On the wettability transparency of graphene-coated silicon surfacesBladimir Ramos-Alvarado, Satish Kumar, and G. P. Peterson Citation: The Journal of Chemical Physics 144, 014701 (2016); doi: 10.1063/1.4938499 View online: http://dx.doi.org/10.1063/1.4938499 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/144/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Wettability of graphitic-carbon and silicon surfaces: MD modeling and theoretical analysis J. Chem. Phys. 143, 044703 (2015); 10.1063/1.4927083 Investigation on the friction coefficient between graphene-coated silicon and glass using barrel compressiontest J. Vac. Sci. Technol. B 33, 031213 (2015); 10.1116/1.4919769 Ab initio and classical molecular dynamics studies of the structural and dynamical behavior of water near ahydrophobic graphene sheet J. Chem. Phys. 138, 204702 (2013); 10.1063/1.4804300 The tunable wettability in multistimuli-responsive smart graphene surfaces Appl. Phys. Lett. 102, 011603 (2013); 10.1063/1.4775360 Effect of surface wettability on liquid density, structure, and diffusion near a solid surface J. Chem. Phys. 126, 034707 (2007); 10.1063/1.2424934

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THE JOURNAL OF CHEMICAL PHYSICS 144, 014701 (2016)

On the wettability transparency of graphene-coated silicon surfacesBladimir Ramos-Alvarado, Satish Kumar, and G. P. Petersona)

The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology,Atlanta, Georgia 30332, USA

(Received 8 October 2015; accepted 10 December 2015; published online 6 January 2016)

In order to better understand the behavior and governing characteristics of the wetting transparencyphenomenon observed in graphene-coated surfaces, molecular dynamics simulations were coupledwith a theoretical model. Graphene-coated silicon was selected for this analysis, due to potentialapplications of hybrid silicon-graphene materials as detectors in aqueous environments. The resultsindicate good agreement between the theory and simulations at the macroscopic conditions requiredto observe wetting transparency. A microscopic analysis was also conducted in order to identify theparameters, such as the interaction potential energy landscape and the interfacial liquid structure thatgovern the wetting behavior of graphene-coated surfaces. The interfacial liquid structure was foundto be different between uncoated Si(100) and the graphene-coated version and very similar betweenuncoated Si(111) and the graphene-coated version. However, the concentration of liquid particles forboth silicon surfaces was found to be very similar under transparent wetting conditions. C 2016 AIPPublishing LLC. [http://dx.doi.org/10.1063/1.4938499]

I. INTRODUCTION

The thermal, electrical, and mechanical properties ofgraphene films have been the subject of significant interestfollowing the realization that a monolayer of carbon atoms thatis stable at room temperature could be fabricated.1 Becausegraphene is a 2-D material, its surface properties are ofsignificant importance in situations where the graphene servesas an interface between different media. The many optionsfor chemically functionalizing graphene make it suitable foruse as a passivation film with tunable wettability. Severalexamples of this have been identified in the literature,including superhydrophobic graphene aerogels synthetizedto obtain contact angles greater than 150◦;2 graphene foamscoated with Teflon that can generate surfaces with advancingand receding contact angles of 163◦ and 143◦, respectively;3

few-layer graphene films supported on silicon substrates thathave been chemically functionalized to exhibit the entire rangeof wettability from superhydrophilic to superhydrophobic;4

and first principles simulations that have demonstratedthe possibility of tuning the wettability of graphene bymeans of aluminum doping.5 Although the applications offunctionalized graphene surfaces such as these are still in thedevelopmental stage, a wide range of applications has alreadybeen proposed, including maintenance-free solar cells, vaporcondensation, high-performance electrical actuators,6 and useas electrode materials.7

Due to its chemical properties, a graphene coating onmaterials such as copper and silicon serves as an anticorrosionbarrier. Interestingly, the changes produced in the wettabilityof a given surface after being coated with graphene havebeen a controversial subject among the scientific community.Experimental and theoretical analyses support the theories

a)E-mail address: bud.peterson@gatech.edu

of wettability opaqueness, transparency, and translucency ofgraphene-coated surfaces. Shin et al.8 found that the contactangle on a silicon carbide surface coated with graphene wassimilar to that of graphite and independent of the number ofstacked graphene layers, indicating wettability opaqueness.Raffie et al.9 exfoliated and functionalized graphene inaqueous solutions with varying concentrations of acetone tomodify the wettability of graphene and then coated differentsubstrates with graphene; contact angle dependence on thesupporting substrate was observed. Later on, Raffie et al.10

first reported the wettability transparency of graphene. Singleand multiple layer graphene were used to coat materialssuch as gold, copper, silicon, and glass. The results indicatedthat the contact angle for gold, copper, and silicon wasnot significantly affected by coating these surfaces with asingle graphene layer. Alternatively, the contact angle ofglass, a highly hydrophilic material, was significantly affectedby a single layer of graphene. Simulations and theoreticalcalculations supported the idea that surfaces for whichwettability was dominated by van der Waals forces couldexhibit wetting transparency unlike surfaces like glass whereshort-range hydrogen bonding is also important. Shih et al.11

used molecular dynamics (MD) simulations and a mean-field-theory-based model, to formulate the partial wettabilitytransparency or wettability translucency theory, in which thecontact angle on a graphene-coated surface is affected by thewater-substrate and water-graphene interactions. This idea iscontrary to that of the wetting transparency theory in whichthe van der Waals interactions between water and graphene arenegligible and the substrate properties are transmitted throughthe graphene sheet. Raj et al.12 investigated the wettabilityof copper, silicon oxide, and glass substrates, coated withCVD-grown graphene, by measuring the advancing, receding,and static contact angles. It was reported that the additionof a single graphene layer altered the contact angle of

