Article pubs.acs.org/Langmuir
Molecular Dynamics Study of Alkylsilane Monolayers on Realistic Amorphous Silica Surfaces Jana E. Black,†,‡ Christopher R. Iacovella,†,‡ Peter T. Cummings,†,‡ and Clare McCabe*,†,‡,§ †
Department of Chemical and Biomolecular Engineering, ‡Multiscale Modeling and Simulation (MuMS), and §Department of Chemistry, Vanderbilt University, Nashville, Tennessee 37235, United States S Supporting Information *
ABSTRACT: Interfacial properties of n-alkylsilane monolayers on silica have been investigated with molecular dynamics simulations using both reactive and classical (i.e., nonreactive) force fields. A synthesis mimetic simulation (SMS) procedure using the reactive force field ReaxFF has been developed to mimic the experimental processing of silicon wafers involved in the preparation of alkylsilane monolayers; in the SMS procedure, amorphous silica surfaces are generated and exposed to hydrogen peroxide (H2O2) to create a hydroxide surface layer. Alkylsilane monolayers are then assembled on these surfaces, and their behavior is studied. To investigate the impact of the SMS procedure on monolayer properties, simulations have also been performed using more idealized monolayers assembled on crystalline surfaces and non-H2O2-processed amorphous surfaces. The simulations reported here demonstrate that processing-induced silica surface roughness plays a key role in the structure and frictional performance of monolayers. Furthermore, ignoring these effects results in a significant underestimation of the coefficient of friction and an overestimation of the orientational ordering of the monolayers.
■
INTRODUCTION Micro- and nano-electromechanical systems (MEMS and NEMS) have been used to develop smaller and more efficient sensors to detect chemical signals, stresses, vibrations, and forces at the atomic level;1,2 examples include tips and cantilever beams in atomic force microscopy3 and inertial navigation system accelerometers and gyroscopes.4 MEMS/ NEMS devices have small lateral dimensions and therefore large surface-area-to-volume ratios, which without lubrication can result in significant surface interactions, e.g., adhesion and friction, that can lead to surface damage and eventual device failure.1,5 An effective method to protect and lubricate contacting surfaces in such devices is to employ chemisorbed monolayers. Different types of monolayers can be assembled on a 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 surfaces from oxidation and wear.4,6−12,33 Several fundamental studies of alkylsilanes have been reported to gain insight into which monomer and monolayer properties can be used to enhance tribological performance. For example, recent experimental work on alkylsilane monolayers assembled on silica7 and mica32 demonstrated a decrease in friction as alkylsilane chain length increases; in both cases the authors concluded that increased disorder in monolayers constructed from shorter alkylsilane chains (5−8 backbone carbons), as compared to those constructed from longer chains (12−18 backbone carbons), was the cause of increased friction.32 Experiments have also shown that the chemistry of the terminal contacting groups of the monolayer © 2015 American Chemical Society
molecules has a significant impact on friction and adhesive forces.7 Additionally, Flater et al. conducted AFM experiments in which the AFM tip and/or the silicon surface was coated by an alkylsilane monolayer and demonstrated that friction and adhesion decrease when either surface is coated and that the effect is cumulative when both surfaces are coated.34 Molecular simulation has also been used to increase our understanding of the molecular-level behavior of alkylsilane monolayers.6−12,22,33 For example, molecular dynamics simulation has demonstrated that pure alkylsilane monolayers yield lower coefficients of friction than pure perfluoroalkylsilane monolayers while undergoing shear.6,11,12 Furthermore, mixed alkylsilane/perfluoroalkylsilane monolayers were shown to provide better protection against friction than either of the pure monolayers by combining the advantageous properties of high surface coverage in alkylsilane monolayers with the low surface energy of perfluoroalkylsilane monolayers.11 We note however that many prior simulation studies have examined monolayers assembled on ideal crystalline surfaces. While crystalline surfaces appropriately represent gold28,30 and diamond15,29,35,36 surfaces, they introduce an approximation when used to represent silica surfaces since the comparable experimental surfaces are typically amorphous.4,17−19,37 As a result, there may be discrepancies between the system properties predicted by the simulations and those observed in experiments. For example, simulations have historically overReceived: December 23, 2014 Revised: February 21, 2015 Published: February 26, 2015 3086
DOI: 10.1021/la5049858 Langmuir 2015, 31, 3086−3093
Article
Langmuir
