Monte Carlo Simulations of Thin Hydrocarbon Films - American

Feb 24, 2014 - Department of Chemistry, Roanoke College, 221 College Lane, Salem, Virginia 24153, United States. §. Department of Chemical Engineerin...
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Monte Carlo Simulations of Thin Hydrocarbon Films: Composition Heterogeneity and Structure at the Solid−Liquid and Liquid−Vapor Interfaces Sara Wenzel,† Hannah Nemec,‡ Kelly E. Anderson,*,†,‡ and J. Ilja Siepmann*,†,§ †

Department of Chemistry and Chemical Theory Center, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455, United States ‡ Department of Chemistry, Roanoke College, 221 College Lane, Salem, Virginia 24153, United States § Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, United States ABSTRACT: The structural properties of 10 nm thick lubricant films consisting of binary and ternary n-alkane mixtures (8 ≤ n ≤ 12) adsorbed on a structureless metal substrate were studied for several temperatures and compositions using Monte Carlo simulations. Configurational-bias Monte Carlo identity switch moves are essential to sample the spatial distribution in these mixtures. Longer alkanes are found to preferentially adsorb onto the substrate while shorter alkanes are enriched at the liquid−vapor interface. This preferential adsorption is evident even when the two chains differ by only one methylene unit and the longer chain is the minor component. Enhanced composition heterogeneity and orientational ordering and fewer gauche defects are characteristic features of the first layer near the substrate.

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INTRODUCTION

Molecular simulations have also been used to examine these effects. Xia and Landman10 used molecular dynamics to study the adsorption of n-hexadecane versus n-hexane from a 1:1 mixture by weight onto an Au(001) surface. Hexadecane was the major component at the solid interface and adopted a partially ordered lamellar structure in the plane of the surface. Also using molecular dynamics, Smith et al.23 examined the solid−liquid and liquid−vapor interfaces of a 1:1 mixture by weight of n-octane and n-butane adsorbed on a wax-like substrate. Structured layers were found near the substrate− liquid interface. While molecular mobility within this layer was greatly reduced relative to the bulk, a solid “frozen” layer was not found. Smith et al. concluded that the solid layer seen by Castro et al. was a result of stronger interactions with the substrate than with the bulk liquid. Looking at the composition of the layers, Smith et al. found more octane than butane in the second and third layers but not in the first (i.e., the layer closest to the substrate). In this paper, we use Monte Carlo simulations with advanced sampling techniques to explore thin films containing mixtures of linear alkanes differing by one to four methylene units. We examine compositional heterogeneity, out-of-plane and in-plane structure near the solid−liquid and liquid−vapor interfaces, and conformational ordering over a range of temperatures well above the bulk melting point.

Understanding the properties of liquid films of articulated molecules near solid surfaces is of interest for many diverse applications, including lubrication, adhesion, and chromatography. The formation of molecular layers in liquids near solid substrates is a well-documented phenomenon.1−35 The structural and dynamic properties within these layers differ from the bulk liquid. For example, the viscosity is generally higher within the layers than in the bulk.23,30,35 Preferential adsorption at the liquid−solid interface is seen in a variety of mixtures.1,10,14,19−26,33 A few experimental studies of linear alkane mixtures indicate that longer alkanes are preferentially adsorbed onto graphite, even when the chains differ by only one methylene unit.1,19−22,25,32 Castro et al. examined a variety of binary mixtures of linear alkanes adsorbed on graphite near the bulk melting point using differential scanning calorimetry and incoherent elastic neutron scattering.19−22 At temperatures slightly above the bulk melting point, these studies indicate the formation of a solid monolayer next to the substrate when either pure liquids or mixtures are adsorbed. In mixtures, the longer component is preferentially adsorbed at the interface, even when it is the minor component.19 Cousty and Pham Van25 used scanning tunneling microscopy to examine binary mixtures of n-alkanes with a length ratio of 2. Their studies also show a strong preference for the longer alkane, C36H74, to adsorb at a graphite surface. This monolayer, though, is not pure C36H74. Two C17H36 molecules are able to occupy one C36H74 vacancy in the layer. The result is a partially demixed solid solution. © 2014 American Chemical Society

