Microscopic Origins of the Variability of Water Contact Angle with

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Microscopic Origins of the Variability of Water Contact Angle with Adsorbed Contaminants on Layered Materials Yao Zhou, and Evan J. Reed J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b04934 • Publication Date (Web): 24 Jul 2018 Downloaded from http://pubs.acs.org on July 26, 2018

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The Journal of Physical Chemistry

Microscopic Origins of the Variability of Water Contact Angle with Adsorbed Contaminants on Layered Materials Yao Zhou and Evan J. Reed*

Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, United States *E-mail: [email protected]. Tel: [+1] (650) 723 2971. Fax: [+1] (650) 725-4034

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ABSTRACT Significant variation in literature reports of water contact angles on layered materials have been interpreted to suggest that the wettability of layered materials can be very sensitive to contamination in an ambient environment. However, the theoretical potential for contamination to account for this variation has yet to be quantitatively fully explored. To address this gap, we combined a Lifshitz-based contact angle model with density functional theory calculations of optical properties to study the wettability of graphite and MoS2. We first demonstrated the layer dependence and substrate dependence of wettability. We find that the contact angle generally decreases with increasing number of layers for a suspended layered material, while for a layered material on a substrate, the contact angle change depends on the dielectric functions of both the layered material and the substrate. Then, to study in depth the effect of contamination, we considered a spectrum of potential contaminating molecules in air, including N2, O2, CO2, CH4 and 1-octadecene. Specifically, our results show that contamination between the liquid and layered material leads to significantly larger changes in contact angle than contaminants that are intercalated within the layered material. We find that layered materials generally appear more hydrophobic after contamination. Our model has potential application of guiding the design of more hydrophobic layered materials. In contrast to other common Lifshitz approaches, these conclusions are independent of any fitting to experimental contact angle results.


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Introduction Layered materials in monolayer, few-layer and bulk forms have received great attention in the past decade, but have been studied in bulk forms for many decades prior. Among the broad spectrum of technologically important layered materials are graphite and transition metal dichalcogenides such as MoS2. The wettability of layered materials plays an important role in the study of many surface properties, including coating1, adhesion2 and nanofluidics3. Intense experimental efforts have been focused on studying wettability of layered materials4,5,6,7,8,9. It has been previously reported that wettability can be very sensitive to surface contamination. To be specific, airborne contamination has been reported to have a great impact on the wettability of graphene6,7 and also affect transition metal dichalcogenides8,9,10, including MoS2 and WS2. These contaminations are usually unintentional and poorly controlled, and can originate from contaminants in air. Although the specific set of contaminating molecules are not completely known, infrared spectroscopy and X-ray photoelectron spectroscopy has been used to monitor hydrocarbon peaks and demonstrate hydrocarbon accumulation on graphene surfaces with exposure to air6. Other molecules in air may also cause contamination: layered materials are known to be subject to small molecule or atom adsorption11,12,13 and intercalation14,15. Even large organic molecules, like stearamide, have been reported to be able to intercalate between the layers16. It has been reported that relative humidity can also impact water wettability of graphitic surfaces17 by inhibiting the adsorption of airborne contaminants. In this work, we consider common molecules in air, including N2, O2, CO2 and CH4, and one hydrocarbon volatile organic compound molecule, 1-octadecene. Volatile organic compounds have been reported to exist in air18, possibly emitted by automotive combustion and plastics such



as polyvinyl chloride (PVC). Here we focused on 1-octadecene as an example because it has been previously studied in a control experiment and has been reported to affect the wettability of graphene by a significant amount6. Despite the advances in the experimental study of the effect of contamination on wettability of layered materials, models demonstrating theoretical potential for contamination to impact contact angles have yet to be quantitatively fully explored. There is a previous theoretical study using polyethylene covered bulk graphite to study the effect of potential -CH2- contamination19. In the modeling of water contact angles, the van der Waals (vdW) interaction plays a significant role. Previous studies have shown the effect of carbon-water interactions on wettabilities20,21,22,23. However, the computation of the vdW interaction can be challenging for standard electronic structure approaches. The practical methods of computing vdW interactions range from a simple pairwise-only parameterized Lennard-Jones potential to an advanced adiabatic-connection fluctuation-dissipation theorem within random phase approximation (ACFDT-RPA)24 applied on top of mean field electronic structure calculations. Although the ACFDT-RPA has been empirically reported to be the most accurate for layered materials25, the applications of the ACFDT-RPA are inhibited by its demanding computational cost. As an alternative to the ACFDT-RPA, the Lifshitz model26 combined with calculations of the macroscopic electromagnetic response provides faster computation for layered geometries, while still being able to describe some non-pairwise effects. The Lifshitz-based model has been applied to layered materials with suitably defined separation and thickness recently and it has been found to provide total vdW binding energies within 8-20% percent of ACFDT-RPA energies for a variety of layered heterostructures27. In this work, we applied the Lifshitz-based model to the study of wettability of layered materials


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and the effect of contamination in ambient environment. Combining the Lifshitz-based model with density functional theory (DFT) calculations of macroscopic optical properties, we computed the optical property change of the materials and, in turn, the contact angle change before and after contamination. We also studied the layer thickness dependence and substrate dependence of wettability of layered materials.

