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Wetting transition from Cassie-Baxter state to Wenzel state on regularly nanostructured surfaces induced by an electric field Ben-Xi Zhang, Shuo-Lin Wang, and Xiao-Dong Wang Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b03808 • Publication Date (Web): 02 Jan 2019 Downloaded from http://pubs.acs.org on January 5, 2019

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Wetting transition from Cassie-Baxter state to Wenzel state on regularly nanostructured surfaces induced by an electric field

Ben-Xi Zhang1,2,3, Shuo-Lin Wang1,2,3, Xiao-Dong Wang1,2,3* 1. State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China; 2. Research Center of Engineering Thermophysics, North China Electric Power University, Beijing 102206, China; 3. Key Laboratory of Condition Monitoring and Control for Power Plant Equipment of Ministry of Education, North China Electric Power University, Beijing 102206, China.

Keywords: Cassie-Baxter state; Wenzel state; wetting transition; energy barrier; free energy; molecular dynamics simulations.

*Corresponding

Author:

Xiao-Dong

Wang,

Tel.

and

[email protected].

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Abstract: When droplets are placed on hydrophobic textured surfaces, different wetting state Cassie-Baxter (CB) state or Wenzel (W) state may occur depending on materials and structures of surfaces, types and sizes of droplets, thermal fluctuations, and external stimuli. The wetting transition from the CB to the W state and the opposite process have attracted a great deal of attention due to their primary importance for designing and fabricating textured surfaces. In this work, molecular dynamics (MD) simulations are employed to understand the mechanism behind the CB-to-W transition for a nanoscale water film placed on a surface decorated with a single nanogroove when an external electric field is applied. The free energy variation during the transition process is computed on the basis of the restrained MD simulations. Water intrusion into the groove is observed by simulation snapshots, which provides a direct evidence for the electric-field-induced CB-to-W transition. In the previous experiments, however, only a sharp reduction in the apparent contact angle is employed to judge whether the transition takes place. The free energy curves reveal that there are two energy barriers separating the CB and W states (∆E1) as well as separating the W and CB states (∆E2). Owing to the presence of ∆E1, although the CB state has a higher free energy than the W state, it cannot spontaneously convert to the W state. When the external energy input exceeds ∆E1, the CBto-W transition can be triggered, otherwise the transition will stop, and the water film will return to the CB state. Moreover, it is found that the maximum of free energy always occurs after the film touches the groove bottom. Thus, the requirement of the film touching the groove bottom is responsible for the presence of the energy barrier ∆E1. Finally, the dependences of the two energy barriers on the electric field strength, groove aspect ratio, and intrinsic contact angle of the groove are also discussed.


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■ INTRODUCTION In nature, many plant leaves and bird feathers have the ability to resist the infiltration of water droplets because of their superhydrophobicity with an apparent contact angle larger than 150° and a very small contact angle hysteresis. For instance, a 164° contact angle was observed on lotus leaves with the contact angle hysteresis smaller than 3°, and hence a water droplet can roll off the surface arbitrarily instead of sliding [1-3]. This unique phenomenon has attracted great interests in recent years due to its potential applications in drag reduction, self-cleaning, anti-icing, anti-dew, condensation heat transfer enhancement, and so forth [4-6]. It has been confirmed that superhydrophobic surfaces are commonly formed or fabricated by patterning hydrophobic surfaces with nano-/micro-structures [7]. When a droplet is placed on a rough surface with regular or irregular nano-/micro-structures, two different wetting states can be distinguished. One is the Wenzel (W) state with liquid penetrating into the asperities of nano-/microstructures. The other one is the Cassie-Baxter (CB) state, in which air pockets are trapped into the asperities so that the droplet actually wets a mixed solid-gas surface. As compared with the W state, the CB state possesses a larger apparent contact angle; thus, to maintain surface superhydrophobicity, the CB state needs to be sustained. Similar to the Young equation [8] proposed for ideal surfaces, two different models were employed to describe the W and the CB state. For the W state, the contact angle follows cosθW=rfcosθY [9], where θW is the apparent contact angle in the W state, θY is the Young contact angle or the intrinsic contact angle of the material of which the rough surface is made, rf is a roughness factor defined as the ratio of the real area of the rough surface to the geometric projected area. For the CB state, cosθC=fcosθY+(1-f)cos180° =fcosθY+f-1 is valid [10], where θC is the apparent


