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Cite this: Phys. Chem. Chem. Phys., 2014, 16, 5613

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Molecular dynamics study on the wettability of a hydrophobic surface textured with nanoscale pillars Zhengqing Zhang,a Hyojeong Kim,a Man Yeong Hab and Joonkyung Jang*a Using molecular dynamics simulation, we studied the wetting properties of a surface textured with hydrophobic pillars, several nanometers in size. The drying transition of water confined between square or circular pillars was related to the Wenzel (WZ) to Cassie–Baxter (CB) transition of a water droplet

Received 26th November 2013, Accepted 20th January 2014 DOI: 10.1039/c3cp54976c

deposited on periodic pillars. The inter-pillar spacing at which the drying occurs was compared to that predicted from the continuum theory. Such a comparison revealed that the line tension plays an important role in the drying behavior of the present nm-sized pillars. The water molecules near the pillar walls were layered and ordered in orientation. Our simulation showed a long-lived CB state which eventually turns into the WZ state. In this transition, water slowly penetrated down into the inter-pillar

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gap until it reached the half height of the pillar, and then quickly reached the base of the pillar.

Introduction Super-hydrophobic surfaces1–3 find widespread application, such as self-cleaning windows,4 microfluidics,5 and reduction of fluid resistance, just to name a few.6 On a typical superhydrophobic surface, a water droplet has a high contact angle (>1501) as well as a small sliding angle (o101).7 Changing the texture of a surface greatly enhances the hydrophobicity of the surface.2,8–13 In particular, the presence of nano- or micro-sized pillars can make a normal hydrophobic surface (with a contact angle of 1201 or less) super-hydrophobic. Examples of such surfaces abound in nature, including luffas,14 lotus leaves,15,16 water strider legs,17 butterfly wings,18,19 gecko foot-hairs20 and petals.21,22 Texturing a surface with nm- or mm-sized pillars can be achieved by using micro- and nano-electromechanical systems (MEMS and NEMS) technologies.23–30 Various shapes of pillars have been constructed. Most commonly, square,23–26 circular,27–29 and domeshaped30 pillars were produced. Hierarchical pillar structures such as nano-hairs on micropillars31–33 and the pillars with re-entrant geometries34–36 were constructed as well. A water droplet deposited on such a pillared surface can be impaled by the pillars, which is called the Wenzel (WZ) state37 (Fig. 1a). On the other hand, a water droplet that sits on top of the pillars without penetrating the gap between the pillars is in the Cassie–Baxter (CB) state38 (Fig. 1b). Compared to a droplet in the WZ state, a CB droplet a

Department of Nanomaterials Engineering, Pusan National University, Busan 609-735, Republic of Korea. E-mail: [email protected]; Fax: +82-51-514-2358; Tel: +82-51-510-7348 b School of Mechanical Engineering, Pusan National University, Busan 609-735, Republic of Korea

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Fig. 1 Simulation snapshot of the water confined between pillars. The Wenzel (a) and Cassie–Baxter (b) states of water deposited on a periodic array of square pillars. Only the periodic cell of the simulation (drawn as boxes) is shown. A macroscopic water droplet sitting on top of pillars was emulated as a bulk liquid. Oxygen and carbon atoms are drawn as spheres and dots, respectively. Hydrogen atoms are not drawn for visual clarity.

(having a reduced contact area with solid) has an enhanced contact angle and surface mobility.1,39 It is therefore desirable to design pillars that preferentially induce the CB state of a droplet. It is both practically important and scientifically interesting to understand how the CB or WZ state of a droplet depends on the shape and size of pillars and the spacing between pillars. Qualitatively, as the inter-pillar spacing reduces to zero, the gap between the pillars vanishes and no water can penetrate down into the gap. A water droplet in this limiting case will be in the CB state. On the other hand, for a large inter-pillar spacing, a water droplet sitting on top of the pillars is likely to penetrate down into the gap between pillars, which is the WZ state.