Methods The water contact angle was calculated using the Young-Dupre equation28 as the following: = −1 −

wvs wv

(1)

where wv is the experimentally measured water surface energy29 72.8 mJ/m2 and wvs is the interaction between water and the solid material. In the Owens-Wendt-Rabel-Kaelble method30, wvs consists of a dispersive component and a polar component, where the polar component is a geometric mean of the polar components of the water surface tension and the solid material surface tension. Assuming the solid material lacks a polar component of dielectric response, wvs has only a dispersive component and thus can be expressed as the vdW interactions between water and the solid material31. Here, wvs was calculated using the Lifshitz-based model as shown below. Lifshitz-based model The vdW interactions were calculated using a suitably defined Lifshitz-based model reported recently for layered materials27. In the Lifshitz-based model, macroscopic frequency-dependent



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dielectric functions of the materials are required to evaluate the vdW interactions. Here, the Lifshitz-based model does not account for the wavevector dependence of the dielectric functions and is essentially a macroscopic theory. The frequency-dependent dielectric functions of semiconducting or insulating materials consist only of interband contributions. The interband contributions of solid materials were computed using the independent-particle Kohn Sham wavefunctions (no local field effects) with DFT32. For metallic materials, as for graphene and Cu in this work, the frequency-dependent dielectric functions were computed by adding the intraband contributions from free carriers to the interband contributions computed with DFT. The added intraband contributions were computed with the Drude model33: △ = −

(2)

The plasma frequency P and was set to experimental values. For Cu: P =7.39 eV and =4.6×10-13s;34 For graphite: P =0.44 eV and =2×10-13s.35 A modified Kramers-Kronig transformation was used to convert the imaginary part of the frequency-dependent dielectric functions to the imaginary-frequency response required for the Lifshitz-based model:

+ & ''

!" = 1 + %, $

( ) (

Here, !" is sampled at Matsubara frequencies "- =

*

$./ ℏ

(3)

1, 1 = 0, 1, 2 …. T was set to 300 K

in our calculations of the frequency dependent dielectric response.


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For water, the imaginary-frequency response is computed using the Lorentzian-type oscillator model with previously reported coefficients36,37, which were determined by fitting to experimental values36: & w )6 & w )

= ∑

89 : ( ;9 : ( 9 9

(4)

Here, ? =0.154, ? =0.186, ?A =0.004, ?B =0.020, ?< =0.202; =3.64×1013rad/s, =1.32×1014rad/s, A =3.10×1014rad/s, B =6.59×1014rad/s, < =1.90×1016rad/s; =5.0×1013rad/s, =1.0×1014rad/s, A=2.6×1013rad/s, B=1.3×1014rad/s,

, ,

(5)

where ∆Jeff vsv is defined as: R(STs V: /Ts V: Z[

xx W zz W ∆Jsv 6Q ∆Jeff = vsv s s V: /T V: Z[ R(STxx W zz W 6∆Jsv ( Q

(6)

Here, D is the electromagnetic surface mode wave vector, \ is the separation between the bulk water and the slab of the solid material and * is the thickness of the slab of the solid material. ACS Paragon Plus Environment


The prime in the summation indicates that the 1 = 0 term needs to be halved. Terms involving ∆J are defined below.

Figure 1. The effect of contamination adsorbed above or intercalated below the surface layer. (a) shows a schematic representation of a suspended monolayer before and after a full coverage of contamination. Two different cases are illustrated: contaminating molecules above the monolayer and below the monolayer. (b) shows the contact angle change at different watermonolayer separations. We find that contamination above the surface layer leads to change of the contact angle and the change of the contact angle diminishes with increasing separation. For the case of a suspended monolayer after contamination, we considered two cases: contaminating molecules above the monolayer (assuming molecules separated from water, not dissolved) or contaminating molecules below the monolayer. These two possible cases represent two different ways of contamination of layered materials: adsorption above the layer or intercalation between the layers. To understand the nature of the contamination, we studied both possibilities as shown in Figure 1 (a) after contamination, assuming a full coverage of


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contaminants. Here, a full coverage is assumed to be the case when contaminating molecules form a layer of crystalline solid on top of the layered materials. For the case of molecules above the monolayer, the vdW interaction energy per area between bulk water (w) and a suspended slab of solid material (s) with molecules (m) above mediated by vacuum (v) can be expressed as the following38: + ./ 6NO wvs = ∑+ ′ % DdDln[1 − ∆Jwv ∆Jeff ] vsmv M $ ->, ,

(7)

where ∆Jeff vsmv is defined as:

∆Jeff vsm =

∆Jeff vsmv =

∆Jvs Q

R(STsxx V:W /Tszz V:W Z[

∆Jvs ∆Jsm Q

∆Jeff vsm Q

∆Jsm


m R(STm xx V:W /Tzz V:W Z[m

J ∆Jeff vsm ∆mv Q

∆Jmv


(8)

(9)

