Parametrizing Nonbonded Interactions from Wetting Experiments via

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Parameterizing Non-Bonded Interactions from Wetting Experiments via the Work of Adhesion: The Example of Water on Graphene Surfaces Frédéric Leroy, Shengyuan Liu, and Jianguo Zhang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b10267 • Publication Date (Web): 25 Nov 2015 Downloaded from http://pubs.acs.org on November 26, 2015

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The Journal of Physical Chemistry

Parameterizing Non-Bonded Interactions from Wetting Experiments via the Work of Adhesion: The Example of Water on Graphene Surfaces Frédéric Leroy, 1,2,* Shengyuan Liu2 and Jianguo Zhang2 1

Institut für Chemie, Universität Kassel, Heinrich-Plett-Strasse 40, 34132 Kassel, Germany

2

Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität

Darmstadt, Alarich-Weiss-Strasse 4, 64287 Darmstadt, Germany

ABSTRACT

The question of the parameterization of interfacial non-bonded interactions for heterogeneous solid-liquid systems is addressed through the example of water on graphene surfaces. We suggest that a reference value of the solid-liquid work of adhesion WSL rather than the corresponding

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wetting contact angle should be the quantity to reproduce through molecular simulations when deriving and testing interaction parameters. A relationship between WSL and the adsorption energy of water on graphene is established almost independently of the water model. It is shown that this relationship also holds for water on graphite. The ability of different Lennard-Jones interaction potential parameters to reproduce the experimental value of WSL of water on graphite is evaluated. Furthermore, it is shown that the relationship mentioned above is able to predict quantitatively the value of WSL for a classical model of water on hexagonal boron-nitride and is in good agreement with the value of WSL for a classical model of water on gold. We use this relationship to establish a direct connection between values of WSL that can be obtained from macroscopic measurements of wetting contact angles and the adsorption energy of single water molecules obtained by quantum mechanical calculations.

1. INTRODUCTION The last five years have witnessed intense experimental activity around the question of the wetting properties of graphite and graphene.1 From the macroscopic standpoint, the wetting contact angle formed by a water droplet on graphite is the visible manifestation of the interaction between water and graphitic carbon. The balance of interactions at the three-phase contact line that lead to the equilibrium contact angle θ is expressed in quantitative terms following:

γ LV cosθ = γ SV − γ SL

(1)

γLV is the liquid surface tension, γSL is the solid-liquid interfacial tension and γSV is the solidvapor surface tension. The precise knowledge of the contact angle of water on graphite is of


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crucial importance for molecular simulations. Because it depends on the solid-liquid interactions, it constitutes an observable against which interaction potential parameters have been optimized. The experimental works on the wetting properties of graphene coated surfaces showed that the interaction between pure water and graphitic carbon is short ranged in nature.2-6 Consequently, it may satisfactorily be modeled by the Lennard-Jones potential. A common approach to obtain Lennard-Jones parameters for the water-carbon interaction is to perform molecular dynamics (MD) simulations of nanometer-sized droplets. The parameters that lead to a value of the simulated contact angle equal to the macroscopic experimental one are chosen to represent the water-carbon interaction.7 The droplet simulations are also used to test whether a given set of parameters obtained by other means like first-principle calculations is consistent with experimental contact angle values.8 It is important to note that θ also depends on the water-water interaction through γLV (eq 1). Water models generally lead to values of γLV which often differ from the experimental one by more than 10%.9 We will show that these differences have a nonnegligible influence on θ and must be taken into account in the parameterization or the test of water-carbon interaction parameters. We introduce the idea that the solid-liquid work of adhesion WSL rather than the contact angle alone should be the quantity to reproduce. In fact WSL is connected to θ, but also depends on γLV through the Young-Dupré equation:

WSL = γ LV (1+ cosθ )

(2)

We will show by means of MD simulations that contrary to θ, WSL only weakly depends on the water model for a given set of Lennard-Jones potential parameters for the water-carbon interaction.


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As mentioned above, the parameterization of an interaction potential requires wellcharacterized experimental data. It was found experimentally that airborne contaminants that adsorb on graphene-coated and graphite surfaces strongly influence wetting contact angle measurements.10-17 Due to their hydrophobic nature, these molecules increase the apparent wetting contact angle of water compared with clean surfaces. This phenomenon was systematically studied only very recently. Ashraf et al.13 measured experimentally a value of 45±3°, in agreement with the earlier measurement by Schrader (42±7°).10 Mücksch et al.17 and Kozbial et al.14 reported values of 56°±3° and 64.4°±2.9°, respectively. A consensus of agreement has then emerged around the idea that graphite surfaces are less hydrophobic than previously thought, i.e. with contact angle values significantly smaller than 90°. Previous parameterizations of the Lennard-Jones potential for water on graphite were performed to reproduce a value of 86°.7, 18 Equation 1 shows that a decrease in the contact angle from 86° to approximately 60° implies that γSV-γSL is roughly reduced by a factor of two. Sizeable changes corresponding to this modification are thus expected in the interaction potential parameters for models of the water-carbon interaction.19 In this contribution, we applied the methodology based on the solid-liquid work of adhesion mentioned above to evaluate the ability of various interaction potentials to reproduce contact angle values of water on graphite in the range 45°-60°. We will show that there is a simple relationship between WSL and the adsorption energy of single water molecules on a given surface. We also found that this relationship depends weakly on the water model and that it describes both the water-graphene and water-graphite systems. Simultaneously to the intense experimental activity on the wetting properties of graphene and graphite, a significant number of quantum calculation studies with various methods addressed the question of the interaction between water and graphitic surfaces.8, 20-32 We refer to


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the work of Wu and Aluru8 for a detailed discussion on the recent efforts in this direction. Most of the works cited above deal with the adsorption properties of single water molecules on polycyclic aromatic hydrocarbons and monolayer graphene. In the corresponding calculations the adsorption energy of water at a given adsorption site on the graphene surface is determined at 0 K, while observables such as contact angles depend on the collective behavior of water molecules at a given temperature. Thus, it is a priori not straightforward to connect a microscopic quantity such as the adsorption energy of a single molecule and a macroscopic one like the wetting contact angle of a droplet. The adsorption energy at a given site is associated with a given molecular orientation. We found that the molecular orientations which lead to three hydrogen bonds per water molecule on average are the most relevant to describe water on mildly hydrophilic surfaces like graphite and graphene. This water orientation is then used as a criterion to choose the adsorption energy obtained from first-principles calculations that is connected to WSL and consequently to θ through the relationship mentioned above. We develop and validate our approach through classical molecular dynamics (MD) simulations. The simulation methodology and parameters are discussed in the next section. A subsequent section is devoted to a thorough discussion of the results. We summarize our findings and propose future directions to follow to conclude our work.