Received: December 19, 2013 Revised: February 20, 2014 Published: February 24, 2014 3086

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SIMULATION DETAILS Monte Carlo (MC) simulations for several alkane mixtures were performed in the canonical (NVT) ensemble. Alkane− alkane interactions were described by the TraPPE−UA (transferable potentials for phase equilibria−united atom) force field36 which uses the 12−6 Lennard-Jones potential for nonbonded interactions, a cosine series potential for dihedral (1−4) interactions, and a harmonic potential for angle bending, while bond lengths are kept fixed. Alkane−substrate interactions were calculated using the Hautman−Klein 12−3 potential37 with parameters appropriate for a flat Au(111) substrate. By comparing data from simulations of alkane films with this potential to those using an atomistic representation of the surface, Balasubramanian et al.12,13 showed that using a featureless surface, and a very simple interaction potential, has only a small effect on simulation results at temperatures above the melting point. As a result, we chose to simplify these simulations and use an implicit surface representation. The simulated systems consisted of thin, liquid films composed of 600 alkane chains and featured two interfaces: a substrate−liquid interface and a liquid−vapor interface. Periodic boundaries were applied in the xy-plane. A rectangular simulation cell with dimensions 40 Å × 40 Å in the xy-plane was used. In the z-direction, a ceiling was applied at a distance at least 50 Å above the vapor−liquid interface in order to prevent any vaporized molecules from entirely escaping the system. In most cases, this ceiling was applied at 200 Å from the substrate. Monte Carlo trial moves that would result in a center-of-mass location of a molecule above this ceiling were simply rejected. In the analysis, z = 0 Å corresponds to the outer layer of the substrate. This work focuses on mixtures of medium-molecular-weight linear alkanes. In particular, binary mixtures of varying concentrations of octane/nonane, octane/decane, octane/ dodecane, and nonane/decane were simulated and well as an equimolar ternary mixture of octane/nonane/decane. For each binary mixture, three compositions were examined: xshort = 0.125, 0.5, and 0.875, where xshort is the mole fraction of the component with fewer C atoms. Each composition was simulated at three temperatures, T = 250, 300, and 350 K, except for the octane/dodecane mixture, where simulations were performed only at 350 K. To assess system size effects, additional simulations of the equimolar octane/nonane mixture were performed for a larger system (N = 4800 molecules with the linear cell dimensions doubled). The same layering pattern at the substrate surface was exhibited for both system sizes. In order to improve statistics, the larger system is used here for the analysis of the spatial distribution of molecules in the first layer above the substrate. Four independent simulations were performed for each state point, starting from different initial configurations. In some initial configurations, molecules were separated by type into layers (e.g., all octane molecules were nearer to the substrate and all nonane molecules nearer to the vapor interface), while in others, molecules of different types were randomly distributed. At least 50 000 MC cycles (1 cycle = N moves) were performed for equilibration before production runs began. Lower temperatures required longer equilibration periods. The simulations were fully equilibrated when the energy, density, and spatial distributions converged. Production runs were at least 200 000 MC cycles. The statistical uncertainties reflect the

standard error of the mean determined from the four independent simulations. In addition to the standard MC moves (center-of-mass (COM) translations and rigid-body rotations around the COM, configurational-bias Monte Carlo (CBMC) conformation sampling38−40), intrabox identity switch moves were used to accelerated the mixing of all components.41,42 This move allows molecules of different types to exchange positions; e.g., a randomly selected octane molecule may be converted to a nonane molecule by replacing a methyl group through an ethyl group at the chain terminus while the reverse transformation occurs simultaneously on a randomly selected nonane molecule. The location of corresponding units (a heptyl chain in the example above) remains the same, while additional units are grown or removed using CBMC. Utilizing this special move type greatly accelerates the sampling of the spatial distribution of the different components in the mixture. As shown in Figure 1, in the absence of identity switch moves,