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contact angle in the CB state, f is the area fraction of the solid-liquid interface, and 1-f is the area fraction of the solid-air interface. It has been shown that when placed on rough surfaces, droplets can change their wetting state from the W to the CB state or conversely by external stimuli such as pressure or vibration, which is commonly referred to as wetting transition. The occurrence of this transition can be explained from the viewpoint of thermodynamics. The stability of wetting state depends on the free energy of the wetting system, composed of the droplet, solid, and surrounding air. On a rough surface, the free energy of the wetting system has multiple local minima, and the W and the CB state occupy two ones among these local minima [11, 12]. It has been recognized that the W state is more stable than the CB one because of its lower free energy [13]. However, the wetting transition from the CB to the W state (CB-to-W wetting transition) cannot take place spontaneously due to the presence of free energy barrier separating them, implying that there is a local free energy maximum between the CB and W states. The study of the CB-to-W wetting transition is of great importance for many practical applications [14]. For coating, printing, and spraying processes, sustaining a W state is advantageous, while for superhydrophobic applications, a stable CB state is desired. Thus, many efforts have recently been devoted to understanding the mechanism of the wetting transition, and various approaches have been proposed to realize the transition. Tsai et al. [15] reported that evaporating a water droplet deposited on a pillar array surface can drive the CB-to-W transition, and the transition occurs only when the droplet radius reduces to below a critical value. On basis of the global surface energies for the CB and W states, they developed a model to predict the critical radius for the transition. Bartolo et al. [16] experimentally investigated the droplet impacting a hydrophobic 4 ACS Paragon Plus Environment

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microstructured surface, and found that depending on the impacting velocity, the droplet can bounce off the surface (in CB state) or be impaled and strongly stuck on the surface (in W state). They proposed a semi-quantitative model to predict the measured critical velocity for the CB-to-W transition. Yoshimitsu et al. [17] experimentally investigated wetting behaviors of water droplets on various hydrophobic surfaces with pillar or groove structures. By measuring the sliding angle, they presented that water intrusion into the microstructure due to droplet weight induces the CB-to-W transition. Bormashenko et al. [18] experimentally investigated the CB-to-W wetting transition for a droplet deposited on a microscale porous surface induced by vertical and horizontal vibrations of the surface. The driving force of the transition was attributed to the pressure jump coming from the droplet vibration. Despite a variety of approaches have been proposed to trigger the CB-to-W transition, such as evaporation [15], impingement [16], gravity [17], and vibration [18], these approaches have some limitations for practical applications. For example, evaporation and impingement of droplets on solid surfaces are not suitable for switchable lenses, microfluidic devices, and electronic displays. Under microgravity conditions and/or for low-density liquids, the CB-to-W transition cannot be triggered by increasing droplet volume. Moreover, for precision instruments, vibration is not a good choice for wetting transition. Inspired by traditional electrowetting, Krupenkin et al. [19] for the first time experimentally demonstrated that the CB-to-W transition can be triggered by applying an external electric field to droplets. Following Krupenkin et al.’s work, many studies investigated experimentally the electric-field-induced wetting transition [20-31] on textured surfaces, as summarized in Table 1. The critical voltage for the transition was measured for various textured surfaces in Refs. [19-31], and it was found that the critical voltage depends on the arrangement of 5 ACS Paragon Plus Environment

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electrodes, liquid surface tension, and microstructure geometry. It should be noted that, in these studies, determining whether the CB-to-W wetting transition takes place is mainly based on the variation of apparent contact angle. If a sharp reduction in the apparent contact angle is observed during continuously increasing the applied electrical voltage, the CB-to-W transition takes place, otherwise the transition does not occur. However, these studies did not provide a direct evidence for penetration of liquid into the surface asperities, so that whether the transition is indeed triggered is doubtful. Furthermore, the free energy-based analysis for the wetting system during electrowetting process was not implemented in Refs. [19-31]; thus, the mechanisms for the electric-field-induced wetting transition are not yet fully understood. On the basis of the reasons mentioned above, molecular dynamics simulations are implemented to investigate the electric-field-induced CB-to-W wetting transition of nano water films on a superhydrophobic gold surface with regular pillar array structure in this work. Detailed dynamics of liquid infiltration into a single groove is shown to provide a direct evidence of the transition. The free energy variation of the wetting system during the electrowetting process is calculated and employed to elucidate the transition mechanisms. Finally, the energy barrier separating the CB and W wetting states is discussed for various electrical field strengths, surface wettabilities, and pillar aspect ratios.

