Molecular Dynamics Study of Alkylsilane Monolayers on RealisticAmorphous Silica SurfacesJana E. Black,†,‡ Christopher R. Iacovella,†,‡ Peter T. Cummings,†,‡ and Clare McCabe*,†,‡,§

†Department of Chemical and Biomolecular Engineering, ‡Multiscale Modeling and Simulation (MuMS), and §Department ofChemistry, Vanderbilt University, Nashville, Tennessee 37235, United States

*S Supporting Information

ABSTRACT: Interfacial properties of n-alkylsilane monolayers on silica have beeninvestigated with molecular dynamics simulations using both reactive and classical (i.e.,nonreactive) force fields. A synthesis mimetic simulation (SMS) procedure using thereactive force field ReaxFF has been developed to mimic the experimental processing ofsilicon wafers involved in the preparation of alkylsilane monolayers; in the SMSprocedure, amorphous silica surfaces are generated and exposed to hydrogen peroxide(H2O2) to create a hydroxide surface layer. Alkylsilane monolayers are then assembled onthese surfaces, and their behavior is studied. To investigate the impact of the SMSprocedure on monolayer properties, simulations have also been performed using moreidealized monolayers assembled on crystalline surfaces and non-H2O2-processedamorphous surfaces. The simulations reported here demonstrate that processing-inducedsilica surface roughness plays a key role in the structure and frictional performance ofmonolayers. Furthermore, ignoring these effects results in a significant underestimation ofthe coefficient of friction and an overestimation of the orientational ordering of the monolayers.

■ INTRODUCTION

Micro- and nano-electromechanical systems (MEMS andNEMS) have been used to develop smaller and more efficientsensors to detect chemical signals, stresses, vibrations, andforces at the atomic level;1,2 examples include tips andcantilever beams in atomic force microscopy3 and inertialnavigation system accelerometers and gyroscopes.4 MEMS/NEMS devices have small lateral dimensions and thereforelarge surface-area-to-volume ratios, which without lubricationcan result in significant surface interactions, e.g., adhesion andfriction, that can lead to surface damage and eventual devicefailure.1,5 An effective method to protect and lubricatecontacting surfaces in such devices is to employ chemisorbedmonolayers. Different types of monolayers can be assembled ona wide variety of surfaces,6−33 including n-alkylsilane[CH3(CH2)n−1Si(OH)3] monolayers on silicon and silica,which have been shown to reduce stiction and protect surfacesfrom oxidation and wear.4,6−12,33

Several fundamental studies of alkylsilanes have beenreported to gain insight into which monomer and monolayerproperties can be used to enhance tribological performance.For example, recent experimental work on alkylsilanemonolayers assembled on silica7 and mica32 demonstrated adecrease in friction as alkylsilane chain length increases; in bothcases the authors concluded that increased disorder inmonolayers constructed from shorter alkylsilane chains (5−8backbone carbons), as compared to those constructed fromlonger chains (12−18 backbone carbons), was the cause ofincreased friction.32 Experiments have also shown that thechemistry of the terminal contacting groups of the monolayer

molecules has a significant impact on friction and adhesiveforces.7 Additionally, Flater et al. conducted AFM experimentsin which the AFM tip and/or the silicon surface was coated byan alkylsilane monolayer and demonstrated that friction andadhesion decrease when either surface is coated and that theeffect is cumulative when both surfaces are coated.34

Molecular simulation has also been used to increase ourunderstanding of the molecular-level behavior of alkylsilanemonolayers.6−12,22,33 For example, molecular dynamics simu-lation has demonstrated that pure alkylsilane monolayers yieldlower coefficients of friction than pure perfluoroalkylsilanemonolayers while undergoing shear.6,11,12 Furthermore, mixedalkylsilane/perfluoroalkylsilane monolayers were shown toprovide better protection against friction than either of thepure monolayers by combining the advantageous properties ofhigh surface coverage in alkylsilane monolayers with the lowsurface energy of perfluoroalkylsilane monolayers.11 We notehowever that many prior simulation studies have examinedmonolayers assembled on ideal crystalline surfaces. Whilecrystalline surfaces appropriately represent gold28,30 anddiamond15,29,35,36 surfaces, they introduce an approximationwhen used to represent silica surfaces since the comparableexperimental surfaces are typically amorphous.4,17−19,37 As aresult, there may be discrepancies between the systemproperties predicted by the simulations and those observed inexperiments. For example, simulations have historically over-