Here, \ is the separation between the bulk water and the slab of the solid material with molecules above, * is the thickness of the slab of the solid material and *m is the thickness of the slab of molecules. For the case of molecules below the monolayer, the vdW interaction energy per area between bulk water (w) and a suspended slab of solid material (s) with molecules (m) below mediated by vacuum (v) can be expressed as the following38: + ./ 6NO wvs = ∑+ ′ % DdDln[1 − ∆Jwv ∆Jeff ] vmsv M $ ->, ,

where ∆Jeff vmsv is defined as:


(10)


∆Jeff vms =

∆Jvm Q


∆Jvm ∆Jms Q

∆Jeff vmsv =

∆Jeff vms Q

∆Jms



J ∆Jeff vms ∆sv Q

∆Jsv


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(11)

(12)

Here, \ is the separation between the bulk water and the slab of the solid material with molecules below, * is the thickness of the slab of the solid material and *m is the thickness of the slab of molecules. To illustrate the effect of contamination for the two cases, Figure 1 (b) shows the results of N2 contamination of graphene. By comparing the two possible cases after contamination, N2 above graphene or N2 below graphene, to the case before contamination, we find that contamination above the graphene layer leads to the change of the contact angle. The water predominantly interacts with a portion of the material of thickness equal to the vacuum spacing, as shown in Figure 1. Therefore, from now on we only consider contamination above the layered materials. Figure 2 is a schematic representation of three substrate scenarios studied in this work. In general, the coverage of contaminants may vary depending on the type of layered substrate material, type of contaminants and time of exposure to contaminants in the air. To account for potential variations in coverage, we model the solid materials after contamination to be a mix of materials with contamination and without contamination. Thus, the vdW interaction energy per area between bulk water and the solid material can be expressed as the following: w/o_contam

wvs = 1 − ^wvs

w_contam + αwvs


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w/o_contam

Here, linear mixing parameter ^ is the coverage of the contaminating molecules, wvs

is

the vdW interaction energy per area between bulk water and the solid material without w_contam contamination, and wvs is the vdW interaction energy per area between bulk water and the

solid material with contamination. The expressions for the case of Figure 2 (a) are discussed in detail above. For the case of Figure 2 (b) without contamination, the vdW interaction energy per area between bulk water (w) and a bulk solid material (s) mediated by vacuum (v) can be expressed as the following38: wvs = ∑+ ′ % DdDln[1 − ∆Jwv ∆Jsv M 6NO ] $ ->, , ./

+

(13)

Here, \ is the separation between the bulk water and the bulk solid material.



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Figure 2. Schematic representation of three cases before and after contamination: (a) bulk water on a suspended slab of layered solid material with vacuum in between. (b) bulk water on a bulk solid material with vacuum in between. (c) bulk water on a slab of solid material on a bulk substrate with vacuum in between. After contamination, we assume that the solid material turns into a mix of materials with contamination and without contamination. For the case of Figure 2 (b) with contamination, the vdW interaction energy per area between bulk water (w) with molecules (m) above and a bulk solid material (s) mediated by vacuum (v) can be expressed as the following38: 6NO wvs = ∑+ ] ′ % DdDln[1 − ∆Jwv ∆Jeff smv M $ ->, , +

./

∆Jeff smv =

∆Jsm Q


∆Jsm ∆Jmv Q

∆Jmv


(14)

(15)

Here, \ is the separation between the bulk water and the bulk solid material and *m is the thickness of the slab of molecules. For the case of Figure 2 (c) without contamination, the vdW interaction energy per area between bulk water (w) and a slab of solid material (s) on a bulk substrate (sub) mediated by vacuum (v) can be expressed as the following38: + ./ 6NO wvs = ∑+ ′ % DdDln[1 − ∆Jwv ∆Jeff ] subsv M $ ->, ,

where ∆Jeff subsv is defined as:


(16)

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∆Jeff subsv =

∆Jsubs Q


∆Jsubs ∆Jsv Q

∆Jsv


(17)

Here, \ is the separation between the bulk water and the slab of the solid material on the bulk substrate, * is the thickness of the slab of the solid material. For the case of Figure 2 (c) with contamination, the vdW interaction energy per area between bulk water (w) and a slab of solid material (s) with molecules (m) above on a bulk substrate (sub) mediated by vacuum (v) can be expressed as the following38: + ./ 6NO wvs = ∑+ ] ′ % DdDln[1 − ∆Jwv ∆Jeff subsmv M $ ->, ,

(18)

where ∆Jeff subsmv is defined as:

R(STs V: /Ts V: Z[

xx W zz W ∆Jsubs Q ∆Jsm ∆Jeff = subsm R(STsxx V:W /Tszz V:W Z[ ∆Jsubs ∆Jsm Q

∆Jeff subsmv =

∆Jeff subsm Q


J ∆Jeff subsm ∆mv Q

∆Jmv


(19)

(20)

Here, \ is the separation between the bulk water and the slab of the solid material with molecules below, * is the thickness of the slab of the solid material and *m is the thickness of the slab of molecules. The above terms involving the difference of imaginary-frequency response ∆J are defined as38: w