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Consider a liquid confined between square pillars with a width, W, and height, H, which are periodically replicated with an inter-pillar spacing of S (Fig. 2a). A macroscopic droplet sitting on top of these pillars was modelled as a bulk liquid filling the space above the pillars (see Fig. 1). As the inter-pillar spacing S decreases, the volume and therefore the cohesion of water confined between the pillars decrease. At the same time, the water-pillar interfacial energy becomes increasingly important. As S becomes smaller than a critical value, SC, the water confined between pillar walls becomes unstable and evaporates. The resulting CB state is something like that shown in Fig. 1b. By comparing the grand potentials for the liquid and vapour phases of the confined water, SC can be derived for a periodic array of square pillars as follows:40 "sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi # 4aDg 1 ; (1) SC ¼ W 1þ fðDPÞaW  Dg þ gLV g Fig. 2 Geometric parameters of the present periodic pillars. Shown are the periodic cells of surfaces textured with square (a) and circular (b) pillars. The height and width of the pillar and the spacing between pillars are represented as H, W and S, respectively. Also drawn in (a) is the present coordinate system, where the surface normal lies along the Z axis.

Therefore, there will be a critical inter-pillar spacing at which the transition between the CB and WZ states occurs. This critical spacing should depend on the size and shape of pillars. We note that the WZ-to-CB (CB-to-WZ) transition can be viewed as the drying (wetting) transition of a liquid confined between pillar walls. The drying transition in particular40 has been studied extensively in the context of protein folding41–45 and capillary evaporation in pores.46,47 With this perspective, we studied the WZ-to-CB state transition (drying) using Monte Carlo simulation.40 Unfortunately, this simulation was based on a crude model, the lattice gas model. A fully atomistic off-lattice simulation is needed to realistically model the confined water with molecular details, such as the molecular orientation and packing structure. Herein, using all-atom molecular dynamics (MD) simulations, we investigated the water deposited on a periodic array of square or circular pillars (which are common shapes of pillars made by MEMS or NEMS, Fig. 2a and b). By varying the inter-pillar spacing S, we investigated the WZ-to-CB (and CB-to-WZ) transition of the water confined in the inter-pillar gap. We delved into the molecular details of the confined water. We examined the dynamics of the transition from a long-lived CB (WZ) state to a WZ (CB) state. The present MD simulation was compared with a continuum theory. By taking the line tension effect into account, the continuum theory was in agreement with the molecular simulations, even for pillars as small as a few nanometers in width and height.

Continuum theory and molecular simulation methods We first summarize the continuum theory for the inter-pillar spacing, where a transition between the WZ and CB states occurs.40

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where DP is the liquid pressure, PL, minus the vapour pressure, PV. gLV is the liquid–vapour interfacial tension, and Dg  gLS  gVS, where gLS and gVS are the liquid–solid and vapour–solid interfacial tensions, respectively. a is the aspect ratio of the pillar, a = H/W. Similarly, the SC for a periodic array of circular pillars (Fig. 2b) can be expressed as follows:40 "pffiffiffisffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi # 4aDg p 1þ 1 : (2) SC ¼ W 2 fðDPÞaW  Dg þ gLV g Dg in eqn (1) and (2) can be obtained by using the Young equation, Dg = gLV cos yc, where yc is the intrinsic contact angle of a droplet in contact with a flat surface. The present SC is similar to the cut-off distance of the hydrophobic interaction between a pair of solid objects. Our work deals with periodically replicated pillars on a surface, not the pair interaction of two pillars. A given pillar has 4 neighbour pillars, and the bottom surface further promotes the drying of water confined between pillars. Therefore, SC is not straightforwardly related to the cut-off distance of hydrophobic interaction between two solid objects such as studied by Singh et al.48 In the present MD simulation, the pillars were carved out from the face-centred cubic (FCC) lattice of carbon atoms (lattice spacing of 3.567 Å). This FCC carbon structure was used to model hydrophobic pillars which are compact and smooth on surface. Although an FCC carbon structure exists under an exotic condition such as under a plasma treatment, it is not a common material for hydrophobic pillars. The height, H, and width, W, of each pillar were 2.854 and 1.606 nm, respectively. We chose an aspect ratio, a = 1.78, typical for the pillars made by MEMS or NEMS. The inter-pillar spacing was varied as 3.57, 5.35, 8.92, 12.49, 16.06 and 19.62 Å. The extended simple point charge model (SPC/E)49 of water was used. In this model, the oxygen and hydrogen atoms are treated as point charges of 0.8476 and +0.4238, respectively. These partial charges interact via the Coulomb potential, as follows: U C ðrij Þ ¼