for the Si/O interactions and Rahaman et al.41 for the C/O/H interactions. A full description of the ReaxFF potential is given by van Duin et al.39 The classical simulations were performed using the optimized potentials for liquid simulations all-atom (OPLS-AA) force field.42 The OPLS-AA parameters used in this work were taken from Lorenz et al.10 for silica and Jorgensen et al. for the alkanes,42 in accordance with prior simulation studies of alkylsilane monolayers on silica.6,7,11,12 All simulations were performed using the LAMMPS simulation engine43 in the NVT ensemble (constant number of atoms, volume, and temperature) with periodic boundary conditions in the surface plane (i.e., the xy-plane) in order to mimic the behavior of an infinite surface; simulations did not interact across the z-boundary. Temperature was controlled via the Nosé−Hoover thermostat44,45 with a temperature damping parameter of 50 fs. Simulations using the ReaxFF potential employed a 0.5 fs time step.39 In all simulations using the OPLS-AA potential, the equations of motion were integrated using the multiple time step algorithm rRESPA with timesteps of 0.3 fs for bond interactions, 0.6 fs for angle interactions (valence and dihedral), and 1.2 fs for Lennard-Jones and electrostatic interactions, which were computed using the particle−particle, particle-mesh algorithm for slabs (i.e., electrostatic interactions were not calculated across the nonperiodic boundary). Lennard-Jones interactions were computed using a cutoff radius of 10 Å, in accordance with prior simulation studies.6,7,11,12 Unless stated otherwise, each system was simulated at room temperature (300 K) with the outer 50% of the silica surface (i.e., the portion not in contact with the monolayer) immobilized to prevent bulk translation of the system. Postequilibration trajectory lengths were 2 ns for the equilibrium molecular dynamics simulations used to study the structural properties of monolayers, which were conducted using the ReaxFF potential. Postequilibration trajectory lengths ranged from 5 to 10 ns for the nonequilibrium molecular dynamics simulations used to study the frictional performance of monolayers, which were conducted using the OPLS-AA potential. These trajectory lengths were found to be sufficient in order for the simulations to converge to a steady state and yield data with reasonably low uncertainty. SMS Procedure. Previously, Litton and Garofalini46 performed molecular dynamics simulations using a multibody potential to generate amorphous silica; 2:1 mixtures of silicon and oxygen atoms were heated to 10 000 K and then rapidly quenched to room temperature. Using ReaxFF to create bulk amorphous silica, the same general procedure has been implemented in this work. Specifically, 4800 oxygen atoms and 2400 silicon atoms were confined to a periodic box of dimensions 4.77 × 4.13 × 5.52 nm3; the atoms were organized in a regular alternating pattern similar to patterns observed in crystalline silica. The system was then heated from room temperature to 5000 K over the course of 1.0 ps such that it melted and was then quenched back to room temperature over the course of 1.0 ps; the system was then simulated at room temperature for 1.0 ps to form bulk amorphous silica. 4.77 × 4.13 × 2.30 nm3 slices of the bulk silica were selected and then used as amorphous silica surfaces. Prior work has shown that systems of this size are sufficiently large to avoid system size effects due to periodic boundary conditions.33 To mimic the treatment of silica surfaces with piranha solution, the amorphous silica surfaces were then exposed to H2O2. Two nonidentical silica surfaces were placed at opposing ends of a box of dimensions 4.77 × 4.13 × 15.0 nm3
estimated the average tilt angle (relative to the normal to the surface) of chains in alkylsilane monolayers, which has been attributed to the idealized nature of the silica surfaces used in the simulations. Simulations of amorphous silica surfaces have demonstrated increased coefficients of friction compared to crystalline surfaces, and the differences have been attributed to the nonuniform arrangement of the alkylsilane chains on the surface and the resulting presence of voids.8−10,20 However, the amorphous surfaces used in prior simulation studies may still not be fully representative of the silica surfaces used in experiment, since the effects of the postsynthesis processing of silica done experimentally are not taken into account. Specifically, in the experimental procedure to prepare alkylsilane monolayers, silicon wafers are typically first treated with a “piranha” solution (H2SO4/H2O2) to generate a silica layer containing surface hydroxide groups. Trichloroalkylsilane molecules then readily bond to these hydroxide groups in the presence of water to generate an alkylsilane monolayer.7,33 The strong oxidation present during this process has been shown to introduce atomic-scale surface roughness and alter the surface structure relative to an untreated amorphous silica surface.38 In order to determine the impact of this surface preparation on surfaces and monolayers, chemical reactions, which are not permitted in molecular dynamics simulations using classical force fields, must be taken into account. In this work, a synthesis mimetic simulation (SMS) procedure using the ReaxFF force field39 has been developed to create realistic hydroxylated silica surfaces and alkylsilane monolayers. In the SMS procedure, amorphous silica surfaces are generated and then exposed to H2O2 to create a hydroxide surface layer to which alkylsilane chains are bonded. This process closely mimics the postsynthesis processing of silicon wafers with piranha solution. Monolayer properties and coefficients of friction have been determined for these SMSbased configurations and compared to the properties of more idealized configurations (i.e., idealized monolayers on crystalline silica, monolayers with defects on crystalline silica, and monolayers on non-H2O2-processed amorphous silica of varying atomic-scale roughness). This study demonstrates the importance of using realistic models that consider the synthesis and processing steps associated with the creation of monolayers and provides insight into the key factors that influence the frictional performance of monolayers.