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014701-2 Ramos-Alvarado, Kumar, and Peterson J. Chem. Phys. 144, 014701 (2016)

the substrates, while the addition of more layers had noobservable impact on the contact angle. These findingswere used to formulate the idea that graphene is actuallyopaque to wettability changes since the equilibrium spacingbetween the substrate and graphene is too large for anysubstrate force potential to be transferred to the wettingliquid.

Li et al.13 investigated the effects of atmospherichydrocarbon contamination on the wettability of graphene-coated surfaces exposed to air. Airborne hydrocarbons werefound to be absorbed onto graphitic substrates, therebyincreasing the surface energy, and hence, creating morehydrophobic surfaces, as a function of the exposure time.These findings indicate that graphitic surfaces are more hydro-philic than previously thought. Lai et al.14 reported similarobservations for graphene-coated copper when exposedto airborne hydrocarbons. AFM-based force reconstructionwas used to perform a nanoscopic characterization of theinterface under different ambient humidity conditions, whichled to the hypothesis that ambient water absorption alsocontributes to the observed ambient-exposure wettabilitydependence. The observed similarity between the wettingbehavior of graphene coated surfaces and that of graphiticcarbon prompted Lai et al.14 to support the idea of thewettability opaqueness of graphene. Conversely, a recentexperimental investigation conducted by Kim et al.15 sup-ported the wettability transparency theory when using in situCVD-grown graphene on copper substrates, since the growthprocess involves surface adsorption that uniformly covers anyimperfections.

Shih et al.16 described the wettability of graphene-coatedsurfaces by means of the classical Young-Dupré model. Thecontributions to the total work of adhesion were assumed to beadditive (water-graphene and water-substrate interactions) andthat the substrate-graphene interactions did not alter the totalcontact angle. By separating both solid-liquid interactions, aclearer understanding of the conditions for transparent andopaque wettability was obtained. In the current investigation,we adopted the ideas explaining the wettability of graphene-coated surfaces proposed by Shih et al.,16 and used the mean-field theory to develop an analytical model of wettability ofgraphene-coated silicon to predict the macroscopic conditionsrequired for observing wettability transparency. The effectsof the silicon anisotropy on the wettability of differentatomic planes were accounted for in the theoretical model,obtaining a remarkable accuracy to predict contact anglesderived from MD simulations. This model represents animprovement on the previous model developed by Shihet al.11 and also implemented by Li et al.,13 The recentlyreported contact angles of clean graphitic carbon13,14,17 wereutilized for the calibration of the water-carbon interactionpotential, while the wettability of silicon was artificiallycontrolled by varying the water-silicon interaction strength.In addition to report on the macroscopic conditions leadingto observe wettability transparency, microscopic conditionssuch as the energy landscape generated due to the substrate-water interaction and the interfacial concentration of liquidparticles were used to explain the wettability of graphene-coated silicon.

II. ANALYTICAL MODEL OF WETTABILITYOF GRAPHENE-COATED SURFACES

Shih et al.16 proposed that the wettability of graphene-coated substrates can be explained by considering theindividual contributions to the total work of adhesion (W T

A)by the water-substrate and the water-graphene interactions,which can be expressed as

W TA = W WG

A +W WSA = γlv (1 + cos θc) , (1)

where W WGA is the water-graphene work of adhesion, W WS

A isthe water-substrate work of adhesion, γlv is the experimentalsurface tension of water, and θc is the contact angle ona graphene-coated substrate. The work of adhesion hasinterfacial energy and entropy contributions18 given by

WA =1A(∆UWS − T∆SWS) , (2)

