Acta Mechanica Sinica (2013) 29(4):543–549DOI 10.1007/s10409-013-0063-9

RESEARCH PAPER

Control of surface wettability via strain engineering

Wei Xiong ··· Jefferson Zhe Liu ··· Zhi-Liang Zhang ··· Quan-Shui Zheng

Received: 31 March 2013/ Accepted: 8 July 2013©The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag Berlin Heidelberg 2013

Abstract Reversible control of surface wettability has wideapplications in lab-on-chip systems, tunable optical lenses,and microfluidic tools. Using a graphene sheet as a sam-ple material and molecular dynamic simulations, we demon-strate that strain engineering can serve as an effective wayto control the surface wettability. The contact anglesθ ofwater droplets on a graphene vary from 72.5◦ to 106◦ underbiaxial strains ranging from−10% to 10% that are appliedon the graphene layer. For an intrinsic hydrophilic surface(at zero strain), the variation ofθ upon the applied strains ismore sensitive, i.e., from 0◦ to 74.8◦. Overall the cosines ofthe contact angles exhibit a linear relation with respect to thestrains. In light of the inherent dependence of the contact an-gle on liquid-solid interfacial energy, we develop an analyticmodel to show the cosθ as a linear function of the adsorptionenergyEadsof a single water molecule over the substrate sur-face. This model agrees with our molecular dynamic resultsvery well. Together with the linear dependence ofEadson bi-axial strains, we can thus understand the effect of strains onthe surface wettability. Thanks to the ease of reversibly ap-plying mechanical strains in micro/nano-electromechanicalsystems, we believe that strain engineering can be a promis-ing means to achieve the reversibly control of surface wetta-bility.

The project was supported by the National Natural Science Foun-dation of China (11172149).

W. Xiong · Q.-S. Zheng (�)Department of Engineering Mechanics and Center for Nanoand Micro Mechanics, Tsinghua University, 100084 Beijing, Chinae-mail: zhengqs@tsinghua.edu.cn

J.-Z. Liu (�)Department of Mechanical and Aerospace Engineering,Monash University, Clayton, VIC 3800, Australiae-mail: zhe.liu@monash.edu

Z.-L. ZhangDepartment of Structural Engineering,Norwegian University of Science and Technology (NTNU),N-7491 Trondheim, Norway

Keywords Wettability · Strain engineering· Molecular dy-namics simulation

1 Introduction

Understanding the surface characteristics and controlling thewettability of solid surfaces are fundamental topics in chem-ical physics and serves as a basis in many applications [1].The lotus-leaf-like superhydrophobic surface, for example,has attracted enormous attention in the past decades be-cause of the superior water-repellent and self-cleaning prop-erties [2]. On the other hand, superhydrophilicity of surfaceshas also seen itself wide applications, e.g., improving thefiltration efficiency of polymer filter thin films [3] and theboiling heat transfer efficiency in heat pipes [4, 5]. Recentlyactive and reversible control of the surface wettability is be-coming a very attractive research topic and various applica-tions are proposed and demonstrated.

Engineering the solid surface structures is the mostwidely used method to control the wettability, e.g., via in-troduction of surface roughness/defects and changes of thechemical properties [2, 3, 6, 7]. It is reported that the surfaceenergy of graphene increased as more defects were induced,leading to a hydrophilic nature [8]. Rafiee et al. [9] foundthat the contact angle of graphene film can be controlledwhen the graphene film was dispersed on a substrate by per-forming high-power ultra-sonication in the solvent with acontrolled proportion of acetone and water. Despite the greatsuccess of this approach, there are several trade-offs. Induc-ing roughness, defects and chemical groups will affect thestructural integrity and thus reduce the robustness of the per-formance in practice (e.g., under harsh environments) [10],together with some other undesired consequences, e.g., en-hanced slip friction force for the motion of fluid droplets,and so on. Additionally, most of the methods to change thesolid surface structure and wettability are usually permanentand lack of active controllability and reversibility, which arehighly desired in novel micro/nano-fluidic devices [10, 11].