■
SIMULATION METHODS Molecular dynamics simulations were carried out using both reactive and classical force fields. Specifically, reactive simulations were used to generate amorphous substrates, both unprocessed and processed using the SMS procedure (described below), and to investigate the structural properties of monolayers under equilibrium conditions. Since classical simulations are less computationally expensive than reactive simulations by a factor of ∼50, the OPLS-AA potential was used rather than the ReaxFF potential to study the coefficients of friction of monolayers under nonequilibrium conditions in order to capture longer trajectories more efficiently. The reactive simulations were performed using ReaxFF, which uses a bond order/bond distance relationship with a polarizable charge description and bond-order-dependent three- and fourbody interactions in addition to van der Waals and Coulombic forces, in order to accurately model chemical reactions.39 The parameters used in this work were taken from Fogarty et al.40 3087
DOI: 10.1021/la5049858 Langmuir 2015, 31, 3086−3093
Article
Langmuir
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−O bonds 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
groups/nm2. Unbound molecules were then removed from the system. 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 following hydroxylation by H2O2. The new surface hydroxide groups were considered eligible bonding sites for alkylsilane chains; if two hydroxide groups were less than 2.0 Å apart, only one was considered an eligible bonding site due to steric hindrance. C6−C18 alkylsilane monolayers (i.e., monolayers of alkylsilane chains with uniform lengths of 6−18 carbons) with densities of 3.9, 4.3, and 4.9
perpendicular to the surface plane (i.e., in the z-direction) with 600 H2O2 molecules between the surfaces. The surfaces were then pushed toward each other at a rate of 0.1 nm/fs until the volume available to the H2O2 molecules reached the liquid density of pure H2O2 (1.45 g/cm3). The system was then simulated using ReaxFF at room temperature with the outer 67% of each surface fixed to ensure the distance between silica surfaces remained constant. During this time, H2O2 molecules reacted with the surface of the silica to form hydroxide groups. After ∼60 ps, the number of surface bound hydroxide groups reached a plateau and attained a density of ∼5.8 hydroxide 3088
DOI: 10.1021/la5049858 Langmuir 2015, 31, 3086−3093
Article
Langmuir chains/nm2 and 77, 85, and 96 alkylsilane chains, respectively, were generated using this procedure by varying the minimum cutoff distance between bonding sites from 2.0 to 2.5 Å and randomly choosing between the available sites. These surface coverages are consistent with experimental alkylsilane monolayers assembled on silica, which have been reported to have densities of ∼4.0−4.5 chains/nm2.33 High-energy states due to steric hindrance and the overlap of particles typically do not cause fundamental issues in classical molecular dynamics simulations since all bonds are permanent; however, in simulations using ReaxFF, high-energy states and stress on alkylsilane chains cause them to break and/or become detached from the silica surface if the chains are simply placed at the desired bonding sites. In order to avoid this issue, OPLSAA was used to relax the grafted alkylsilane chains, and once the system reached a stable low-energy state, the simulation was run using ReaxFF. A system generated using this procedure is shown in Figure 1A. Additional details of this procedure are provided 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
The amorphous systems (Figure 1D) were created using the idealized systems as starting configurations (i.e., 100-monomer monolayers of varying densities grafted onto expanded βcristobalite). For each system, the substrate was heated to 5000 K until it melted, again using ReaxFF and following the general procedure of Litton and Garofalini,46 while the alkylsilane chains were fixed; upon cooling to room temperature, oxygen atoms on the silica surface formed bonds to the fixed attachment sites (i.e., silicon atoms) of the alkylsilane chains. Following the re-formation of the bonds, the monolayer was allowed to relax. This procedure generated monolayers with a relatively uniform in-plane arrangement of chains (i.e., minimal defects) grafted to amorphous silica substrates with RMS roughness values of ∼0.4 Å. We consider these to be smooth surfaces. Additional systems in which the silica surfaces have higher RMS roughness values were also generated by randomly perturbing the center of mass of individual alkylsilane chains normal to the surface prior to heating/quenching of the substrate. We define the medium amorphous system as that with RMS roughness of ∼0.9 Å and the rough amorphous system as that with RMS roughness of ∼1.2 Å. A full description of this procedure is given in the Supporting Information. In order to quantify the structural properties and frictional performance of all the alkylsilane monolayers studied, the tilt angle and nematic order parameter of the chains within the monolayers and the RMS roughness of surfaces, as well as the coefficient of friction of monolayers undergoing shear, have been determined. The average tilt angle of a monolayer is defined such that a monolayer in perfect alignment with a vector normal to the silica surface yields a tilt angle of 0°. The nematic order parameter (S2) is used to quantify global orientational ordering of the monolayer. A value of S2 = 1 indicates perfect orientational ordering within the monolayer, and values of S2 less than unity represent proportionately less orientational ordering. The RMS roughness of surfaces has been estimated by the standard deviation of the positions of the surface oxygen atoms that are bonded to alkylsilane chains normal to the surface plane. Simulations of monolayers undergoing shear were conducted at several different normal forces, and the coefficient of friction was approximated by the slope of the line generated by plotting friction force as a function of normal force. A detailed description of the calculation of each of these metrics is provided in the Supporting Information.