where ∆UWS/A is the total solid-liquid interaction energy perunit area, −∆SWS/A is the interfacial entropy loss due to theliquid layering imposed on the interfacial water moleculesclose to the solid surface, and T is the absolute temperature.Taherian et al.18 found that the interfacial entropy contributionaccounts for as much as 30% of the total work of adhesionon graphitic surfaces. A model based on the free-energyperturbation theory was developed to obtain the interfacialentropy, but its accuracy was restricted to a very limitedrange of hydrophobic conditions.18 Mean-field-theory-basedmodels of wettability rely on the reduction of a many-body problem to a one-body problem (single-body potentialintegrated over a function that represents the distribution ofparticles) and the assumption that WA ≈ ∆UWS/A. Driskillet al.19 investigated the wettability transparency of graphenein water; in other words, instead of having a crystalline solidsubstrate coated with graphene, they studied the effect ofhaving a water slab “coated” with graphene. MD simulationsand a theoretical model of wettability transparency weredeveloped. In the theoretical model, they included the water-water electrostatic interactions, a requirement when studyingpolar particles interactions. Previously, we developed amean-field model of wettability where the main differencewith respect to previous models was the calibration of theBoltzmann distribution used to represent the interfacial liquidstructure.20 This simple modification led to a better matchbetween the MD and theoretical calculations of the contactangle when compared with analytical models based on thesharp-kink-approximation (SKA). By neglecting ∆SWS/A, ourmodel was self-compensated under hydrophilic conditions,where ∆SWS/A is important but our model underpredicted∆UWS/A. Alternatively, slight underpredictions of the contactangle were observed for hydrophobic surfaces where themagnitude of ∆SWS/A is small but the theoretical values of∆UWS/A were slightly smaller than MD calculations; seethe supplementary material of Ref. 20. These observationsallowed to justify ignoring ∆SWS/A in the calculation of thework of adhesion. The same model will be used here forinvestigating the wettability of silicon and graphene-coatedsilicon; specific details on the model development can beconsulted in Ref. 20.

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014701-3 Ramos-Alvarado, Kumar, and Peterson J. Chem. Phys. 144, 014701 (2016)

The approximation to the work of adhesion for thegraphene-coated silicon substrate can be determined from

W WGA +W WS

A ≈ −rc

zref

ρL (z) [wWG (z) + wWS (z)] dz, (3)

where ρL(z) is the density distribution of liquid particlesnormal to the wetted plane, and the integration is performedfrom a reference value zref ≈ 0 to a large value of rcin order to capture the bulk behavior. The definition ofa proper ρL(z) function is the major limitation of thesekinds of wettability models. Taherian et al.18 found thata Boltzmann distribution significantly overestimates theconcentration of interfacial liquid particles and that the SKA

generates poor predictions of wettability when compared tonumerical simulations. Recently, Ramos-Alvarado et al.20

suggested a simple but effective calibration to the Boltzmanndistribution in which ρL (z) = ρL,0 exp [−w (z) /ηkBT], whereρL,0 is the bulk density of the liquid particles, w (z) is thetotal single-particle interaction potential, and η is the onlytuning parameter of the model. The single-particle interactionpotentials for the graphene layer (wWG) and the bulk siliconsubstrate (wWS) are

wWG (z) = 4πρCs εCOσ

2CO

*,

σ10CO

5z10 −σ4

CO

2z4+-− *,

σ2CO

5r10c−σ2

CO

2r4c

+-

,

(4)

wWS (z) = 4πρSis εSiOσ

2SiO

N−1k=0

σ10SiO

5(z + δGS + khi)10 −σ4

SiO

2(z + δGS + khi)4− *,

σ10SiO

5(rc + δGS + khi)10 −σ4

SiO

2(rc + δGS + khi)4+-

, (5)

where ρSis is the atomic surface density of the silicon plane

under consideration (7.83 nm−2 for Si(111) and 6.78 nm−2 forSi(100)), ρCs = 38.16 nm−2 is the atomic surface density ofcarbon atoms in graphene, N is the number of atomic planes,(εCO,σCO) and (εSiO,σSiO) are the Lennard-Jones potentialparameters for carbon-oxygen and silicon-oxygen pairs, δGSis equilibrium separation between graphene and silicon, andhi is the interlayer distance between silicon planes, wherehi can take a fixed value (h3 = 1.357 Å) between Si(100)planes or alternating values (h1 = 0.784 Å, h2 = 2.352 Å)in order to capture the triple-bilayer periodic structure ofSi(111); see Fig. 1. This kind of modelling approach was firstintroduced by Steele21 for modeling graphite-gas interactions.In summary, the definition of ρL(z) and Eqs. (1)–(5) close themodel for calculating the contact angle on a graphene-coatedsurface.

The implementation of the wettability model with acalibration for ρL(z) is referred to as the Boltzmann-calibratedmodel (BCM), and was inspired by the similarity betweenthe MD-derived density profiles of liquid particles and theBoltzmann distribution. Figure 2(a) depicts a comparisonbetween the different functional forms of ρL(z) and thatobtained from MD simulations. The implementation of theBCM resulted in a remarkably accurate prediction of thecontact angles obtained from MD simulations taken fromRef. 18 for graphitic-carbon under a wide range of interactionpotentials. Figure 2(b) illustrates a comparison between the

analytical prediction of graphite wettability using the BCMand SKA to represent ρL(z), and MD simulation results fordifferent interaction potentials. A value of η = 7.25 was foundto be appropriate to generate an accurate prediction of theMD-calculated contact angles; additionally, a good matchbetween the MD and theoretical calculations of the interfacialconcentration of liquid particles for different values of ε wasreported in Ref. 20. Thus, the BCM is not only forcing amodel to predict a given behavior, but also captures some ofthe interfacial properties of the wetting phenomenon.