& ) 6 ∆Jwv = w )W &

W

(21)



s

s

g& )W &zz )W 6 ∆Jsv = −∆Jvs = xx s ) & s ) g&xx

s

W

zz

s

(22)

W

m

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m

g& )W &zz )W 6g&xx )W &zz )W ∆Jsm = −∆Jms = xx s s m m

(23)

g&xx )W &zz )W g&xx )W &zz )W m

m

g& )W &zz )W 6 ∆Jmv = −∆Jvm = xx m m g&xx )W &zz )W

∆Jsubs =

sub ) & sub ) 6g& s ) & s ) S&xx W zz W W zz W xx sub ) & sub ) g& s ) & s ) S&xx W zz W W zz W xx

(24)

(25)

Electronic structure calculations DFT calculations were used to compute the interband contributions of the frequency-dependent dielectric functions. All DFT calculations were performed with the Vienna Ab Initio Simulation Package (VASP)39 with the Projected-Augmented Wave (PAW) method40,41. Electron exchange and correlation effects were treated using the generalized gradient approximation (GGA) functional of Perdew, Burke and Ernzerhof42. We used a plane-wave basis set with a kinetic energy cutoff of 550 eV. To determine the thickness of the slab of contaminating molecules for each layered material, layered bulk forms with two layers per computational cell were relaxed with intercalated molecules. The relaxed interlayer distance with intercalated molecules was utilized to determine the thickness of the contaminants *m . The summarized results of *m are shown in Table 1. A 2×2×1 computational cell with 16 C or 8 MoS2 and 1 molecule per layer were used. Except for the cases of 1-octadecene, because of the large size of the molecule, we used a 4×4×1


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computational cell with 64 C and 1 molecule per layer or a 3×3×1 computational cell with 18 MoS2 and 1 molecule per layer. We sampled the Brillouin zone using a 0.1-0.2 Å-1 MonkhorstPack43 k-point grid. All structures were relaxed at zero stress conditions, with vdW interactions included using the D3 correction method of Grimme (DFT-D3)44. N2 O2 CO2 CH4 *m (Å) graphite 2.56 2.02 2.52 2.9 MoS2 2.78 2.43 2.86 3.08 Table 1. Thicknesses *m of contaminant layers for graphite and MoS2.

1-octadecene 9.61 10.30

To compute the frequency-dependent dielectric functions, we used bulk forms of layered materials and solid experimentally characterized crystalline forms of contaminating molecules. In the case of 1-octadecene, we used the relaxed structure obtained from the intercalated calculation above since there is no crystalline solid form available. We set the number of bands large enough to provide a dielectric response spectrum up to greater than 45 eV for all cases. Figure 3 shows the imaginary parts of the frequency-dependent dielectric functions, which represent the absorption spectra, of all materials included in this work. Both in-plane and out-ofplane components are shown.



Figure 3. Computed independent particle DFT based frequency-dependent interband only electronic absorption spectra of bulk layered materials, contaminating molecules and substrates. '' '' (a) and (b) show in-plane and out-of-plane components, xx and zz , of the frequency-dependent

imaginary dielectric function of graphite and MoS2, respectively. (c) and (d) show in-plane and '' '' out-of-plane components, xx and zz , of the frequency-dependent imaginary dielectric function

of contaminating molecules: N2, O2, CO2, CH4 and 1-octadecene. (e) and (f) show in-plane and '' '' out-of-plane components, xx and zz , of the frequency-dependent imaginary dielectric function

of Cu and sapphire (Copper is cubic and therefore isotropic, and sapphire is trigonal with zz direction corresponding to its rotation axis). Fitting of Lifshitz-based model


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Because the Lifshitz model is inherently a macroscopic one, the separation distance l between the water and solid material must be determined. The microscopic nature of this distance introduces a degree of ambiguity. Here, we use this distance as a fit parameter to reproduce experimentally measured water contact angles on fresh samples. Contact angle data of fresh bulk graphite within the past few years has been summarized to range from 53 degrees to 69 degrees (63.6 degrees ± 4.6 degrees for a total of 9 reported contact angle values)45. The contact angle of fresh bulk MoS2 has been reported to be 67.2 degrees8 or 69 degrees10. Here, the experimentally reported value we used to fit our model is 64.4 degrees for graphite6 and 67.2 degrees for MoS28. We fitted the Lifshitz-based water contact angle model for the case of bulk solid material as shown in Eq. (13) corresponding to Figure 2 (b) without contamination. Figure 4 (a) and (b) show the calculated water contact angles of bulk graphite and bulk MoS2 without contamination as a function of separation l respectively. We then fitted the calculated contact angle of bulk graphite and MoS2 without contamination to the experimentally measured water contact angle on fresh samples6,8 to get the equilibrium separation \, , as indicated by the blue dashed lines. We find \, =1.399 Å for graphite and \, =1.532 Å for MoS2, and these values were used for all the cases we studied in this work. In Figure 4, for reference, we also show an estimated range of possible vacuum separations, as indicated by the green shaded region. This estimated range is computed based on previous molecular dynamics reports of water density profiles normal to graphite22 or MoS246 surfaces. We use the first peak position z in the water density profile to estimate the range to be from z-z0-rO to z-z0-rH, where rO and rH are the covalent radii of atoms O and H, and z0 is determined in a previous study27 for Lifshitz model using ACFDT-RPA calculations for graphite or z0 is the covalent radius rS of atom S for MoS2.



