~i.e., the number of layers in the film athe bottom of each step is decreased by one from that cosponding to the film at the top of the step~and the plateau!.On the other hand, for the squalane film the variationnc fn associated with the layering transitions is overall montonic and continuous in nature, with the development oweak step-like feature only at the limit of a very thin [email protected]., see transition from a 3- to a 2-layer film, forD&15 Å,in Fig. 5~b!#.

These characteristics of the layering transitions arether found~see Fig. 5! in plots of nc fn /D versusD ~wherenc fn /D is proportional to the number density of moleculsegments in the gap, since the area of the confining ssurfaces is constant for all values ofD). These plots illus-



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trate that for the squalane film the confined segmental dsity remains approximately constant throughout the narroing ~squeezing! process~except in the limit of a very thinfilm, D&15 Å!, while for n-hexadecane reducing the gawidth is accompanied by marked variations in the dens~becoming increasingly more pronounced as the film thdown!. Furthermore, in the latter case the local maximathe film density, corresponding to well-formed layered cofigurations, are of equal value.

These results suggest that the confined squalane filmhaves in a liquid-like manner throughout most of the ganarrowing sequence; that is the equilibrium confined filwhich is in contact with the surrounding bulk liquid, maintains a constant density for varying widths of the confinigap by gradually expelling molecules into the surroundliquid when the gap width is reduced. In contrast the cofined n-hexadecane film of sufficiently small thickness~i.e.,

No. 10, 8 March 1997


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below about 5 layers, or<25 Å! exhibits certain featurescharacteristic to solid-like response; that is, when the coning gap width is slightly reduced@typically DD;1–2 Å!,starting from one of the well-formed layered configuratioof the film with nL layers~corresponding to the maxima ithe solvation force shown in Fig. 5~a!#, the film ‘‘yields’’through expulsion of approximately a layer-worth of moleclar segments into the surrounding liquid, causing a shdecrease in the confined film density. During further redtion of the gap width, the number of confined molecusegments remains almost constant@corresponding to the plateaus ofnnc f shown in Fig. 5~a!#, with an associated increasof the confined film density@seenc fn /D in Fig. 5~a!# whichis accompanied by enhancement of the order in the layestructure of the film. This process continues until a gap wicorresponding to a maximally ordered layered film~withnL21 layers! is reached, for which the confined film densimaximizes. This sequence of events repeats with a perio;4.5–5 Å.

At this juncture we reemphasize that the states ofconfined films which we analyze here are all at equilibriuconditions. Consequently, we argue that the different naof the layering transitions in then-hexadecane and squalanfilms, reflects differences in the equilibrium properties of tconfined films of the two materials. In particular, we assoate the aforementioned solid-like characteristics with a hdegree of order in the layeredn-hexadecane confined filmwhile the liquid-like nature found for the squalane casecorrelated with frustration of the order in the confined filmcaused mainly by branching.44

FIG. 6. Side views of the equilibrium 4-layern-hexadecane~bottom! andsqualane~top! systems. Note the enhanced order in then-hexadecane con-fined film. Different shades of molecular segments have been used tovisualization.



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B. Structure and dynamics

As alluded to above, while organization of the confinfilm density into layered structures, with the number of laers dependent on the gap width, occurs for bothn-hexadecane and squalane films, the degree of order intwo films is different with that in the shorter linear alkanbeing higher. This may be ascertained from close inspecof the density profiles of the two systems shown in Figsand 3, where the minima between layers are deepern-hexadecane along with the occurrence, on each side osqualane film, of small peaks between the density maxcorresponding to the layer closest to the solid interfacethe second layer in, as well as from inspection of molecuconfigurations of the films, such as those shown forequilibrated 4-layer films in Figs. 6 and 7. The side viewsthe films in Fig. 6 show enhanced layering order in tn-hexadecane film as compared to the squalane one, andegree of in-plane intermolecular order in the first layer~in-terfacial layer closest to the solid surface! is clearly larger~see Fig. 7! in the linear alkane film~similarly for the secondlayer in, not shown!. Indeed statistical analysis shows thfor the 4-layer films the probabilities for one end of a moecule to be in the interfacial layer~designated as the firslayer; note that by symmetry the interfacial layers on bosides of the film are equivalent, therefore we averageresults for both interfaces! and the other end to be locateeither at the first, second, or third layer, arf ee(1,i )~n-hexadecane! 5 0.8, 0.12, and 0.08 fori51,2,3, re-spectively, while for the squalane film these probabilitiesalmost evenly distributed,f ee