Received: December 23, 2014Revised: February 21, 2015Published: February 26, 2015

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estimated the average tilt angle (relative to the normal to thesurface) of chains in alkylsilane monolayers, which has beenattributed to the idealized nature of the silica surfaces used inthe simulations.Simulations of amorphous silica surfaces have demonstrated

increased coefficients of friction compared to crystallinesurfaces, and the differences have been attributed to thenonuniform arrangement of the alkylsilane chains on thesurface and the resulting presence of voids.8−10,20 However, theamorphous surfaces used in prior simulation studies may stillnot be fully representative of the silica surfaces used inexperiment, since the effects of the postsynthesis processing ofsilica done experimentally are not taken into account.Specifically, in the experimental procedure to preparealkylsilane monolayers, silicon wafers are typically first treatedwith a “piranha” solution (H2SO4/H2O2) to generate a silicalayer containing surface hydroxide groups. Trichloroalkylsilanemolecules then readily bond to these hydroxide groups in thepresence of water to generate an alkylsilane monolayer.7,33 Thestrong oxidation present during this process has been shown tointroduce atomic-scale surface roughness and alter the surfacestructure relative to an untreated amorphous silica surface.38 Inorder to determine the impact of this surface preparation onsurfaces and monolayers, chemical reactions, which are notpermitted in molecular dynamics simulations using classicalforce fields, must be taken into account.In this work, a synthesis mimetic simulation (SMS)

procedure using the ReaxFF force field39 has been developedto create realistic hydroxylated silica surfaces and alkylsilanemonolayers. In the SMS procedure, amorphous silica surfacesare generated and then exposed to H2O2 to create a hydroxidesurface layer to which alkylsilane chains are bonded. Thisprocess closely mimics the postsynthesis processing of siliconwafers with piranha solution. Monolayer properties andcoefficients of friction have been determined for these SMS-based configurations and compared to the properties of moreidealized configurations (i.e., idealized monolayers on crystal-line silica, monolayers with defects on crystalline silica, andmonolayers on non-H2O2-processed amorphous silica ofvarying atomic-scale roughness). This study demonstrates theimportance of using realistic models that consider the synthesisand processing steps associated with the creation of monolayersand provides insight into the key factors that influence thefrictional performance of monolayers.

■ SIMULATION METHODSMolecular dynamics simulations were carried out using bothreactive and classical force fields. Specifically, reactivesimulations were used to generate amorphous substrates,both unprocessed and processed using the SMS procedure(described below), and to investigate the structural propertiesof monolayers under equilibrium conditions. Since classicalsimulations are less computationally expensive than reactivesimulations by a factor of ∼50, the OPLS-AA potential wasused rather than the ReaxFF potential to study the coefficientsof friction of monolayers under nonequilibrium conditions inorder to capture longer trajectories more efficiently. Thereactive simulations were performed using ReaxFF, which usesa bond order/bond distance relationship with a polarizablecharge description and bond-order-dependent three- and four-body interactions in addition to van der Waals and Coulombicforces, in order to accurately model chemical reactions.39 Theparameters used in this work were taken from Fogarty et al.40

for the Si/O interactions and Rahaman et al.41 for the C/O/Hinteractions. A full description of the ReaxFF potential is givenby van Duin et al.39 The classical simulations were performedusing the optimized potentials for liquid simulations all-atom(OPLS-AA) force field.42 The OPLS-AA parameters used inthis work were taken from Lorenz et al.10 for silica andJorgensen et al. for the alkanes,42 in accordance with priorsimulation studies of alkylsilane monolayers on silica.6,7,11,12