Table 1. Key Structural Properties of the Alkylsilane Monolayer Systems Studied system SMS idealized defected amorphous
smooth medium rough
arrangement of chains in monolayer
atomic-scale properties of silica
RMS roughness of silica (Å)
nonuniform uniform nonuniform uniform uniform uniform
amorphous crystalline crystalline amorphous amorphous amorphous
1.3 0.0 0.0 0.4 0.9 1.2
were also examined.8−13,24,33 Systems with three distinct levels of nonideality were studied: uniform monolayers grafted onto crystalline surfaces (which we refer to as “idealized”), monolayers grafted onto crystalline surfaces with defects induced by removing individual alkylsilane chains (which we refer to as “defected”), and monolayers grafted onto untreated amorphous surfaces (which we refer to as “amorphous”) with varying 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 4.9 chains/nm2) assembled on a crystalline silica surface that is based on the structure of β-cristobalite. While alkylsilane monolayers assembled on β-cristobalite have a density of 5.1 chains/nm2, the lower monolayer densities used here were achieved by expanding a β-cristobalite silica surface with initial dimensions 4.77 × 4.13 × 1.05 nm3 by a factor of 1.02−1.14. The defected model (Figure 1C) consists of alkylsilane monolayers assembled on the original unexpanded βcristobalite substrate. In these systems, monolayer densities of 3.9, 4.3, and 4.9 chains/nm2 were achieved by removing 4−23 chains (out of 100) at random and terminating the unused bonding sites with hydrogen ions. In equilibrium simulations of the idealized and defected systems, atoms in the silica surfaces were immobilized since stretching of Si−O bonds (e.g., during the expansion of β-cristobalite) could lead to rupture in ReaxFF simulations.
■
RESULTS AND DISCUSSION Since ReaxFF has not been used extensively to study monolayers, equilibrium simulations using the idealized model were conducted using ReaxFF and OPLS-AA to compare 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, nematic order parameter, and monolayer thickness of C10 −C 18 monolayers; in the case of C6 monolayers, the ReaxFF results appear to be in better agreement with experiment.7 Thus, simulations using both force fields should provide quantitative agreement regarding the structural properties of C10−C18 monolayers and can be used interchangeably and directly compared 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 order parameter), equilibrium simulations using the ReaxFF potential 3089
DOI: 10.1021/la5049858 Langmuir 2015, 31, 3086−3093
Article
Langmuir have been performed for the idealized, defected, smooth amorphous, and SMS systems. Tilt angle (Table 2) and nematic Table 2. Average Tilt Angle (deg) as a Function of Monolayer Density and Chain Lengtha 4.9 chains/nm2
a
C6 C10 C14 C18
30.6 27.4 27.5 32.0
± ± ± ±
C6 C10 C14 C18
31.0 39.6 37.1 38.6
± ± ± ±
C6 C10 C14 C18
31.7 31.5 32.3 34.8
± ± ± ±
C6 C10 C14 C18
29.7 30.6 32.4 31.9
± ± ± ±
4.3 chains/nm2
SMS 37.1 ± 20.9 34.6 ± 17.4 32.3 ± 13.6 37.1 ± 11.9 idealized 10.1 37.3 ± 9.1 3.6 39.1 ± 9.5 5.5 38.4 ± 8.4 4.6 38.6 ± 7.2 defected 11.6 35.6 ± 10.8 9.4 37.3 ± 13.2 10.4 36.1 ± 12.5 10.7 35.3 ± 10.8 smooth amorphous 8.4 33.6 ± 10.1 6.0 35.1 ± 8.4 7.3 34.7 ± 6.5 5.4 34.2 ± 7.3 16.5 14.2 13.5 9.0
3.9 chains/nm2 37.7 37.2 37.7 36.0
± ± ± ±
20.3 17.8 15.4 16.3
42.9 39.8 38.5 39.2
± ± ± ±
9.1 8.3 9.5 8.2
41.3 39.8 42.4 39.6
± ± ± ±
16.3 16.0 13.8 14.6
37.2 35.7 36.5 37.4
± ± ± ±
11.2 7.1 8.5 9.1
Error in measurements is one standard deviation. Figure 2. Average nematic order parameter (S2) as a function of monolayer 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. Error bars represent one standard deviation.
