Molecular Dynamics Study of the Hydrophilic-to-HydrophobicSwitching in the Wettability of a Gold Surface Corrugated withSpherical CavitiesZhengqing Zhang,†,∥ Mohammad A. Matin,§,∥ Man Yeong Ha,‡ and Joonkyung Jang*,†

†Department of Nanoenergy Engineering and ‡Department of Mechanical Engineering, Pusan National University, Busan, 609-735,Republic of Korea§Center for Advanced Research in Sciences (CARS), University of Dhaka, Dhaka-1000, Dhaka Bangladesh

ABSTRACT: This paper reports a large scale moleculardynamics (MD) simulation study of the wettability of a goldsurface engraved with (hemi)spherical cavities. By increasing thedepth of cavities, the contact angle (CA) of a water droplet onthe surface was varied from a hydrophilic (69°) to ahydrophobic value (>109°). The nonmonotonic behavior ofthe CA vs the depth of the cavities was consistent with theCassie−Baxter theory, as found in the experiment by Abdelsalam et al. (Abdelsalam, M. E.; Bartlett, P. N.; Kelf, T.; Baumberg, J.Wetting of Regularly Structured Gold Surfaces. Langmuir 2005, 21, 1753−1757). Depending on the depth of cavities, however,the droplet existed not only in the Cassie−Baxter state, but also in the Wenzel or an intermediate state, where the cavities werepenetrated partially by the droplet.

■ INTRODUCTION

The wettability of a solid surface is influenced greatly by thesurface roughness.1−5 In particular, the hydrophobicity of asurface increases drastically in the presence of nano- ormicroscale corrugations. This way, a hydrophobic surface with acontact angle (CA) < 120° can be turned into a super-hydrophobic one with a CA > 150°. With the help of micro-and nano-electromechanical systems technologies, arrays ofrectangular, cylindrical, and dome-shaped pillars are con-structed routinely on the μm- or nm- scale. Recently, moresophisticated corrugated structures, such as the hierarchicalstructures (e.g., nm-sized hairs on μm-scale pillars)6−8 andpillars with re-entrant geometries, have been constructed.9−11

Abdelsalam et al.12 reported that even a hydrophilic goldsurface can be turned a hydrophobic surface by carving outspherical cavities on it (Figure 1a). Specifically, a hydrophilicgold surface, whose intrinsic CA is ∼70°, had a CA> 90° whenit was engraved with (hemi)spherical cavities, a few hundrednanometers in diameter. In the experiment, the depth of thecavities (t) relative to the diameter of the spheres (d), ξ = t/d(see Figure 1a), increased continuously from a near zero (flat)to half (hemispherical) and to near one (spherical) value. Bychanging the shape of the cavities from almost hemispherical toa spherical one (as shown in the change from the top to bottomof Figure 1a), the intrinsically hydrophilic gold surfacetransformed to a hydrophobic surface. This extraordinaryswitching in the surface wettability is not completely under-stood, especially at the molecular level. Thermodynamically, themeasured (apparent) CA of a droplet on a corrugated surface,θ*, is determined by both the material property (surfaceenergy) and surface geometry. The material property can becharacterized by the intrinsic CA of the droplet in contact with

a flat surface, θ. On the other hand, the effects of the surfacegeometry on θ* can be considered only when the exact shapeof the droplet in contact with the corrugations (i.e., sphericalcavities in the present case) is known. For this purpose, twoextreme cases are commonly invoked. In the so-called Wenzel(WZ) state, the droplet completely wets a corrugated surface,filling in the cavities (pits) of the surface (Figure 1b). Theapparent CA, θ*, of the droplet in the WZ state is then given by

θ ϕ θ* =cos cos (1)

where ϕ is the ratio of the area of the corrugated surface to thearea of the horizontal plane (>1).13 On the other hand, thedroplet in the Cassie−Baxter (CB) state is assumed to contactonly the top of the corrugated surface, while the cavities of thesurface remain intact (Figure 1c). The apparent CA in the CBstate is given by

θ θ* = − −f fcos cos (1 )1 1 (2)

where f1 (<1) is the fraction of the top of the corrugated surfaceprojected onto the horizontal plane.14 Whether a droplet on acorrugated surface exists in the WZ, CB, or some intermediatestate cannot be determined a priori. Therefore, the CA (θ*)measured in experiments is compared with the WZ and CBtheories, eqs 1 and 2, to deduce the actual state of the droplet.Based on free energy analysis, Patankar15 studied theoret-

ically the wetting behavior of a gold surface engraved withspherical cavities. According to his theory, the CB state is only