Figure 4. Water contact angles of bulk materials calculated at different water-bulk material separations: (a) bulk graphite. By fitting the water contact angle of bulk graphite to 64.4 degrees, an experimentally reported value of a fresh sample6, we find that \, =1.399 Å for graphite. (b) bulk MoS2. By fitting the water contact angle of bulk MoS2 to 67.2 degrees, an experimentally measured value of a fresh sample8, we find that \, =1.532 Å for MoS2. The green shaded region shows an estimated range of vacuum separations based on previous molecular dynamics studies on water density profiles normal to graphite22 or MoS246 surfaces.

Results and Discussion In this section, we discuss the results of our application of the Lifshitz-based model to study the wettability of layered materials. Specifically, we studied the wettability of graphene and MoS2 in bulk, few-layer and monolayer forms with or without contaminations. The contaminants we considered here include some common molecules in air: N2, O2, CO2 and CH4, and one volatile organic compound: 1-octadecene.


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The wettability of a layered material can potentially change with the number of layers. The existence of a substrate supporting a layered material can also potentially influence the wettability. To obtain the layer dependence and the substrate dependence of wettability, we calculated the water contact angles with different number of layers for four cases: suspended graphite, graphite on a Cu substrate, suspended MoS2 and MoS2 on a sapphire substrate. We chose the substrate Cu for graphite and the substrate sapphire for MoS2, respectively, to facilitate a comparison with the substrates used in reported experimental measurements6,8. Eq. (5) and (6) corresponding to the case of Figure 1 (a) or Figure 2 (a) without contamination required definition of the thickness of the slab of the layered material d. Our earlier work suggested using the covalent radius of atoms to define the thickness for transition metal dichalcogenides such as MoS2, or using thickness fitted to ACFDT-RPA for graphite provides total vdW binding energies between layers that are within 8-20% percent of ACFDT – RPA energies for a variety of layered heterostructures.27 Thus, the thickness of the slab of the layered material is defined as the following: * = * + j − 1*interlayer

(26)

where N is the number of layers, * is the thickness of the monolayer defined according to the previous study27: * =2.84 Å for graphite and * =5.17 Å for MoS2. *interlayer is the interlayer distance defined using the equilibrium distance calculated with the ACFDT-RPA27: *interlayer=3.3 Å for graphite and *interlayer=6.3 Å for MoS2. In the computed model results in Figure 5, the blue and yellow curve show that the contact angle of a suspended layered material, specifically graphite and MoS2, decreases with the number of layers. The contact angle of suspended graphite is more sensitive to the change of the number of



layers than that of suspended MoS2. When a substrate is added, Eq. (16) - (17) corresponding to the case of Figure 2 (c) without contamination indicate the vdW interaction between water and a slab of solid material on a substrate depends on the dielectric functions of both the solid layered material and the substrate. Thus, the layer dependence of the contact angle on top of a particular layered material may vary with a choice of substrate. The red curve in Figure 5 shows that the contact angle of graphite on a Cu substrate increases with the number of layers. This is an qualitative agreement with an earlier experimental report6 depicted in figure 5, though the magnitude of the increase is larger in the experiments than in our prediction. In contrast, the purple curve in Figure 5 shows that the contact angle of MoS2 on a sapphire substrate decreases slightly with the number of layers, which agrees well with previous experimental measurements8 shown in figure 5. The contact angles for large numbers of layers in figure 5 have been constrained to the experimentally reported bulk values by construction.

Figure 5. Computed water contact angles on suspended graphite, graphite on a Cu substrate, suspended MoS2, and MoS2 on a sapphire substrate as a function of the number of layers. Our


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results show that the contact angle decreases with increasing number of layers for suspended graphite and MoS2, and the magnitude of decrease is larger for suspended graphite than MoS2. For a layered material on a substrate, the contact angle depends on the dielectric functions of both the layered material and the substrate. As the figure shows, the contact angle increases with increasing number of layers for graphite on a Cu substrate and the contact angle decreases with increasing number of layers for MoS2 on a sapphire substrate. Experimental values45,8,10,6,7,47 for the monolayers on the substrates and the bulk materials are shown as numbers in the figure for comparison, qualitatively consistent with the trends of calculated contact angle with number of layers.

The effect of contamination on wettability of layered materials can also vary with the number of layers and existence of a substrate. Here, we computed the contact angle change with contamination for graphite and MoS2 in bulk and monolayer forms, suspended or on a substrate. Figure 6 shows the three cases of contact angle change for graphite and MoS2: a suspended monolayer, a bulk material and a monolayer material on a substrate. We find that the change of contact angle is positive for all cases, which shows that the layered materials generally turn more hydrophobic after contamination, regardless of the number of layers or existence of a substrate. This contact angle increase with contamination agrees well with earlier experimental reports for both materials6,48,7,19,49,50,47,51,8,10, as indicated by the circle dots on the right of Figure 6 (a) and Figure 6 (b). Note that the magnitude of the increase strongly depends on the coverage of contaminants and hence may explain the different magnitudes of increase experimentally reported for the effect of contamination. Moreover, note that the adsorption energies for the



small molecules including N2, O2, CO2 and CH4 are likely to be small and thus may lead to a low coverage at room temperature.