All simulations were performed using the LAMMPSsimulation engine43 in the NVT ensemble (constant numberof atoms, volume, and temperature) with periodic boundaryconditions in the surface plane (i.e., the xy-plane) in order tomimic the behavior of an infinite surface; simulations did notinteract across the z-boundary. Temperature was controlled viathe Nose−́Hoover thermostat44,45 with a temperature dampingparameter of 50 fs. Simulations using the ReaxFF potentialemployed a 0.5 fs time step.39 In all simulations using theOPLS-AA potential, the equations of motion were integratedusing the multiple time step algorithm rRESPA with timestepsof 0.3 fs for bond interactions, 0.6 fs for angle interactions(valence and dihedral), and 1.2 fs for Lennard-Jones andelectrostatic interactions, which were computed using theparticle−particle, particle-mesh algorithm for slabs (i.e., electro-static interactions were not calculated across the nonperiodicboundary). Lennard-Jones interactions were computed using acutoff radius of 10 Å, in accordance with prior simulationstudies.6,7,11,12 Unless stated otherwise, each system wassimulated at room temperature (300 K) with the outer 50%of the silica surface (i.e., the portion not in contact with themonolayer) immobilized to prevent bulk translation of thesystem. Postequilibration trajectory lengths were 2 ns for theequilibrium molecular dynamics simulations used to study thestructural properties of monolayers, which were conductedusing the ReaxFF potential. Postequilibration trajectory lengthsranged from 5 to 10 ns for the nonequilibrium moleculardynamics simulations used to study the frictional performanceof monolayers, which were conducted using the OPLS-AApotential. These trajectory lengths were found to be sufficientin order for the simulations to converge to a steady state andyield data with reasonably low uncertainty.

SMS Procedure. Previously, Litton and Garofalini46

performed molecular dynamics simulations using a multibodypotential to generate amorphous silica; 2:1 mixtures of siliconand oxygen atoms were heated to 10 000 K and then rapidlyquenched to room temperature. Using ReaxFF to create bulkamorphous silica, the same general procedure has beenimplemented in this work. Specifically, 4800 oxygen atomsand 2400 silicon atoms were confined to a periodic box ofdimensions 4.77 × 4.13 × 5.52 nm3; the atoms were organizedin a regular alternating pattern similar to patterns observed incrystalline silica. The system was then heated from roomtemperature to 5000 K over the course of 1.0 ps such that itmelted and was then quenched back to room temperature overthe course of 1.0 ps; the system was then simulated at roomtemperature for 1.0 ps to form bulk amorphous silica. 4.77 ×4.13 × 2.30 nm3 slices of the bulk silica were selected and thenused as amorphous silica surfaces. Prior work has shown thatsystems of this size are sufficiently large to avoid system sizeeffects due to periodic boundary conditions.33

To mimic the treatment of silica surfaces with piranhasolution, the amorphous silica surfaces were then exposed toH2O2. Two nonidentical silica surfaces were placed at opposingends of a box of dimensions 4.77 × 4.13 × 15.0 nm3

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perpendicular to the surface plane (i.e., in the z-direction) with600 H2O2 molecules between the surfaces. The surfaces werethen pushed toward each other at a rate of 0.1 nm/fs until thevolume available to the H2O2 molecules reached the liquiddensity of pure H2O2 (1.45 g/cm3). The system was thensimulated using ReaxFF at room temperature with the outer67% of each surface fixed to ensure the distance between silicasurfaces remained constant. During this time, H2O2 moleculesreacted with the surface of the silica to form hydroxide groups.After ∼60 ps, the number of surface bound hydroxide groupsreached a plateau and attained a density of ∼5.8 hydroxide

groups/nm2. Unbound molecules were then removed from thesystem. Prior to H2O2 treatment, the root-mean-squared(RMS) roughness values of the silica surfaces were ∼0.3 Å,but the roughness of the surfaces increased to ∼1.3 Å followinghydroxylation by H2O2.The new surface hydroxide groups were considered eligible

bonding sites for alkylsilane chains; if two hydroxide groupswere less than 2.0 Å apart, only one was considered an eligiblebonding site due to steric hindrance. C6−C18 alkylsilanemonolayers (i.e., monolayers of alkylsilane chains with uniformlengths of 6−18 carbons) with densities of 3.9, 4.3, and 4.9