(1,i )~squalane!5 0.33, 0.37, 0.30,indicating a high degree of interlayer interdigitation~bridg-ing! in the longer branched alkane film. Additionally, fomolecules with one end in one of the middle layers~desig-

id

FIG. 7. Top views~in thexy plane! of the interfacial layers ofn-hexadecane~bottom! and squalane~top! corresponding to the equilibrium 4-layer film~see Fig. 6!. The confined film is the region between the solid lines. Noenhanced intramolecular and intermolecular order in the confin-hexadecane film.

No. 10, 8 March 1997


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nated as layers 2 and 3! the probabilities that one end of thmolecule is in one of these layers and the other is foueither in the same layer or in the other one af ee(2,i )~n-hexadecane! 5 0.6 and 0.4 fori52 and 3, respec-tively, and f ee

(2,i )~squalane! 5 0.38 and 0.62, respectively, indicating a higher degree of interlayer interdigitation for mecules in the middle layers of the films, with a larger degfor the squalane film. A similar analysis but for the probabties of one end of a molecule to be in the interfacial lay~layer 1 or 4! and the middle segment of the molecule tolocated either in the same layer or in the middle layers offilm ~layers 2 and 3! yields f em

(1,i )~n-hexadecane! 5 0.9, 0.08,and 0.02 for i5 1, 2, and 3, respectively, anf em(1,i )~squalane! 5 0.5, 0.39, 0.11, indicating that for thhexadecane film the small amount of interlayer interdigtion involves mainly the molecular tails, while for thsqualane film a larger part of the molecule may be distuted between neighboring layers; the corresponding resfor the middle layers of the films,f em

(2,i )( i52,3), are: forn-hexadecanef em

(2,2)50.79, f em(2,3)50.21, and for the squalan

film f em(2,2)50.63 andf em

(2,3)50.37. A similar analysis for the3-layern-hexadecane film gives:f ee

(1,i ) 5 0.9, 0.1 andf em(1,i ) 5

0.94, 0.06 fori51,2, respectively, and for the squalane filmf ee(1,i ) 5 0.32, 0.55, and 0.13 fori51,2,3, respectively~indi-cating that over 10% of the molecules bridge the two intfaces in the 3-layer squalane system!, and f em

(1,i ) 5 0.65, 0.3,and 0.05. The selected molecular configurations displayeFig. 8 illustrate interlayer interdigitation in a 3-layesqualane film and no interdigitation in a correspondn-hexadecane film.

The degree of order in the films can also be analyzed

FIG. 8. Side views~in slices! through then-hexadecane~bottom! andsqualane~top! films, illustrating molecular interlayer interdigitation~darkshaded molecule! in the squalane film. The small spheres correspond tosurface layers of the gold substrates.



d:

e

r

e

-

-lts

-

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in

terms of the order parameterP2(cosu)5^(3 cos2u21)/2&,whereu is the angle formed between bond vectors conneing neighboring segments of the molecules and the direcnormal to the surface, and the angular brackets denote aaging over all bonds in the regions~confined or bulk! andover the MD simulation. The results displayed in Fig.show that in the bulk regions the molecular bonds doexhibit any orientational order, i.e.,P2(cosu)'0. On theother hand in the confined films they show a tendency topreferentially parallel to the confining surfaces with the dgree of that preferred orientation being larger in tn-hexadecane film. Furthermore, the degree of preferenorientational [email protected]., more negative values ofP2(cosu)]oscillates as a function of the gap width, with local maximorientational ordering achieved for gap widths correspondto well-formed layers~i.e., solvation force maxima in Fig. 5!,with intervening states of reduced orientational order corsponding to the transitions between layered states offilms asD is varied.

