Molecular Dynamics Study of the Hydrophilic-to-Hydrophobic

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Molecular Dynamics Study of the Hydrophilic-to-Hydrophobic Switching in the Wettability of a Gold Surface Corrugated with Spherical Cavities Zhengqing Zhang, Mohammad A. Matin, Man Yeong Ha, and Joonkyung Jang Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b02378 • Publication Date (Web): 01 Sep 2016 Downloaded from http://pubs.acs.org on September 4, 2016

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Molecular Dynamics Study of the Hydrophilic-to-Hydrophobic Switching in the Wettability of a Gold Surface Corrugated with Spherical Cavities Zhengqing Zhang, 1,§ Mohammad A. Matin,2,§ Man Yeong Ha,3 and Joonkyung Jang1,* 1

Department of Nanoenergy Engineering, Pusan National University, Busan, 609-735, Republic of Korea

2

Center for Advanced Research in Sciences (CARS), University of Dhaka, Dhaka-1000, Dhaka, Bangladesh 3

Department of Mechanical Engineering, Pusan National University, Busan, 609-735, Republic of Korea

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ABSTRACT

This paper reports a large scale molecular dynamics (MD) simulation study of the wettability of a gold surface engraved with (hemi)spherical cavities. By increasing the depth of cavities, the contact angle (CA) of a water droplet on the surface was varied from a hydrophilic (69°) to a hydrophobic value (> 109°). The non-monotonic behavior of the CA vs. the depth of the cavities was consistent with the Cassie-Baxter theory, as found in the experiment by Abdelsalam et al.. 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 were penetrated partially by the droplet.


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INTRODUCTION

The wettability of a solid surface is influenced greatly by the surface roughness.1-5 In particular, the hydrophobicity of a surface increases drastically in the presence of nanoor micro- scale corrugations. This way, a hydrophobic surface with a contact 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 of rectangular, cylindrical, and dome-shaped pillars are constructed routinely on the µm- or nm- scale. Recently, more sophisticated corrugated structures, such as the hierarchical structures (e.g., nm-sized hairs on µm-scale pillars)

6-8

and pillars with re-entrant geometries, have

been constructed.9-11 Abdelsalam et al.12 reported that even a hydrophilic gold surface can be turned a hydrophobic surface by carving out spherical cavities on it (Figure 1a). Specifically, a hydrophilic gold surface, whose intrinsic CA is ~70°, had a CA> 90° when it was engraved with (hemi) spherical cavities, a few hundred nm in diameter. In the experiment, the depth of the cavities (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. By changing the shape of the cavities from almost hemispherical to a spherical one (as shown in the change from the top to bottom of Figure 1a), the intrinsically hydrophilic gold surface transformed to a hydrophobic surface. This extraordinary switching in the surface wettability is not completely understood, especially at the molecular level. Thermodynamically, the measured (apparent) CA of a droplet on a corrugated surface, θ * , is determined by both the material property (surface


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Figure 1. Wetting property of a surface textured with (hemi)spherical cavities. (a) Schematic diagram of gold surfaces with approximately hemispherical (top) and spherical (bottom) cavities. The dimensionless depth of the spherical cavities, ξ , is defined as the ratio of the cavity depth (t) to the diameter of the spheres (d). The top and bottom show cases, where

ξ = 0.21 and ξ = 0.88 . (b) Wenzel state of a droplet on the surface

engraved with nearly hemispherical cavities. (c) Cassie-Baxter state of a droplet on the surface with almost spherical cavities.


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energy) and surface geometry. The material property can be characterized by the intrinsic CA of the droplet in contact with a flat surface, θ . On the other hand, the effects of the surface geometry on θ * can be considered only when the exact shape of the droplet in contact with the corrugations (i.e. spherical cavities in the present case) is known. For this purpose, two extreme 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). The apparent CA, θ * , of the droplet in the WZ state is then given by cosθ * = φ cosθ

(1)

where φ is the ratio of the area of the corrugated surface to the area of the horizontal plane (>1).13 On the other hand, the droplet in the Cassie-Baxter (CB) state is assumed to contact only the top of the corrugated surface, while the cavities of the surface remain intact (Figure 1c). The apparent CA in the CB state is given by cos θ * = f1 cos θ − (1 − f1 )

( 2)

where f1 ( (1 + cosθ ) / 2 (=0.67 for θ=70°). Otherwise, the spherical cavities are either partially or fully (WZ) filled with the droplets. Patankar proposed several partially filled states, such as crescent and bubble-like geometries inside 5 ACS Paragon Plus Environment