Figure 1. Simulation snapshots showing C10 alkylsilane monolayers at a density of 3.9 chains/nm2. Side (left) and top down (right) views of (A) the

SMS system, (B) the idealized system, (C) the defected system, and (D) the smooth amorphous system (i.e., RMS roughness of ∼0.4 Å). Si−Obonds within the silica surfaces are shown in yellow (silicon) and red (oxygen) and atoms within the alkylsilane chains are shown in cyan (silicon)and black (carbon). Hydrogen atoms have been removed for clarity. Images were generated using the Visual Molecular Dynamics (VMD)software.47

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chains/nm2 and 77, 85, and 96 alkylsilane chains, respectively,were generated using this procedure by varying the minimumcutoff distance between bonding sites from 2.0 to 2.5 Å andrandomly choosing between the available sites. These surfacecoverages are consistent with experimental alkylsilane mono-layers assembled on silica, which have been reported to havedensities of ∼4.0−4.5 chains/nm2.33

High-energy states due to steric hindrance and the overlap ofparticles typically do not cause fundamental issues in classicalmolecular dynamics simulations since all bonds are permanent;however, in simulations using ReaxFF, high-energy states andstress on alkylsilane chains cause them to break and/or becomedetached from the silica surface if the chains are simply placedat the desired bonding sites. In order to avoid this issue, OPLS-AA was used to relax the grafted alkylsilane chains, and oncethe system reached a stable low-energy state, the simulation wasrun using ReaxFF. A system generated using this procedure isshown in Figure 1A. Additional details of this procedure areprovided in the Supporting Information.Idealized Models. In order to determine the impact of the

experimental silica processing on monolayer properties,idealized systems (Table 1) used in previous simulation studies

were also examined.8−13,24,33 Systems with three distinct levelsof nonideality were studied: uniform monolayers grafted ontocrystalline surfaces (which we refer to as “idealized”),monolayers grafted onto crystalline surfaces with defectsinduced by removing individual alkylsilane chains (which werefer to as “defected”), and monolayers grafted onto untreatedamorphous surfaces (which we refer to as “amorphous”) withvarying atomic-scale roughness (e.g., “smooth”, “medium”, and“rough”).The idealized model (Figure 1B) consists of 100-monomer

alkylsilane monolayers of varying densities (3.9, 4.3, and 4.9chains/nm2) assembled on a crystalline silica surface that isbased on the structure of β-cristobalite. While alkylsilanemonolayers assembled on β-cristobalite have a density of 5.1chains/nm2, the lower monolayer densities used here wereachieved by expanding a β-cristobalite silica surface with initialdimensions 4.77 × 4.13 × 1.05 nm3 by a factor of 1.02−1.14.The defected model (Figure 1C) consists of alkylsilanemonolayers assembled on the original unexpanded β-cristobalite substrate. In these systems, monolayer densities of3.9, 4.3, and 4.9 chains/nm2 were achieved by removing 4−23chains (out of 100) at random and terminating the unusedbonding sites with hydrogen ions. In equilibrium simulations ofthe idealized and defected systems, atoms in the silica surfaceswere immobilized since stretching of Si−O bonds (e.g., duringthe expansion of β-cristobalite) could lead to rupture in ReaxFFsimulations.

The amorphous systems (Figure 1D) were created using theidealized systems as starting configurations (i.e., 100-monomermonolayers of varying densities grafted onto expanded β-cristobalite). For each system, the substrate was heated to 5000K until it melted, again using ReaxFF and following the generalprocedure of Litton and Garofalini,46 while the alkylsilanechains were fixed; upon cooling to room temperature, oxygenatoms on the silica surface formed bonds to the fixedattachment sites (i.e., silicon atoms) of the alkylsilane chains.Following the re-formation of the bonds, the monolayer wasallowed to relax. This procedure generated monolayers with arelatively uniform in-plane arrangement of chains (i.e., minimaldefects) grafted to amorphous silica substrates with RMSroughness values of ∼0.4 Å. We consider these to be smoothsurfaces. Additional systems in which the silica surfaces havehigher RMS roughness values were also generated by randomlyperturbing the center of mass of individual alkylsilane chainsnormal to the surface prior to heating/quenching of thesubstrate. We define the medium amorphous system as thatwith RMS roughness of ∼0.9 Å and the rough amorphoussystem as that with RMS roughness of ∼1.2 Å. A fulldescription of this procedure is given in the SupportingInformation.In order to quantify the structural properties and frictional