Reversible controls of wettability have been recentlydemonstrated by some elegant methods, including the light

544 W. Xiong, et al.

irradiation [12, 13], the electrochemical surface modifica-tions [14, 15], applying an electric field [16], and the thermaltreatment [17]. For example, Zhao’s group [18, 19] in Chinahas applied electric field to realize the controllable and re-versible process of elasto-capillarity, which they named theelectro-elasto-capillarity. But these methods still suffer somelimitations, e.g., a small controllable range of contact angles(about 11◦ [3, 13]), a large hysteresis loop [12, 16], delayeddynamic motion of liquid droplets [12], and a low number oflife cycles [13]. Most of these limitations can be attributedto the fact that the wettability changes are accomplished bythe conformational transition of the surface molecular struc-tures.

In this paper, we will demonstrate that the strain en-gineering can serve as an effective way to reversely controlthe wettability of an atomically smooth surface without dam-aging the structure. Graphene is selected as the solid sub-strate, because of its superior mechanical, electronic, andbio-compatibility properties, which render it an ideal ma-terial building-block in the nanofluidic devices [20]. Westudied the wetting behaviour of water droplets on graphenesheets with a biaxial strainε range from−10% to 10% usingmolecular dynamics (MD) simulations. The contact anglesθ of water droplets on the graphene surface vary from 72.5◦

to 106◦ in this strain range. For the intrinsic hydrophilic sur-faces (i.e., at zero strain), the variation ofθ upon the appliedstrains is even more sensitive than that of intrinsic hydropho-bic surfaces (e.g., from 0◦ to 74.8◦). Overall we find a linearrelationship between the cosθ andε. In the end, an analyticalmodel will be presented to explain this observation.

2 Simulations and methodology

Our molecular system is illustrated in Fig.1a: a water dropleton a single graphene sheet. The graphene sheet is biax-ially strained, ranging from−10% to 10%. Accordingly,the carbon-carbon bond lengthaCC changes from 0.9aCC0 to1.1aCC0, whereaCC0 denotes the carbon-carbon bond lengthof strain-free graphene (e.g.,aCC0 = 0.142 nm). We placedfour different sizes of water droplets on the strained graphenesheets, i.e., 748, 1 885, 3 709, 6 600 water molecules, respec-tively. In our MD simulations, the positions of carbon atomsare fixed. We have tried flexible graphene substrates withapplied 0% and 10% biaxial strain and found a less than 5◦

difference in the calculated contact angles from those of thecorresponding rigid substrates.

All MD simulations were performed with theLAMMPS code [21]. A time step of 1.0 fs was usedand the total simulations time was about a few nanosec-onds. We used the CHARMM force field and the SPC/Emodel [22] for water with the SHAKE algorithm [23]. Thevan der Waals (vdW) interactions between water moleculesand carbon atoms were described by a Lennard–Jones(L–J) potential between oxygen and carbon atoms, i.e.,φ(r) = 4ε[(σ/r)12 − (σ/r)6]. The vdW forces were trun-cated at 1.2 nm with long-range Coulomb interactions com-

puted using the particle-particle particle-mesh (PPPM) algo-rithm [24]. Water molecules were kept at a constant temper-ature of 300 K using the Nosé–Hoover thermostat.

Fig. 1 a A water droplet on strained graphene where the carbonatoms are fixed;b Density map of a water droplet with 6 600 watermolecules on graphene sheet at 0% strain, which has been averagedalong the radial direction;c Determination of the contact angleθand the base curvature 1/rB by fitting a circle to the free surface ofthe water droplet in plotb

While maintain the same hexagonal lattice withgraphene for the monolayer solid substrates, we select threesets of L–J parameter for the water-solid interactions, corre-sponding to macroscopic contact angles of 91.2◦, 52.1◦, and133◦ on the zero strained solid surfaces. There are two moti-vations. First, we can study the strain engineering effects onthe contact angles for substrates with different wettability.Second, the contact angle of graphite measured in experi-ments is scattered, varying from 0◦ to over 115◦. It should benoted that value of about 90◦ is commonly accepted [25, 26].The parameters ofσ = 0.319 0 nm andε = 4.063 meV wereadopted to reproduce such an angle [25]. We kept the sameσvalue but altered the parameterε as 5.848 meV or 1.949 meVto represent the hydrophilic or hydrophobic strain-free solidsubstrates, respectively [25]. We label these substrates asgraphene, hydrophilic-surface and hydrophobic-surface, ac-cordingly.