Finally, we show in Fig. 9 the torsional angle transitiorates betweentrans and gaucheconformations of the mol-ecules. We observe that in the bulk region ofn-hexadecanethe transition rates are higher than in the bulk squalaneuid. The transition rates in the confined systems are lothan their corresponding bulk values, and exhibit an oscitory behavior as a function of the gap width, with locminima of the transition rates occurring for values ofD cor-responding to well-formed layers. The amplitudes of thecillations of the transition rates versusD are larger for then-hexadecane film and they increase as the confiningwidth is reduced.

These results correlate with those discussed abovetaining to structural properties, showing that both structuand dynamical characteristics of complex liquids are inflenced greatly by their confinement. Moreover, our simutions revealed dependencies of the various degrees of oin the films~layering, in-plane order, and orientational ordeing! on the complexity of the molecular constituents, andthe degree of confinement.

IV. SUMMARY

In this paper, equilibrium structures, solvation forceand conformational dynamics of thin confined filmsn-hexadecane and squalane were investigated using agrand canonical ensemble molecular dynamics methodsimulations of confined liquids. The method combines costant pressure simulations with a computational cell containg solid surfaces and both bulk and confined liquid regioin equilibrium with each other~Fig. 1!, allowing investiga-tions of confined films under conditions similar to those usin surface force apparatus and tip-based experiments.

Our studies provide insights into the nature of equilrium confined liquids and the effects of molecular structuon the properties of such systems. For both the straightlecular chain liquid~n-hexadecane! and for the branched on~squalane! layered density oscillations in the confined filmwere found, with the number of layers depending on

e

No. 10, 8 March 1997


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FIG. 9. Segment-bond order parameter,P2(cosu), in the top panels, andtrans-gauche~and vice versa! transition rates,Tf ~in units of 1/ns! in thebottom panels, plotted versus the gap width,D, in Å, for the equilibriumstates of then-hexadecane~a! and squalane~b! systems. The crosses correspond to values obtained for the bulk liquids outside the confinement,the solid lines connect values calculated for the confined films.



width of the confinement. Then-hexadecane confined filmexhibits enhanced layered order, as well as a higher deof in-plane molecular ordering, compared to those foundthe squalane film, with the latter showing a high tendencyinterlayer molecular interdigitation~see Figs. 2, 3, 6–8!. Re-duced conformational~trans-guache! transition rates in theconfined films, compared to their bulk values, are found, atheir oscillatory dependence on the degree of confinemenanalyzed, showing smaller transition rates for the weformed layered states of the films~Fig. 9!.

The solvation force oscillations as a function of the gwidth for the straight chain,n-hexadecane, liquid are morpronounced exhibiting attractive and repulsive regions, whfor the branched alkane the solvation forces are mostlypulsive, with the development of shallow local attractive rgions for small values of the gap width~Fig. 4!. These resultscorrelate with recent observations using SFA measuremon confined films of squalane,18,19 showing the influence ofmolecular structure~i.e., moderate degree of branching! onthe character of the solvation forces. Furthermore, the naof the transitions, and equilibrium intermediate states,tween well-formed layered configurations is different in ttwo systems, with then-hexadecane film exhibiting solidlike characteristics portrayed by step-like variations in tnumber of confined segments occurring in response tsmall decrease~;1–2 Å! in the gap width, starting fromwell-layered states of the film@Fig. 5~a!#. On the other handthe behavior of the squalane film is liquid-like, exhibitingmonotonic continuous decrease in the number of confisegments as the gap width is decreased@Fig. 5~b!#. Thesecharacteristics, which are correlated with the above mtioned structural properties of the confined films, suggestliquids with molecular structures which are more conducto formation of ordered configurations~such as globular, orlow-molecular weight straight chain molecules! would de-velop solid-like characteristics under confinement, whconfined films made of more complex molecular structu~e.g., a moderate degree of branching, as in squalane!, whereordering is frustrated due to the molecular structural coplexity, would exhibit a higher tendency to behave inliquid-like manner. In this context we remark that indesolid-like behavior, under the sole effect of confinement~i.e.,with no lateral relative shear motion between the confinsurfaces! has been observed recently19 in SFA experimentsfor semispherical molecules~OMCTS!.

ACKNOWLEDGMENTS

This work is supported by the DOE, and the AFOSComputations were performed on CRAY Computers atPittsburgh Supercomputing Center and at the GIT CenterComputational Materials Science.

1For a recent review see, B. Bhushan, J. N. Israelachvili, and U. LandmNature374, 607 ~1995!.