■ MODEL AND METHODS Simulation setup Molecular dynamics simulations are employed to investigate the electric-field-induced wetting transition of a nano water film on a pillar array gold surface based on LAMMPS (Large Atomic and Molecular Massively Parallel Simulator). With consideration of the symmetry, only one unit is 6 ACS Paragon Plus Environment

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selected as the simulated system, which is composed of a water film and a gold plate with a single groove. The initial configuration of the simulated system is illustrated in Fig 1. The system is a cuboid box with dimensions of 9.792×45×1.632 nm3. The groove has a height h and a width w. To simulate the effect of groove geometry on wetting transition, the groove width is kept at a constant value of w=4.896 nm, while its height is taken as h=2.448, 3.672, and 4.896 nm, respectively, so that three different aspect ratios of h/w=0.5, 0.75, and 1.0 are obtained. The gold atom numbers are 3500, 4052, and 4604 for the three plates. The water film has 2.1 nm thickness and includes 1125 water molecules. The gold plate (100) is constructed by face-centered cubic crystals with lattice constant of 4.08 Å. The plate consists of 12 layers and the gold atoms at the lowest layer are fixed to prevent from the plate deformation. Water molecules are modeled by the SPC/E model, which has been shown to reproduce many of the properties of water [32]. The O-H bond length of 0.1 nm and the H-O-H bond angle of 109.47° remain constant by the SHAKE algorithm. A combination of the Coulombic and Lennard-Jones 126 potentials is used to model the interactions between water molecules, as follows,

U ij 

qi q j rij

  ij  4 ij   r  ij 

12

   ij      rij

  

6

   

(1)

where Uij is the potential energy between particles i and j, qi, and qj are the charge of particles i and j, rij is the distance between particles i and j, εij is the depth of the potential well, and σij is the zerocrossing distance between particles i and j. The embedded atom model (EAM) potentials have the many-body nature which makes them well suited for modeling metals [33]. Therefore, the EAM potential is employed here to describe the interactions between the gold atoms. The parameter values of the potential can be found in Ref. [34]. 7 ACS Paragon Plus Environment

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To generate an external electric field, the gold atoms in the inner surface of the groove are charged and each atom in the first layer of the groove bears an equal positive charge. Thus, the total charge carried by the inner surface of the groove is the summation of the charge carried by each atom. The surface charge density, qe, can be calculated through dividing the total charge by the inner surface area of the groove. Similar method was also employed in Ref. [35]. The interactions between water molecules and gold atoms are also modeled by the combination of the Coulombic and Lennard-Jones 12-6 potentials [35]. It should be noted that for the gold atoms without surface charge, the interactions can be simplified to the Lennard-Jones 12-6 potential. The Coulombic interaction between gold atoms with surface charge is ignored due to that it is far less than EAM potential. The values of parameter for the water-water and water-gold interactions are listed in Table 2. The spherical truncation is adopted for the Lennard-Jones potentials with a cut-off radius of 10 Å. The long-range electrostatic interactions are computed by particle-particle/particle mesh method (PPPM) with an accuracy of 104.

Two different surface wettabilities are used in the present simulations, which are obtained by adjusting the energy parameter between water molecules and gold atoms (εO-Au) [35]. With a prespecified εO-Au, spreading of a spherical water droplet on the gold plate is implemented. The contact angle can be measured by fitting the equilibrated droplet contour. The simulations show that the contact angle is 85.6° for εO-Au=0.0114 eV and 116.9° for εO-Au=0.0056 eV, as shown in Fig. S1 in the Supporting Information. Periodic boundary conditions are applied to all three directions of the box. After building the initial configuration, the system relaxes 1000 ps under the NVT ensemble at 298 K to reach an equilibrium. Subsequently, the inner surface of the groove is charged with a 8 ACS Paragon Plus Environment

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constant charge density (qe) to trigger the wetting transition. The time step for all simulations is taken to be 1 fs, and the Velocity-Verlet algorithm is used to solve the Newton's motion equation of each particle.