qi qj ; 4pe0 rij

(3)

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where qi is the partial charge on atom i and e0 is the vacuum permittivity. rij is the distance between two atoms, i and j. The long-ranged Coulomb interaction between point charges was handled using the Ewald sum method.50 Oxygen atoms also interact with each other through the Lennard-Jones (LJ) potential,50 "   6 # sij 12 sij LJ ; (4) U ðrij Þ ¼ 4eij  rij rij where the LJ size and well-depth parameters, sij and eij, are set to 3.166 Å and 0.6502 kJ mol1, respectively.51 The LJ size and well-depth parameters for the carbon–oxygen inter-atomic interaction were set to 3.190 Å and 0.4389 kJ mol1, respectively.52 The present model of water has been widely used in the study of a confined water. For example, the MD simulation using the SPC/E model captured the salient features of the force-distance curve measured for the water confined between a silicon tip and a surface.53 We will also show the present model of water gives a layering of water which was observed in the firstprinciples MD simulation (see below). We found that employing a flexible model of water54 is not practical for the present largescale simulation. Constant number, pressure and temperature (NPT) MD simulations were run by fixing pressure and temperature to 2 atm and 300 K, respectively. The desired pressure and temperature were obtained by coupling the system to the Berendsen barostat and thermostat, respectively.55 Note the spherical curvature of a droplet gives the pressure inside the droplet higher than the ambient pressure. According to the Young–Laplace equation, DP = (2gLV)/R, where R is the radius of a droplet, the present pressure (2 atm) is that of a droplet with a radius of 712 nm. This radius is much larger than the size of the pillar (only a few nanometers in width and height), as assumed in the derivation of the continuum theory (the droplet size was assumed to be infinite compared to the size of the pillar gap). Also, the radius of water droplets (712 nm) is less than the capillary length of water (i.e., 2.7 mm), so that the gravity can be neglected in the simulation.56 Reyssat et al. reported that a droplet with a diameter of tens of micrometers evaporates within a few seconds.57 Presumably, the present

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droplet will last for times shorter than several seconds, as it is ten times smaller than the one studied by Reyssat et al. It is reasonable however to assume that the lifetime of the present droplet is not much shorter than a few seconds and therefore our droplet will remain stable within the timescale of the present MD simulation (20 ns long). The periodic array of pillars was emulated by applying the periodic boundary conditions in the simulation. The top boundary of the simulation box was 4.8 nm above from the top of the pillars. Due to the periodic image of the bottom surface, the density of water was low near the top boundary. It is well known however that the depleted density of water near a hydrophobic wall approaches the bulk value within the distance of 1 nm from the wall.54 Therefore, our simulation box is tall enough to remove the artefacts due to the fictitious wall replicated at the top boundary. Moreover, by increasing the box height from 8 to 10 nm, we found no change in the present simulation results. The simulation box varied in size during the present NPT simulation. As a result, the lattice spacing of the carbon atoms comprising the pillars slightly changed (by less than 0.5 Å). Two different initial conditions of simulation were used: one where the inter-pillar gap was empty while liquid water filled the space above the pillars, and the other was where the entire simulation box was filled with liquid. The former and latter correspond to the CB and the WZ state of a droplet, respectively (initially). A 0.5 ns long NVT simulation was run to generate both of the initial conditions for the NPT simulations. And the first 0.5 ns portion of the NPT simulation was discarded for equilibration. The time integration for the MD trajectory was performed by using the velocity Verlet algorithm50 with a time step of 1.0 fs. All MD simulations were run for 20 ns by using the DL POLY simulation package.58 To implement the continuum theory for SC, we need the intrinsic contact angle, yc, which refers to the contact angle of a macroscopic droplet.59,60 yc was extrapolated by running NVT MD simulations for droplets of varying sizes. Specifically, water droplets containing 2184, 3150, 4000 and 5023 water molecules on a flat carbon surface were simulated (see Fig. 3a and b). The base radii of these droplets, RBs, were 25.14, 27.53, 29.86 and 32.51 Å. For each droplet, the surface normal, which passes through the centre of mass of the droplet, was set up.