It usually took a few hundred picoseconds to reachequilibrium and the simulations were then continued fortwo more nanoseconds to collect data. From the MD tra-jectories, water density maps were obtained by introduc-ing a 3-dimensional (3D) grid with the size of each cell as0.05 nm×0.05 nm×0.05 nm. Reducing the 3D mesh into a2-dimensional (2D) density map by averaging along radialdirection leads to Fig. 1b, which is the density map of thedroplet with 6 600 water molecules on a graphene sheet with0% strain. We further averaged the 2D density maps of10 000 frames of the trajectory in a total of 2 ns duration.To obtain the water contact angle from such a map, a two-step procedure was adopted following the Ref. [25]. First,

Control of surface wettability via strain engineering 545

the boundary of the droplet surface was determined withinevery single layer that was vertical toz direction by using0.5 g/cm3 as a critical density [27]. Second, a circular bestfit through these points was extrapolated to the solid surfacewhere the contact angleθ was measured as shown in Fig. 1c.Note that the points of the surface below a height of 0.8 nmfrom the solid surface were not taken into account for the fit,to avoid the influence from density fluctuations at the liquid-solid interface.

3 Results and discussions

Figure 2 summarized the contact angles of the waterdroplets with different sizes on the strained sheets ofgraphene (Figs. 2a, 2b), hydrophilic-surface (Figs. 2c, 2d),and hydrophobic-surface (Figs. 2e, 2f)). The measured mi-croscopic contact anglesθ depend on the size of the droplets.According to the modified Young’s equation [25, 28], themacroscopic contact angleθ∞ can be related to the micro-scopic contact angles as

cosθ = cosθ∞ −τ

γLV

1rB, (1)

whereτ is the line tension, 1/rB is the fitted base curvature ofthe water droplets, andγLV is the interfacial free energy perunit area for the liquid-vapor interface. In Fig. 2, the cosinesof contact angles measured in our MD simulations follow thelinear relation very well with respect to 1/rB (Eq. (1)). Ex-trapolating the linear relations in Figs. 2a, 2c, 2e yields themacroscopic contact anglesθ∞.

Figures 2b, 2d, and 2f depict the contact anglesθ andθ∞(hexagon symbols) as a function of the applied strains. Thecosines of the (macroscopic) contact angles exhibit a linearrelation with the mechanical strains. For the three types ofsurfaces, positive strains (stretching) always result in a de-crease of cosθ and thus the increase of contact angleθ, andvice versa. The magnitude of the angle changes is, however,quite different for the three types of solid surfaces. Theθ∞of graphene varies from 72.5◦ to 106◦ for the applied strainfrom −10% to 10%. On the hydrophobic-surface, theθ∞varies from 121◦ to 140◦. For the hydrophilic-surface, thechange is much more significant, from 0◦ to 74.8◦. In com-parison, other methods have a smaller controllable range ofcontact angles. For example, by using an electric field, the(receding) contact angles of water droplets on a low den-sity monolayer can be reversibly controlled between 20◦ and50◦ [16]. The largest photoinduced contact angle changeon langmuir-blodgett films with photoresponsive fluorine-containing azobenzene polymer is about 11◦ [13].

Fitting the contact angle vs. droplet size to Eq. (1)yields the values of line tensionτ as well. The results areshown in Fig. 3. They are on the order of 10–30 pJ/m, de-pending on the wetting properties of the substrates and ap-plied strains (Fig. 3). The obtained magnitude ofτ is con-sistent with the theoretical predictions and some recent ex-periments [29]. It is known that a substrate with a highersurface atom density and better wettability usually has a

larger line tensionτ [30, 31]. Stretching the graphene andthe hydrophobic-surface will reduce the surface atom den-sity and the wettability, thus leading to a dropped line ten-sion value as observed in Fig. 3. In contrast, Fig. 3 suggeststhat the hydrophilic-surface (a nearly constant line tension,27 pJ/m) is almost independent on these two factors. It isworth noting that there is still a debate on the quantitativevalue ofτ and data reported often have differences in severalorders of magnitude [27, 28].