Calculation of free energy When placed on a rough surface, a droplet may possess many observable apparent contact angles, this phenomenon is referred to as contact angle hysteresis [36]. Metastable state theory has been employed to explain the contact angle hysteresis. According to this theory, the wetting system involving a droplet, a solid, and a surrounding gas has multiple local minima of free energy, and every minimum corresponds to an observable apparent contact angle [37]. Therefore, when a droplet is in the CB or the W state on a rough surface, the wetting system is in a metastable state and has a local minimum of free energy. To understand the mechanism of the CB-to-W wetting transition, the free energy of the wetting system is calculated as follow. In the process of CB-to-W wetting transition, the red region in Fig 1 is taken as a collective variable space (CVs). The collective variable is denoted by s(r), which is defined as the number of particles inside the CVs, where r=(r1,…,rN) is the coordinates of the particles. Obviously, the value of s(r) varies with the wetting transition. Thus, different s(r) corresponds to different wetting state. For example, when the system is in the CB state, the water film is suspended above the groove, the value of s(r) is low. On the contrary, when the system is in the W state, the water film collapses into the groove, the value of s(r) is high. For a given positive integer a, which is referred to as the target value of the collective variable s(r), the probability Ps(s(r)=a) can be calculated by the following equation [11, 38], 9 ACS Paragon Plus Environment

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Ps  s  r   a      s  r   a w  r  dr

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(2)

where w(r) is the invariant distribution of the system. Since the simulated system is in the NVT ensemble, w(r) is the Boltzmann distribution. Thus, the Landau free energy (also referred to as the microscopic expression of free energy) can be expressed as [11, 38]: F ( s (r )  a )  kBT ln Ps ( s (r )  a )

(3)

where kB is the Boltzmann constant. Different probability presents different free energy. A low probability region corresponds to a local maximum of free energy. In contrast, a high probability region corresponds to a local minimum of free energy. It is well known that the stability of the wetting state depends on the free energy value. Metastable states such as the CB state or the W state are associated with the local minimum of free energy, while the transition state is the global maximum of free energy. The difference of free energy between a local minimum and the neighboring maximum is defined as the free energy barrier ∆E. Once the energy input to a wetting system by external stimuli exceeds the energy barrier, the wetting transition will be triggered. The free energy barrier dictates the kinetics of the wetting transition; thus, we have [39] l = l0 exp(E kBT )

(4)

where l is the average time required to complete the CB-to-W wetting transition and l0 is a prefactor. According to Eq. (4), the wetting transition will take a very long time for the wetting system with larger free energy barriers. Considering that the infrequent transitions between the metastable states make the calculation of Ps(s(r)=a) and F(s(r)=a) very difficult through the standard MD, the restrained MD method is employed to reconstruct the potential of mean force (PMF) profile. In the restrained MD, the system is restrained so that it is close to the condition of s(r)=a by a restraining potential. The form of the 10 ACS Paragon Plus Environment

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restraining potential is that Ures(r)=k/2(s(r)-a)2, where k is a suitable constant. The restraining potential with suitably large values of the constant k restrains the system close to the condition of s(r)=a, and hence allows one to sample the low probability regions of the phase space [11, 38]. In the restrained MD, the free energy F(s(r)=a) is not calculated directly, but is reconstructed by integration of the free energy gradient dF/da. Therefore, the computation of dF/da becomes a key issue. In the restrained MD, dF/da can be evaluated by the time average of the mean force of the restraining potential [11, 38, 39]:

dF 1   k ( s (r (t )  a ))dt da  0

(5)

where τ is the duration of the restrained MD. The right-hand-side of Eq. (5) can be estimated based on a series of ai fixed points corresponding to independent restrained MD simulations. Finally, the free energy F(s(r)=a) can be reconstructed by numerically integrating the free energy gradient dF/da. On the basis of the above method, the free energy is calculated by LAMMPS software combining with the modified version of PLUMED plug-in [40], and more details can refer to Refs. [11, 38-40].