Fig. 3 Contact angle of a water droplet on a flat surface. Side (a) and top (b) views of a water droplet (made of 3150 molecules) on a flat carbon surface. For a given height from the surface z, the density of oxygen atoms r is plotted as a function of the distance from the surface normal axis r (circles). The solid line shows the fit by using the hyperbolic function, eqn (5), (c). The droplet radius R vs. the vertical height from the surface z (circles), (d). The solid line is the fit using the parabolic function of z.

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The droplet was then divided into slabs by dividing the Z coordinates into 1 Å-thick intervals. In each slab, the distances of oxygen atoms from the surface normal, rs, were binned into 1 Å long intervals. The density of oxygen atom, r, (circles in Fig. 3c) was fitted to the following function (drawn as the line in Fig. 3c),   1 1 2ðr  re Þ rðrÞ ¼ ðrl þ rv Þ  ðrl  rv Þ tanh ; (5) 2 2 d where the fitting parameters, rl and rv, are the liquid and vapour densities, respectively, re is the location of the Gibbs dividing surface, and d is the thickness of the liquid–vapour interface. The radius of a droplet for a given slab R(z) was taken to be the value of r which gives 0.2 g cm3 for the r(r) in eqn (5). After obtaining R(z) (drawn as circles in Fig. 3d) as a function of the vertical height from the surface, z, the R(z) values greater than 25 Å were fitted to a parabolic function of z (solid curve, Fig. 3d). The contact angle was taken from the tangential line of the parabola at z = 0.51,60 The contact angles for these finitesized droplets, ys, with RBs of 25.14, 27.53, 29.86 and 32.51 Å were found to be 116.58, 115.79, 115.66 and 114.311, respectively, showing a decrease with increasing droplet size. According to the modified Young’s equation,61 cos y = cos yc  gSLV/(RBgLV),

(6)

cos y is a linear function of 1/RB. By fitting the four values of cos y to a linear function of 1/RB, cos yc was estimated from the fit value at 1/RB = 0. The resulting yc was found to be 107.741. A line tension, gSLV, of 2.30  1011 J m1 was obtained from the slope of the fitting function, eqn (6) and the gLV previously calculated using the SPC/E model of water (= 0.0636 N m1).62 If the gLV value taken from the experimental value, 0.0721 N m1, was used, the resulting gSLV (= 2.61  1011 J m1) remained similar to the value above.

Results and discussion By varying the inter-pillar spacing S, we examined the density of water in the gap between pillar walls (0 r z r H, see Fig. 2). In case S is greater than a critical value SC, the inter-pillar gap was filled with water, giving rise to a WZ state (Fig. 1a). On the other hand, for S o SC, the inter-pillar gap was in the vapour phase (empty), meaning that the droplet was in a CB state (Fig. 1b). The top (bottom) of Fig. 4 shows the cross-sectional density profiles of the WZ (CB) state for square pillars. The left two panels present the density profiles projected onto the planes which are parallel to the XY plane and in the range 0 r z r H (the bottom of the pillar is located at z = 0). The right panels show the density profiles projected onto the planes parallel to the XZ plane (side view of the system) and in the range, 0 r y r W/2 (see Fig. 2a for the geometry and coordinate system). In the WZ state shown in the top panels of Fig. 4, three black stripes separated by almost 2.7 Å are visible. As this separation is close to the effective diameter of a water molecule,40,63 water is layered between the pillars. This layering is incomplete at the corners of the pillars, where the black stripe vanishes (top left). Similarly, layering has been observed for the liquids confined