Figure 1. Equilibration of the spatial composition of octane in an equimolar octane/nonane mixture started from a demixed initial configuration. The instantaneous mole fraction was determined for a 5 Å wide slab centered 40 Å from the substrate. The cyan and magenta lines show the evolution of the mole fraction from simulations without identity switch moves (composition recorded every 1000 MC cycles) and with identity switch moves (composition recorded every 25 MC cycles), respectively.

600 000 MC cycles were insufficient to equilibrate the spatial distribution of components when starting from a layered configuration (i.e., completely demixed with nonane molecules placed near the substrate). In contrast, after only 10 000 MC cycles using the identity switch moves, the mole fraction of each component reached the bulk component mole fraction in a representative slice 40 Å from the substrate. During all CBMC regrowth steps during conformational moves and identity switch moves, 10 trial positions are explored. This choice has been shown previously to provide satisfactory sampling efficiency for united-atom alkane models.36,43 3087

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RESULTS AND DISCUSSION Total Density Profiles. Experimental research on thin liquid films on solid substrates has indicated density oscillations in the vicinity of the substrate.5,31 Analysis of the present simulations also demonstrates the presence of strong density oscillations in the liquid within 20 Å of the substrate (see Figure 2). The peak heights are found to decrease for successive

temperature for each composition examined here. In Figure 2E, the total densities for equimolar mixtures of octane with longer alkanes are shown. Included is the density profile for the ternary octane/nonane/decane mixture. Note that the total mass of this film is equal to that of the octane/decane film. When comparing the density profile of all CHx units, these systems behave identically. The composition has a minor effect on the density of the bulk region with larger values for mixtures involving longer chains or higher fractions of the longer chains, and the same also applies not surprisingly to the total film thickness. Mole Fraction Enhancement. Incoherent elastic neutron scattering measurements on solid binary mixtures of alkanes by Castro et al. suggest that longer alkanes preferentially adsorb to graphite, unless there is a large excess of shorter alkanes.19 Figure 3 shows the effects of increasing difference in the chain

Figure 3. CH3 density profiles for equimolar mixtures of n-octane and a longer n-alkane at T = 350 K [top] and for different temperatures for an equimolar mixture of n-octane (red dashed line) and n-nonane (green solid line) [bottom]. Figure 2. Total density profiles for (A, B) equimolar octane/nonane mixture at T = 250 K (black), 300 K (red), and 350 K (green); (C, D) octane/nonane mixture at 300 K for xoct = 0.125 (cyan), xoct = 0.500 (red), and xoct = 0.875 (purple); (E, F) equimolar mixtures at 350 K of octane/nonane (green), octane/decane (blue), octane/dodecane (orange), and octane/nonane/decane (dashed red). Figures on the left side show details of the density profiles for the first 30 Å above the substrate. Figures on the right side show the remainder of the density profiles. The vertical dashed lines indicate the location of the Gibbs dividing surfaces.

length and of temperature on the density profiles of CH3 units for each chain type in equimolar mixtures. Since each compound possesses two CH3 units, these profiles allow for a straightforward comparison between molecule types. Additionally, we examined the mole fraction enhancement or depletion of each species within this first layer (see Table 1). The mole fraction enhancement is the ratio of the mole fraction of one component in a given interval in the z-direction to the overall bulk mole fraction. The position of a molecule is determined by the z-component of its center of mass. Data are provided for an interval in the bulk region of the liquid films, for reference. The top row of Figure 3 shows the CH3 density profiles for mixture of n-octane with a longer n-alkane (compound B). As the length difference increases, it is clear that for each mixture the density of CH3 units from B in the first layer exceeds that of octane to a greater extent. The difference in density between CH3(octane) and CH3(B) increases from 14% for octane/ nonane to 25% for octane/dodecane. Concomitantly, the overall density of CH3 units in the first layer decreases because of the larger footprint of the longer B chains. The bottom row of Figure 3 shows the effect of temperature on CH3 density in equimolar mixtures of octane/nonane. The density of nonane CH3 units in the first layer is greater than that of octane CH3