■ RESULTS AND DISCUSSION The CB-to-W wetting transition In this section, the morphology evolution of water films on a single groove with or without electric filed is simulated. The simulations are implemented with the groove aspect ratio of h/w=0.75 and the intrinsic contact angle of θ0=85.6°, and a surface charge density of qe=0.02 C m-2 is employed. As shown in Fig. 2, the water film exhibits distinctly different wetting states for the groove with or without surface charge. When the groove is not charged, although a relative hydrophilic surface is 11 ACS Paragon Plus Environment

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employed, water intrusion into the groove does not take place such that the water film is always in the CB state. It worth noting that the present result of the stable CB state occurring on an intrinsic hydrophilic grooved-surface seems contradictory with the macroscopic theories [41]. However, recent studies have shown that, even when the intrinsic contact angle of a surface is lower than 90°, it is possible to design a superhydrophobic surface with the CB state for sessile droplets placed on the surface, so long as nanoscale (not microscale) structures are properly patterned on the surface [11, 42-44]. When surface charge is applied, it is observed that the water film gradually penetrates into the groove and finally the groove is filled with water molecules, forming a W state. The present observation provides a clear evidence that the CB-to-W transition can be triggered by applying an electric field. In continuum calculations of free energy, it is commonly assumed that a flat meniscus is maintained during the water intrusion into grooves [45]. However, our MD simulations exhibit an interesting phenomenon that an asymmetric water intrusion into the groove takes place. As shown in Fig. 2(b), the water film initially sustains a flat meniscus, subsequently, the meniscus starts to bend and advance along the right sidewall of the groove until it touches the groove bottom. After that, the meniscus moves along both the groove bottom and the left sidewall, and finally the water film completely penetrates into the groove. The asymmetric path for the CB-to-W transition was also reported by Giacomello et al. [11] and Pashos et al. [46], and it was explained by means of a simple macroscopic argument based on the minimization of surface free energy. When the groove is filled with only a small amount of liquid, the liquid with a flat meniscus has the minimum free energy, whereas when enough liquid penetrates into the groove, the meniscus confined between the bottom


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and sidewall of the groove has a smaller liquid-vapor area and hence has a lower free energy than the plat meniscus.

The mechanism of the CB-to-W transition To understand the mechanism behind the CB-to-W transition when an electric field is applied to a groove, the snapshots of water film morphology evolution and the corresponding variations of free energy during the transition process for the grooves with various surface charges are shown in Figs. 3 and 4, respectively. The surface charge density is qe=0.003, 0.01, and 0.02 C m-2, respectively. The groove height and width are both 4.896 nm with h/w=1, and the intrinsic contact angle of the groove surface is θ0=85.6°. As shown in Fig. 3(a), for the low surface charge density of 0.003 C m-2, the film is always suspended above the groove and water intrusion does not take place, indicating that a low electric field is not enough to trigger the CB-to-W transition. Accordingly, the free energy of the water film maintains a constant value, as shown in Fig. 4(a). When surface charge density increases to 0.01 C m-2, it can be seen from Fig. 3(b) that the water intrusion is triggered; however, the water film does not completely penetrate into groove. Figure 4(b) shows that during this period, the free energy of the film slightly increases. It should be noted that the partial intrusion does not lead to the CB-to-W transition, the film is still in the CB state. However, the partial intrusion may lead to a sharp reduction in apparent contact angles. Thus, in the previous experiments as listed in Table 1, when an electric filed is applied to droplets on textured surfaces, judging whether the CB-to-W transition takes place only by the sharp reduction in apparent contact angles may be inadequate, at least is doubtful.