Figure 6. Change of contact angle with contamination for graphite and MoS2 in forms of a suspended monolayer, a bulk material and a monolayer material on a substrate. We find that the contact angle generally increases after contamination and the magnitude of increase depends strongly on the coverage of contaminating molecule above the surface layer. Note that such dependence as shown in the figure is close to linear. Various experimental values6,48,7,19,49,50,47,51,8,10 for contaminated materials are indicated as circle dots on the right of the figure for comparison. In Figure 1, we have shown that the contamination above the surface layer leads to change of contact angle and that the water interacts mostly with the top layer of the material. The trends in figures 5 and 6 can be approximately understood and summarized by noting that figure 5 indicates that the water sees only a few layers, or a length of order 1 nm into the adjacent


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material. If high dielectric materials like copper are added to that 1 nm region, interactions will strengthen and the contact angle will decrease. If a vacuum or air is added to that 1 nm region, interactions will weaken and the contact angle will increase. Likewise, adding a layer of organic contaminants between the water and substrate effectively lowers the average dielectric in that 1 nm region, resulting in an increase in contact angle for these materials. We have demonstrated the application of the Lifshitz-based model to the study of water contact angle. In addition, we have provided important insights into the theory behind the effect of contaminations on wettability of layered materials using the Lifshitz-based contact angle model: contamination above the surface layer leads to change of water contact angles and the change of contact angle is generally positive and strongly depends on coverage of contaminants. Based on these findings, we can potentially apply the Lifshitz-based contact angle model to the design of a layered material with desired wetting properties, by introducing targeted molecule adsorption to a layered material. Some of our results are qualitatively or even quantitatively verified by experimental reports, while other results are predictions of the model that we hope will drive experimental work. The prediction that the contact angle increases with decreasing number of layers when freely suspended is a prediction of this model. The relatively small impact of intercalated contaminants on contact angle is also a prediction of this model.

Conclusions In this work, we applied a Lifshitz-based model with DFT-calculated frequency-dependent dielectric functions to the study of wettability of layered materials. We have determined the water-graphite and the water-MoS2 separation by fitting the Lifshitz-based contact angle model



to experimentally measured water contact angles in the case of not-contaminated bulk materials. Our results also demonstrate the layer dependence and substrate dependence of wettability of layered materials. Last, we have shown the change of water contact angles of layered materials with contamination of a spectrum of molecules above the surface layer, rather than from intercalated contaminants. Our results demonstrate that, generally, layered materials appear more hydrophobic after contamination. Our model thus provides theoretical support for previous experimental observations and also provides guidance in the design of more hydrophobic layered materials using organic molecules or other coatings.

Acknowledgment This work was partially supported by Army Research Office grant W911NF-15-1-0570, by Office of Naval Research grant N00014-15-1-2697, by the US Army Research Laboratory through the Army High Performance Computing Research Center, Cooperative Agreement W911NF-07–0027, by NSF grant DMR-1455050, and by the Alma M. Collins Stanford Graduate Fellowship.

References (1) Ghodssi, R.; Lin, P. MEMS Materials and Processes Handbook; Springer Science & Business Media, 2011. (2) Meuler, A. J.; Smith, J. D.; Varanasi, K. K.; Mabry, J. M.; McKinley, G. H.; Cohen, R. E. Relationships between Water Wettability and Ice Adhesion. ACS Appl. Mater. Interfaces 2010, 2 (11), 3100–3110. (3) Werder, T.; Walther, J. H.; Jaffe, R. L.; Halicioglu, T.; Noca, F.; Koumoutsakos, P. Molecular Dynamics Simulation of Contact Angles of Water Droplets in Carbon Nanotubes. Nano Lett. 2001, 1 (12), 697–702.