2. METHODOLOGY 2.1 Simulation and force-field parameters. Simulations of water on a single layer of carbon atoms with the hexagonal structure of graphene were performed. We will refer to these surfaces as monolayer graphene or simply graphene. Owing to the short range nature of the water-


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graphene interaction, a stack of a few graphene layers is sufficient to model the water-graphite system.7, 18, 33 We used a stack of four graphene layers with AB stacking to model the watergraphite system. The simulations were performed with the simulation package LAMMPS.34 The SPC/E,35 TIP3P36 and TIP4P/200537 rigid water models were employed to model the water-water interactions. These models were chosen because they are widely used in simulations involving solid-liquid interfacial systems and because they lead to relatively different values of water interfacial tension.9 The surfaces mentioned above had their atoms rigidly maintained at their crystallographic position. The carbon-carbon distance for the graphene and graphite surfaces was 0.142 nm. The interlayer distance for graphite was 0.34 nm. In the case of monolayer graphene and graphite, the cross sectional area of the surface was A=4.26×3.689 nm2. Each carbon layer contained 600 atoms. The systems contained 5000 water molecules. Each system was arranged such that initially a film of water of approximate thickness 10 nm was in contact with the atoms of the respective solid upper layer (Figure S1). Since the liquid film was in contact with a single surface, the systems contained a solid-liquid and a liquid-vapor interface (Figure S1). Periodic boundary conditions were employed in the three directions of space. The size of the simulation box in the direction perpendicular to the surfaces was set to 45 nm to avoid interactions between periodic images of the system through electrostatic forces. For each system, a repulsive single atomic layer was rigidly placed at 15 nm from the bottom solid layer so that the few water molecules that evaporated from the film during a given simulation were sent back to it after they collided with the repulsive surface (Figure S1).


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System OPLS-TIP3P OPLS-TIP4P OPLS-SPCE Werder Aluru Steele h-BN

εCO (kJ/mol) 0.4317 0.4764 0.4364 0.3920 0.3556 0.3891 εBO (kJ/mol) 0.5081

σCO (nm) 0.33444 0.33487 0.33525 0.31900 0.34360 0.32800 σBO (nm) 0.33095

εCH (kJ/mol) 0.1602 0.1290 εNO (kJ/mol) 0.6277

σCH (nm) 0.26900 0.28100 σNO (nm) 0.32655

Table 1. Energy and distance parameters for the Lennard-Jones pair potentials for the watergraphene and water-graphite, as well as water-hexagonal boron nitride systems. For all systems, the 12-6 Lennard-Jones inter-atomic potential was adopted to model the watercarbon interaction. The OPLS parameters for aromatic carbon atoms38 (with no electrostatic charge) were combined with the water parameters using the geometric mixing rules. In these simulations, there was no explicit interaction between the carbon and hydrogen atoms. Simulations were also carried out with the parameters of Werder et al.,7 with the parameters of Wu and Aluru8 and with the parameters used by Gordillo and Martí39 after Steele40 in combination with the SPC/E water model. Note that explicit Lennard-Jones interactions between carbon and hydrogen are present in the model of Wu and Aluru and in the model of Steele. The energy and distance parameters of the systems mentioned above are summarized in Table 1. In Table 1 and in what follows, OPLS-SPCE, OPLS-TIP3P and OPLS-TIP4P refer to the simulations performed with the OPLS parameters for carbon combined with the SPC/E, TIP3P and TIP4P/2005 parameters, respectively. Werder refers to the simulations performed with the model of Werder et al.,7 Aluru refers to the simulation performed with the model of Wu and Aluru8 and Steele refers to the simulations with the model of Steele as used by Gordillo and Martí.39 We also performed calculations where the distance parameters σCO and σCH were taken from the models above, but where the corresponding energy parameters εCO and εCH were


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changed. For example, we carried out calculations with the value of σCO for OPLS-TIP3P, but with a value of εCO different than what is reported in Table 1. We will also refer to OPLS-TIP3P to describe these calculations, but we will clearly indicate the value of εCO that was employed. A similar nomenclature will be used to discuss the other models. The electrostatic interactions were calculated using the particle-particle particle-mesh approach to the Ewald summation as implemented in LAMMPS.34 Both the electrostatic interactions in the real space and the Lennard-Jones interactions were calculated with a cutoff distance of 1.3 nm unless specified otherwise. This value was chosen relatively large to minimize the missing tail corrections in the calculation of the Lennard-Jones interactions. This point will be discussed in more detail in Section 3.1. A time-step of 2 fs was employed to integrate the equations of motion. The simulations were performed at constant temperature, constant volume and constant number of particles. The average temperature was maintained at 298 K with the Berendsen thermostat.41 In addition to the simulations of water films on graphene, simulations were also performed of water droplets on the graphene surface. Cylindrical droplets, i.e. periodic along the y direction of the simulation cell, were used. These droplets were made up of 5000 water molecules. Cylindrical droplets were employed because droplets with a larger radius of the liquid-vapor interface may be obtained with a given number of molecules in this configuration compared with spherical droplets. Moreover, cylindrical droplets are expected to be less sensitive to the curvature of the three-phase contact line than the spherical ones. The size of the simulation cell was 42.6×3.689×45 nm3. The enlarged dimension in the x direction was chosen such that the distance between the contact lines of the droplets was much larger than the cutoff distance rcut


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and such that the electrostatic interactions between the periodic images of the droplet were negligible. As in the simulations with the water films, a repulsive graphene surface was placed at a distance of 15 nm from the graphene layer on which the droplet resided. The initial configuration of the water droplet had a cubic shape as generated by PACKMOL.42 The system was allowed to relax during at least 2 ns. After this relaxation period, the position of the droplet center of mass in the direction perpendicular to the solid fluctuated around an equilibrium value. Additional simulations of 4 to 6 ns were run depending on the strength of the interaction between water and the surface. The longest simulations correspond to the lowest equilibrium contact angle. The spatial average mass density distribution of the droplet in the reference frame of its center of mass was obtained by time averaging runs of 1ns. The contour of the droplet was defined to be formed by the points of the distribution whose mass-density value was within five percent of the water model’s bulk density. All points within 1 nm from the upper atom layer of the solid surface were disregarded, in order to exclude possible artefacts from ordering effects of the surface on the first few molecular water layers.7 A circle was subsequently fitted to the thusdefined droplet contour. The contact angle was determined from the line tangent to the circle where the fitting circle crossed the plane of the surface atoms. 2.2 Solid-liquid work of adhesion calculations. The solid-liquid work of adhesion WSL is the work required to separate unit areas of solid and liquid in vacuum and to bring them to a distance where they no longer interact. It depends on the solid surface tension γS, on γLV and on γSL through the following relationship:

WSL = γ S + γ LV − γ SL

(3)


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In eq 3, it is assumed that vapor has no influence on the process of separating solid and liquid.4345

This assumption is valid for water at ambient condition owing to its relatively low vapor

pressure. The difference between γSV and γS is thus negligible, i.e. γSV≈γS. Combining eq 3 with eq 1 shows that WSL is directly related to the contact angle through the equation of Young and Dupré (eq 2). Equation 2 shows that WSL is accessible through the experimental determination of θ and γLV. In our approach, the graphene model is rigid, meaning that its surface and interfacial tensions can be identified with its surface and interfacial excess free energies, respectively. Thus WSL is the free energy per unit area necessary to separate water from graphene or graphite. We calculated WSL by means of the dry-surface method. We refer to ref

45

for the

derivation of the corresponding algorithm. Following this method, WSL is calculated as the change in Helmholtz free energy per unit area of the solid-liquid interface to turn the interface of interest (denoted as state B of the system) into an effectively repulsive interface (denoted as state A). Thermodynamic integration is used for this purpose. The interfacial tension of the solidliquid interface in state B is γSL. State A is defined such that its solid-liquid interfacial tension is γLV+γS. Thus turning the system from state B into state A leads to WSL. This is realized in practice by changing the energy parameter of the carbon atom ε from its actual value εB to a value εA. εA is chosen such that the average solid-liquid interaction energy in state A, /A is of the order of -0.01 mJ/m2, i.e. negligible compared with the expected value of WSL.45 The thermodynamic integration formalism for this process takes the form:45 εA

W SL

1 = A

∫

εB

∂USL ∂ ε

d ε

(4)

NVT


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where USL is the total Lennard-Jones interaction energy between water and graphene or graphite. The bracket denotes an ensemble average at constant temperature, constant volume and constant number of particles at a given value of ε. The explicit dependence of USL on the force-field parameters reads  σ USL = ∑ ∑ 4ε CO  CO  rij i =1 j =1  NC NO

12 6    σ CO   N C N H  −   + ∑∑ 4ε CH  σ CH    r   i =1 k =1  rik   ij  

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 σ  −  CH   rik

  

6

  

(5)

NO is the number of oxygen atoms (number of water molecules), NH the number of hydrogen atoms and NC the number of carbon atoms in the graphene layer. σCO is a constant that depends on the model that is considered (Table 1). Since ε CO = ε O ε and ε CH = ε H ε (geometric mixing rule) with εO and εH the Lennard-Jones energy parameters for oxygen and hydrogen, respectively, eq 5 leads to εB

W SL

4 =− A

NC

    

NO

∫ ∑∑ εA

i =1

j =1

 σ ε O  CO   rij 

   

12

σ −  CO  rij 

   

6

+  

NH

∑ k =1

12  σ σ CH   −  CH   r  rik   ik 

ε H 

   

6 

   

d ε

(6)

NVT

Note that for the models with εH=0 (OPLS-type and Werder models), to each value of εB corresponds a value of εCO obtained from ε CO = ε ε O . In the cases of the models of Aluru and of Steele, we used εH=0.13201 kJ/mol and εH=0.071536 kJ/mol, respectively. For each model, a system with ε=εB was equilibrated for 500 ps. The initial configuration of this simulation was prepared by putting the liquid film equilibrated at bulk density next to the solid surfaces. Simulations, each with a different value of ε were performed for 4.5 ns following the equilibration step. The last 2 ns were used to calculate the integrand in eq 6. The integral was


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computed by the trapezoidal rule. Typical variation of the integrand with respect to

ε can be

seen in Figure 4 of ref 45. The values of ε that were used for each model are reported in Table 2. OPLS-TIP3P ε×105 kJ/mol 0.15717 5.6581 22.632 76.070 277.25 604.16 1056.8 2738.5 5793.9 9980.8 16296 24151 35015 47890 64779

OPLS-TIP4P ε×105 kJ/mol 0.12905 4.6458 18.583 62.460 227.64 496.06 867.72 2248.5 4757.3 8195.1 13380 19830 28750 39322 53189

OPLS-SPCE ε×105 kJ/mol 0.15381 5.5370 22.148 74.442 271.31 591.23 1034.2 2679.9 5669.9 9767.3 15947 23634 34265 46865 63393

Werder ε×105 kJ/mol 0.15381 5.5370 22.148 74.442 271.31 591.23 1034.2 2679.9 5669.9 9767.3 15947 23634 34265 46865 63393

Aluru ε×105 kJ/mol 0.038452 0.15381 5.5370 22.148 74.442 271.31 591.23 1034.2 2679.9 5669.9 9767.3 15947 19453

Steele ε×105 kJ/mol 0.038452 0.15381 5.5370 22.148 74.442 271.31 591.23 1034.2 2679.9 5669.9 9767.3 15947 23282

Table 2. Values of ε used to calculate WSL by thermodynamic integration with the dry-surface method. We also studied the interface between hexagonal boron nitride (h-BN) and a water film. Similarly to the water-graphene simulations, the layer of h-BN was made up of 600 atoms with a cross sectional area of 4.334×3.753 nm2. The distance between two bonded boron and nitrogen atoms was 0.144 nm. The systems contained 5000 water molecules. The Lennard-Jones parameters of Kang and Hwang46 in combination with the SPC/E model with the LorentzBerthelot mixing rules were employed (see Table 1). Note that more elaborated models of the interaction between water and h-BN have been developed, especially in regard of the charge alternation between boron and nitride.47 We employed a model with no charges on B or N to test our approach. A comparison between the water-graphene and water-h-BN systems is performed in the light of recent quantum calculation results in Section 3.4. WSL for the interface between


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water and h-BN was calculated in two steps by thermodynamic integration. We first calculated the free energy change per unit area to turn all boron atoms into nitrogen atoms, i.e. to turn the potential energy parameter εBO into εNO. We then calculated the Helmholtz free-energy change for turning the interface between water and the surface containing only nitrogen atoms into an effectively repulsive interface by the approach in eq 6. We also calculated WSL by first turning the nitrogen atoms into boron atoms, and then by using the approach in eq 6 to obtain the free energy change per unit area to turn the boron interface into an effectively repulsive interface. We found no difference in WSL compared with the foregoing procedure, i.e. when first turning boron into nitrogen.