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Fig. 4 Density profiles of the wet (WZ) and dry (CB) states of water confined between square pillars. The left two panels present the contour plot of the density profile projected onto the planes which are parallel to the XY plane and in the range 0 r z r H. The right panels show the crosssectional (projected onto the planes parallel to the XZ plane) density profile averaged over the range 0 r y r W/2. In each panel, the dotted lines represent the boundaries of pillars. The left panels have the same axis labels, as do the figures on the right. In each figure, the liquid sitting on top of the pillar (z > H) is not drawn. The inter-pillar spacings for the WZ and CB states are 12.49 and 8.92 Å, respectively.

between plates64 and between an AFM tip and surface.63,65–67 Although not shown here, we examined the cross-sectional density profile projected onto the plane x = y. Along this diagonal direction, where the confinement between pillar walls is minimal, layering is not as significant as that found above (which is along the direction perpendicular to the pillar walls, where the spatial confinement is maximal). Fig. 5 presents the density profiles for circular pillars. As in Fig. 4, the left two panels show the cross-sectional density profiles projected to the planes parallel to the XY plane and in the range, 0 r z r H. The right two panels present the crosssectional density profiles projected onto the planes parallel to the XZ plane and in the range, 0 r y r W/4. Here too, layering of water can be seen in the WZ state (shown in the top two panels). Both the top (top left) and side (top right) views of the WZ state illustrate three black stripes of water. The distance between the black stripes is approximately 2.6 Å, which is again close to the molecular diameter of water. The bottom right shows that water slightly penetrates down into the gap between the pillars. We point out that the ab initio MD simulation of water confined between graphene sheets68 also reported a layering of water. Therefore, the layering shown in Fig. 4 and 5 is likely a robust feature of a confined liquid, not an artefact of the present rigid body model of water. We investigated the orientational order of water molecules confined between square pillars (with the inter-pillar spacing of 19.62 Å). Shown in the top of Fig. 6 is the probability density of cos y, where y is defined as the angle between the electric dipole of water molecule and the surface normal to the pillar wall (normal to the YZ plane). As shown in the top of Fig. 6, the probability

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Fig. 5 Density profiles of the wet (WZ) and dry (CB) states of water confined between circular pillars. Drawn in the left two panels are the contour plot of the cross-sectional density profile projected onto the planes which are parallel to the XY plane and in the range 0 r z r H. The right panels show the cross-sectional density profile projected onto the planes parallel to the XZ plane and in the range, 0 r y r W/4. In each panel, the broken lines represent the boundaries of the pillars. The figures on the left have the same axis labels, as do figures on the right. In each figure, liquid sits on top of the pillar (z > H) but it is not drawn. The interpillar spacings for the WZ and CB states are 12.49 and 5.35 Å, respectively.

density for molecules in the first layer (within 3 Å from the wall) is peaked at y B 901, signifying that the diploes tend to be parallel to the pillar wall. A similar orientational distribution of the dipoles was found in the MD simulation of water confined between two hydrophobic plates.69–71 The orientational order of molecules in the upper layers (>3 Å apart from the pillar wall) was checked by dividing the vertical distances of molecules from the wall into 3 Å long intervals. The orientation of molecules in the second and third layers is uniform and indistinguishable from that of the bulk water. We additionally checked the probability distribution of the inter-atomic vector connecting two hydrogen atoms of the water molecule (bottom of Fig. 6). The H–H inter-atomic vectors in the first layer are predominantly parallel to the pillar wall (bottom of Fig. 6). The interatomic vectors of molecules in the upper layers are uniformly distributed as in the bulk water. Therefore, we conclude that the H–O–H planes of water molecules close to the pillar wall (less than 3 Å apart from the pillar wall) are predominantly parallel to the pillar wall. Our finding is similar to that reported in the MD simulation of water in contact with a hydrophobic surface.72 The orientation of water molecules in the upper layers (more than 3 Å away from the pillar wall) is random and bulk-like. Although not shown here, we observed the same qualitative behaviour for the orientation of water molecules confined between circular pillars. Our model does not account for the van der Waals interaction between carbon and hydrogen. Given that the liquid structure is largely governed by the short-ranged repulsive part of the van der Waals interaction, the H–C interaction can be neglected compared to the O–C interaction. The present model