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Figure 3(c) illustrates that for the high surface charge density of 0.02 C m-2, the groove is finally filled with water molecules, and hence the CB-to-W transition is triggered. We also implement a series of extra simulations to find the minimum surface charge density triggering the transition, the results show that the critical value is qe=0.013 C m-2. The variation of free energy corresponding to the complete transition reveals that the free energy first continuously increases with time until it reaches a maximum value, subsequently the free energy starts to reduce and finally keeps a constant value, as shown in Fig. 4(c). The state corresponding to the maximum of free energy is commonly referred as to transition state [13]. The free energy difference between the CB state and the transition state is defined as the energy barrier ∆E1. Apparently, owing to the presence of ∆E1, although the CB state has a higher free energy than the W state, it cannot spontaneously convert to the W state. Thus, a large enough energy needs to be input to the water film to overcome this energy barrier. As a result, there is a critical surface charge density or electric field to trigger the CB-to-W transition. Figure 4(c) also shows that there is another an energy barrier ∆E2 defined as the free energy difference between the transition state and the W state. Likewise, the presence of ∆E2 hinders the transition from the W state to the CB state. It should be noted that ∆E2 is much larger than ∆E1, leading to an asymmetric energy barrier. The asymmetric energy barrier has been extensively reported in the wetting transition with various external stimuli, and it was employed to explain the strongly hysteretic behavior of intrusion and extrusion cycle experimentally observed on hydrophobic nanotextured surfaces [13]. To further understand the effect of energy barrier, three extra simulations are carried out. Three points in Fig. 4(c) are selected, which correspond to three non-equilibrium wetting states. One point is located in the left part of the maximum of free energy, while two other points in the right part. In every extra simulation, once the water film reaches one of these three states, the surface charge 14 ACS Paragon Plus Environment

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applied to the groove is removed. Our simulations demonstrate that two different wetting paths and final wetting states are achieved, as shown in Fig. 5. For the water film in the left part of the maximum of free energy, after the electric field is removed the water intrusion cannot proceed; oppositely, the water extrusion takes place and finally the film returns to the previous CB state, as shown in Fig. 5(a). On the contrary, for the water films in the right part, although the electric field is removed, the films continue to penetrate into the groove until the groove is filled with water molecules, as shown in Figs. 5(b) and 5(c). The above results indicate that the mechanism behind the CB-to-W transition induced by electric field is similar to the other transition approaches, i.e. when the external energy input exceeds the energy barrier separating the CB and W wetting states, the wetting transition will be triggered, otherwise the transition will stop, and the system will return to the CB state. It is worth noting that the critical value of an external stimulus to trigger the CB-to-W transition was also explained from the viewpoint of mechanics [16, 47]. More in detail, once the pressure exerted on the meniscus above the groove exceeds the Young-Laplace pressure p=2γ/w, the liquid will penetrate into the groove leading to the occurrence of the CB-to-W transition, where γ is the liquid surface tension. So far, the detailed analysis for the CB-to-W transition using the force method has not been constructed well. The Young-Laplace equation p=2γ/w is employed to only explain why there is a critical pressure to trigger the liquid intrusion into grooves. According to the Young-Laplace equation, the critical pressure is dependent only on the groove width and increases with the reduction in the groove width. However, it has been shown that with a constant groove width, the CB state is more stable for a larger groove height [16]. Our simulations also demonstrate that the energy barrier separating the CB and the W state increases with the groove height (see Section 3.3). Therefore, the Young-Laplace equation is not completely valid for the explanation of the CB-to-W transition. Figure 15 ACS Paragon Plus Environment

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5(a) shows that even if the external energy input exceeds the critical value or the pressure exceeds p=2γ/w, which triggers the film intrusion into the groove, the CB-to-W transition still cannot take place when the electric field is removed. This result confirms that the force criterion is not always true. Moreover, by checking the snapshots of film intrusion and the corresponding free energy curves, an interesting result is found. Because of the asymmetric water intrusion into the groove, the film starts to touch the groove bottom always from a sidewall of the groove, and the maximum of free energy always occurs after the film touching the groove bottom. Thus, the requirement of the film touching the groove bottom is responsible for the presence of the energy barrier, ∆E1, and the critical surface charge density (or the electric field strength). This finding further confirms that the force criterion is not always true. The present film consists of only 1125 water molecules, its volume is slightly larger than that of the grooves with h/w=0.5 and 0.75, even is smaller than that of the groove with h/w=1. Thus, when the CB-to-W transition occurs, the film must break up, as shown in Figs. 2 and 3. To examine the contribution of the resistance of the film breakup to the energy barrier of the CB-to-W transition, we implement an extra simulation with the following conditions of 2250 water molecules in the film as well as h/w=0.5 and θ0=85.6° for the groove. As shown in Fig. S2 in the Supporting Information, when the surface charge is not applied to the groove surface, the film is always in the CB state; however, when the surface charge with qe= 0.02 C m-2 is applied, the water intrusion into the groove is observed, and finally the CB state is converted into the W state. It is observed that, in the whole transition process, the film breakup does not take place due to that the volume of the film is far larger than that of the groove. The free energy variation of the water films with 1125 and 2250 water molecules on the groove with h/w=0.5 and qe=0.02 C m-2 is shown in Fig. S3 in the Supporting 16 ACS Paragon Plus Environment