3. RESULTS 3.1 Contact angles on graphene. As mentioned in Section 1, a procedure which is commonly used to obtain or to validate the Lennard-Jones potential parameters of a given solid-liquid interaction is to perform droplet simulations (see for example refs 7, 48-49). The aim is to understand whether given interaction potential parameters reproduce a reference value of the contact angle. In this section we show that this approach depends on the choice of the water model when liquid water is involved. If neglected, as seems to have been the case in the literature, the influence of the water model may have unwanted consequences. For example values of the interaction potential parameter εCO may be thought to be too large and thus disregarded. This may happen because the difference between the experimental value of γLV and the value for the model has to be compensated by an equivalent difference between the simulated and the actual solid-liquid interactions in order to reproduce the experimental contact angle. In


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other words, in order to reproduce an experimental value of cosθ, one has to compensate a possible error in γLV of the water model by an equal error in γS-γSL. We substantiate our reasoning through contact angle calculations on the water-graphene system. We show in Figure 1 the contact angle θ of cylindrical water droplets on monolayer graphene for systems with the distance parameter σCO of OPLS-SPCE, OPLS-TIP3P and OPLSTIP4P (Table 1) depending on select values of the energy parameter εCO. To test our simulation approach, we also performed a simulation with the model of Wu and Aluru,8 for which we obtained a value of 55±2°, in quantitative agreement with the result reported by these authors. It can be seen that θ strongly depends on the water model for a given εCO, especially in the range of values we are interested in (below 70°). The contact angle θ follows the ordering TIP4P>SPCE>TIP3P. This behavior is unexpected in regard of the value of σCO for the different models. It can be seen in Table 1 that σCO differs between OPLS-TIP4P and OPLS-TIP3P by approximately 0.12%. The fact that such a small difference may induce variations of the contact angle as large as 30° (see e.g. the results at εCO=0.472 kJ/mol in Figure 1) calls for a clarification. Before we demonstrate the determining role played by γLV, we extend our understanding of the graphene-water interface by exploring its interfacial structure and interfacial energy properties.


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Figure 1. Contact angle of cylindrical droplets made up of 5000 water molecules on monolayer graphene modeled with the SPC/E (black circle), the TIP3P (red triangle down) and the TIP4P/2005 (blue triangle up) water models depending on the Lennard-Jones potential energy parameter εCO between carbon and oxygen.

We show in Figure 2 the number density of the oxygen atoms in the direction perpendicular to graphene for OPLS-SPCE, OPLS-TIP3P and OPLS-TIP4 depending on εCO. The corresponding simulations were performed with the adsorbed liquid film setup. It can be observed that the structure of water is only weakly dependent on the water model. The main difference is observed in the intensity of the second peak located around 0.6 nm from the surface. Similar observations were reported in ref

50

. This result is consistent with the fact that the

distance parameter σCO in Table 1 is almost independent of the water model. We thus conclude that the dependence of the interfacial water structure on the water model cannot sufficiently explain the variations of θ in Figure 1.


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Figure 2. Number density distribution of oxygen atoms perpendicular to the graphene surfaces for OPLS-SPCE (black), OPLS-TIP3P (red) and OPLS-TIP4P/2005 (blue) at different values of εCO. We now discuss the energy properties of the water-graphene interface. We analyzed the simulation trajectories of the water film systems to calculate the effective water-surface interaction potential Epot,SL depending on the distance z from the surface. Epot,SL at a given height z is defined as the total average interaction energy between a given water molecule whose oxygen atom is located at z and the whole surface. We show in Figure 3 the variation of Epot,SL(z) with the choice of water model for εCO=0.472 kJ/mol and εCO=0.322 kJ/mol. It is straightforward to see that the choice of the water model at a given value of εCO has no effect on Epot,SL. Note that this result was obtained for all tested values of εCO between 0.001 and 0.642 kJ/mol (not shown). Note also that the shape of these curves can be analytically described by Epot,SL(z)=4πεd(σ12/5z10σ6/2z4),33, 51 where d is the carbon surface density in graphene and ε and σ are the carbon-oxygen

Lennard-Jones parameters as reported in Table 1. Given the behavior of the oxygen number density (Figure 2) and of Epot,SL(z) (Figure 3), it is not surprising to find that the average total water-graphene interaction energy per unit area /A is also almost independent of the


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water model for all εCO. For example, at εCO=0.552 kJ/mol, we obtained -152.1 mJ/m2, -148.8 mJ/m2 and -146.9 mJ/m2 for σCO taken from OPLS-SPCE, OPLS-TIP3P and OPLS-TIP4P, respectively. The difference in /A between the water models at a given εCO is of the order of 2-4 mJ/m2, which is more than one order of magnitude smaller than the surface tension of the water models (> 50 mJ/m2). Thus, a change in /A from one model to another cannot explain the difference in contact angle observed in Figure 1.

Figure 3. Effective potential energy of a given water molecule with the whole graphene surface depending on the distance of the oxygen atom from the graphene plane for the OPLS-SPCE (black), OPLS-TIP3P (red) and OPLS-TIP4P/2005 (blue) for εCO=0.472 kJ/mol (left) and εCO=0.332 kJ/mol (right). The red curves and the blue curves were shifted by 0.075 nm and 0.15 nm to the right, respectively, for better readability. Without this manipulation, the three curves are indistinguishable.

We found that neither the interfacial structure of water on graphene, nor the corresponding interfacial energy can explain the dependence of θ on the water model shown in Figure 1. The reason for this behavior is found in the behavior of γLV. Vega et al.9 showed that γLV for water follows the order TIP4P/2005>SPCE>TIP3P over a range of approximately 15


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mJ/m2, i.e. significantly larger than the range of /A values discussed above. This result qualitatively explains why droplets with the TIP3P model spread more than with SPC/E, which in turn spread more than with TIP4P/2005 at a given εCO. A more quantitative analysis that supports this explanation is given below. The discussion above clearly shows that γLV influences the contact angle when different water models are compared. We now discuss in more concrete terms the consequences of this dependence on the optimization process for the water-carbon interaction through droplet simulations. Assume for example that one chooses εCO with the TIP4P/2005 model to reproduce a given experimental value of θ by means of droplet calculations. If one now uses the obtained parameter in combination with the TIP3P model, a lower contact angle is obtained. In the range of contact angles we are interested in, i.e. below 70°, the difference can be as large as 30°. One would then conclude that a new optimization is required, in contradiction with the observation that both TIP3P and TIP4P/2005 lead to similar structure and energy properties of the interface. There are even values of εCO such as 0.6 kJ/mol for which the TIP3P model predicts fully wetting behavior of the system (θ=0°), while the TIP4P/2005 model leads to a measurable contact angle. The discussion above suggests that contact angle is generally not the right observable to use to derive or to validate solid-liquid interaction potentials because of the dependence of θ on γLV. This task can only be achieved through droplet simulations if γLV of the considered water model is equal to the corresponding experimental value. This constraint is in practice almost impossible to meet. In the first place most of the common water models do not reproduce the experimental value of γLV but rather differ from it, in several cases by more than 10%.9 Moreover, it is unknown whether a given water model is able to reproduce the