order parameter (Figure 2) have been determined as a function of chain length (C6−C18) and monolayer density (3.9, 4.3, and 4.9 chains/nm2). Uniform monolayers (i.e., idealized and amorphous) were found to yield lower standard deviations in tilt angle than nonuniform monolayers (i.e., defected and SMS), suggesting voids/defects in the monolayers allow the chains to explore new conformations and as a result have a wider range of tilt angles. Monolayers assembled on amorphous surfaces (i.e., amorphous and SMS) have slightly lower average tilt angles than those assembled on crystalline surfaces (i.e., idealized and defected), which suggests that atomically rough surfaces may cause the chains to stand slightly more upright. As previously mentioned, simulations of alkylsilane monolayers have historically overestimated the chain tilt, and our results support the suggestion that this is due to the idealized nature of the crystalline silica surfaces used. In all cases, tilt angle increases as monolayer density decreases, but there does not appear to be a meaningful correlation between monomer length and tilt angle. The nematic order parameter (S2) decreases as additional levels of nonideality are introduced into the system and as monolayer density and monomer length decrease. Monolayers assembled on crystalline surfaces (i.e., idealized and defected) have significantly higher orientational order than monolayers assembled on amorphous surfaces (i.e., amorphous and SMS). The difference in S2 between monolayers assembled on crystalline surfaces and amorphous surfaces is more significant than the difference in S2 between uniform monolayers (i.e., idealized and amorphous) and nonuniform monolayers (i.e., defected and SMS). These results suggest that atomic-scale surface roughness may play a larger role in global orientational ordering than in-plane monolayer organization. To further investigate the effects of atomic-scale silica surface roughness on monolayer properties, equilibrium simulations using the ReaxFF potential have been performed using C10
monolayers grafted onto amorphous surfaces of varying RMS roughness; the monolayers have densities of 3.9 chains/nm2, and the RMS roughness of the silica surfaces varies from ∼0.5 to 1.0 Å. Tilt angle (Figure 3A) and nematic order parameter
Figure 3. Average tilt angle (A) and nematic order parameter (S2) (B) as a function of RMS roughness for C10 alkylsilane monolayers on silica with densities of 3.9 chains/nm2. Error bars represent one standard deviation. 3090
DOI: 10.1021/la5049858 Langmuir 2015, 31, 3086−3093
Article
Langmuir
time and used to calculate the coefficient of friction. For simulations of the amorphous and SMS systems, permanent bonds required for OPLS-AA simulations were determined via the ReaxFF bond order calculation, with angles and dihedrals determined from this bonding topology following the OPLSAA parameter set. The results of the nonequilibrium simulations are reported in Figure 4 and Table 3. The coefficient of friction values
(Figure 3B) have been determined as a function of RMS roughness. As surface roughness increases, tilt angle decreases slightly, and the standard deviation increases slightly; this observation suggests that increasing atomic-scale surface roughness causes the chains to stand more upright on the surface and have a wider range of tilt angles. These results further support the idea that many prior simulation studies have overestimated the tilt angle of alkylsilane monolayers due to the idealized nature of the crystalline silica surfaces used. As surface roughness increases, global order decreases dramatically, as evidenced by the nematic order parameter (S2); these data further support the suggestion that atomic-scale surface roughness significantly impacts the global ordering of alkylsilane 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 processing on the frictional performance of alkylsilane monolayers undergoing shear. As previously mentioned, OPLS-AA was used here rather than ReaxFF for computational efficiency and to avoid the possibility of chain breakage. Although we recognize that chain breakage is important in the determination of wear mechanisms, it is not within the scope of this study and will be considered in future work. Furthermore, since equilibrium ReaxFF and OPLS-AA simulations were shown to provide quantitative agreement regarding the structural properties of alkylsilane monolayers, fundamental differences are not expected by using OPLS-AA. Shearing simulations were conducted using C10 monolayers with densities of 3.9 chains/ nm2; this monolayer density was chosen because it most closely approximates the density of real alkylsilane monolayers (∼4.0 chains/nm2). All systems described here were assigned identical monomer lengths and monolayer densities so that the impact of key structural properties (i.e., the arrangement of chains in the monolayers and structure of the silica surfaces) on frictional performance could be examined directly. Identical monolayer-covered surfaces were mirrored over the surface plane to create two monolayers in contact. To conduct shearing simulations at different normal forces, independent shearing runs were performed at 4−5 different fixed separation distances for each system. During each shearing run, the distance between the inner surfaces of opposing silica substrates (i.e., the silica−monolayer boundaries) was assigned a fixed value between 1.8 and 3.0 nm. This separation distance was quantified by the average distance normal to the surface between bonding sites (i.e., oxygen atoms in the silica bonded to alkylsilane chains) on opposing surfaces. The positions of atoms in the silica surfaces were not integrated through time, so the relative positions of atoms within a substrate remained constant (i.e., the silica substrates behaved as rigid bodies). Constant velocities of 5 and −5 m/s were applied to the upper and lower silica surfaces, respectively, in the x-direction; alkylsilane chains bonded to the rigid silica surfaces were free to move. While shearing speeds of 10 m/s are higher than those normally used in experiment, several studies8−11,33 report that shearing velocities of this magnitude do occur between monolayer-covered surfaces in nanotribological systems, including MEMS/NEMS. Furthermore, prior studies have shown that frictional forces do not significantly depend on sliding velocity at moderate loads.8−11,33 The friction force on each monolayer (i.e., the sum of the forces in the x-direction) and the normal force on each monolayer (i.e., the sum of the forces in the z-direction) were determined periodically over
Figure 4. Friction force per area as a function of normal force per area for C10 alkylsilane monolayers with densities of 3.9 chains/nm2. Error bars represent standard error of the mean.