Received: June 25, 2016Revised: August 31, 2016Published: September 1, 2016

Article

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© 2016 American Chemical Society 9658 DOI: 10.1021/acs.langmuir.6b02378Langmuir 2016, 32, 9658−9663

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allowed for the cavity depths ξ > (1 + cos θ)/2 (= 0.67 for θ =70°). Otherwise, the spherical cavities are either partially orfully (WZ) filled with the droplets. Patankar proposed severalpartially filled states, such as crescent and bubblelike geometriesinside the cavities. This theoretical prediction contrasts with theexperiment by Abdelsalam et al., in which the CAs alwaysagreed with the CB theory. Patankar concluded that theagreement of the CB theory with the measured CAs does notguarantee that the droplets actually exist in the CB states.Similarly, this study shows that the CAs of nm-sized dropletscan be close to the CB values even if the droplets exist in theWZ states (see below).Thermodynamic theories, including those by Patankar, WZ,

and CB, regard the droplet and surface as featureless continua,instead of collections of discrete molecules and atomsinteracting with each other via various interatomic interactions.Therefore, these theories cannot deliver the molecular insightson the surface wettability. Herein, a molecular dynamics (MD)simulation was performed to study the switching behavior in

the wettability of a gold surface carved out with sphericalcavities. Using a coarse grained model of water, droplets of81 170 molecules and surfaces made of 149 000 gold atomswere simulated, which far exceeds those simulated inconventional MD simulations. The present MD simulationindeed reproduced the hydrophilic-to-hydrophobic transition inthe wettability of a gold surface with increasing cavity depth. Asin the experiment by Abdelsalam et al., the overall tendency ofthe CA vs the cavity depth was consistent with CB theory.Quantitatively, however, CB theory deviated significantly fromthe MD simulation. Moreover, the droplets were not always inthe CB state, but in the WZ or some intermediate statespartially filling the cavities. The molecular details of the partiallyfilled states are provided.

■ MODEL AND SIMULATION METHODThe gold surfaces carved out with the periodic arrays of (hemi)spherical cavities (Figure 2a) were simulated. Sixteen (hemi)spherical

cavities, 6 nm in diameter, were carved out from a flat gold surface. Atleast three layers were kept below the bottom of the cavities in thesimulations. The lateral dimension of the surfaces was 36.2 × 36.2 nm2

(Figure 2a). Eight different values of ξ, ranging from 0.136 to 0.884,were simulated. Depending the value of ξ, the gold surfaces consistedof 78 000 to 149 000 atoms. The gold surfaces were held rigid and theperiodic boundary conditions were applied along the horizontaldirections.

The water droplet was modeled by employing MARTINI modelversion 2.0,16 which treats four water molecules as a single bead.Designed to account for the strong polar interaction between watermolecules,16 the present model has proven to preserve the majorproperties, such as the diffusivities, surface tension, and solvationenergy, of the SPC point charge model.17,18 Also, this model wassuccessful in modeling the surface property of water.19 A water dropletcomposed of 20 290 beads, corresponding to 81 170 water moleculesand 13.2 nm in diameter, was prepared. The present water droplet ismuch larger than the typical size in previous MD simulations.20 Theinteratomic or intermolecular interaction u(r) was modeled using theLennard−Jones (LJ) potential function, u(r) = 4ε[(σ/r)12 − (σ/r)6],where σ and ε are, respectively, the length and energy parametersinherent to atomic or molecular species. The LJ parameters of watermolecules and gold atoms were σw = 0.47 nm and εw = 1.195 kcal/mol,and σAu = 0.2935 nm and εAu = 0.1365 kcal/mol, respectively. Thewater−gold LJ potential parameters were determined using the

Figure 1. Wetting property of a surface textured with (hemi)sphericalcavities. (a) Schematic diagram of gold surfaces with approximatelyhemispherical (top) and spherical (bottom) cavities. The dimension-less depth of the spherical cavities,ξ, is defined as the ratio of the cavitydepth (t) to the diameter of the spheres (d). The top and bottomshow cases where ξ = 0.21 and ξ = 0.88. (b) Wenzel state of a dropleton the surface engraved with nearly hemispherical cavities. (c) Cassie−Baxter state of a droplet on the surface with almost spherical cavities.