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experimental value of γLV for the case of nanometer-sized, rather than macroscopic, droplets. At the nanometer scale, the value of γLV depends on the curvature of the liquid-vapor interface49, 52 and on the thickness of the liquid phase (height of the droplet).53 Furthermore, it has been suggested that tail corrections to the Lennard-Jones interactions should be applied.9 How they should be implemented with the geometry of spherical or cylindrical nano-caps remains to be established. It is thus expected that γLV generally depends on the system size at the nanometer scale. This size dependence is a priori unknown. The contact angle may also depend on the droplet size through other quantities. An important factor in this respect is the curvature of the three-phase contact line (see for example the references reference

45

4

and

7

as well as the introduction of

). However, the precise quantification of this effect remains an open question.54-55

The discussion above shows that a quantity different from θ should be employed to derive or to test solid-liquid interaction potential parameters. We show in the next section that the solidliquid work of adhesion is a strong candidate. 3.2 Solid-liquid work of adhesion. In Section 2.2, the solid-liquid work of adhesion WSL has been defined as the free energy change per unit area for separating water from a given surface. This is strictly correct in the present study because graphene is modeled as a rigid structure. Note that graphene lattice vibrations were found to have no effect on contact angle when compared with rigid substrates.7 Our results are thus expected to be independent of graphene flexibility. Because it is a free energy, WSL is the sum of an energy term and an entropy term.33 Moreover, the intermolecular interactions are modeled with pair potentials. Thus it is possible to separate clearly liquid-liquid and solid-liquid contributions to WSL through the relationship A⋅WSL=∆ULL+∆USL-T(∆SLL+∆SSL).33 ∆ULL and ∆USL represent the changes in internal energy upon separating liquid and solid arising from the changes in the liquid-liquid and solid-liquid


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interactions, respectively. ∆SLL and ∆SSL are the corresponding entropy changes. Owing to the energy/entropy compensation ∆ULL=T∆SLL,56 WSL only depends on the solid-liquid energy and entropy components through:33

WSL =

∆U SL T∆S SL − A A

(7)

Although θ and WSL depend on the same interfacial thermodynamic quantities (see eq 1 and eq 3, respectively), the explicit contribution of the water-water interactions vanishes in eq 7. This result is the fundament on which our approach is based. It suggests that WSL rather than θ is an appropriate choice to evaluate the ability of a given force-field to model solid-liquid interfacial interactions. In fact, WSL only depends on the solid-liquid interactions in an explicit way. The role of the water-water interactions is implicit. We showed in Section 3.1 that all water models lead to similar distribution of the oxygen number density when they interact with graphene with the same interfacial potential ESL,pot. We thus expect no significant influence of the water model on WSL for systems under similar interfacial energy conditions. We calculated WSL for σCO taken from OPLS-SPCE, OPLS-TIP3P and OPLS-TIP4P depending on εCO by means of the dry-surface approach (see Section 2.2). We present in Figure 4 the variation of WSL with respect to εCO in the range between 0.322 and 0.642 kJ/mol for OPLSSPCE, OPLS-TIP3P and OPLS-TIP4P, both for water on monolayer graphene and on graphite (four carbon layers). It can be readily seen that in both cases, for all εCO values there is quantitative agreement between the values of the OPLS-TIP3P and OPLS-TIP4P models. Moreover, the largest deviation between OPLS-TIP3P and OPLS-SPCE occurs at εCO=0.642 kJ/mol, for which the OPLS-SPCE value exceeds the OPLS-TIP3P value by only 2.7%. Note


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that the uncertainty on each WSL value is of the order of 1%. There is then a strong contrast between the dependence of the contact angle and the dependence of WSL on the water model at a given εCO.

Figure 4. Variation of the solid-liquid work of adhesion WSL depending on the energy parameter εCO for OPLS-SPCE (black), OPLS-TIP3P (red) and OPLS-TIP4P (blue). Filled symbols: water on graphite, empty symbols: water on monolayer graphene. The dotted lines are guide to the eye. The statistical uncertainty on WSL is of the order of 1%.

We now show that the behavior of WSL is consistent with the behavior of θ observed in Figure 1. We consider two water models denoted as model 1 and model 2. They lead to the values of the work of adhesion WSL,1 and WSL,2, respectively. The relationship WSL,1≈WSL,2 suggested in Figure 2 combined with eq 3 leads to cos θ 2 ≈ γ LV ,1 γ LV , 2 (1 + cos θ1 ) − 1 , where θ1 and θ2 are the contact angles for model 1 and for model 2, respectively. γLV,1 and γLV,2 are the liquid surface tension for model 1 and model 2, respectively. We use OPLS-SPCE as system 1. We calculated the value of θ2 for OPLS-TIP3P and OPLS-TIP4P from the relationship between cosθ1 and cosθ2 above. The values of γLV without tail correction given in ref

9

were taken for


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γLV,1 and γLV,2. We present in Table 3 the comparison between the actual values of θ and the

values predicted from the knowledge of θ1 and γLV,1 as well as γLV,2. There is good agreement between the predicted and actual values of θ for OPLS-TIP3P and OPLS-TIP4P. This result highlights the role played by γLV and the dependence of θ on the water model. Note that a strict quantitative comparison between the predicted and simulated contact angles is not possible because it is unknown how γLV is influenced by the size of the droplet. Differences in the contact angle between values obtained from simulated droplets and values predicted by the independent calculation of the surface tensions were also reported for water on diamond surfaces.53 Similarly to our results, the difference between the approaches increased as θ decreased. θ1=θOPLS-SPCE

97.6° 81.8° 60.5°

θ2=θOPLS-TIP3P Predicted / Measured 86.5° / 89.7° 66.6° / 69.8° 34.5° / 40.4°

θ2=θOPLS-TIP4P Predicted / Measured 101.6° / 103.7° 86.7° / 90.2° 67.8° / 71.6°

Table 3. Contact angle θ2 for OPLS-TIP3P and OPLS-TIP4P predicted from θ1 for OPLS-SPCE. Comparison with the corresponding measured angle in the droplets simulations. The error on the measured angle is ±2°. The conclusion that WSL is weakly dependent on the water model for a given interfacial interaction potential opens a new methodological perspective. WSL may be taken as a quantity to reproduce in order to obtain potential parameters like εCO. We assume that a hypothetical water model that strictly reproduces the experimental value of γLV (72 mJ/m2 at 298 K ) leads to a value of WSL that can be predicted by the variation of OPLS-TIP4P in Figure 4. This is a reasonable assumption because the TIP4P/2005 model leads to the value of γLV which is the closest to the experimental one.9 If one considers the value of 45° for the experimental contact angle of water on graphite, one obtains 123 mJ/m2 as the reference experimental value for WSL (with 72 mJ/m2