determined for the idealized, defected, and smooth amorphous systems are consistent and provide close agreement with prior results.9,11,48 Specifically, Lewis et al. obtained a coefficient of friction of 0.15 for idealized C10 monolayers11 as compared to the value of 0.14 obtained for idealized C10 monolayers in this work. Chandross et al. obtained a coefficient of friction of 0.19 for C8 monolayers containing defects,9 which compares well with the value of 0.17 obtained for C10 monolayers with comparable defects in this work. Chandross et al. also reported a coefficient of friction of 0.21 for C8 monolayers on amorphous silica surfaces with no induced surface roughness,48 which is comparable to the value of 0.26 determined here for C10 monolayers assembled on smooth amorphous silica. In combination, the results presented in this work, along with the literature values, demonstrate that the introduction of defects to uniform monolayers assembled on crystalline silica leads to a small increase in the coefficient of friction, while assembling monolayers on amorphous silica rather than crystalline silica results 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 values found for the smooth amorphous, idealized, and defected systems. The smooth amorphous silica and SMS-based silica have RMS roughnesses of 0.4 and 1.3 Å, respectively (the crystalline surfaces have roughnesses of 0 Å). To determine if a correlation exists between surface roughness and coefficient of friction, shearing studies of the medium amorphous system (0.9 Å) and rough amorphous system (1.2 Å) were also conducted; these systems demonstrated coefficients of friction of 0.32 and 0.34, respectively. Thus, a positive correlation between surface roughness and coefficient of friction is observed. The coefficient of friction is still higher for the SMS-based system than the rough amorphous system, likely due to the fact that the rough amorphous monolayer is more uniform in its in-plane 3091
DOI: 10.1021/la5049858 Langmuir 2015, 31, 3086−3093
Article
Langmuir
Table 3. RMS Roughness Values and Coefficients of Friction for C10 Alkylsilane Monolayers with Densities of 3.9 chains/nm2 a
a
system
coefficient of friction
arrangement of chains in monolayer
atomic-scale properties of silica
RMS roughness of silica (Å)
SMS idealized defected amorphous smooth medium rough
0.40 ± 0.02 0.14 ± 0.01 0.17 ± 0.02 0.26 ± 0.03 0.32 ± 0.04 0.34 ± 0.02
nonuniform uniform nonuniform uniform uniform uniform
amorphous crystalline crystalline amorphous amorphous amorphous
1.3 0.0 0.0 0.4 0.9 1.2
Error bars represent standard error of the mean.
■
arrangement (i.e., contains minimal defects) compared to the SMS-based monolayer. These results indicate that defects present in monolayers and atomic-scale surface roughness both increase the friction between monolayers. The difference in friction coefficient between monolayers assembled on crystalline surfaces (i.e., idealized and defected) and those assembled on amorphous surfaces (i.e., amorphous and SMS) is more significant than the difference in friction between uniform monolayers (i.e., idealized and amorphous) and nonuniform monolayers (i.e., defected and SMS). Thus, atomic-scale surface roughness can be concluded to be a larger contributor to friction, but the presence of defects and surface roughness demonstrate a cumulative effect, as evidenced by the SMS system. These results, in conjunction with the aforementioned orientational ordering results of isolated monolayer systems, suggest that there is a negative correlation between the global orientational ordering of monolayers and the coefficient of friction of the monolayers undergoing shear, as was suggested in the experimental work of refs 7 and 32.
■
ASSOCIATED CONTENT
S Supporting Information *
Additional details of the simulation methods and descriptions of the calculations performed to quantify the structural properties and frictional performance of the monolayers. This material is available free of charge via the Internet at http:// pubs.acs.org.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected] (C.M.). Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS This work is supported by the National Science Foundation (NSF) through Grant OCI-1047828. Computational resources were provided by the National Energy Research Scientific Computing Center (NERSC), which is supported by the Office of Science of the U.S. Department of Energy under Contract DE-AC02-05CH11231. Jana E. Black also acknowledges support from the Department of Education for Graduate Assistance in Areas of National Need (GAANN) Fellowship under Grant P200A090323.
CONCLUSIONS
A synthesis mimetic scheme (SMS) using the ReaxFF force field has been developed to create realistic silica surfaces and alkylsilane monolayers on those surfaces. Equilibrium simulations have been conducted using ReaxFF and OPLS-AA to compare monolayer properties predicted by both force fields; since very close agreement was obtained, results from ReaxFF and OPLS-AA simulations can be directly compared. For the SMS systems and more idealized systems, monolayer properties were determined using ReaxFF equilibrium simulations, and coefficients of friction were determined using OPLS-AA nonequilibrium simulations. The results suggest that there is a negative correlation between the coefficient of friction during monolayer−monolayer shearing and the global orientational ordering of the monolayers. The introduction of defects into the monolayers yields a slight decrease in orientational ordering and a slight increase in friction, while the introduction of atomic-scale roughness into the silica surfaces leads to a more significant decrease in orientational ordering and increase in friction. Furthermore, monolayer defects and surface roughness appear to have a cumulative impact on both global orientational ordering and friction, as evidenced by the simulations of the SMS systems. These results demonstrate the importance of using realistic models that consider the synthesis and processing steps associated with the creation of alkylsilane monolayers and provide insight into the key factors that influence the frictional performance of monolayers.