Figure 2. (a) Simulation geometry of a gold surface engraved with 16spherical cavities, 6 nm in diameter (in this case, ξ = 0.443). The cross-sectional side view of the surface is shown on the right. (b) MDsimulation snapshot of a water droplet in the WZ state. (c) MDsnapshot of a water droplet in the CB-like state.

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Lorentz−Berthelot combination rules.21 Using these LJ parameters,the present MD simulation reproduced the experimental CA on a flatgold surface (see below).The MD simulations were run at constant number (N), volume

(V), and temperature (T) using the Evans thermostat22 at 300 K. Thecutoff distance for the LJ interaction was 12 Å. The MD trajectorieswere propagated using the velocity Verlet algorithm21 with a 30 fs timestep, which conserved the energies in the simulations. 600 snapshots of12 ns long simulations were collected to calculate the averagequantities. The DLPOLY simulation package23 was used to implementthe MD methods described above.The intrinsic CA, θ, was obtained by running an MD simulation of a

droplet on a flat gold surface at 300 K for 12 ns. For a given MDsnapshot of the droplet (Figure 3a), the surface normal passingthrough the center of the droplet was set up along the Z axis. Thedroplet was then sliced into 5 Å − thick slabs. In each slab, thedistances of the water beads from the Z axis, r s, were binned at 5 Å

intervals. By averaging more than 600 snapshots, the horizontal densityprofile ρ(r) was calculated for each slab located at z (drawn as circlesin Figure 3b). The density ρ(r) was calculated by counting the numberof molecules located at r ∼ r+dr (dr = size of bin). This number wasthen converted to ρ(r) by dividing it by the Jacobian factor, 2πr. Thisconversion sometimes caused a numerical instability near r = 0, givingrise to a decreasing, rather than a leveling-off, density near the centerof the droplet (as shown in Figure 3b). This numerical artifact can beovercome by using an unequal binning of r as in Werder et al.’s work.24

Note however ρ(r) is only calculated to locate the periphery of thedroplet where ρ(r) drops down to zero. For this purpose, the presentbinning method is sufficient. The data were then fit to a function,ρ(r)= (ρl + ρν)/2 − (1/2)(ρl − ρν)tanh(2(r − re)/w), where ρ

l and ρν arethe liquid and vapor densities, re is the position of the Gibbs dividingsurface, and w is the width of the liquid−vapor interface (drawn as thesolid line in Figure 3b). The Levenberg−Marquardt method was usedto determine the fitting parameters, ρl, ρν, w, and re.

25 The distanceabove which ρ falls below 0.2 g cm−3 is defined as the radius of thedroplet at that z value, Rdrop(z). Figure 3c shows a plot of Rdrop vs z(drawn as circles). Finally, Rdrop was fitted to a parabolic function of zdrawn as the solid line in Figure 3c. We used a parabolic fit, instead ofa circular fit,24,26 because the droplets were not circular near thesurfaces. The parabolic fit, including a circular fit as a special case,closely reproduced the peripheries of the droplets. The parabolic fitshave been widely used in the previous studies of the liquid−vaporinterfaces.27−29 θ is given by the slope of the tangential line of theparabola at z = 0.29 The resulting value of θ was 73°, which is close tothe experimental value measured for a macroscopic droplet (70°).

■ RESULTS AND DISCUSSIONThis study investigated how the CA θ* depends on the cavitydepth, ξ. In Figure 4, the CAs from the MD simulations are

drawn as filled or open circles when the droplets are in the WZ-like or CB-like states, respectively. The CAs predicted from theCB (solid line) and WZ (dotted line) theories were alsoplotted. The simulated CAs indeed showed a hydrophilic-to-hydrophobic transition: the CA increased from 73° to 109°with increasing ξ from 0 to 0.544. Upon further increases in ξto 0.884, the CA decreased to 99.23°. The simulated CAs arethe upper and lower bounded by the CB and WZ theoreticalvalues, respectively.The simulated CAs deviate significantly from both the CB

and WZ theories, especially for intermediate values of ξ (0.24−0.78). This deviation can be ascribed partly to the finite size ofthe present droplet (13.2 nm in diameter) relative to that of the

Figure 3. Calculation of the intrinsic contact angle of a water dropleton a flat gold surface. (a) MD snapshot of a water droplet on a gold(111) surface. (b) Density of water ρ vs the distance from the surfacenormal axis r (circles) for a given height from the surface. The solidline is the fit using the hyperbolic function. (c) Droplet radius Rdrop vsthe vertical height from the surface z (circles). The solid line is the fitusing the parabolic function of z.