layers away from the substrate, and as many as five layers are evident at 250 K and as few as three at 350 K (see Figure 2A). At each temperature and for each mixture, the first peak occurs at the same position, z = 3.8 Å, because of the strong CHx− substrate interactions. However, the locations of subsequent peaks shifts further from the surface as the temperature increases. In contrast to the large temperature effects, neither changing concentration ratios nor chain length appears to have a significant effect on the density profiles near the substrate (see Figures 2C,E). Each mixture reaches a region with bulk density at z ≈ 25 Å from the surface. When the molar masses of the two components are similar, e.g., octane/nonane (see Figure 2C), there is no concentration effect on the number of layers formed; i.e., the same number of layers form at a given 3088

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In an effort to explore this effect, MC simulations for the butane/octane mixture were performed for conditions similar to those of Smith et al. (T = 223 K, xC8 = 0.333, N = 336 molecules, and four independent simulations of 400 000 MC cycles) but using the TraPPE−UA force field for alkane−alkane interactions and the Hautman−Klein potential for alkane− substrate interactions. As can be seen from the density profiles presented in Figure 4, the present simulations yield a strong

Table 1. Mole Fraction Enhancement/Depletion of the Longer (Longest) Compound Obtained for Different Regions of Mixtures with Various Chain Length Differences, Bulk Compositions, and at Different Temperaturesa system

T [K]

xtotal

xregion/xtotal first layerb central regionc LV interfaced

C8/C9

250 300

C8/C10

350 250 300

C9/C10

350 250 300

C8/C9/C10

C8/C12

350 250 300 350 350

0.500 0.875 0.500 0.125 0.500 0.500 0.875 0.500 0.125 0.500 0.500 0.875 0.500 0.125 0.500 0.500 0.500 0.500 0.500

1.112 1.011 1.072 1.143 1.061 1.293 1.021 1.121 1.305 1.102 1.142 1.001 1.091 1.122 1.043 1.224 1.082 1.001 1.202

1.011 1.001 0.991 1.011 0.991 0.983 1.001 1.011 1.031 1.001 1.011 1.001 1.011 0.972 1.002 1.021 1.031 1.012 1.001

0.972 0.991 0.961 0.942 0.971 0.902 0.981 0.942 0.872 0.961 0.941 1.001 0.981 0.952 0.981 0.821 0.851 0.973 0.871

a

Subscripts denote the standard error of the mean in the last digit. zCOM ≤ 6 Å. c57 Å ≤ zCOM ≤ 63 Å. dzCOM within the 10−90 interfacial region. b

units at each temperature (e.g., by about 28% and 14% at 250 and 350 K, respectively). The trend of enhanced long chain adsorption at the solid− liquid interface is also reflected in the mole fraction enhancement data presented in Table 1. The mole fraction enhancement is larger for larger chain length differences; e.g., the composition of dodecane is increased by 20% compared to only 6% for nonane at T = 350 K and for lower temperatures, e.g., an 11% increase for nonane at 250 K. The enthalpy gain for adsorption of longer alkanes outweighs the entropic penalty for partial demixing. The reason for the enthalpic gain is that methylene units occupy a smaller incremental surface area than methyl units, and hence, the total number of CHx units in contact with the substrate is increased when more of the longer chains are present in the first layer. In addition to the chain length difference and the temperature, the composition is found to also play a role in the extent of the partial demixing at the solid−liquid interface (see data given in Table 1). For mixtures at T = 300 K, the extent of the enhancement increases as the overall mole fraction of the longer chain decreases. For example, for the octane/decane mixture, enhancements of 1.30 and 1.02 occur for bulk mole fraction of xC10 = 0.125 and 0.875, respectively. Our findings are in agreement with the work of Xia and Landman, who simulated a 1:1 mixture by weight of n-hexane and n-hexadecane (xC16 = 0.276) and found a significant enrichment of hexadecane at the solid−liquid interface.10 In contrast, Smith et al. studied a 1:1 mixture by weight of nbutane and n-octane (xC8 = 0.337) and found a higher concentration of butane than octane in the first layer near the surface.23 Smith et al. attributed this to the efficient packing of butane between octane molecules.