■
REFERENCES
(1) Berman, D.; Krim, J. Surface science, MEMS and NEMS: Progress and opportunities for surface science research performed on, or by, microdevices. Prog. Surf. Sci. 2013, 88 (2), 171−211. (2) di Ventra, M.; Evoy, S.; Helfin, J. R. Introduction to Nanoscale Science and Technology; Springer: Berlin, Germany, 2004. (3) Willemsen, O. H.; et al. Biomolecular Interactions Measured by Atomic Force Microscopy. Biophys. J. 2000, 79 (6), 3267−3281. (4) Bush, B. G.; et al. Interfacial Mechanical Properties of nAlkylsilane Monolayers on Silicon Substrates. J. Microelectromech. Syst. 2013, 22 (1), 34−43. (5) Maboudian, R. Surface processes in MEMS technology. Surf. Sci. Rep. 1998, 30 (6−8), 207−269. (6) Booth, B. D.; et al. Tribological Durability of Silane Monolayers on Silicon. Langmuir 2011, 27 (10), 5909−5917. (7) Vilt, S. G.; et al. Surface and Frictional Properties of TwoComponent Alkylsilane Monolayers and Hydroxyl-Terminated Monolayers on Silicon. J. Phys. Chem. C 2009, 113 (33), 14972− 14977. (8) Lorenz, C. D.; et al. Tribological Properties of Alkylsilane SelfAssembled Monolayers. Langmuir 2005, 21 (25), 11744−11748. (9) Chandross, M.; et al. Systematic Study of the Effect of Disorder on Nanotribology of Self-Assembled Monolayers. Phys. Rev. Lett. 2004, 93 (16), 166103. (10) Lorenz, C. D.; et al. Frictional dynamics of perfluorinated selfassembled monolayers on amorphous SiO2. Tribol. Lett. 2005, 19 (2), 93−98. 3092
DOI: 10.1021/la5049858 Langmuir 2015, 31, 3086−3093
Article
Langmuir (11) Lewis, J. B.; et al. Frictional Properties of Mixed Fluorocarbon/ Hydrocarbon Silane Monolayers: A Simulation Study. Langmuir 2012, 28 (40), 14218−14226. (12) Rivera, J. L.; Jennings, G. K.; McCabe, C. Examining the frictional forces between mixed hydrophobic−hydrophilic alkylsilane monolayers. . J. Chem. Phys. 2012, 136 (24), 244701. (13) Cione, A. M.; et al. Deposition and Wettability of [bmim][triflate] on Self-Assembled Monolayers. J. Phys. Chem. C 2009, 113 (6), 2384−2392. (14) Knippenberg, M. T.; et al. Atomic contributions to friction and load for tip−self-assembled monolayers interactions. Phys. Rev. B 2008, 78 (23), 235409. (15) Tutein, A. B.; Stuart, S. J.; Harrison, J. A. Indentation Analysis of Linear-Chain Hydrocarbon Monolayers Anchored to Diamond. J. Phys. Chem. B 1999, 103 (51), 11357−11365. (16) Mazyar, O. A.; Jennings, G. K.; McCabe, C. Frictional Dynamics of Alkylsilane Monolayers on SiO2: Effect of 1-n-Butyl-3-methylimidazolium Nitrate as a Lubricant. Langmuir 2009, 25 (9), 5103− 5110. (17) Bhushan, B.; et al. AFM study of perfluoroalkylsilane and alkylsilane self-assembled monolayers for anti-stiction in MEMS/ NEMS. Ultramicroscopy 2005, 105 (1−4), 176−188. (18) Kasai, T.; et al. Micro/nanotribological study of perfluorosilane SAMs for antistiction and low wear. J. Vac. Sci. Technol., B 2005, 23 (3), 995−1003. (19) Jones, R. L.; Pearsall, N. C.; Batteas, J. D. Disorder in Alkylsilane Monolayers Assembled on Surfaces with Nanoscopic Curvature. J. Phys. Chem. C 2009, 113 (11), 4507−4514. (20) Chandross, M.; et al. Simulations of Nanotribology with Realistic Probe Tip Models. Langmuir 2008, 24 (4), 1240−1246. (21) Lane, J. M. D.; et al. Water Penetration of Damaged SelfAssembled Monolayers. Langmuir 2008, 24 (11), 5734−5739. (22) Vivek, K.; Pierre, A. D.; Srini, R. Molecular dynamics simulations of friction between alkylsilane monolayers. Modell. Simul. Mater. Sci. Eng. 2006, 14 (2), 283. (23) Christian, D. L.; et al. Nanotribology of water confined between hydrophilic alkylsilane self-assembled monolayers. Modell. Simul. Mater. Sci. Eng. 2010, 18 (3), 034005. (24) Lorenz, C. D.; et al. Molecular Dynamics Simulations of Water Confined between Matched Pairs of Hydrophobic and Hydrophilic Self-Assembled Monolayers. Langmuir 2009, 25 (8), 4535−4542. (25) Lorenz, C. D.; Chandross, M.; Grest, G. S. Large Scale Molecular Dynamics Simulations of Vapor Phase Lubrication for MEMS. J. Adhes. Sci. Technol. 