2Fundamentals of Friction: Macroscopic and Microscopic Processes, ed-ited by I. L. Singer and H. M. Pollock~Kluwer, Dordrecht, 1992!.

3Physics of Sliding Friction, edited by B. N. J. Persson and E. Tosa~Kluwer, Dordrecht, 1996!.

d

No. 10, 8 March 1997


.

ms

hy

tu

, J

plt.

, J

les

ereght.ofull.

.

akeof the

ett.

dsound

ell

entased


4Handbook of Micro/Nano Tribology, edited by B. Bhushan~CRC, BocaRaton, Florida, 1995!.

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17J. N. Israelachvili and R. G. Horn, J. Chem. Phys.35, 1400~1981!.18S. Granick, A. L. Demirel, L. L. Cai, and J. Peanasky, Isr. J. Chem.35, 75

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21M. W. Ribarsky and U. Landman, J. Chem. Phys.97, 1937 ~1992!, andreferences therein.

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23U. Landman and W. D. Luedtke, MRS Bull.17, 36 ~1993!.24S. Gupta, D. C. Koopman, G. B. Westerman-Clark, and I. A. BitsanisChem. Phys.100, 8444~1994!.

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28For simulations of confined alkanes with a single pendant methyl, whforce oscillations similar to those found for the corresponding straichain alkanes, see:~a! Y. Yang, K. Hill, and J. G. Harris, J. Chem. Phys100, 3276 ~1994!; ~b! J. Ouyang, Ph.D. dissertation, Georgia InstituteTechnology, 1995; J. Ouyang, W. D. Luedtke, and U. Landman, BAm. Phys. Soc.40, 425 ~1995!.

29J. N. Israelachvili~private communication!.30S. Granick, Science253, 1374~1991!.31D. Y. C. Chan and R. G. Horn, J. Chem. Phys.83, 5311~1985!.32J. N. Israelachvili, J. Colloid. Interface Sci.110, 263 ~1986!.33G. Reiter, A. L. Demirel, and S. Granick, Science263, 1741~1994!.34H. Yoshizawa, P. McGuiggan, and J. N. Israelachvili, Science259, 1305

~1993!.35P. A. Thompson and M. O. Robbins, Science250, 792 ~1990!; M. O.Robbins and P. A. Thompson,ibid. 253, 916 ~1991!.

36B. N. J. Persson, Phys. Rev. B50, 4771~1994!.37J. Gao, W. D. Luedtke, and U. Landman, Science270, 605 ~1995!.38J, van Alsten and S. Granick, Macromolecules23, 4856~1990!; S. Gran-ick and H.-W. Hu, Langmuir10, 3857~1994!; J. Peanasky, L. Cai, C. RKessel, and S. Granick,ibid. 10, 3874~1994!.

39I. K. Snook and W. J. van Megen, J. Chem. Phys.72, 2907~1980!.40W. J. van Megen and I. K. Snook, J. Chem. Phys.74, 1409~1981!.41M. Parrinello and A. Rahman, J. Appl. Phys.52, 7182~1981!. In derivingthe equations of motion within the Parrinello-Rahman formalism, we tas our Lagrangian dynamical variables the scaled-space coordinatesfluid particles and the component of the calculation cell along thex direc-

tion.42M. Mondello and G. S. Grest, J. Chem. Phys.103, 7156~1995!.43T. K. Xia, J. Ouyang, M. W. Ribarsky, and U. Landman, Phys. Rev. L69, 1967~1992!.

44Similar simulations which we performed for simple spherical LJ fluihave shown an even more pronounced step-like behavior than that fby us forn-hexadecane@see Fig. 5~a!#. This indicates that solid-like be-havior is enhanced in sufficiently thin confined liquids which pack wand exhibit a high degree of ordering, as in OMCTS~Ref. 19!. Further-more, recent simulations forn-tetracosane~n-C24H50! show a similar be-haviour to that ofn-hexadecane, leading us to conclude that the differbehaviour of squalane is caused by branching rather than by increchain-length; J. Gao, W. D. Luedtke, and U. Landman~in preparation!.

No. 10, 8 March 1997


Documents

Structure and solvation forces in confined films: Linear and branched alkanes