Figure 4. Total density profile for a 1:1 mixture by weight of butane (blue) and octane (red) at T = 223 K.

preference for octane being adsorbed in the first layer closest to the substrate instead of the preference for butane found by Smith et al.23 Considering the larger relative difference in chain length and the lower temperature, the strong preference for octane in this mixture is consistent with the other systems studied in the present work. Within the layer adjacent to the substrate, on average 15.3 octane and 7.2 butane molecules are found. In the second layer, the contributions of butane and octane to the mass density are similar, whereas a slight preference for butane is found in the third and fourth layers. A similar inversion of the preference but to a smaller extent is found here also for the octane/decane and octane/dodecane mixtures (see Figure 3). The underlying cause for this inversion is likely the greater entropic penalty associated with layering of the larger molecule that is not compensated for by a sufficiently strong interaction with the substrate in these layers at z = 8−20 Å. In contrast, Smith et al.23 report an enhancement of the octane concentration in the second to fourth layer. A key difference between these studies is the choice of substrate−molecule interaction potential. The Hautman−Klein potential has been shown to accurately describe the interactions of alkanes with a gold surface, correctly predicting the magnitude and chain length dependence of the heat of adsorption for alkanes.12 In contrast, the substrate potential developed by Smith et al. represents the weaker interactions with a waxy surface. Clearly the differences in the strength of substrate−molecule interactions influences the structural 3089

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properties of the liquid phase in the vicinity of the substrate and must be considered carefully in simulations of this nature. Liquid−Vapor Interface. A substantial bulk liquid region is present through the central portion of each liquid slab before reaching the vapor−liquid interface at z > 100 Å (see Figure 2). This interface is more diffuse, and it does not exhibit the pronounced density oscillations found near the solid substrate. Furthermore, the film thickness and, hence, the location of the vapor−liquid interface depend on film composition and temperature. To this end, we use a hyperbolic tangent fit to the total density profile to locate the Gibbs dividing surface (GDS) and to define the width of the interface44,45 ρ (z ) =

ρliq + ρvap ⎡ ⎛ z − zGDS ⎞⎤ ⎢1 − tanh⎜ ⎟⎥ ⎢⎣ 2 ⎝ δGDS ⎠⎦⎥

where ρliq and ρvap are the densities of the bulk liquid and vapor, respectively, and zGDS and δGDS are the location of the GDS and the interface thickness parameter. The GDS location is indicated in Figure 2. In this discussion, we use the “10−90” range of the liquid density to define the interfacial region. In contrast to the solid−liquid interface, the shorter alkane is generally preferentially found near the vapor−liquid interface. Table 1 also lists the mole fraction enhancement/depletion of the longer molecule in the 10−90 interfacial region. With regard to composition and temperature effects, the vapor− liquid interface mirrors the solid−liquid interace, i.e., larger chain length difference, long chains being the minority compound, and lower temperature lead to a larger depletion of the longer alkane at the vapor−liquid interface compared to the bulk region (and, of course, also compared to the solid− liquid interface with its enhancement of the longer alkane). For normal alkanes, the surface tension increases with increasing chain length. This behavior is caused by the larger enthalpic and entropic penalty (with respect to orientation and conformation, see below) for adsorption of the longer alkane at the vapor− liquid interface.46 Molecular Alignment. Near a flat substrate (z ≤ 20 Å), alkane molecules are known to align themselves with the long axis of the linear chain parallel to the substrate.6,11,13,31 This alignment can be quantified via the orientational order parameter defined as47,48 S=