In light of the inherent relation between the contact an-gle and the water-solid interfacial energyγSL, in the follow-ings, we will report a linear relation between the cosθ∞ andthe adsorption energyEads of a single water molecule overa solid surface, which will help us understand the effects ofstrain on the cosθ∞ (Fig. 2). The Young–Dupré equation [32]correlated the macroscopic contact angle and the work of ad-hesion

γLV (1+ cosθ∞) =W/A0, (2)

whereW = (γLV + γSV − γSL)A0 is the work of adhesion,A0 is the contact area,γSV, γSL andγLV are the interfacialfree energy per unit area for the solid-vapor, solid-liquid, andliquid-vapor interfaces, respectively.

In our molecular model, the water-solid interaction en-ergy is zero when they are separated infinitely far away fromeach other. Thus we can calculate the work of adhesionW bysummarizing the molecular pair-wise interactions betweenthe water molecule and the solid surface atoms [20, 32, 33],i.e.,

W = −∫ ∞

0E(h)ρ(h)A(h)dh, (3)

where E(h) is the interaction energy of a single watermolecule with a distanceh from the substrate,ρ(h) are num-ber density of the water molecules per unit area, andA(h)is the cross section area of the water droplet. As usual, thesummation of pair-wise vdW interactions between one wa-ter molecule and all carbon atoms on the monolayer surfacecan be replaced by an integration assuming the continuousdistribution of carbon atoms [32]

E(h) =∫ ∞

0

4

3√

3a2CCφ(√

r2 + h2)dr

=16πε

3√

3a2CC

(σ12

5h10− σ

6

2h4

)=

(5σ43h4− 2σ

10

3h10

)Eads, (4)

where Eads is the lowest point of the potential wellE(h),which occurs ath = σ,

Eads= E(h = σ) = −8πε

5√

3

(σ

aCC

)2= − 8πε

5√

3

[σ

(1+ ε)aCC0

]2≈ − 8πε

5√

3

(σ

aCC0

)2(1− 2ε). (5)

546 W. Xiong, et al.

Fig. 2 Cosine of the contact angleθ as a function of the base curvature 1/rB of the droplets ona graphene,c hydrophilic-surface andehydrophobic-surface; Cosine of the contact angleθ as a function of the biaxial strains applied onb graphene,d hydrophilic-surface,f hydrophobic-surface

The value ofEads represents the adsorption energy of asingle water molecule over a solid surface, which is linearlycorrelated with the applied mechanical strainε on the solidsurface in Eq. (5).

Our previous MD study [34] showed that there is a de-

pletion layer at the interface with a thickness of 0.2 nm, be-tween 0.2 nm and 0.5 nm is the so called “first water layer”with a peak densityρ about 2–3 times higher than the bulkvalue, between 0.5 nm and 1.0 nm is a second layer with den-sity exhibit small oscillation around bulk water density, be-

Control of surface wettability via strain engineering 547

Fig. 3 Line tension fitted from Fig. 2 using Eq. (1) as a function ofthe applied strain on the substrate

yond 1.0 nm is the bulk water with a constant densityρ0.This density profileρ(h) has a weak dependence on thestrains applied on the surface. Similar density profiles arealso observed for the hydrophilic and hydrophobic surfacesin this study. Thus, we can perform the integration (Eq. (3))in two separate parts

1+ cosθ∞

= − 1γLV

∫ huhl

ρ(h)E(h)dh− ρ0γLV A0

∫ ∞hu

E(h)A(h)dh

= − 1γLV

∫ huhl

ρ(h)E(h)dh− ∆tail

=

[ −1γLV

∫ huhl

ρ(h)(5σ4

3h4− 2σ

10

3h10

)dh]Eads− ∆tail, (6)

wherehl andhu represent the lower bound of the first waterlayer and the upper bound of the second, respectively.