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the cavities. This theoretical prediction contrasts with the experiment by Abdelsalam, in which the CAs always agreed with the CB theory. Patankar concluded that the agreement of the CB theory with the measured CAs does not guarantee that the droplets actually exist in the CB states. Similarly, this study shows that the CAs of nm-sized droplets can be close to the CB values even if the droplets exist in the WZ 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 atoms interacting with each other via various interatomic interactions. Therefore, these theories cannot deliver the molecular insights on 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 spherical cavities. Using a coarse grained model of water, droplets of 81,170 molecules and surfaces made of 149,000 gold atoms were simulated, which far exceeds those simulated in conventional MD simulations. The present MD simulation indeed reproduced the hydrophilic-to-hydrophobic transition in the wettability of a gold surface with increasing cavity depth. As in the experiment by Abdelsalam, the overall tendency of the CA vs. the cavity depth was consistent with CB theory. Quantitatively, however, CB theory deviated significantly from the MD simulation. Moreover, the droplets were not always in the CB state, but in the WZ or some intermediate states partially filling the cavities. The molecular details of the partially filled states are provided. MODEL AND SIMULATION METHOD The 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


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carved out from a flat gold surface. At least three layers were kept below the bottom of the cavities in the simulations. 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 consisted of 78,000 to 149,000 atoms. The gold surfaces were held rigid and the periodic boundary conditions were applied along the horizontal directions. The water droplet was modeled by employing MARTINI model version 2.016, which treats 4 water molecules as a single bead. Designed to account for the strong polar interaction between water molecules16, the present model has proven to preserve the major properties, such as the diffusivities, surface tension, and solvation energy, of the SPC point charge model17,18. Also, this model was successful in modeling the surface

Figure 2. (a) Simulation geometry of a gold surface engraved with 16 spherical 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) MD simulation snapshot of a water droplet in the WZ state. (c) MD snapshot of a water droplet in the CB-like state. 7 ACS Paragon Plus Environment

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property of water.19 A water droplet composed of 20,290 beads, corresponding to 81,170 water molecules and 13.2 nm in diameter, was prepared. The present water droplet is much larger than the typical size in previous MD simulations.20 The interatomic or intermolecular interaction u(r) was modeled using the Lennard-Jones (LJ) potential

[

12

6

function, u (r ) = 4ε (σ r ) − (σ r )

] , where σ and ε

are, respectively, the length and

energy parameters inherent to atomic or molecular species. The LJ parameters of water molecules and gold atoms were σ w = 0.47 nm and ε w = 1.195 kcal/mol, and

σ Au = 0.2935 nm and ε Au = 0.1365 kcal/mol, respectively. The water-gold LJ potential parameters were determined using the Lorentz-Berthelot combination rules.21 Using these LJ parameters, the present MD simulation reproduced the experimental CA on a flat gold surface (see below). The MD simulations were run at constant number (N), volume (V), and temperature (T) using the Evans thermostat22 at 300 K. The cutoff distance for the LJ interaction was 12 Å. The MD trajectories were propagated using the velocity Verlet algorithm21 with a 30 fs time step, which conserved the energies in the simulations. 600 snapshots of 12 ns long simulations were collected to calculate the average quantities. The DLPOLY simulation package 23 was used to implement the 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 MD snapshot of the droplet (Figure 3a), the surface normal passing through the center of the droplet was set up along the Z axis. The droplet was then sliced into 5 Å –thick slabs. In each slab, the distances of the water


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Figure 3. Calculation of the intrinsic contact angle of a water droplet on 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 surface normal axis r (circles) for a given height from the surface. The solid line is the fit using the hyperbolic function. (c) Droplet radius Rdrop vs. the vertical height from the surface z (circles). The solid line is the fit using the parabolic function of z . 9 ACS Paragon Plus Environment

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beads from the Z axis, r s, were binned at 5 Å intervals. By averaging more than 600 snapshots, the horizontal density profile ρ(r) was calculated for each slab located at z (drawn as circles in Figure 3b). The density ρ(r) was calculated by counting the number of molecules located at r~r+dr (dr=size of bin). This number was then converted to ρ(r) by dividing it by the Jacobian factor, 2πr. This conversion sometimes caused a numerical instability near r=0, giving rise to a decreasing, rather than a leveling-off, density near the center of the droplet (as shown in Figure 3b). This numerical artefact can be overcome by using an unequal binning of r as in Werder et al.’s work24. Note however ρ(r) is only calculated to locate the periphery of the droplet where ρ(r) drops down to zero. For this purpose, the present binning method is sufficient. The data were then fit to a function,