performance of all the alkylsilane monolayers studied, the tiltangle and nematic order parameter of the chains within themonolayers and the RMS roughness of surfaces, as well as thecoefficient of friction of monolayers undergoing shear, havebeen determined. The average tilt angle of a monolayer isdefined such that a monolayer in perfect alignment with avector normal to the silica surface yields a tilt angle of 0°. Thenematic order parameter (S2) is used to quantify globalorientational ordering of the monolayer. A value of S2 = 1indicates perfect orientational ordering within the monolayer,and values of S2 less than unity represent proportionately lessorientational ordering. The RMS roughness of surfaces hasbeen estimated by the standard deviation of the positions of thesurface oxygen atoms that are bonded to alkylsilane chainsnormal to the surface plane. Simulations of monolayersundergoing shear were conducted at several different normalforces, and the coefficient of friction was approximated by theslope of the line generated by plotting friction force as afunction of normal force. A detailed description of thecalculation of each of these metrics is provided in theSupporting Information.

■ RESULTS AND DISCUSSIONSince ReaxFF has not been used extensively to studymonolayers, equilibrium simulations using the idealizedmodel were conducted using ReaxFF and OPLS-AA tocompare monolayer properties predicted by both force fields.As the results presented in the Supporting Information show,very close agreement was obtained for the tilt angle, nematicorder parameter, and monolayer thickness of C10−C18monolayers; in the case of C6 monolayers, the ReaxFF resultsappear to be in better agreement with experiment.7 Thus,simulations using both force fields should provide quantitativeagreement regarding the structural properties of C10−C18monolayers and can be used interchangeably and directlycompared for the purposes of this study.To ascertain the impact of silica processing on the structural

properties of monolayers (i.e., tilt angle and nematic orderparameter), equilibrium simulations using the ReaxFF potential

Table 1. Key Structural Properties of the AlkylsilaneMonolayer Systems Studied

system

arrangement ofchains inmonolayer

atomic-scaleproperties of

silica

RMSroughness ofsilica (Å)

SMS nonuniform amorphous 1.3idealized uniform crystalline 0.0defected nonuniform crystalline 0.0amorphous smooth uniform amorphous 0.4

medium uniform amorphous 0.9rough uniform amorphous 1.2

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have been performed for the idealized, defected, smoothamorphous, and SMS systems. Tilt angle (Table 2) and nematic

order parameter (Figure 2) have been determined as a functionof chain length (C6−C18) and monolayer density (3.9, 4.3, and4.9 chains/nm2). Uniform monolayers (i.e., idealized andamorphous) were found to yield lower standard deviations intilt angle than nonuniform monolayers (i.e., defected andSMS), suggesting voids/defects in the monolayers allow thechains to explore new conformations and as a result have awider range of tilt angles. Monolayers assembled on amorphoussurfaces (i.e., amorphous and SMS) have slightly lower averagetilt angles than those assembled on crystalline surfaces (i.e.,idealized and defected), which suggests that atomically roughsurfaces may cause the chains to stand slightly more upright. Aspreviously mentioned, simulations of alkylsilane monolayershave historically overestimated the chain tilt, and our resultssupport the suggestion that this is due to the idealized nature ofthe crystalline silica surfaces used. In all cases, tilt angleincreases as monolayer density decreases, but there does notappear to be a meaningful correlation between monomer lengthand tilt angle. The nematic order parameter (S2) decreases asadditional levels of nonideality are introduced into the systemand as monolayer density and monomer length decrease.Monolayers assembled on crystalline surfaces (i.e., idealized anddefected) have significantly higher orientational order thanmonolayers assembled on amorphous surfaces (i.e., amorphousand SMS). The difference in S2 between monolayers assembledon crystalline surfaces and amorphous surfaces is moresignificant than the difference in S2 between uniformmonolayers (i.e., idealized and amorphous) and nonuniformmonolayers (i.e., defected and SMS). These results suggest thatatomic-scale surface roughness may play a larger role in globalorientational ordering than in-plane monolayer organization.To further investigate the effects of atomic-scale silica surface