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for γLV). The results in Figure 4 indicate that simulations performed with the TIP4P/2005, TIP3P or SPC/E water models with εCO≈0.54-0.55 kJ/mol reproduce this value. If one now assumes that this value of εCO is transferable between graphite and monolayer graphene, one predicts from Figure 4 that the contact angle of a water droplet on an isolated graphene sheet is approximately 62°, a value which remains to be confirmed experimentally. A similar calculation performed for the case θ≈60° on graphite leads to θ≈72° on isolated monolayer graphene. Note that mean-field calculations may be performed to establish a connection between WSL and εCO.53,

57

The

effectiveness of these approaches has been critically discussed in ref 45. Their main drawback is that they neglect the entropy component -T∆SSL of WSL (eq 7) while it was showed that this contribution can be as large as approximately 30% in the water-graphene and water-graphite cases.33 The non-negligible entropy contribution seems in fact to be a general feature, as was recently shown by the analysis of the temperature dependence of WSL of several experimental systems performed by Weber and Stanjek.58

Figure 5. Variation of WSL with respect to εCO for the OPLS-SPCE model (black), for the model of Werder (dark green) with the following values for the cutoff distance rcut: 1.1 nm (square), 1.3 nm (circle) and 1.5 nm (diamond) and as obtained by Kumar and Errington59 (magenta right triangle). The dotted lines are guide to the eye.


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We now discuss the results obtained with the model of Werder.7 This model has a value for σCO that significantly differs from the values with the OPLS force-field (see Table 1). We consider not only the original value of εCO reported in Table 1 but we also study the dependence of WSL on this parameter. We compare in Figure 5 the variation of WSL with respect to εCO for the model OPLS-SPCE and the model of Werder. It can clearly be seen that the distance between the two curves diverges, with no intersection in the considered range of εCO values. We have also plotted in Figure 5 the results obtained with different values of the cutoff distance rcut for the simulations with the model of Werder. It is observed that WSL is also influenced by this parameter. Note that rcut was also found to influence contact angles.8, 18 The common feature behind the effect of σCO and rcut is that they modify the solid-liquid interaction energies even if εCO is maintained constant. We call effective binding energy Emin the energy value at the minimum of the potential energy curve Epot,SL. We found that Emin=-6.96 kJ/mol for OPLS-SPCE at εCO=0.392 kJ/mol, while Emin=-6.25 kJ/mol for the model of Werder, both with rcut=1.3 nm. It is thus understandable that this model leads to values of WSL that are smaller than with OPLS-SPCE. The effect of rcut is also easily explained. The larger rcut is, the larger the number of water-carbon pairs with an attractive contribution that are included in the calculation of Epot,SL. In fact we obtained Emin=-6.17 kJ/mol and Emin=-6.26 kJ/mol for rcut=1.1 nm and rcut=1.5 nm, respectively. The influence of rcut on Emin is a consequence of the absence of tail corrections to the solid-liquid energies. Although the treatment of such corrections is well established for bulk simulations and liquid-vapor interfacial tensions with planar interface,60 it remains to be developed for heterogeneous systems like solid-liquid interfaces. It should be noted that the value of Emin with rcut=1.3 nm and rcut=1.5 nm differ by less than 0.5%. It is thus expected that corrections to


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account for the solid-liquid interactions beyond this value would be negligible. This observation justifies our choice to perform the simulations with rcut=1.3 nm. For comparison we also included the data of Kumar and Errington59 who employed a value of 1.0 nm for rcut and a slightly different water model to obtain WSL by a Monte Carlo approach. The results of these authors shown in Figure 5 are consistent with the trend obtained with the dry-surface approach, according to which WSL decreases with rcut at a given εCO. It is important to observe that Emin contains information on all simulation parameters which influence WSL or θ, like rcut and σCO, in addition to εCO. It thus appears that the values of WSL obtained with different force-fields may be better compared if the variation of WSL is plotted against Emin rather than with respect to εCO. We show such a plot in Figure 6 for the OPLS graphene and graphite systems, as well as the graphite system with the model of Werder at different rcut values. It is interesting to observe that for a given OPLS model, the graphene and graphite results follow the same variation. Thus all results for OPLS-TIP3P and OPLS-TIP4P are described by a single curve. The graphene and graphite results with OPLS-SPCE also belong to a single curve, which is close to the OPLS-TIP4P one, i.e. within less than 5 mJ/m2. The graphite results with the model of Werder are also well described by the dependence of WSL on Emin obtained for the OPLS systems. The system with rcut=1.1 nm shows the strongest deviation from the OPLS curves, being still within 8-10 mJ/m2. The variation of WSL with Emin in Figure 6 may be interpreted in qualitative terms. Figure 3 shows that the ESL,pot(z) is a short ranged function of the distance z. Figure 2 shows that the molecules of the first adsorbed layer are located in the well of ESL,pot(z). Thus most of the contribution to the total solid-liquid interaction energy of the system arises from the molecules with the solid-liquid energy Emin. Because the energy component is the dominating contribution to WSL,33 it is qualitatively understandable that WSL


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seems to be proportional to Emin. Nevertheless, we mentioned that the entropy contribution is in fact not negligible at all,33 but that it also depends on the solid-liquid interaction, as can be qualitatively understood from eq 7 and eq 8. Since we focus in the present publication on how the results reported in Figure 6 may be exploited for the question of deriving force-field parameters, we defer a more detailed discussion of the relative role of energy and entropy and of the simple dependence of WSL on Emin to a another publication.

Figure 6. Variation of WSL depending |Emin| for OPLS-SPCE, OPLS-TIP3P and OPLS-TIP4P models as well as the model of Werder (green). The symbols have the same meaning as in Figure 4 and Figure 5.

3.3 Comparison of WSL of water-graphite models with experiments. We can now perform a direct comparison between experimental values of WSL on graphite and the determination of this quantity with various interaction potentials by the MD simulations. We show the result of this investigation in Figure 7. We present the values obtained for εCO given in Table 1, i.e. for parameters as found in the literature. We also show the values of WSL that correspond to the experimental values θ=64.4° and θ=45° as well as θ=90°. It is found that the force-field of Wu


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and Aluru8 and the force field of Steele39 lead to similar values and fall in the range of contact angle values between 45° and 60°. These values define the interval where recent13-14, 17 and less recent10 experimental measurements were reported. It can also be observed that the combination of the TIP4P/2005 water model with the OPLS force field for aromatic carbon through the geometric mixing rule is also in agreement with θ≈64°. The other models lead to larger contact angles (lower WSL values). We also present in Figure 7 a continuous curve for the dependence of WSL on Emin for OPLS/TIP4P (black dotted line). This curve was obtained in two stages. We first found that there is linear relationship between Emin and εCO with Emin=17.7088 εCO (error on the fitting parameter 0.053%). We then found empirically that WSL=aEmin+bEmin1.1 with a=(29.03±0.59) and b=(33.36±0.48) with WSL expressed in mJ/m2 and Emin in kJ/mol. This curve gives a good description of the variation of WSL with Emin for all systems. The reason why WSL is not a linear function of Emin will be discussed in another publication.