ρ (r ) = (ρ l + ρ v )/ 2 − (1 / 2)(ρ l − ρ v )tanh (2(r − re ) w) , where ρ l and ρ v are the liquid and vapor densities, re is the position of the Gibbs dividing surface, and w is the width of the liquid-vapor interface (drawn as the solid line in Figure 3b). The LevenbergMarquardt method was used to determine the fitting parameters, ρ l , ρ v , w, and re .25 The distance above which ρ falls below 0.2 g cm-3 is defined as the radius of the droplet 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 z drawn as the solid line in Figure 3c. We used a parabolic fit, instead of a circular fit24,26, because the droplets were not circular near the surfaces. The parabolic fit, including a circular fit as a special case, closely reproduced the peripheries of the droplets. The parabolic fits have been widely used in the previous studies of the liquid-vapor interfaces.27-29. θ is given by the slope of the tangential line of


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the parabola at z = 0 .29 The resulting value of θ was 73°, which is close to the experimental value measured for a macroscopic droplet (70°).

RESULTS AND DISCUSSION This study investigated how the CA θ * depends on the cavity depth, 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 the CB (solid line) and WZ (dotted line) theories were also plotted. 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 ξ to 0.884, the CA decreased to 99.23°. The simulated CAs are the upper and lower bounded by the CB and WZ theoretical values, respectively.

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


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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 of the present droplet (13.2 nm in diameter) relative to that of the spherical cavities (6 nm in diameter). Both the CB and WZ theories assume that the cavities are negligible in size compared to the (macroscopic) droplet. The effects of the droplet size can be estimated approximately by referring to the modified Young’s equation, cos θ = cos θ ∞ − (τ / γ ) / rB , where rB is the base radius , γ and τ are the surface tension

and line tension of the water droplet, and θ ∞ is the CA of a macroscopic droplet ( rB → ∞ ). Typically, the line tension, τ , measured experimentally30 is negative and is in the order of 10 −10 J m −1 ; hence, the CA increases with increasing the droplet size. Similarly, the MD simulation of Santiso et al. showed that the CA on a hydrophilic surface increases with increasing droplet size.31 We simulated droplets of varying sizes on a flat surface. The droplets made of 3996, 5050, 6160, 6994, 7988 and 9625 beads were simulated. The contact angles and the base radii of the droplets varied as 68.98, 67.94, 69.94, 72.08, 73.12, 75.53° and 4.00, 4.55, 4.70, 4.91, 5.40 and 5.64 nm, respectively. According to the modified Young’s equation, we performed a linear fit of the contact angles with respect to the base radii. We obtained, from the fit, a line tension of − 9.65 ×10−10 J m −1 if we used the surface tension value previously calculated by employing the present model of water (= 0.03 N m −1 ) 16. For droplets > 54 nm in diameter (where the macroscopic limit is reached according to Santiso et al.31), the simulated CAs was expected to be close to the CB theory results.


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The CB theory, despite its quantitative deviation from the simulated CAs, reproduced the overall non-monotonic behavior found for the CA vs. ξ curve in Figure 4. According to the CB theory, equation (2), the void fraction ( = 1− f1 ) at the top of the corrugated surface increased with increasing ξ for ξ < 1/ 2 . As a result, the droplet sits more on the void than on the top of a solid, and the surface consequently becomes more hydrophobic. Once ξ reaches more than 0.5, the shape of the cavities switches from a hemispherical to a near spherical one, and the void fraction now decreases with increasing ξ (because the mouths of the cavities shrink as ξ increases from 0.5). This explains the decreasing CA starting from ξ =0.5. In contrast, the WZ theory, equation (1), focuses on the surface area of the corrugated surface, which always increases with increasing ξ . Therefore, the intrinsically hydrophilic gold surface becomes even more hydrophilic with increasing ξ , giving rise to a monotonic decrease in CA with increasing ξ . Abdelsalam et al. reported that the CB theory quantitatively predicts the experimental CAs of droplets on gold surfaces with spherical cavities, regardless of the ξ value.12 Patankar, however, showed that the CB state is unstable for cavity depths,