roughness on monolayer properties, equilibrium simulationsusing the ReaxFF potential have been performed using C10

monolayers grafted onto amorphous surfaces of varying RMSroughness; the monolayers have densities of 3.9 chains/nm2,and the RMS roughness of the silica surfaces varies from ∼0.5to 1.0 Å. Tilt angle (Figure 3A) and nematic order parameter

Table 2. Average Tilt Angle (deg) as a Function ofMonolayer Density and Chain Lengtha

4.9 chains/nm2 4.3 chains/nm2 3.9 chains/nm2

SMSC6 30.6 ± 16.5 37.1 ± 20.9 37.7 ± 20.3C10 27.4 ± 14.2 34.6 ± 17.4 37.2 ± 17.8C14 27.5 ± 13.5 32.3 ± 13.6 37.7 ± 15.4C18 32.0 ± 9.0 37.1 ± 11.9 36.0 ± 16.3

idealizedC6 31.0 ± 10.1 37.3 ± 9.1 42.9 ± 9.1C10 39.6 ± 3.6 39.1 ± 9.5 39.8 ± 8.3C14 37.1 ± 5.5 38.4 ± 8.4 38.5 ± 9.5C18 38.6 ± 4.6 38.6 ± 7.2 39.2 ± 8.2

defectedC6 31.7 ± 11.6 35.6 ± 10.8 41.3 ± 16.3C10 31.5 ± 9.4 37.3 ± 13.2 39.8 ± 16.0C14 32.3 ± 10.4 36.1 ± 12.5 42.4 ± 13.8C18 34.8 ± 10.7 35.3 ± 10.8 39.6 ± 14.6

smooth amorphousC6 29.7 ± 8.4 33.6 ± 10.1 37.2 ± 11.2C10 30.6 ± 6.0 35.1 ± 8.4 35.7 ± 7.1C14 32.4 ± 7.3 34.7 ± 6.5 36.5 ± 8.5C18 31.9 ± 5.4 34.2 ± 7.3 37.4 ± 9.1

aError in measurements is one standard deviation.Figure 2. Average nematic order parameter (S2) as a function ofmonolayer density and chain length for the SMS, idealized, defected,and smooth amorphous systems studied. Monolayer densities are (A)4.9 chains/nm2, (B) 4.3 chains/nm2, and (C) 3.9 chains/nm2. Errorbars represent one standard deviation.

Figure 3. Average tilt angle (A) and nematic order parameter (S2) (B)as a function of RMS roughness for C10 alkylsilane monolayers onsilica with densities of 3.9 chains/nm2. Error bars represent onestandard deviation.

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(Figure 3B) have been determined as a function of RMSroughness. As surface roughness increases, tilt angle decreasesslightly, and the standard deviation increases slightly; thisobservation suggests that increasing atomic-scale surfaceroughness causes the chains to stand more upright on thesurface and have a wider range of tilt angles. These resultsfurther support the idea that many prior simulation studies haveoverestimated the tilt angle of alkylsilane monolayers due to theidealized nature of the crystalline silica surfaces used. As surfaceroughness increases, global order decreases dramatically, asevidenced by the nematic order parameter (S2); these datafurther support the suggestion that atomic-scale surfaceroughness significantly impacts the global ordering ofalkylsilane monolayers on silica.Nonequilibrium simulations using the OPLS-AA potential