Page 24 of 28

Page 25 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(4) Rafiee, J.; Mi, X.; Gullapalli, H.; Thomas, A. V.; Yavari, F.; Shi, Y.; Ajayan, P. M.; Koratkar, N. A. Wetting Transparency of Graphene. Nat. Mater. 2012, 11 (3), 217–222. (5) Wang, S.; Zhang, Y.; Abidi, N.; Cabrales, L. Wettability and Surface Free Energy of Graphene Films. Langmuir 2009, 25 (18), 11078–11081. (6) Li, Z.; Wang, Y.; Kozbial, A.; Shenoy, G.; Zhou, F.; McGinley, R.; Ireland, P.; Morganstein, B.; Kunkel, A.; Surwade, S. P.; et al. Effect of Airborne Contaminants on the Wettability of Supported Graphene and Graphite. Nat. Mater. 2013, 12 (10), 925–931. (7) Kozbial, A.; Li, Z.; Conaway, C.; McGinley, R.; Dhingra, S.; Vahdat, V.; Zhou, F.; D’Urso, B.; Liu, H.; Li, L. Study on the Surface Energy of Graphene by Contact Angle Measurements. Langmuir 2014, 30 (28), 8598–8606. (8) Gurarslan, A.; Jiao, S.; Li, T.-D.; Li, G.; Yu, Y.; Gao, Y.; Riedo, E.; Xu, Z.; Cao, L. Van Der Waals Force Isolation of Monolayer MoS2. Adv. Mater. 2016, 28 (45), 10055–10060. (9) Chow, P. K.; Singh, E.; Viana, B. C.; Gao, J.; Luo, J.; Li, J.; Lin, Z.; Elías, A. L.; Shi, Y.; Wang, Z.; et al. Wetting of Mono and Few-Layered WS2 and MoS2 Films Supported on Si/SiO2 Substrates. ACS Nano 2015, 9 (3), 3023–3031. (10) Kozbial, A.; Gong, X.; Liu, H.; Li, L. Understanding the Intrinsic Water Wettability of Molybdenum Disulfide (MoS2). Langmuir 2015, 31 (30), 8429–8435. (11) Leenaerts, O.; Partoens, B.; Peeters, F. Adsorption of H2O, NH3, CO, NO2, and NO on Graphene: A First-Principles Study. Phys. Rev. B 2008, 77 (12), 125416. (12) Yue, Q.; Shao, Z.; Chang, S.; Li, J. Adsorption of Gas Molecules on Monolayer MoS2 and Effect of Applied Electric Field. Nanoscale Res. Lett. 2013, 8 (1), 425. (13) Bui, V. Q.; Pham, T.-T.; Le, D. A.; Thi, C. M.; Le, H. M. A First-Principles Investigation of Various Gas (CO, H 2 O, NO, and O 2 ) Absorptions on a WS 2 Monolayer: Stability and Electronic Properties. J. Phys. Condens. Matter 2015, 27 (30), 305005. (14) Jung, Y.; Zhou, Y.; J. Cha, J. Intercalation in Two-Dimensional Transition Metal Chalcogenides. Inorg. Chem. Front. 2016, 3 (4), 452–463. (15) Chhowalla, M.; Shin, H. S.; Eda, G.; Li, L.-J.; Loh, K. P.; Zhang, H. The Chemistry of TwoDimensional Layered Transition Metal Dichalcogenide Nanosheets. Nat. Chem. 2013, 5 (4), 263–275. (16) Gamble, F. R.; Osiecki, J. H.; Cais, M.; Pisharody, R.; DiSalvo, F. J.; Geballe, T. H. Intercalation Complexes of Lewis Bases and Layered Sulfides: A Large Class of New Superconductors. Science 1971, 174 (4008), 493–497. (17) Li, Z.; Kozbial, A.; Nioradze, N.; Parobek, D.; Shenoy, G. J.; Salim, M.; Amemiya, S.; Li, L.; Liu, H. Water Protects Graphitic Surface from Airborne Hydrocarbon Contamination. ACS Nano 2016, 10 (1), 349–359. (18) Millet, D. B.; Donahue, N. M.; Pandis, S. N.; Polidori, A.; Stanier, C. O.; Turpin, B. J.; Goldstein, A. H. Atmospheric Volatile Organic Compound Measurements during the Pittsburgh Air Quality Study: Results, Interpretation, and Quantification of Primary and Secondary Contributions. J. Geophys. Res. Atmospheres 2005, 110 (D7), D07S07. (19) Kozbial, A.; Li, Z.; Sun, J.; Gong, X.; Zhou, F.; Wang, Y.; Xu, H.; Liu, H.; Li, L. Understanding the Intrinsic Water Wettability of Graphite. Carbon 2014, 74, 218–225. (20) Wu, Y.; Aluru, N. R. Graphitic Carbon–Water Nonbonded Interaction Parameters. J. Phys. Chem. B 2013, 117 (29), 8802–8813.