Figure 5. Backbone orientational order parameter (bottom row) near the substrate at T = 250 K for, from left to right, equimolar mixtures of octane (red)/nonane (green), nonane (green)/decane (blue), and octane (red)/decane (blue). Snapshots of each system are shown at top with molecules colored according to the same convention.

layers, leading to orientations parallel to the surface normal for 1−3 vectors centered in these interlayer spaces (see snapshots in Figure 5). At the vapor−liquid interface, there is also an alternating pattern of preferential backbone alignments (see Figure 6), but

1 (3 cos2 ϕ − 1) 2

which is a measure of the tilt angle of the chain backbone relative the surface normal vector. The angle ϕ is defined as the angle between the surface normal and the vector formed by any pair of CHx pseudoatoms separated by two bonds (i.e., an i, i + 2 pair) within a given molecule. When the i, i + 2 vector is found parallel to the surface normal (perpendicular to the surface), then S = 1, while S = −0.5 indicates an orientation of the long axis perpendicular to the surface normal (parallel to the surface). Figure 5 shows the order parameter of the films as a function of the z-coordinate of the intermediate (i.e., i + 1) CH2 pseudoatom. The oscillating pattern in the order parameter plot closely follows the peaks in the total density profiles. Within the layers of linear alkanes near the surface, molecules preferentially align parallel to the surface (perpendicular to the surface normal). This orientation maximizes the interactions between the molecules and the substrate and has been demonstrated both experimentally and via simulation.1,3,10,13,23−25,32 A few molecules are found to span the

Figure 6. Backbone orientational order parameter (bottom row) near the substrate at T = 250 K for, from left to right, equimolar mixtures of octane (red)/nonane (green), nonane (green)/decane (blue), and octane (red)/decane (blue). Snapshots of each system are shown at top with molecules colored according to the same convention. The Gibbs dividing surface for each mixture is indicated by the dashed line.

the magnitude of these orientational preferences is small compared to those at the solid−liquid interface. In a region above the GDS (centered at zGDS + 2 Å), chains are more likely to align parallel to the interface (i.e., perpendicular to the zaxis). Immediately below the GDS within the liquid phase is a region of ≈10 Å depth where molecules align preferentially parallel to the z-axis. Orienting parallel to the interface increases the number of favorable interactions with the denser liquid region for the parts of any given molecule in the outermost 3090

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the liquid−vapor interfacial region show no preference for any given molecule pair. In fact, these 2D-RDFs exhibit little structuring of any kind. This may be due to the greater depth of this interface that allows for a wider variety of angular alignments and for overlap between molecules in the 2D projection (i.e., a nonzero RDF value as the separation approaches zero). Figure 8 shows the correlation between the COM separation of two molecules and their relative orientation, measured by the

region, whereas being preferentially aligned along the interface normal allows for better “anchoring” of the parts within the denser liquid region. 2-Dimensional Spatial and Alignment Distributions. Castro et al.20 have examined the extent of mixing between two components in the first monolayer near the substrate and concluded that n-octane and n-nonane phase separate into near pure-component regions for solid monolayers. Here, we examine the spatial and orientational distribution of molecules in the first layer near the substrate and in the outermost region of the liquid film. In the analysis of the octane/nonane mixture, the data are taken from the larger simulations (N = 4800), where 4 times as many molecules are found at the interface (on average, ≈100 molecules) in order to improve the statistics. At the vapor−liquid interface, there is not a well-defined layer in which to examine the spatial distribution. Instead, a twodimensional projection of all molecules with zCOM within the 10−90 interface was analyzed. The width of this region is generally about 4 times the width of the first layer at the substrate interface and includes approximately twice as many molecules. Figure 7 shows the two-dimensional center-of-mass radial distribution functions (2D-RDF) at each interface. At the