Figure 4. Hydrophilic to hydrophobic transition in the contact anglesfor gold surfaces with various depths of spherical cavities. Thesimulated CAs are plotted as filled or open circles vs ξ. Filled and opencircles correspond to the states of droplets similar to the WZ and CBstates, respectively. For comparison, the CAs from the CB and WZtheories are drawn as solid and dotted lines, respectively.

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spherical cavities (6 nm in diameter). Both the CB and WZtheories assume that the cavities are negligible in size comparedto the (macroscopic) droplet. The effects of the droplet size canbe estimated approximately by referring to the modifiedYoung’s equation, cos θ = cos θ∞ − (τ/γ)/rB, where rB is thebase radius, γ and τ are the surface tension and line tension ofthe water droplet, and θ∞ is the CA of a macroscopic droplet(rB → ∞). Typically, the line tension, τ, measuredexperimentally30 is negative and is in the order of 10−10 Jm−1; hence, the CA increases with increasing the droplet size.Similarly, the MD simulation of Santiso et al. showed that theCA on a hydrophilic surface increases with increasing dropletsize.31 We simulated droplets of varying sizes on a flat surface.The droplets made of 3996, 5050, 6160, 6994, 7988, and 9625beads were simulated. The contact angles and the base radii ofthe droplets varied as 68.98, 67.94, 69.94, 72.08, 73.12, and75.53° and 4.00, 4.55, 4.70, 4.91, 5.40, and 5.64 nm,respectively. According to the modified Young’s equation, weperformed a linear fit of the contact angles with respect to thebase radii. We obtained, from the fit, a line tension of −9.65 ×10−10 J m−1 if we used the surface tension value previouslycalculated by employing the present model of water (=0.03 Nm−1).16 For droplets >54 nm in diameter (where themacroscopic limit is reached according to Santiso et al.31),the simulated CAs was expected to be close to the CB theoryresults.The CB theory, despite its quantitative deviation from the

simulated CAs, reproduced the overall nonmonotonic behaviorfound for the CA vs ξ curve in Figure 4. According to the CBtheory, eq 2, the void fraction (=1 − f1) at the top of thecorrugated surface increased with increasing ξ for ξ < 1/2. As aresult, the droplet sits more on the void than on the top of asolid, and the surface consequently becomes more hydro-phobic. Once ξ reaches more than 0.5, the shape of the cavitiesswitches from a hemispherical to a near spherical one, and thevoid fraction now decreases with increasing ξ (because themouths of the cavities shrink as ξ increases from 0.5). Thisexplains the decreasing CA starting from ξ = 0.5. In contrast,the WZ theory, eq 1, focuses on the surface area of thecorrugated surface, which always increases with increasing ξ.Therefore, the intrinsically hydrophilic gold surface becomeseven more hydrophilic with increasing ξ, giving rise to amonotonic decrease in CA with increasing ξ.Abdelsalam et al. reported that the CB theory quantitatively

predicts the experimental CAs of droplets on gold surfaces withspherical cavities, regardless of the ξ value.12 Patankar, however,showed that the CB state is unstable for cavity depths, ξ <(1+cos θ)/2 = 0.65 if we use the intrinsic CA calculated in thepresent simulation.15 Similarly, the droplets in the presentsimulation completely penetrated into the cavities (WZ states,drawn as filled circles in Figure 4) for ξ < 0.68 and the CBstates of droplets were only possible for ξ > 0.68 (=0.78 and0.88, drawn as open circles in Figure 4). The present thresholdvalue of ξ (=0.68) slightly differed from the theoretical value ofPatankar (=0.65) presumably due to the finite size of droplet inour simulation. Note the simulated CAs of these WZ dropletswas closer to the values of CB theory. Moreover, the simulateddroplets for ξ = 0.78 and 0.88 were not in the pure CB state,but they also partially penetrated the cavities, as shown inFigure 2c. In the following, the partial filling of the cavities isexamined in detail for the case of a macroscopic droplet.The partial filling of the cavities with liquid was further

investigated by continuously varying ξ from 0.65 to 0.85. For

this purpose, a macroscopic droplet, instead of a finite-sizeddroplet above, was simulated. The macroscopic droplet wassimulated by placing 72 layers of water molecules on top of asingle spherical cavity by applying the periodic boundaryconditions along the horizontal direction. For ξ = 0.65, 0.68,0.71, 0.78, 0.82, and 0.85, 24 ns long NPT MD simulations at 1atm and 300 K were run using the Berendsen barostat andthermostat.32 Figure 5 presents illustrative MD snapshots of the