ξ < (1+ cosθ ) / 2 = 0.65 if we use the intrinsic CA calculated in the present simulation.15 Similarly, the droplets in the present simulation completely penetrated into the cavities (WZ states, drawn as filled circles in Figure 4) for ξ 0.68 (=0.78 and 0.88, drawn as open circles in Figure 4). The present threshold value of ξ (=0.68) slightly differed from the theoretical value of Patankar (=0.65) presumably due to the finite size of droplet in our simulation. Note the simulated CAs of these WZ droplets was closer to the values of CB theory. Moreover, the 13 ACS Paragon Plus Environment

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simulated droplets for ξ =0.78 and 0.88 were not in the pure CB state, but they also partially penetrated the cavities, as shown in Figure 2c. In the following, the partial filling of the cavities is examined 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 finitesized droplet above, was simulated. The macroscopic droplet was simulated by placing 72 layers of water molecules on top of a single spherical cavity by applying the periodic boundary conditions 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 1 atm and 300 K were run using the Berendsen barostat and thermostat.32 Figure 5 presents illustrative MD snapshots of the NPT simulations. As for the finite-sized droplets, the macroscopic droplets penetrated the

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


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spherical cavities completely with ξ ≤0.68 (Figure 5a). On the surfaces with ξ >0.68, the droplet was in the CB-like state. The partial penetration of the water droplet into the cavities was noticeable, especially for ξ =0.71 and 0.78 (Figures 5c and 5d, respectively). In these cases, water molecules almost completely covered the cavity surface. Unlike the prediction of Patankar, however, a bubble like structure, where water molecules completely 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 cavities were only partly covered with water molecules, forming crescent structures

Figure 6. Influence of the size of cavities on the contact angle. Spherical cavities with five different diameters were simulated using similar 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 ξ values 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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inside the cavities, which are closer to the pure CB state. We have not found however a pure CB state where 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 from 4 nm to 8 nm (default diameter was 6 nm). All the cavities were similar in shape by choosing similar ξ values (0.12 to 0.16). As the present gold surface has a discrete lattice spacing, the size of the cavities cannot be controlled continuously. The present values of the depth of the cavities are as close to each other as they can be in the MD simulation. Figure 6 presents the simulated CAs along with the CB theory prediction (solid line). The CA did not change much, even though the diameter of the cavities was doubled (in the change from a to e in the figure). This illustrates that the CA is determined mainly by the shape ξ , not by the size, of the cavities. Therefore, similar switching behavior is expected for the wettability of the surfaces with spherical cavities smaller or larger than the present ones.

CONCLUSION The wettability of a surface can be controlled by introducing nano- or micro- scale corrugations. The possible shapes of the corrugations are limitless, but previous studies focused on simple shapes, such as rectangular, cylindrical, and dome-shaped pillars. Surfaces carved out with spherical cavities have received less attention. A previous study showed experimentally that the intrinsically hydrophilic gold surface turned hydrophobic when the surface was engraved with spherical cavities. Presently, this extraordinary switching behavior is not fully understood, especially at the molecular level.


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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 varied systematically to examine the change in the surface wettability. In accordance with the experiment by Abdelsalam et al., the CA of the water droplet varied from a hydrophilic (73°) to a hydrophobic (>90°) with increasing depth of the cavities. The nonmonotonic behavior of CA with increasing cavity depth was consistent with CB theory, but the droplet actually existed in various states, including the CB, WZ, and intermediate states, in which 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 pictures of the wetting of the cavities even at the nanoscale. The primary goal of our work was to test these WZ and CB pictures against the molecular views provided by MD simulations. A numerical coincidence of the CB or WZ theory with MD results does not necessarily mean that the underlying pictures of these theories are correct at the molecular level. Certainly, these theories can be improved to give a better agreement with MD results. Such an improvement is beyond the scope of the current work however.

AUTHOR INFORMATION Corresponding author *E-mail: [email protected], Tel.: +82-51-510-7348

Author Contributions §These

two authors contributed equally to this work.

Notes The authors declare no competing financial interests 17 ACS Paragon Plus Environment

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ACKNOWLEDGMENTS This study was supported by the National Research Foundation of Korea (NRF) grant funded

by

the

Korea

government

(NRF-2015R1A2A2A01004208

and

NRF-

2014R1A4A1001690).

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TOC Graphics


Molecular Dynamics Study of the Hydrophilic-to-Hydrophobic

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