Previously, Shih et al.11 developed a similar modelto explain the wettability of a graphene-coated substrate.However, their model was limited in that (1) only long-rangeattractive forces were considered in the definition of theinteraction potential between a water monomer and the solidatoms, (2) a Boltzmann distribution was used to representρL(z) and in order to avoid divergence to infinity of the densityclose to the wall, an arbitrary definition of the equilibriumdistance between water and the substrate was assumed, (3)the calculation of ∆UWS/A was very sensitive to the definitionof the water-solid equilibrium distance, and (4) the substratewas characterized by a bulk volumetric density to accountfor a wide variety of materials. Conversely, the current modelincludes both attractive and repulsive interactions, thus thewater-solid equilibrium distance results in a model that closelymatches the MD simulation results. The evaluation of Eq. (3)is not restricted, with the exception of the case that zref = 0

FIG. 1. (a) Unit cell for generating graphene-coated Si(111), (b) underlying structure of a graphene-coated Si(111) surface where h1 and h2 characterize theperiodic triple bilayer, and (c) underlying structure of a graphene-coated Si(100) surface where h3 is the inter-plane distance.

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014701-4 Ramos-Alvarado, Kumar, and Peterson J. Chem. Phys. 144, 014701 (2016)

FIG. 2. (a) Schematic view of the different functional forms to represent the density distribution of liquid particles in mean-field models of wettability withMD data for comparison. (b) Implementation of the SKA and the BCM approximations for predicting the wettability of graphitic carbon compared with MDsimulations.

because of numerical divergence. In addition, the anisotropyof crystalline substrates was considered, since the wettabilityis dependent upon the planar atomic density as observed fordifferent silicon surfaces.20

III. MOLECULAR DYNAMICS MODEL

The wettability of pristine silicon surfaces, Si(100)and Si(111), and the graphene-coated version of similarsurfaces was numerically investigated using MD simulationsof cylindrical water droplets to determine the contact angle.Unlike the simulations for hemispherical droplets, cylindricalliquid slabs offer a number of benefits such as being lessaffected by the size and line tension as described by theYoung’s modified equation.10,22 Water was used as the workingfluid and the SPC/E model23 was utilized due to its goodpredictive capabilities, its low computational cost, and forcomparison purposes due to being amply used in the literature.The Coulombic interactions in the water model were treatedwith the PPPM24 algorithm with an accuracy of 1 × 10−6

and the rigidity of the model was enforced through theSHAKE25 algorithm. The solid dynamics were not solvedin the simulations, since it has been demonstrated that havingfixed or mobile solid atoms does not alter the contact anglecalculation in a significant manner.26 The equilibrium distancebetween the graphene layer and the substrate was varied asillustrated in Fig 1. The structure of Tersoff graphene27

was stretched 4% in order to create periodic graphene-coatedsilicon structures. Figure 1(a) depicts the unit cell used tocreate the graphene-coated Si(111) structure. The Si(100)imposed a greater challenge for matching with graphene,but a good periodic structure approximation was found byconsidering a unit cell of a combined structure which wasmade of 5 unit cells of graphene and 4 of Si in thex-direction and 11 cells of graphene and 5 of Si in they-direction. The stability of the graphene-silicon structureswas investigated by obtaining the equilibrium configurationsfrom independent MD simulations of stretched graphenesupported on silicon. The results indicated that the struc-tures maintained their original periodic configuration afterequilibration. It is noteworthy that a recent investigation ofgraphene-coated silicon wettability did not report any detailson the structure of the graphene-silicon system.28

The carbon and water molecules (oxygen atoms)interacted through a truncated Lennard-Jones potentialwith σCO = 3.19 Å, εCO = 0.4736 kJ/mol, and rc = 15 Å(parameters calibrated to obtain a contact angle of 64.4◦ on aclean graphite surface).20 For the silicon substrate, the distanceparameter σSiO = 2.63 Å was kept constant while εSiO wasvaried to artificially modify the wettability of silicon.29 Waterdroplets containing 2500-8300 molecules were simulated todiscard any size effects on the contact angle calculation. TheMD code LAMMPS30 was used to perform the simulationsand VMD31 for visualization. Periodic boundary conditionswere imposed on the three directions of the computationaldomain. The time step for integration of the governingequations was 1 fs; the neighbor lists were updated everytime step, and the center of mass of the water molecules wasreset to its initial position every time step in order to avoiddrifting due to random perturbations. A snapshot of the initialmolecular setup is illustrated in Fig. 3(a) and an equilibriumconfiguration is illustrated in Fig. 3(b). The simulationsfollowed the process: (1) minimization of energy in order toeliminate any excess potential energy from the initial config-uration; (2) equilibration at 298 K using the Nosé-Hooverthermostat32 with a time constant of 0.1 ps during 0.5 ns;(3) a microcanonical ensemble run for 0.5 ns under purelyNewtonian dynamics; (4) production run (3-4 ns) for collectingsnapshots of the water molecules every 0.5 ps.