(21) Svoboda, M.; Malijevský, A.; Lísal, M. Wetting Properties of Molecularly Rough Surfaces. J. Chem. Phys. 2015, 143 (10), 104701. (22) Werder, T.; Walther, J. H.; Jaffe, R. L.; Halicioglu, T.; Koumoutsakos, P. On the Water−Carbon InteracMon for Use in Molecular Dynamics SimulaMons of Graphite and Carbon Nanotubes. J. Phys. Chem. B 2003, 107 (6), 1345–1352. (23) Ramos-Alvarado, B.; Kumar, S.; Peterson, G. P. On the Wettability Transparency of Graphene-Coated Silicon Surfaces. J. Chem. Phys. 2016, 144 (1), 014701. (24) Harl, J.; Schimka, L.; Kresse, G. Assessing the Quality of the Random Phase Approximation for Lattice Constants and Atomization Energies of Solids. Phys. Rev. B 2010, 81 (11), 115126. (25) Björkman, T.; Gulans, a; Krasheninnikov, a V.; Nieminen, R. M. Are We van Der Waals Ready? J. Phys. Condens. Matter Inst. Phys. J. 2012, 24 (42), 424218. (26) Dzyaloshinskii, I. E.; Lifshitz, E. M.; Pitaevskii, L. P. The General Theory of van Der Waals Forces. Adv. Phys. 1961, 10 (38), 165–209. (27) Zhou, Y.; Pellouchoud, L. A.; Reed, E. J. The Potential for Fast van Der Waals Computations for Layered Materials Using a Lifshitz Model. 2D Mater. 2017, 4 (2), 025005. (28) Schrader, M. E. Young-Dupre Revisited. Langmuir 1995, 11, 3585–3589. (29) Harkins, W. D.; Brown, F. E. The Determination of Surface Tension (Free Surface Energy), and the Weight of Falling Drops: The Surface Tension of Water and Benzene by the Capillary Height Method. J. Am. Chem. Soc. 1919, 41 (4), 499–524. (30) Kaelble, D. H. Dispersion-Polar Surface Tension Properties of Organic Solids. J. Adhes. 1970, 2 (2), 66–81. (31) Drummond, C. J.; Chan, D. Y. C. Van Der Waals Interaction, Surface Free Energies, and Contact Angles: Dispersive Polymers and Liquids. Langmuir 1997, 13 (14), 3890–3895. (32) Gajdoš, M.; Hummer, K.; Kresse, G.; Furthmüller, J.; Bechstedt, F. Linear Optical Properties in the Projector-Augmented Wave Methodology. Phys. Rev. B 2006, 73 (4), 045112. (33) Kittel, C. Introduction to Solid State Physics; John Wiley & Sons, Inc, 2004. (34) Ordal, M. A.; Bell, R. J.; Alexander, R. W.; Long, L. L.; Querry, M. R. Optical Properties of Fourteen Metals in the Infrared and Far Infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W. Appl. Opt. 1985, 24 (24), 4493–4499. (35) Philipp, H. R. Infrared Optical Properties of Graphite. Phys. Rev. B 1977, 16 (6), 2896– 2900. (36) Nir, S.; Adams, S.; Rein, R. Polarizability Calculations on Water, Hydrogen, Oxygen, and Carbon Dioxide. J. Chem. Phys. 1973, 59 (6), 3341–3355. (37) Chun, J.; Mundy, C. J.; Schenter, G. K. The Role of Solvent Heterogeneity in Determining the Dispersion Interaction between Nanoassemblies. J. Phys. Chem. B 2015, 119 (18), 5873–5881. (38) Parsegian, V. A. Van Der Waals Forces: A Handbook for Biologists, Chemists, Engineers, and Physicists; Cambridge University Press: Cambridge, 2005. (39) Kresse, G. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54 (16), 11169–11186.


Page 26 of 28

Page 27 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(40) Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B 1994, 50 (24), 17953– 17979. (41) Kresse, G. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B 1999, 59 (3), 1758–1775. (42) Perdew, J. P.; Burke, K.; Ernzerhof, M.; of Physics, D.; Quantum Theory Group Tulane University, N. O. L. 70118 J. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77 (3), 3865–3868. (43) Pack, J. D.; Monkhorst, H. J. Special Points for Brillouin-Zone Integrations. Phys. Rev. B 1977, 16 (12), 1748–1749. (44) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys. 2010, 132 (15), 154104. (45) Kozbial, A.; Trouba, C.; Liu, H.; Li, L. Characterization of the Intrinsic Water Wettability of Graphite Using Contact Angle Measurements: Effect of Defects on Static and Dynamic Contact Angles. Langmuir 2017, 33 (4), 959–967. (46) Luan, B.; Zhou, R. Wettability and Friction of Water on a MoS2 Nanosheet. Appl. Phys. Lett. 2016, 108 (13), 131601. (47) Aria, A. I.; Kidambi, P. R.; Weatherup, R. S.; Xiao, L.; Williams, J. A.; Hofmann, S. Time Evolution of the Wettability of Supported Graphene under Ambient Air Exposure. J. Phys. Chem. C 2016, 120 (4), 2215–2224. (48) Ashraf, A.; Wu, Y.; Wang, M. C.; Aluru, N. R.; Dastgheib, S. A.; Nam, S. Spectroscopic Investigation of the Wettability of Multilayer Graphene Using Highly Ordered Pyrolytic Graphite as a Model Material. Langmuir 2014, 30 (43), 12827–12836. (49) Amadei, C. A.; Lai, C.-Y.; Heskes, D.; Chiesa, M. Time Dependent Wettability of Graphite upon Ambient Exposure: The Role of Water Adsorption. J. Chem. Phys. 2014, 141 (8), 084709. (50) Wei, Y.; Jia, C. Q. Intrinsic Wettability of Graphitic Carbon. Carbon 2015, 87, 10–17. (51) Ondarçuhu, T.; Thomas, V.; Nuñez, M.; Dujardin, E.; Rahman, A.; Black, C. T.; Checco, A. Wettability of Partially Suspended Graphene. Sci. Rep. 2016, 6, 24237.

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Microscopic Origins of the Variability of Water Contact Angle with

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