Figure 7. Solid-liquid work of adhesion of different models of water on graphite, monolayer graphene and hexagonal boron nitride.


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3.4 Connecting adsorption energy and solid-liquid work of adhesion. The importance of the simple relationship between WSL and Emin shown in Figure 7 and discussed above is of particular interest. In fact Emin is closely related to the adsorption energy Eads that is obtained by quantum calculations. The energy Eads calculated by these methods is the minimum of the total watersurface interaction energy at 0 K of an isolated water molecule with a given orientation at a given interaction site on the surface as a function of the surface-oxygen distance z. We calculated the average Lennard-Jones interaction energy at 0 K between an isolated water molecule that was sequentially placed on lattice points (spacing 0.05 nm×0.05 nm) in the plane parallel to the surface at a given distance from it. We repeated this operation at different values of z to obtain the z-dependent interaction potential VSL between a given molecule and the whole surface. We found that Epot,SL and VSL never differ by more than 0.5% for a given z value. Note that we performed these calculations for the models with no explicit interaction between hydrogen and carbon, i.e. water was interacting with graphite through the oxygen atom only. We assume that Emin which is the minimum value of Epot,SL is a good approximation of the average value of Eads of water on graphene. We now discuss the validity of this assumption.

Figure 8. Schematic representation of the major orientations of water molecules in the first adsorbed layer on hydrophobic and mildly hydrophilic surfaces.


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Depending on the adsorption site, different water orientations and energies that may differ by several kJ/mol are obtained in quantum calculations. A criterion is thus required to select the adsorption energy that is most appropriate to be identified with Emin. In this context, it is important to observe that only specific orientations are taken by the water molecules in the layer adsorbed on the surface, i.e. in the well of Epot,SL(z). Several classical MD studies61-62 and a recent ab initio MD work32 showed that these water molecules form on average three hydrogen bonds (HBs). The two most probable water orientations which are compatible with this number are characterized for example in ref 53 and represented in Figure 8. The ab initio MD simulations of Tocci et al.32 suggest that the distribution of water-graphene interaction energies in the first adsorbed layer is relatively narrow. We thus suggest that the adsorption energy of the singlemolecule quantum calculations that leads to one of the orientations mentioned above can be used as an estimate of Emin. This energy is expected to be close to the average energy, owing to the narrowness of the distribution of water-graphene energies suggested by the work of Tocci et al. It may then be possible to perform a direct connection between the microscopic adsorption energy Eads evaluated at the quantum level and the value of WSL obtained from the measurement of contact angles on macroscopic droplets. It is interesting to note that the parameters of the model of Wu and Aluru8 for the C-H and C-O pair interactions were obtained from the result of random-phase approximation (RPA) calculations that led to a water orientation with the two bonds of the molecule pointing towards the surface.8,

24

The corresponding adsorption energy is -9.5 kJ/mol as found in the RPA

calculations.24 This value significantly differs from Emin=-8.0 kJ/mol that we obtained. We have found that the water molecules of the first adsorbed layer rarely have the orientation of the RPA calculation despite the explicit C-H pair interaction. On average, they take instead the two


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orientations discussed above (Figure 8) in approximately equal proportions. Thus only the energies compatible with these orientations are effectively sampled and the energy -9.5 kJ/mol never occurs. The RPA calculations of Ma et al. which led to the water orientation as represented on the left of Figure 8 and denoted by these authors as "one-leg" water structure yielded a value of Eads=-7.9 kJ/mol. It would be interesting to derive Lennard-Jones potential parameters for the C-H and C-O pairs based on the one-leg RPA potential energy curve and compare the obtained classical Emin with the quantum Eads. It would then be possible to understand whether the one-leg curve leads to a result different than the two-leg curve used by Wu and Aluru. On non-polar surfaces, the adsorption energy is of the order of -10 kJ/mol at most (Figure 7). This is of the order of or even lower than the energy of a hydrogen bond. Thus the system cannot gain free energy by disrupting the interfacial structure which minimizes the perturbation of the HB network and replace it with a structure that leads to equivalent solid-liquid energy, but a considerable loss of water-water energy.61, 63 Note that the structure with three HBs per molecule was obtained in simulations with a broad range of solid-liquid energies on hydrophobic nonpolar surfaces53 and in simulations with polarizable water models.62 This highlights the important role played by the HBs to determine the orientation of the adsorbed molecules on substrates with hydrophobic or mildly-hydrophilic character. We now show how our approach may be used to address systems other than the graphene surfaces. We found that the dependence of WSL with respect to simulation parameters such as the water model or the cutoff distance can be described by a simple function of the effective binding energy of water. We conclude that the graphene and the graphite surfaces may simply be described by an external field with a single well located within a few Ångströms from the surface. The water molecules interact with it depending on the distance perpendicular to the


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surface and depending on its depth, i.e. the effective binding energy. This conclusion suggests that WSL for surfaces other than graphene or graphite may also be predicted by the variation of WSL for graphene. Calculations carried out with a classical non-polar force-field for water on hBN (see Section 2.1) lead to WSL=104 mJ/m2 and Emin=-8.5 kJ/mol. These values indeed fall on the curve plotted in Figure 7. Our recent work on the gold water interface described by the Lennard-Jones potential of Heinz et al. led to WSL=317 mJ/m2 for Emin=-19.8 kJ/mol through free-energy calculations.45 From the relationship between WSL and Emin established on the OPLSTIP4P model, we predict WSL=316 mJ/m2 at Emin =-19.8 kJ/mol. Both values of WSL are in excellent agreement, showing that the relationship between WSL and Emin derived here seems to be valid for water on non-polar substrates in general. We note that Al-Hamdani et al.64 recently reported a value of -8.1±0.5 kJ/mol for the adsorption energy of water on h-BN obtained by quantum Monte Carlo simulations. According to Figure 7, this value is comparable with the value of the effective binding energy we obtained for water on graphene through the model of Wu and Aluru8 (-8.0 kJ/mol). This model was obtained from random phase approximation calculations.8, 24 It is interesting to see that the agreement between the two results is consistent with the work of Tocci et al. who found by ab initio MD calculations that the water density distribution and HB structure on graphene and h-BN are identical. Note that different quantum mechanical methods were considered in the discussion above. Thus the comparison between the results obtained through different approaches should be considered in a qualitative way. Nevertheless, this comparison indicates that it is worth investigating our assumption regarding the role of water orientation when deriving force-field parameters from quantum mechanical results. From the knowledge of WSL on graphene (97±1 mJ/m2) reported in


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Figure 7, we predict that the contact angle on an isolated monolayer of h-BN is approximately 70°. This value remains to be confirmed experimentally.