The shape of the water droplets was determined by time-averaging the density contours obtained from the particlecount into several bins of dimensions 0.25 × 0.25 Å in thex − z plane. The y-dimension of the computational box wasused as a whole for the calculation of the bin volume. Afteranalyzing several data sets, the density of the water dropletwas obtained as function ρ = ρ(x, z), see the inset of Fig. 3(c)and a sigmoidal function33 was used to fit the density profile as

ρ (z) = 12(ρl + ρv) − 1

2(ρl − ρv) tanh

(z − ze

de/2

), (6)

where ρl is the bulk liquid density, ρv is the bulk vapor density,ze is the position of the equimolar distance, and de is anapproximation of the liquid-vapor interface thickness. ρv wasassumed zero and the data fit was carried out neglecting thehighly distorted region near the solid surface, see Fig. 3(c). Thedroplet interface was defined by placing markers at the outer

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014701-5 Ramos-Alvarado, Kumar, and Peterson J. Chem. Phys. 144, 014701 (2016)

FIG. 3. Schematic description of the MD modeling and postprocessing of cylindrical droplet wettability. (a) Initial water block sitting on Si(100) coated withgraphene, (b) equilibrium configuration of a water droplet on the same surface, and (c) typical center-line density profile with sigmoidal fit and density contours(inset).

bins where ρ(x, z) = ρl/2, then the interface was refined bymeans of a linear interpolation algorithm. The interface pointswere reconstructed using a circular approximation and thecontact angle was obtained from the slope at the intersectionwith the solid surface. The contact angle calculation wasthe last step of the postprocessing stage and was performedevery ten snapshots, allowing accumulation of the data overtime. From this point on, the MRPM method20 was usedfor assessing the quality of the calculations performed forobtaining the contact angle as a function of the data setsanalyzed over time, to determine the steadiness of thecalculations, and finally to obtain a reliable calculation ofthe contact angle.

IV. RESULTS AND DISCUSSION

A. Macroscopic conditions for wettabilitytransparency

The theoretical model developed in Sec. II was used topredict the wettability of graphene-coated silicon and baresilicon surfaces, and MD simulations were used as a source of“experimental” data. The wettability of silicon was artificiallycontrolled by holding the silicon-oxygen interaction potentialparameter σSiO constant, while varying the energy parameterεSiO, similar to the previous investigation by Barisik andBeskok,29 where the analysis was focused on the wettability

of the Si(100) plane. It was found that using the same silicon-oxygen interaction potential for the Si(100) and Si(111)surfaces leads to the observation of different contact anglesdue to the silicon structure anisotropy. This observation wasverified by MD simulations and theoretical calculations. Forcomparison purposes, in terms of the observed contact angles,the contact angle of the two silicon surfaces was adjusted from∼50◦ to ∼150◦, a range amply covering the experimentallyreported wettability of clean silicon.29,34 Three independentsimulation runs were conducted for each εSiO value and thecontact angles on the two silicon surfaces are illustrated inFig. 4(a). The MD simulation results were consistent withthe theoretical predictions of the BCM, where η = 2.7 forSi(111) and η = 2.1 for Si(100), although η = 2.5 producesgood prediction for both surfaces. The theoretical predictionsappeared to be more accurate for hydrophilic surfaces thanfor hydrophobic surfaces. This behavior is understandable,since the BCM compensates the lack of accountability forinterfacial entropy under hydrophilic conditions (due to anunderprediction of the energy contribution to the work ofadhesion) and slightly overpredicts the work of adhesion inhydrophobic surfaces, as demonstrated in the supplementarymaterial of Ref. 20.

Figure 4(a) illustrates the strong effect of the crystalstructure on the wettability of anisotropic materials, such assilicon. When the two silicon surfaces and water interactthrough the same potential, the less atomically dense Si(100)

FIG. 4. Theoretical and numerical contact angle calculations for (a) silicon surfaces as a function of εSiO and (b) for graphene-coated silicon surfaces as afunction of εSiO. All data points have error bars.

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014701-6 Ramos-Alvarado, Kumar, and Peterson J. Chem. Phys. 144, 014701 (2016)

surface exhibits a more hydrophobic behavior than theatomically denser Si(111) surface, a feature taken as anadvantage for anisotropic microfabrication by the MEMScommunity. By having lower atomic planar density, the energycontribution to the work of adhesion is reduced and the water-solid affinity decreases. Differences of ∼25◦ exist betweenSi(111) and Si(100) under hydrophilic conditions (large εSiO)and the difference decreases to ∼4◦ under very hydrophobicconditions where the interaction between water and the siliconsurfaces becomes highly repulsive (small εSiO). At this point,two important aspects can be highlighted: (1) the theoreticalmodel developed here has the capability of accounting forthe effects of the surface and structural anisotropy on thewettability of crystals; and (2) the wide range of contactangles numerically obtained serve as a calibration exercisefor future investigations of silicon wettability on the planesconsidered here; the required interaction potentials can bederived from Fig. 4(a). On a note on the nature of the fittingparameter η, it could be thought that η apparently depends onlyon the planar density of the wetted surfaces; however, it mustbe remembered that the matching of wettability experimentswith size-independent MD simulations leads to calibrate twoindependent interaction potential parameters and also that thesolid structure (planar density and atomic interlayer spacing)plays a major role as indicated in Eqs. (4) and (5). Hence,unraveling the nature of η for every possible system poses achallenging task beyond the practical application featured inthis investigation.