In Eq. (6), the first water layer has a monolayer thick-ness so that its cross section area is approximately the dropletcontact areaA0. The rapid decay ofE(h) for h > σ impliesthat the second term on the right side of Eq. (6) is muchsmaller than the first one. Indeed, our calculations showedthat∆tail is less than 5% of the first term in all our calcula-tions. Because theσ is a constant (L–J potential betweenwater and carbon atoms), the liquid-vapor interfacial energyγLV is independent of the solid surfaces, and the change ofwater densityρ(h) upon strain engineering has a small effectin the integral term, which we will discuss in detail later, wecan conclude that cosine of the macroscopic contact angleθ∞should exhibit an approximate linear relation with respect tothe adsorption energyEads. It is important to note that, asthe contact areaA0 is close to zero when the contact angle isalmost 180◦, the linear relationship should have deviation atsuperhydrophobic region.

Figure 4 summarizes the cosθ∞ directly obtained fromour MD simulations (Fig. 2) as a function of the ad-sorption energyEads for the differently strained graphene,hydrophilic-surface and hydrophobic-surface. Indeed, it is a

linear function, as predicted in Eq. (6). The fitted value of theslope is−22.0 eV−1. The contact angle data from Werder etal. [25] are also included in Fig. 4 and the agreement is good.SinceEads is a linear function of the applied strain (Eq. (5)),we can understand the linear relation between cosθ∞ andεdepicted in Fig. 2.

It is interesting to investigate the changes of waterstructures upon the strain of graphene substrates and howsuch changes would determine the contact angle. In our pre-vious publication [34], we analyzed the water structure (den-sity, radial density function and structure factor) at the inter-face of the strained “real” graphene. The two-dimensionalradial distribution and structure factors of the first water lay-ers on the−10%, 0%, and 10% strained graphene substratesare almost identical, while the water density profiles alongthe perpendicular direction of the substrates are similar ex-cept a±15% change in the peak density of the first waterlayers. We have carried out analysis on MD simulations re-sults on hydrophobic and hydrophilic surfaces. Similar con-clusions are obtained. We found that the change of waterdensity profile upon strain engineering has a small effect inthe integral term in Eq. (6). For “real” graphene, the inte-gral term varies from−22.2 eV−1 to −20.7 eV−1 at a strainfrom −10% to 10%. For hydrophobic surface, it varies from−18.9 eV−1 to −17.0 eV−1. And for hydrophilic surface, it isfrom −22.5 eV−1 to −22.2 eV−1. All of them are close to thefitted slope−22.0 eV−1 in Fig. 4. This shows our analyticalmodel is consistent quite well with our MD results. This alsoindicates the change ofEads upon strain engineering plays adominant role on cosine of the contact angle.

Fig. 4 Cosine of the macroscopic contact angleθ∞ as a functionof the adsorption energy of a single water molecule on top of thestrained graphene, hydrophilic-surface, hydrophobic-surface. Wealso included the simulated microscopic contact angle results ofWerder et al. [25]

It is worth noting that in Ref. [25], Werder et al. corre-lated the contact angleθ∞ to the equilibrium adsorption en-ergy, in which they concluded that only in a certain range, thecontact angle follows a linear relationship with theEads. We

548 W. Xiong, et al.

believe that Eq. (6) (Fig. 4) is a better model to understandthe relation between the surface wettability and the chemi-cal/physical interactions of liquid and solid surfaces.

Since our model is derived without presumption on theatomic structures of the substrate, it can be easily applied to3-dimensional substrates (e.g., graphite) by summing the in-teraction energy between water molecules and the differentatomic layers of the substrate, although the surface atomicdensity of a substrate and the averagedEads might not nec-essary be linear functions of the applied strain/stress. It isworth noting that since the Lennard–Jones interaction de-cays rapidly over distances, the interfacial energy is mainlydetermined by the first atomic layer of substrates [9, 35]. Webelieve our results can provide some valid indications for abroad class of three dimensional substrates.