Figure 8. Orientational-spatial correlation of the end-to-end vector angular distribution versus the 2D-RDF for molecules in the first layer above the substrate for equimolar mixtures of octane with nonane (left) and dodecane (right) at T = 350 K. In both columns, the top, middle, and bottom graphs show the correlations for octane pairs, nonane or dodecane pairs, and pairs of unlike molecules, respectively.

cosine of the angle between the end-to-end vectors of molecule A and molecule B. Regardless of which molecule pair in a mixture is considered, the molecules in the first layer above the substrate exhibit a very strong preference for parallel mutual alignment at short COM separation distances. Beyond the first solvation shell, there is a minor tendency for molecules to align parallel to one another, and this tendency is slightly stronger at the location of the second peak in the 2D-RDF. For the octane/dodecane mixture, the orientational alignment is also stronger for the C12−C12 pair than for the C8−C8 pair, whereas the correlations for the C8−C8 and C9−C9 pairs in the octane/nonane mixture do not show any significant difference. Representative snapshots of the first layer near the substrate for the octane/nonane and octane/dodecane mixtures are shown in Figure 9. These snapshots clearly illustrate the preference of the molecules to pack locally in stacks with their long axis parallel to each other and parallel to the substrate, i.e.,

Figure 7. Two-dimensional radial distribution functions of the centerof-mass separation for molecules in the first layer near the substrate (top row) and in the vapor−liquid interfacial region (bottom row) at T = 350 K for equimolar octane/nonane (left column) and octane/ dodecane (right column).

solid−liquid interface, the first peak for each molecule pair is located at r = 5.1 Å. In contrast, the location of the first minimum moves to slightly longer distances for pairs involving the longer component (e.g., rC8−C8 < rC8−C9 < rC9−C9 min min min ) as does the location of the second peak. The heights of the peaks are similar for all pairs in the octane/nonane mixture, and the 2DRDFs do not provide evidence of enhanced octane−octane and nonane−nonane interactions. There is significantly more noise in the 2D-RDFs for the octane/dodecane mixture because of the smaller system size. Nevertheless, it appears that the height of the first peak for dodecane−dodecane pairs is somewhat lower than for either 2D-RDF with octane. The 2D-RDFs for 3091

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Figure 10. Fraction of molecules with n gauche defects at T = 350 K for equimolar mixtures of octane with longer linear alkanes. The distributions for different sections of the film are presented as dotted, solid, and striped bars for the first layer near the substrate, the bulk-like liquid region, and the liquid−vapor interfacial region. The z-ranges for each region follow Table 1. Figure 9. Snapshots of molecules belonging to the first layer near the substrate in the octane/nonane (top, large system size, L = 80 Å) and octane/dodecane (bottom, small system size, L = 40 Å) mixtures at T = 350 K. Octane, nonane, and dodecane molecules are shown in red, green, and orange, respectively.

given probability to find a gauche defect, the probability to find an all-trans conformer decreases with increasing number of dihedral angles (ranging from 5 for n-octane to 9 for ndodecane). The fraction of molecules near the substrate (zCOM ≤ 6 Å) with no gauche defects is 2−5 times greater than the fraction of molecules with no gauche defects within the bulk region (57 Å ≤ zCOM ≤ 63 Å) or at the vapor interface (see Figure 10). As the length of the alkane increases, the fraction of molecules in the bulk-like region with no gauche defects drops from 12% to 2% moving from octane to dodecane, while at the substrate, 21% and 11% of octane and dodecane molecules are all-trans, respectively. The distribution of chains with a given number of gauche defects is shifted toward fewer defects for molecules in the layer next to the substrate compared to the bulk-like and liquid−vapor interfacial regions. There is not any statistically significant difference for the populations found in the bulk-like and liquid−vapor interfacial regions. Similarly, the populations found for n-octane are independent of the other molecule type in the mixture. In the bulk-like region, the average number of gauche defects per molecule at T = 350 K is 1.5 for octane and 2.7 for dodecane (i.e., 0.3 per dihedral angle), whereas these values shift to 1.3 and 2.0, respectively, for the strongly adsorbed layer. Conformations that minimize the number of gauche defects allow not only for tighter packing of molecules within the plane but also maximize the number of interactions between the molecule and the substrate, allowing for a strongly adsorbed layer with a density that is significantly higher than the bulk density (see Figure 2). The enthalpic gain from the chain− substrate interactions and the fewer gauche defects overcomes