NPT simulations. As for the finite-sized droplets, themacroscopic droplets penetrated thespherical cavities com-pletely with ξ ≤ 0.68 (Figure 5a). On the surfaces with ξ >0.68, the droplet was in the CB-like state. The partialpenetration of the water droplet into the cavities wasnoticeable, especially for ξ = 0.71 and 0.78 (Figure 5c and d,respectively). In these cases, water molecules almost completelycovered the cavity surface. Unlike the prediction of Patankar,however, a bubble like structure, where water moleculescompletely cover the surface of cavity and form a thin film,was not observed. With further increases in ξ from 0.72 to 0.82(Figure 5e) and 0.85 (Figure 5f), the surfaces of the cavitieswere only partly covered with water molecules, formingcrescent structures inside the cavities, which are closer to thepure CB state. We have not found however a pure CB statewhere the cavity is entirely void of water molecules.We then examined how the size of the cavities affects the CA

by simulating cavities with five different diameters ranging from4 to 8 nm (default diameter was 6 nm). All the cavities weresimilar in shape by choosing similar ξ values (0.12 to 0.16). Asthe present gold surface has a discrete lattice spacing, the size ofthe cavities cannot be controlled continuously. The presentvalues of the depth of the cavities are as close to each other asthey can be in the MD simulation. Figure 6 presents thesimulated CAs along with the CB theory prediction (solid line).The CA did not change much, even though the diameter of thecavities was doubled (in the change from (a) to (e) in thefigure). This illustrates that the CA is determined mainly by theshape ξ, not by the size, of the cavities. Therefore, similarswitching behavior is expected for the wettability of the surfaceswith spherical cavities smaller or larger than the present ones.

Figure 5.Wetting of spherical cavities by macroscopic droplets. Shownare MD snapshots for six different cavity depths ξs of 0.65 (a), 0.68(b), 0.71 (c), 0.78 (d), 0.82 (e), and 0.85 (f). In each panel, the finalMD snapshot (taken after 24 ns) is shown.

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■ CONCLUSIONThe wettability of a surface can be controlled by introducingnano- or microscale corrugations. The possible shapes of thecorrugations are limitless, but previous studies focused onsimple shapes, such as rectangular, cylindrical, and dome-shaped pillars. Surfaces carved out with spherical cavities havereceived less attention. A previous study showed experimentallythat the intrinsically hydrophilic gold surface turned hydro-phobic when the surface was engraved with spherical cavities.Presently, this extraordinary switching behavior is not fullyunderstood, especially at the molecular level.Using large scale MD simulations, this study investigated the

wettability of a gold surface engraved with nanoscale (hemi)-spherical cavities. The depth of the cavities was variedsystematically to examine the change in the surface wettability.In accordance with the experiment by Abdelsalam et al., the CAof the water droplet varied from a hydrophilic (73°) to ahydrophobic (>90°) with increasing depth of the cavities. Thenonmonotonic behavior of CA with increasing cavity depth wasconsistent with CB theory, but the droplet actually existed invarious states, including the CB, WZ, and intermediate states, inwhich the cavities were partially filled with liquid.Although the WZ and CB theories are designed for

macroscopic droplets, the WZ and CB states are valid picturesof the wetting of the cavities even at the nanoscale. The primarygoal of our work was to test these WZ and CB pictures againstthe molecular views provided by MD simulations. A numericalcoincidence of the CB or WZ theory with MD results does notnecessarily mean that the underlying pictures of these theoriesare correct at the molecular level. Certainly, these theories canbe improved to give a better agreement with MD results. Suchan improvement is beyond the scope of the current workhowever.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: jkjang@pusan.ac.kr. Tel.: +82-51-510-7348.

Author Contributions∥Z.Z. and M.A.M. contributed equally to this work.

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

This study was supported by the National Research Foundationof Korea (NRF) grant funded by the Korea government (NRF-2015R1A2A2A01004208 and NRF-2014R1A4A1001690).

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Figure 6. Influence of the size of cavities on the contact angle.Spherical cavities with five different diameters were simulated usingsimilar values of ξ. The simulated diameters of the cavities were 4 nm(a), 5 nm (b), 6 nm (c), 7 nm (d), and 8 nm (e). The corresponding ξvalues were 0.161 (a), 0.129 (b), 0.136(c), 0.117(d), and 0.130 (e).Plotted in (f) are the CAs for the five different surfaces shown in (a)−(e).

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