have been performed for the idealized, defected, amorphous,and SMS systems to determine the impact of silica processingon the frictional performance of alkylsilane monolayersundergoing shear. As previously mentioned, OPLS-AA wasused here rather than ReaxFF for computational efficiency andto avoid the possibility of chain breakage. Although werecognize that chain breakage is important in the determinationof wear mechanisms, it is not within the scope of this study andwill be considered in future work. Furthermore, sinceequilibrium ReaxFF and OPLS-AA simulations were shownto provide quantitative agreement regarding the structuralproperties of alkylsilane monolayers, fundamental differencesare not expected by using OPLS-AA. Shearing simulations wereconducted using C10 monolayers with densities of 3.9 chains/nm2; this monolayer density was chosen because it most closelyapproximates the density of real alkylsilane monolayers (∼4.0chains/nm2). All systems described here were assigned identicalmonomer lengths and monolayer densities so that the impact ofkey structural properties (i.e., the arrangement of chains in themonolayers and structure of the silica surfaces) on frictionalperformance could be examined directly.Identical monolayer-covered surfaces were mirrored over the

surface plane to create two monolayers in contact. To conductshearing simulations at different normal forces, independentshearing runs were performed at 4−5 different fixed separationdistances for each system. During each shearing run, thedistance between the inner surfaces of opposing silica substrates(i.e., the silica−monolayer boundaries) was assigned a fixedvalue between 1.8 and 3.0 nm. This separation distance wasquantified by the average distance normal to the surfacebetween bonding sites (i.e., oxygen atoms in the silica bondedto alkylsilane chains) on opposing surfaces. The positions ofatoms in the silica surfaces were not integrated through time, sothe relative positions of atoms within a substrate remainedconstant (i.e., the silica substrates behaved as rigid bodies).Constant velocities of 5 and −5 m/s were applied to the upperand lower silica surfaces, respectively, in the x-direction;alkylsilane chains bonded to the rigid silica surfaces were freeto move. While shearing speeds of 10 m/s are higher than thosenormally used in experiment, several studies8−11,33 report thatshearing velocities of this magnitude do occur betweenmonolayer-covered surfaces in nanotribological systems,including MEMS/NEMS. Furthermore, prior studies haveshown that frictional forces do not significantly depend onsliding velocity at moderate loads.8−11,33 The friction force oneach monolayer (i.e., the sum of the forces in the x-direction)and the normal force on each monolayer (i.e., the sum of theforces in the z-direction) were determined periodically over

time and used to calculate the coefficient of friction. Forsimulations of the amorphous and SMS systems, permanentbonds required for OPLS-AA simulations were determined viathe ReaxFF bond order calculation, with angles and dihedralsdetermined from this bonding topology following the OPLS-AA parameter set.The results of the nonequilibrium simulations are reported in

Figure 4 and Table 3. The coefficient of friction values

determined for the idealized, defected, and smooth amorphoussystems are consistent and provide close agreement with priorresults.9,11,48 Specifically, Lewis et al. obtained a coefficient offriction of 0.15 for idealized C10 monolayers

11 as compared tothe value of 0.14 obtained for idealized C10 monolayers in thiswork. Chandross et al. obtained a coefficient of friction of 0.19for C8 monolayers containing defects,9 which compares wellwith the value of 0.17 obtained for C10 monolayers withcomparable defects in this work. Chandross et al. also reporteda coefficient of friction of 0.21 for C8 monolayers onamorphous silica surfaces with no induced surface roughness,48

which is comparable to the value of 0.26 determined here forC10 monolayers assembled on smooth amorphous silica. Incombination, the results presented in this work, along with theliterature values, demonstrate that the introduction of defects touniform monolayers assembled on crystalline silica leads to asmall increase in the coefficient of friction, while assemblingmonolayers on amorphous silica rather than crystalline silicaresults in more significant increases in friction.If we now consider the SMS system, the coefficient of friction

is found to be 0.40, which is considerably larger than the valuesfound for the smooth amorphous, idealized, and defectedsystems. The smooth amorphous silica and SMS-based silicahave RMS roughnesses of 0.4 and 1.3 Å, respectively (thecrystalline surfaces have roughnesses of 0 Å). To determine if acorrelation exists between surface roughness and coefficient offriction, shearing studies of the medium amorphous system (0.9Å) and rough amorphous system (1.2 Å) were also conducted;these systems demonstrated coefficients of friction of 0.32 and0.34, respectively. Thus, a positive correlation between surfaceroughness and coefficient of friction is observed. The coefficientof friction is still higher for the SMS-based system than therough amorphous system, likely due to the fact that the roughamorphous monolayer is more uniform in its in-plane

Figure 4. Friction force per area as a function of normal force per areafor C10 alkylsilane monolayers with densities of 3.9 chains/nm2. Errorbars represent standard error of the mean.