2010, 24 (15−16), 2453−2469. (26) Chandross, M.; et al. Probe-Tip Induced Damage in Compliant Substrates. J. Manuf. Sci. Eng. 2010, 132 (3), 030916−030916. (27) Zhang, L.; Goddard, W. A.; Jiang, S. Molecular simulation study of the c(4×2) superlattice structure of alkanethiol self-assembled monolayers on Au(111). J. Chem. Phys. 2002, 117 (15), 7342−7349. (28) Park, B.; et al. Frictional Dynamics of Fluorine-Terminated Alkanethiol Self-Assembled Monolayers. Langmuir 2004, 20 (23), 10007−10014. (29) Tutein, A. B.; Stuart, S. J.; Harrison, J. A. Role of Defects in Compression and Friction of Anchored Hydrocarbon Chains on Diamond. Langmuir 1999, 16 (2), 291−296. (30) Ghorai, P. K.; Glotzer, S. C. Molecular Dynamics Simulation Study of Self-Assembled Monolayers of Alkanethiol Surfactants on Spherical Gold Nanoparticles. J. Phys. Chem. C 2007, 111 (43), 15857−15862. (31) Ramin, L.; Jabbarzadeh, A. Odd−Even Effects on the Structure, Stability, and Phase Transition of Alkanethiol Self-Assembled Monolayers. Langmuir 2011, 27 (16), 9748−9759. (32) Lio, A.; Charych, D. H.; Salmeron, M. Comparative Atomic Force Microscopy Study of the Chain Length Dependence of Frictional Properties of Alkanethiols on Gold and Alkylsilanes on Mica. J. Phys. Chem. B 1997, 101 (19), 3800−3805. (33) Chandross, M.; Grest, G. S.; Stevens, M. J. Friction between Alkylsilane Monolayers: Molecular Simulation of Ordered Monolayers. Langmuir 2002, 18 (22), 8392−8399.
(34) Flater, E. E.; Ashurst, W. R.; Carpick, R. W. Nanotribology of Octadecyltrichlorosilane Monolayers and Silicon: Self-Mated versus Unmated Interfaces and Local Packing Density Effects. Langmuir 2007, 23 (18), 9242−9252. (35) Piotrowski, P. L.; et al. Atomistic Factors Governing Adhesion between Diamond, Amorphous Carbon and Model Diamond Nanocomposite Surfaces. J. Adhes. Sci. Technol. 2010, 24 (15-16), 2471−2498. (36) Gao, G.; et al. Atomic-Scale Friction on Diamond: A Comparison of Different Sliding Directions on (001) and (111) Surfaces Using MD and AFM. Langmuir 2007, 23 (10), 5394−5405. (37) Clear, S. C.; Nealey, P. F. Chemical Force Microscopy Study of Adhesion and Friction between Surfaces Functionalized with SelfAssembled Monolayers and Immersed in Solvents. J. Colloid Interface Sci. 1999, 213 (1), 238−250. (38) Araki, K.; et al. Dependence of Atomic-Scale Si(110) Surface Roughness on Hydrogen Introduction Temperature after HighTemperature Ar Annealing. J. Surf. Eng. Mater. Adv. Technol. 2014, 04 (05), 249−256. (39) van Duin, A. C. T.; et al. ReaxFF: A Reactive Force Field for Hydrocarbons. J. Phys. Chem. A 2001, 105 (41), 9396−9409. (40) Fogarty, J. C.; et al. A reactive molecular dynamics simulation of the silica-water interface. J. Chem. Phys. 2010, 132 (17), -. (41) Rahaman, O.; et al. Development of a ReaxFF Reactive Force Field for Glycine and Application to Solvent Effect and Tautomerization. J. Phys. Chem. B 2010, 115 (2), 249−261. (42) Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids. J. Am. Chem. Soc. 1996, 118 (45), 11225−11236. (43) Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117 (1), 1−19. (44) Nosé, S. A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys. 1984, 81 (1), 511−519. (45) Hoover, W. G. Canonical dynamics: Equilibrium phase-space distributions. Phys. Rev. A 1985, 31 (3), 1695−1697. (46) Litton, D. A.; Garofalini, S. H. Modeling of hydrophilic wafer bonding by molecular dynamics simulations. J. Appl. Phys. 2001, 89 (11), 6013−6023. (47) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual molecular dynamics. J. Mol. Graphics 1996, 14 (1), 33−38. (48) Chandross, M.; et al. Nanotribology of anti-friction coatings in MEMS. JOM 2005, 57 (9), 55−61.
3093
DOI: 10.1021/la5049858 Langmuir 2015, 31, 3086−3093