Once the silicon and carbon models were calibrated, thecontact angles of graphene-coated silicon were predicted bythe BCM and compared with the MD simulations, as depictedin Fig. 4(b). Because the solid atoms lack internal degreesof freedom during the numerical modeling, the equilibriumdistance between silicon and graphene, normally determinedby the interaction potential between the silicon and carbonatoms, was defined as δGS = 3.0 Å, a reasonable distancebetween a graphene layer physisorbed onto a substrate. Onthis aspect, some authors have indicated that δGS ≈ 2.0 Å35

and others have suggested that δGS ≈ 3.55 Å36 through mixingrule approximations. The value δGS = 3.0 Å was taken asa reference to investigate the accuracy of the BCM whenpredicting the MD wettability of a more complex system than

bare silicon. Figure 4(b) illustrates that the theoretical BCM isable to match the contact angles on graphene-coated surfacescalculated by means of MD simulations. The fitting parameterη = 7.25 was used to predict the wettability of graphene-coated silicon due to the proximity between graphene andwater, see Sec. II. The observed trends coincide, althoughnot as accurately as in the case of bare silicon surfaces. Thiscan be attributed to the fact that the wettability of the coatedsurface is not as sensitive to εSiO as the bare silicon due to theincreased spacing between the water molecules and the siliconsubstrate. It was observed that the graphene-coated versionsof the silicon surfaces have contact angles that vary between∼74◦ and ∼84◦, and the widest gap between the theoreticalpredictions for both surfaces is smaller than 2◦, a smalldifference hardly captured by MD simulations; nevertheless,the “experimental” data points fall within this range for themajority of the values of εSiO.

The theoretical conditions required to achieve wettabilitytransparency as a function of the macroscopic contact angleon a silicon substrate are illustrated in Fig. 5. The equilibriumdistance between graphene and silicon was varied from 3 Åto 5 Å just for purposes of performing a parametric anal-ysis on the BCM; it is important to note that δGS > 3.5 Å isnot physically plausible due to the short range nature of theinteratomic forces. Closely resembling experimental data, theMD simulation results fall along the curve for δGS = 3.0 Åwhich also corresponds to the molecular setup used to obtainthe data illustrated in Figs. 5(a) and 5(b). The region wherewettability transparency was expected appears as a shaded slaband encompasses a condition such that the variation of the con-tact angle of the substrate with respect to its graphene-coatedversion is ±5◦. The results indicate that the exact wettabilitytransparency for δGS = 3.0 Å is achievable if the contact angleof any of the two silicon surfaces is∼76◦. Recent investigationshave reported that the contact angle on a clean silicon surfaceis ∼77◦34 and the wetting transparency of graphene-coatedsilicon surfaces was first reported by Raffie et al.10 There-fore, the theoretical and numerical “experiments” reportedin Fig. 5 support the previous investigations suggesting thepossibility of the wetting transparency of silicon surfaces, inaddition to exploring the overall macroscopic wetting behaviorof graphene-coated silicon surfaces.

FIG. 5. Macroscopic conditions for wettability transparency of (a) graphene-coated Si(111) and (b) graphene-coated Si(100). The shaded regions represent thewettability transparency region with ±5◦. All data points have vertical and horizontal error bars.

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014701-7 Ramos-Alvarado, Kumar, and Peterson J. Chem. Phys. 144, 014701 (2016)

B. Microscopic conditionsfor wettability transparency

In Sec. IV A, the macroscopic properties required toobserve wettability transparency in graphene-coated siliconwere investigated. Microscopic effects are introduced interms of the equilibrium separation between graphene andsilicon, but further assessment of the changes induced inthe interfacial region is required. Therefore, an analysisof the microscopic conditions giving origin to the wettingtransparency phenomenon was conducted by analyzingthe liquid interfacial structure and potential energy fieldcontributions to the wetting transparency phenomenon.

When a silicon surface that exhibits a strong hydrophilicbehavior is coated with a single layer of graphene, thestrong silicon-water interaction is inhibited by increasing theeffective distance between these particles. The equilibriumdistance between graphene and silicon, plus the equilibriumdistance generated between graphene and water, given by thecarbon-water interaction potential, accounts for the diminishedinfluence of the substrate on the water molecules, (seeFig. 6 for details of the silicon-oxygen potential energy fieldgenerated by the silicon atoms of the first two atomic layers).The water-graphene interactions tend to dominate the overallwettability behavior as the surfaces become less hydrophilic,until saturation is reached at superhydrophobic conditions. Inthese situations, it is apparent that the hydrophobic substrateserves as a supporting material and the observed contactangle is approximately that of a single layer of graphene,an argument theoretically supported by Fig. 5. Taking analternative view, it appears that the underlying substrateproperties affect the wettability of the supported graphenelayer. The silicon potential energy granularity is lost when it