4. CONCLUSIONS We showed that the derivation or the evaluation of force-field parameters for the water-graphene interaction by means of droplet calculations is an approach with strong limitations. The dependence of the water surface tension on the water model is an important issue. We found that the solid-liquid work of adhesion WSL is a more robust quantity against which to parameterize. It is related to both the contact angle and liquid surface tension, but it explicitly depends on the solid-liquid interactions only. This feature is the result of the energy/entropy compensation of the change in the water-water interactions upon separating liquid and solid. Note that we have focused on reproducing the solid-liquid work of adhesion. This does not guarantee that other properties are reproduced. Indeed, classical empirical models generally represent compromises and a given model may be more appropriate to tackle a given scientific question.65 We also conclude that the close relation of WSL with the single-molecule adsorption energy Eads is a consequence of the short range nature of the interactions at hand. The work of adhesion is strongly linked to the minimum Emin of the interaction energy of an individual molecule of the liquid with the surface, as the governing descriptor of the interaction; Emin, in turn, shows a close relation to the adsorption energy of a single molecule in vacuum. All systems whose WSL values have been discussed in the present work are modeled through the Lennard-Jones potential. This leads to a surface interaction potential through which the surface mostly interacts with the water molecules of the first adsorbed layer. It would be interesting to understand whether systems with


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other types of interaction (e.g. Coulomb interaction) or modeled with other interaction potentials (e.g. including polarizability of the surface31) follow the behavior of WSL for water on graphene obtained with the Lennard-Jones potential. We obtained a relationship between WSL and the adsorption energy that makes it possible to understand whether the adsorption energy obtained by a given quantum calculation approach is consistent with a given experimental determination of the contact angle. The adsorption energy must be calculated for water orientations that are representative of the orientations taken in a system with many molecules. We found that force-fields which may lead to values of Eads in the range between -9.7 kJ/mol and -8.5 kJ/mol are consistent with the recent experimental contact angles on graphite. i.e. between 45° and 64°. The approach we introduce may be seen as a unifying tool that connects quantum calculations, classical MD simulations and wetting contact angle measurements. As it pertains not only to the example of water on graphene/graphite, but to general apolar or weakly polar surfaces, it should find application for example in the study of the wetting properties of the recently developed twodimensional materials like transition metal dichalcogenides, a topic which has become of interest.16 Finally, it should be noted that this approach has also been used to derive interfacial coarse-grained potentials which are thermodynamically consistent with their parent atomistic model.66 AUTHOR INFORMATION Corresponding Author *Email address: [email protected]


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ACKNOWLEDGMENT We thank Jeffrey Errington for providing the data of the Monte Carlo study presented in Figure 5. We acknowledge Florian Müller-Plathe for encouraging the present work and allowing us to use the computer resource of his group. We are grateful to Florian Müller-Plathe and to Aoife Fogarty for their critical reading of the manuscript and suggestions for improvement. We thank the HPC Center of Technische Universität Darmstadt for allocating computer time on the Lichtenberg-Hochleistungsrechner. We thank the German Research Foundation (DFG) for financial support through the Collaborative Research Center (CRC) Transregio 146 Multiscale Simulation Methods for Soft Matter Systems, the CRC Transregio 75 Droplet Dynamics in Extreme Environments and the Priority Program 1369 Polymer-Solid Contacts: Interfaces and Interphases. ASSOCIATED CONTENT. Supporting Information. Snapshot of the simulation cell in the liquid film configuration. This material is available free of charge via the Internet at http://pubs.acs.org.

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TABLE OF CONTENTS GRAPHIC


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Contact angle of cylindrical droplets made up of 5000 water molecules on monolayer graphene modeled with the SPC/E (black circle), the TIP3P (red triangle down) and the TIP4P/2005 (blue triangle up) water models depending on the Lennard-Jones potential energy parameter εCO between carbon and oxygen. 576x451mm (96 x 96 DPI)



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Number density distribution of oxygen atoms perpendicular to the graphene surfaces for OPLS-SPCE (black), OPLS-TIP3P (red) and OPLS-TIP4P/2005 (blue) at different values of εCO. 568x443mm (96 x 96 DPI)


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Effective potential energy of a given water molecule with the whole graphene surface depending on the distance of the oxygen atom from the graphene plane for the OPLS-SPCE (black), OPLS-TIP3P (red) and OPLS-TIP4P/2005 (blue) for εCO=0.472 kJ/mol (left) and εCO=0.332 kJ/mol (right). The red curves and the blue curves were shifted by 0.075 nm and 0.15 nm to the right, respectively, for better readability. Without this manipulation, the three curves are indistinguishable. 568x444mm (96 x 96 DPI)



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Variation of the solid-liquid work of adhesion WSL depending on the energy parameter εCO for OPLS-SPCE (black), OPLS-TIP3P (red) and OPLS-TIP4P (blue). Filled symbols: water on graphite, empty symbols: water on monolayer graphene. The dotted lines are guide to the eye. The statistical uncertainty on WSL is of the order of 1%. 567x443mm (96 x 96 DPI)


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Variation of WSL with respect to εCO for the OPLS-SPCE model (black), for the model of Werder (dark green) with the following values for the cutoff distance rcut: 1.1 nm (square), 1.3 nm (circle) and 1.5 nm (diamond) and as obtained by Kumar and Errington59 (magenta right triangle). The dotted lines are guide to the eye. 582x443mm (96 x 96 DPI)



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Variation of WSL depending |Emin| for OPLS-SPCE, OPLS-TIP3P and OPLS-TIP4P models as well as the model of Werder (green). The symbols have the same meaning as in Figure 4 and Figure 5. 574x443mm (96 x 96 DPI)


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Solid-liquid work of adhesion of different models of water on graphite, monolayer graphene and hexagonal boron nitride. 581x451mm (96 x 96 DPI)



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Figure 8 Schematic representation of the major orientations of water molecules in the first adsorbed layer on hydrophobic and mildly hydrophilic surfaces. 229x135mm (96 x 96 DPI)


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Parametrizing Nonbonded Interactions from Wetting Experiments via

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