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Fig. 6 Orientational distribution of water molecules confined between square pillars. (top) Distribution of the dipole orientation y of water molecule confined between the pillar walls. For each molecule, y is defined as the angle between the dipole vector and the surface normal to the pillar wall. Plotted is the probability distribution of cos y for molecules lying in different layers from the pillar wall. Each layer is obtained by dividing the vertical distances of molecules from the pillar wall into 3 Å long intervals. For comparison, the orientational distribution of the bulk water is also plotted as triangles. (bottom) Orientational distribution of the vector connecting the two hydrogen atoms within each molecule. Here b is defined as the angle between the H–H inter-atomic vector and the surface normal to the pillar wall. Plotted are the probability distributions of cos b for molecules in different layers from the pillar wall. The orientational distribution of the bulk water is plotted for comparison. Lines are drawn for visual guide.

of the water–carbon interaction however gives an anisotropic structure of water, such as the absence of layering at the corners of square pillars (Fig. 4) and the non-uniform orientation of water shown in Fig. 6. We investigated the density of water in the inter-pillar gap r by changing the inter-pillar spacing S. In Fig. 7, the open (filled) circles are the densities obtained by using the initial condition where the inter-pillar gap is filled with water (empty). Qualitatively, the density was close to zero for a small S. As S increased, the density of vapour steadily increased and then jumped to a liquid density at a critical value SC. With further increases in S, the density gradually increased and converged to a liquid density value (approximately 0.84 g cm3). This converged liquid density is smaller than the bulk water density of 1.00 g cm3, presumably due to the presence of hydrophobic pillars. For circular pillars with an S value near SC, r was dependent on the initial condition of MD simulation. For example, for circular pillars with S = 8.92 Å, r was a vapour density (0.082 g cm3) if the CB-like initial condition (where the inter-pillar gap is empty) was used, but it was a liquid density (0.70 g cm3) when we

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(drawn as vertical dotted lines in Fig. 7). Therefore, the present continuum theory overestimates the SC value for both shapes of pillars. The theoretical prediction of SC can be improved by considering the effects of solid–liquid–vapour line tension. The shift of SC to a new value SC 0 due to the line tension can be estimated as40 0

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SC ¼ SC 

2WgSLV ; fðDPÞaW  Dg þ gLV gðSC þ W Þ

(7)

for the square pillars. For the circular pillars, SC 0 can be expressed as 0

SC ¼ SC 

Fig. 7 Density of water vs. the inter-pillar spacing. The mean density of water confined between the pillar walls r is plotted vs. the inter-pillar spacing S for square (top) and circular (bottom) pillars. The open and filled circles represent the results obtained by using the initial conditions where the inter-pillar gap is filled with water (WZ state) and empty (CB state), respectively. Lines are drawn for visual guide. The inter-pillar spacing S was varied as 3.57, 5.35, 8.92, 12.49, 16.06, and 19.62 Å. Also drawn are the theoretical prediction of SC (vertical dotted line) and its modification by including the effects of line tension SC 0 (vertical broken line). The top panel has the same axis labels as those of the bottom.