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arrangement (i.e., contains minimal defects) compared to theSMS-based monolayer.These results indicate that defects present in monolayers and

atomic-scale surface roughness both increase the frictionbetween monolayers. The difference in friction coefficientbetween monolayers assembled on crystalline surfaces (i.e.,idealized and defected) and those assembled on amorphoussurfaces (i.e., amorphous and SMS) is more significant than thedifference in friction between uniform monolayers (i.e.,idealized and amorphous) and nonuniform monolayers (i.e.,defected and SMS). Thus, atomic-scale surface roughness canbe concluded to be a larger contributor to friction, but thepresence of defects and surface roughness demonstrate acumulative effect, as evidenced by the SMS system. Theseresults, in conjunction with the aforementioned orientationalordering results of isolated monolayer systems, suggest thatthere is a negative correlation between the global orientationalordering of monolayers and the coefficient of friction of themonolayers undergoing shear, as was suggested in theexperimental work of refs 7 and 32.

■ CONCLUSIONS

A synthesis mimetic scheme (SMS) using the ReaxFF forcefield has been developed to create realistic silica surfaces andalkylsilane monolayers on those surfaces. Equilibrium simu-lations have been conducted using ReaxFF and OPLS-AA tocompare monolayer properties predicted by both force fields;since very close agreement was obtained, results from ReaxFFand OPLS-AA simulations can be directly compared. For theSMS systems and more idealized systems, monolayer propertieswere determined using ReaxFF equilibrium simulations, andcoefficients of friction were determined using OPLS-AAnonequilibrium simulations. The results suggest that there isa negative correlation between the coefficient of friction duringmonolayer−monolayer shearing and the global orientationalordering of the monolayers. The introduction of defects intothe monolayers yields a slight decrease in orientational orderingand a slight increase in friction, while the introduction ofatomic-scale roughness into the silica surfaces leads to a moresignificant decrease in orientational ordering and increase infriction. Furthermore, monolayer defects and surface roughnessappear to have a cumulative impact on both global orientationalordering and friction, as evidenced by the simulations of theSMS systems. These results demonstrate the importance ofusing realistic models that consider the synthesis andprocessing steps associated with the creation of alkylsilanemonolayers and provide insight into the key factors thatinfluence the frictional performance of monolayers.

■ ASSOCIATED CONTENT

*S Supporting InformationAdditional details of the simulation methods and descriptionsof the calculations performed to quantify the structuralproperties and frictional performance of the monolayers. Thismaterial is available free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATION

Corresponding Author*E-mail: c.mccabe@vanderbilt.edu (C.M.).

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

This work is supported by the National Science Foundation(NSF) through Grant OCI-1047828. Computational resourceswere provided by the National Energy Research ScientificComputing Center (NERSC), which is supported by the Officeof Science of the U.S. Department of Energy under ContractDE-AC02-05CH11231. Jana E. Black also acknowledgessupport from the Department of Education for GraduateAssistance in Areas of National Need (GAANN) Fellowshipunder Grant P200A090323.

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Table 3. RMS Roughness Values and Coefficients of Friction for C10 Alkylsilane Monolayers with Densities of 3.9 chains/nm2 a

system coefficient of friction arrangement of chains in monolayer atomic-scale properties of silica RMS roughness of silica (Å)

SMS 0.40 ± 0.02 nonuniform amorphous 1.3idealized 0.14 ± 0.01 uniform crystalline 0.0defected 0.17 ± 0.02 nonuniform crystalline 0.0

amorphous smooth 0.26 ± 0.03 uniform amorphous 0.4medium 0.32 ± 0.04 uniform amorphous 0.9rough 0.34 ± 0.02 uniform amorphous 1.2

aError bars represent standard error of the mean.

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