FIG. 6. Silicon-water interaction potential contours generated by the firsttwo layers of (a) Si(100) and (b) Si(111) atoms, z = 0 is the position of thefirst layer of silicon atoms below graphene at z = 3 Å. Note: these contoursrepresent VSiO(x, y) disregarding the strongly repulsive region surroundingthe solid atoms. The energy contours are in kJ/mol.

reaches the water molecules (z ≈ 6 Å) as indicated in Fig. 6.This helps to explain why the two graphene-coated siliconsurfaces exhibit similar contact angles and why the pristinesurfaces exhibit different wettability. The strongly repulsiveregion has been eliminated from the energy potentials depictedin Fig. 6 and appears as a white region surrounding the siliconatoms.

The changes induced in the equilibrium structure of liquidparticles when a silicon surface is coated with graphene aredepicted in Figs. 7 and 8. The upper panels illustrate thedensity contours of droplets for hydrophobic and hydrophilicbare silicon surfaces and the bottom panels depict the samesurfaces coated with graphene. The large interstitial spacingbetween silicon atoms in the (100) plane generates largeenergy potential wells and a rough potential energy landscapeas observed in Fig. 6(a); as a consequence, water moleculeswere observed to become entrained in the large interstitialspaces of the Si(100) surface, (see the right upper panel ofFig. 7). The water molecule entrainment on Si(100) has beenpreviously reported by Barisik and Beskok29 but with ratherlow-resolution contours. Because of the low water-siliconaffinity under hydrophobic conditions, no entrainment wasobserved in this case, (see the left upper panel of Fig. 7).The interfacial structure of the liquid molecules was greatlymodified when the silicon was coated with graphene. Watermolecules did not penetrate the solid structure, due to the lackof potential energy wells caused by a high atomic surfacedensity (the atomic density of graphene is 38.16 nm−2 whilethat of the Si(100) plane is 6.78 nm−2), (see Fig. 7 lowerpanels). Instead, a uniform liquid layering was observed inthe vicinity of the solid.

Figure 8 depicts the density contours of water droplets ona Si(111) surface; similar to the previous case, the left- andright-hand panels are hydrophobic and hydrophilic siliconsurfaces, respectively, while the lower panels are the samesurfaces coated with graphene. The larger atomic surfacedensity of the Si(111) plane (7.83 nm−2) clearly eliminatedthe entrainment effect previously observed on Si(100). Here,the interfacial water structure consisted of a high-density layernear the solid liquid interface, similar to what was observedon the graphene-coated versions. The equilibrium separationbetween the water and the solid atoms is different for thetwo surfaces, due to the interaction potential parameters usedand the potential energy landscape depicted in Fig. 6. This isstrongly related to the length parameter σij.

Figure 9 illustrates the changes observed in the interfacialwater structure under hydrophobic (top panel), hydrophilic(middle panel), and transparent (bottom panel) conditions forboth silicon and graphene-coated silicon surfaces. It shouldbe noted that the observed changes in the density profiles forthe graphene-coated silicon surfaces were minimal; therefore,only one curve is depicted in each panel shown in Fig. 9.Under hydrophobic conditions, major changes in the liquidinterfacial structure were observed after silicon is coated withgraphene; see Fig. 9(a). A large depletion layer was observedon the Si(100) surface as a consequence of the low water-silicon affinity and low atomic surface density, whereas thelarger concentration of solid atoms per unit area on the Si(111)surface alleviated this depletion effect. The graphene-coated

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014701-8 Ramos-Alvarado, Kumar, and Peterson J. Chem. Phys. 144, 014701 (2016)

FIG. 7. Density contours of water droplets on Si(100) surfaces (upper panels) and graphene-coated Si(100) surfaces (lower panels). Hydrophobic silicon surface,left panels; hydrophilic silicon surfaces, right panels. The scale is in g/cm3.

version of the hydrophobic substrates significantly modifiedthe interfacial liquid structure due to the relative strongeraffinity between the carbon atoms and water.

Fig. 9(b) illustrates the microscopic changes producedafter coating a hydrophilic silicon surface. The hydrophilic

Si(100) surface exhibits liquid-layering due to a strongersolid-liquid interaction. The first density peak on the Si(111)surface increased and even surpassed the magnitude of thatof the graphene-coated silicon. The differences observed onboth silicon surfaces can be related to the difference in the

FIG. 8. Density contours of water droplets on Si(111) surfaces (upper panels) and graphene-coated Si(111) surfaces (lower panels). Hydrophobic siliconsurfaces, left panels; hydrophilic silicon surfaces, right panels. The scale is in g/cm3.

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014701-9 Ramos-Alvarado, Kumar, and Peterson J. Chem. Phys. 144, 014701 (2016)

FIG. 9. Droplet center-line density profiles along the z-direction of Si(100),Si(111), and graphene-coated silicon surfaces under (a) hydrophobic, (b)hydrophilic, and (c) transparent conditions.

atomic surface density and the potential energy landscapethey present to the water molecules, see Fig. 6. The Si(100)plane allows for liquid molecules to become entrained in theinterstitia and water density depletion occurred; alternatively,the more closely packed Si(111) structure did not allowentrainment of particles, and as a consequence the liquidparticle concentration near the solid surface increased as thewater-silicon interaction force increased, (see Table I).