showing a large projected area. There are only very few molecules that point away from the substrate, e.g., a nonane molecule found in the lower right-hand corner of the snapshot for the octane/nonane mixture. The snapshots also indicate two other characteristics of the first layer structures: there appears to be partial in-plane demixing (i.e., molecules of the same type are more likely to be nearest neighbors), and the molecules exhibit relatively few conformational defects. To quantify the extent of demixing, the like−like mole fraction was computed from the 2D-RDFs for the first solvation shell. For the octane/dodecane mixture at T = 350 K, the octane mole fraction in the solvation shell of an octane molecule is ≈6% larger than the octane mole fraction in the first layer. The extent of this partial demixing decreases with decreasing length difference and increases with decreasing temperature. Thus, the nearly complete demixing observed by Castro et al.20,21,25 is only present in solid monolayers. In order to maximize the favorable interactions between the chains and the substrate, molecules in the strongly adsorbed first layer preferentially adopt conformations with fewer gauche defects (see Figure 10). In this analysis, a gauche defect is defined as any dihedral angle greater than 60° or less than −60° where an anti rotamer (trans state) has a dihedral angle of 0°. All-trans molecules are those with no gauche defects, but for a 3092

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the entropic cost due to the local ordering within the plane. Additionally, Smith et al.23 note that the free energy penalty for a gauche defect is greater for molecules confined to two dimensions than those moving in three dimensions. This results in a greater stabilization of the all-trans conformation within the strongly adsorbed layer, particularly for longer chains with an overall higher probability for a larger number of gauche defects.

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CONCLUSIONS Using Monte Carlo simulations with efficient sampling strategies, it is shown that for liquid films consisting of binary mixtures of linear alkanes in contact with a metal substrate, the longer component preferentially adsorbs at the solid−liquid interface. This preference is evident even when the two components differ in length by only one methylene unit, although the effect is enhanced as the length difference increases. It is also temperature dependent; the mole fraction enhancement is greatest at lower temperatures. In contrast, the longer component is somewhat depleted at the liquid−vapor interface. In the first layer near the substrate, the favorable interactions with the surface provide a sufficient energetic driving force for the enhanced adsorption of longer molecules (that have a smaller footprint relative to the number of CHx units) and for orientational and conformational ordering, i.e., a strong preference for alignment parallel to the substrate and for conformations with fewer gauche defects. Within the strongly adsorbed layer, there is a small, but statistically significant, tendency for partial lateral demixing, i.e., a small preference for like−like pairs in the first solvation shell. Overall, the concentration enhancements and ordering in these liquid films are much less pronounced than those observed in experimental studies at lower temperatures where the first layer is found to (partially) crystallize19−22 and for mixtures consisting of longer chains and larger chain length differences.25 Future work will examine the effects of chain branching (placement, length, and number of side chains) on the preferential adsorption of hydrocarbon chains, an issue that is important for both lubrication and separation of polyolefins, as well as the influence of a chemically detailed substrate and contaminants, such as water and other oxygenated species.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (K.E.A.). *E-mail: [email protected] (J.I.S.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the National Science Foundation through grants CHE-0851234 (S.W.) and CHE-1152998 (J.I.S.), the Donors of the American Chemical Society Petroleum Research Fund (K.E.A.), and the Thomas F. and Kate Miller Jeffress Memorial Trust (K.E.A.) is gratefully acknowledged. This work was carried out in part using computational resources at the University of Minnesota Supercomputing Institute.

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