used the WZ-like initial condition (where the inter-pillar gap is filled with water). Consequently, the r–S curves formed a hysteresis loop for the circular pillars (drawn as solid and broken lines in Fig. 7). This hysteresis did not vanish even after running a 60 ns long simulation. This type of hysteresis is common in simulations of the first order phase transitions.73 For example, a relatively short (few hundred ps long) MD simulation reported a significant hysteresis in the drying transition of liquid confined between two ellipsoidal particles.45 For the present square pillars (top of Fig. 7) however, we could remove the hysteresis by running a relatively long (>20 ns) simulation. A slight mismatch near SC between the two curves arises from the fact that the simulation box size varies in the present NPT simulation (volume is not fixed). Consequently, the S and r values are slightly different depending on the initial conditions used (CB or WZ state). In each r vs. S curve, we estimated SC as the middle point between the two inter-pillar spacing that gives the highest vapour density and lowest liquid density (drawn as crosses in Fig. 7). The estimated SC values for square pillars were nearly identical regardless of the initial conditions used (they were 9.9 and 10.6 Å, respectively, for the initial conditions where the inter-pillar gap is empty and filled with water). For circular pillars, the SC values were 9.8 and 6.9 Å, respectively, if we used the initial conditions where the inter-pillar gap is empty and filled with water. The true SC is expected to be somewhere in the middle of these values. The SC values from the continuum theory were found to be 16.5 and 12.8 Å for the square and circular pillars, respectively

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pWgSLV : 2fðDPÞaW  Dg þ gLV gðSC þ W Þ

(8)

These SC 0 values were evaluated using the line tension gSLV estimated in Section II (= 2.30  1011 J m1). The resulting SC 0 values were 11.4 and 8.36 Å respectively, for the square and circular pillars (drawn as vertical broken lines in Fig. 7). SC 0 is close to that from the MD simulations for both shapes of pillars (the midpoints of two crosses in Fig. 7 were 10.3 and 8.4 Å, respectively, for square and circular pillars). Therefore, the line tension must be taken into account to accurately predict the drying transition for the present nm-sized pillars. Similarly, Sharma and Debenedetti74 have reported that the line tension is crucial in the capillary evaporation rate of water confined between two circular disks of a few nanometers in diameter. Note the line tension reduces the theoretical value of SC significantly (by 31% and 35% for square and circular pillars, respectively). The line tension effects are negligible for large pillars however: we calculated SC 0 by increasing the size of the pillar. SC 0 differed from SC by less than 1% for square pillars wider than 51 nm (aspect ratio a was fixed to 1.78). Similarly, the difference between SC 0 and SC became smaller than 1% for circular pillars with widths of W Z 63 nm. We investigated the r vs. S by varying temperature from 300 to 360 K. Both for square and circular pillars, increasing temperature slightly decreased r and increased SC. This indicates that the pillars become more hydrophobic with increasing temperature, which is consistent with that found in the MD simulation study of dewetting of hydrophobic plates.69 Mahajan et al. also reported a similar temperature dependence in their MD study of the hydration of hydrophobic solutes.75 They further estimated the entropy change in the hydrophobic hydration by using the thermodynamics perturbation method. Such a calculation of entropy for the present drying transition would be certainly interesting, but is beyond the scope of this work. Pressure also should affect the r–S curves. Intuitively, increasing pressure of water is expected to drive the transition from a CB state to a WZ state. We examined r vs. S by varying pressure from 1 to 4 atm. Indeed, with an increase in pressure, r increased and SC decreased (this trend is opposite of that found for the case where temperature is increased). The changes in r and SC however turned out to be negligible in this range of pressure. It would be interesting to explore a more extensive range of thermodynamics states. This is left as a future work.

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Fig. 8 Transition from a long-lived CB state to a WZ state. Shown in the top 9 panels are the snapshots of water in contact with square pillars (12.49 Å apart). Only the molecules lying in the range, (W/2 r y r W/2 + S), are drawn. Plotted in the bottom is the average height hZi of the bottom surface of water during the transition (W/2 r y r W/2 + S). The broken line represents the half height of pillar.