Strain up to 30% can be readily exerted on graphenein experiments [36–38]. For example, an epitaxial strainof ∼ ±1% builds up in the graphene when it is grown ondifferent substrates [38–41], uniaxial strain up to∼ 1.3%to a graphene monolayer can be applied by using two- andfour-point bending setups [37], and uniaxial strain rangingfrom 0 to 30% can be achieved for large-scale graphenefilms transferred to a pre-stretched substrate [38]. There arealso many ways to reversibly control the strains applied onsubstrate materials by mechanical stresses or electric fields.For example, reversible strain obtained in Fe-Pd single crys-tals by compressive stress-induced martensite variant rear-rangement is reported to exhibit as high as 5% [42], Zhanget al. [43] obtained a large reversible electric-field-inducedstrain of over 5% in BiFeO3 films. We, therefore, believestrain engineering can be a promising way to reversely con-trol the surface wettability in practice. In practice, compres-sive strain often leads to ripples or folding of graphene. Inthis manuscript, the study on the compressive strain serves atheoretical interest. We aim to obtain a more complete pic-ture of the relation between contact angle and molecular ad-sorption energy and substrate strain.

Strain engineering, in our previous study, has been pre-dicted to significantly change the slip length of water over agraphene layer [34]. It is thus interesting to investigate thecorrelation between the wettability and the slip length. It isoften believed that a hydrophobic surface often has a largerslip length than that of a hydrophilic surface [44]. Strainengineering the wettability and the slip length turn to be anexceptional case. In Fig. 2, with a strain from−10% to 10%,the graphene is becoming more hydrophobic (e.g., contactangle increasing from 72.5◦ to 106◦). The slip length ob-tained in our previous MD simulations was reduced from175 nm to 25 nm. Liquid water can slip on a hydrophilic sur-face, even with a larger slip length than that on a hydrophobicsurface [45]. To understand such a counter-intuitive observa-tion, we should note that Eq. (6) implies the dependence ofcontact angle onEads, which is an average of the van derWaals potentials over the whole solid surface (ath = σ),whereas it is the energy barrier (i.e., the corrugation of the

vdW potential profile) experienced by water molecules overa solid surface who defines the slip length [34]. Stretchinga graphene layer results in a smallerEads (Eq. (5)) and thusa higher contact angleθ∞, but it leads to an enhanced en-ergy barrier and thus a reduced slip length [34]. This insightmay help understanding the observed controversial correla-tions between the contact angle and the slip length in exper-iments [44, 46].

4 Conclusions

To summarize, using graphene sheet as a sample material,our MD simulations show that the wettability of a solid sur-face can be controlled by mechanical strains. Overall, thecosines of the contact angles exhibit a linear relation with re-spect to applied strains. For a graphene surface, the contactangles can be tuned from 72.5◦ to 106◦ under biaxial strainsranging from−10% to 10%. For droplets on intrinsic hy-drophilic surfaces (at zero strain), the variation of the contactangle is more sensitive than that of a hydrophobic surface.To understand the strain engineering effect, we developedan analytical model to reveal a linear relationship betweenthe cosθ∞ and the adsorption energyEads of a single watermolecule over the substrate surface. The applied mechani-cal strains change theEadsand consequently alter the contactangle. We believe that the linear relationship between thecosine of the contact angle and the adsorption energyEads isa general model to describe the surface wettability and thechemical/physical interactions of liquids and solid surfaces.Thanks to the ease of reversibly applying mechanical strainsin micro/nano-electromechanical systems, we propose thatstrain engineering can serve as an effective means to achievethe reversibly control of surface wettability.

Acknowledgements

Q.S. Zheng acknowledges the financial support from the IBMWorld Community Grid project “Computing for Clean Water”, andthe Boeing-Tsinghua Joint Research Project “New Air FiltrationMaterials”. J.Z. Liu acknowledges seed grant 2012 from engineer-ing faculty of Monash University. This work was supported by anaward under the Merit Allocation Scheme on the Australia NCI Na-tional Facility at the ANU.

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