The wettability transparency condition for both siliconsurfaces (mildly hydrophilic surfaces) is depicted in Fig. 9(c).It was expected to find similarities between the interfacialwater structure on silicon and graphene-coated silicon surfacesunder wettability transparency conditions. Such an assumptionwas partially and visually verified for the Si(111) surfaceand its graphene-coated counterpart. Both systems exhibiteda similar interfacial structure of liquid particles once theshift between both density curves (∼1 Å) was eliminated.

TABLE I. Interfacial liquid particle concentration per unit area on siliconand graphene-coated silicon surfaces (nm−2). The shaded region indicates thewettability transparency condition.

Si(100) Si(111)

εSiO

(kJ/mol)Bare

substrateGraphene-

coatedεSiO

(kJ/mol)Bare

substrateGraphene-

coated

0.6271 0.4539 10.5079 0.5306 6.2648 10.44191.0709 8.8950 10.5946 0.8973 7.4494 10.49441.4955 9.7170 10.6640 1.2736 9.8698 10.5243

1.9393 10.5242 10.6218 1.5534 10.3221 10.4050

2.0358 10.5684 10.5719 1.6209 10.7569 10.4174

2.1516 11.5913 10.3166 1.8621 11.0525 10.45772.2481 11.6854 10.8280 1.9682 11.3746 10.50222.3445 11.7557 10.5601 2.0454 11.7265 10.5466

When the interfacial concentration of liquid particles wascalculated, from zero to the valley after the first densitypeak, it was found that similarities indeed arise under wettingtransparency conditions for both silicon surfaces, see Table I.It is noteworthy that the density profile at the interface (z = 0)is not zero for the Si(100) plane. This is due to the entrainmentobserved of some liquid particles into Si(100). The interfacialconcentration of liquid particles increases on the bare siliconsurfaces as the energy parameter εSiO increases while it remainsfairly constant on the graphene-coated cases. Interestingly,the concentration of particles is quite similar only underwettability transparency conditions.

It appears that the strong granularity of the energyfield created by the Si(100) surface affected the interfacialwater structure in such a way that water density depletion isobserved; nevertheless, these particles contribute to the totalwork of adhesion and are accounted for in the interfacialconcentration of liquid particles. The rough Si(100) interfacerepresents a major contribution to the wetting behavior of thebare substrate. However, when a graphene coat is applied, theunderlying silicon only adds to the solid-liquid interaction bymeans of a smooth energy landscape. As for the Si(111),the same contribution to the energy potential landscapeexperienced by the water particles was observed, in additionto presenting similar interfacial liquid structures underwetting transparent conditions. Overall, although similaritieswere found between microscopic properties under wettingtransparent conditions, the intricate combination of thesegives origin to a physical macroscopic property such as thecontact angle which eventually serves as a good discriminantfor the conditions required to observe wetting transparency.

V. CONCLUSIONS

A theoretical investigation of the wettability of graphene-coated silicon was conducted in order to predict themacroscopic conditions required to observe wetting trans-parency on these surfaces. The resulting model representsa refinement/upgrade upon previous wettability models.11

Numerical (MD) simulations were used as a source of“experimental” data. The recently reported contact angleson graphitic clean surfaces were used for calibration of the

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014701-10 Ramos-Alvarado, Kumar, and Peterson J. Chem. Phys. 144, 014701 (2016)

water-carbon interaction potentials while the wettability ofdifferent silicon planes was artificially controlled. A goodmatch between theory and simulations was found, indicatingthat in order for graphene-coated silicon to be transparent,the contact angle of silicon should be ∼77◦. The theoreticalmodel of wettability developed herein is inherently unableto fully predict the wettability of a bare surface due tohaving a fitting parameter (η); however, the calibration processperformed for the two pristine surfaces (silicon and graphite)proved to be effective for obtaining a theoretical predictionof the wettability of graphene-coated silicon surfaces andthe conditions required to observe wettability transparency.An analysis of the microscopic conditions required toobserve wettability transparency was conducted by meansof profiling the interfacial liquid density and by observingthe interaction potential between water and silicon atoms.Interfacial structural differences were observed between thedifferent silicon planes due to the strong granularity of theSi(100) surface compared to the smoother Si(111) surface.The interfacial liquid structure was found to be very similarunder wetting transparency conditions on Si(111) whereasthat of Si(100) was quite different. However, calculationsof the interfacial concentration of the liquid particles led toan observed similarity between the concentration of liquidparticles between bare silicon surfaces and their graphene-coated versions under wetting transparency conditions.

ACKNOWLEDGMENTS

While conducting this investigation, Bladimir Ramos-Alvarado was supported by the Mexican Council on Scienceand Technology (CONACyT) under the Scholarship No.312756.

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