Fig. 9 Transition from a long-lived WZ state to a CB state. Top 9 panels illustrate the snapshots of the water confined between square pillars (8.92 Å apart) at different times. Shown are the molecules lying in the range, (W/2 r y r W/2 + S). In the bottom panel, we plot the average height hZi of the bottom surface of water in the course of the transition (W/2 r y r W/2 + S). The broken line represents the half height of pillar.

A spontaneous transition from a metastable CB state to a WZ state has been observed experimentally.57,76 This transition also has been studied theoretically77–82 by focusing on the free energy barrier separating the metastable CB state and the WZ state. However, the dynamics underlying this transition is largely unknown. In the present simulation, we found a longlived (more than 3 ns) CB state which eventually turns into the WZ state: for S values away from SC, r reached its equilibrium value within 0.2 ns, regardless of the initial condition. Near SC however, it took much longer to reach the equilibrium. Fig. 8 illustrates how the long-lived CB state changes into a WZ state. Shown in the top 9 panels are the cross-sectional (along the XZ plane) snapshots of water penetrating down the gap between square pillars (S = 12.49 Å). The bottom surface of water gradually reached down the half height of the pillar with significant up and down movement. Once the bottom surface of water arrived near the half height (at t = 3.14 ns), it quickly dropped down to the base of the pillar (within 0.42 ns). The vapour pocket formed near the base of pillar (at 3.52 and 3.54 ns) is similar to that found in the coarse-grained MD simulation of water confined in a nm-sized trench.81 Plotted in the bottom of Fig. 8 is the average

height of the bottom surface of water hZi vs. time. This height is defined as the average Z position of oxygen atoms located at the bottom surface of water (the base surface is located at Z = 0). As time went by, hZi gradually decreased with significant fluctuation, illustrating the down-and-up movement of the surface of water. As hZi reached the half height of the pillar (drawn as the broken line) at near 3.14 ns, hZi suddenly dropped down to the base surface (hZi B 4 Å). We also found a relatively long lived (0.72 ns long) WZ state which later turns into a CB state. Fig. 9 shows the transition of such a WZ state to a CB state for the square pillars 8.92 Å apart (with an S value near SC). MD snapshots are shown for times ranging from 0 to 1.20 ns. In this transition, a vapour cavity developed at the lower left corner of the inter-pillar gap. Then the surface of water gradually rose to the half height of the pillar with a significant up-and-down movement. After reaching the half height, the surface of water quickly jumped up to the top of the pillar. The bottom of Fig. 9 plots the height of the surface of water hZi as a function of time. Qualitatively, this transition appears as the reverse of the transition from the CB to WZ transition shown in Fig. 8. In both transitions,

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reaching the half of pillar height was the slow, rate determining step, and the rest of the transition was relatively quick.

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Conclusions Using an atomistic MD simulation, we studied the drying transition of water confined between periodic square or circular pillars as the inter-pillar spacing is decreased. By looking into the molecular details of water confined between pillar walls, we found water molecules close to the pillar walls were layered and ordered in orientation. The line tension was important in the wettability of the present small pillars a few nanometers in width and height. The line tension effect however was negligible for the pillars bigger than tens of nanometers in width and height. By considering the line tension, the continuum theory agreed with the molecular simulation. We also studied the transition from a longlived (metastable) CB to the WZ state and vice versa. In these transitions, the surface of water slowly reached the half height of the pillar with a significant up-and-down movement. Once the water surface reached the half height, it quickly penetrated down to the bottom (for the CB-to-WZ transition) or receded to the top of the pillar (for the WZ-to-CB transition).

Acknowledgements This study was supported by National Research Foundation Grants funded by the Korean Government (MEST) (No. 2013-027519 and No. 2013-043992). JJ wishes to thank the Korea Institute of Science and Technology Information for the use of the PLSI supercomputing resources. MYH acknowledges Leading Foreign Research Institute Recruitment Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (No. 2013044133).

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Molecular dynamics study on the wettability of a hydrophobic surface textured with nanoscale pillars.

Using molecular dynamics simulation, we studied the wetting properties of a surface textured with hydrophobic pillars, several nanometers in size. The...
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