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Information. Restated that the breakup occurs for the film with 1125 water molecules when the CBW transition completes, whereas does not take place for the film with 2250 water molecules. Figure S3 shows that although the free energy is larger for the film with 2250 water molecules, the free energy difference between the initial CB state and the transition state is identical for the two cases. In other words, the energy barrier separating the CB and W states is not affected by the film breakup. To explain this result, we check the snapshots of the morphology evolution of the water films with 1125 and 2250 water molecules carefully. It is found that the film breakup always takes place after the maximum of free energy. For example, the maximum of free energy occurs at t=100 ps for the film with 1125 water molecules, whereas the liquid breakup occurs at t=220 ps. Thus, the film breakup cannot affect the energy barrier of the CB-W transition.

The factors affecting the CB-to-W wetting transition According to the foregoing analyses, the free energy barrier ∆E1 plays a crucial role in the CBto-W transition. The previous experiments have demonstrated that the external electric field strength [27] as well as the geometrical structure [48] and intrinsic wettability [20] of textured surfaces affect the CB-to-W transition significantly. Therefore, the effects of the three factors on the energy barrier are discussed in this section. The groove aspect ratio and intrinsic contact angle are maintained at constant values of h/w=0.75 and θ0=85.6°. Two surface charge densities of qe=0.015 and 0.02 C m-2 are applied to the groove to generate different electric field strengths. With the constant h/w=0.75 and θ0=85.6°, our simulations show that the critical charge density is 0.012 C m-2; therefore, the CB-to-W transition is triggered for the both charge densities. Figure 6 shows the free energy variations for the two cases. It can be seen 17 ACS Paragon Plus Environment

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that the free energies corresponding to the CB, transition, and W states are almost the same, indicating the energy barriers ∆E1 and ∆E2 are independent of the electric field strength. This result is reasonable and can be guessed intuitively. However, as the electric field strength increases, the time required to reach the transition and W states reduces. For example, the transition state occurs at t=300 ps for the high surface charge density of qe=0.02 C m-2, whereas occurs at t=450 ps for the low surface charge density of qe=0.015 C m-2. We also implemented an extra simulation with the surface charge placed only on the groove bottom. The simulation shows that the energy barriers separating the CB and W states as well as the W and CB states are the same with those with the surface charge placed on both the sidewalls and the bottom of the groove, which again confirms that the energy barriers are independent of the electric field strength. Thus, it can be concluded that the increase in electric field strength neither change the energy barrier separating the CB and W states nor change the one separating the W and CB states, but it makes the CB-to-W transition evolve faster. The free energy variations corresponding to various groove aspect ratios of h/w=0.5, 0.75, and 1 are illustrated in Fig 7. In these cases, a constant intrinsic contact angle of θ0=85.6° is employed, and qe is 0.02 C m-2 for h/w=0.5, 0.015 C m-2 for h/w=0.75, and 0.03 C m-2 for h/w=1. As shown in Fig. 7, for the groove with a small aspect ratio of h/w=0.5, the energy barrier ∆E1 separating the CB and W states is the lowest among the three grooves, indicating that the CB state is more unstable for small groove aspect ratios, and hence a small external stimulus will cause it collapse to the W state. As the groove aspect ratio increases, ∆E1 increases and the maximum ∆E1 occurs for the groove with h/w=1. Thus, to maintain a stable superhydrophobicity, large groove aspect ratios should be employed in nanotextured surfaces. Recently, Yuan et al. [47] investigated the statics and dynamics of droplets on nanoscale pillar-arrayed surfaces via MD simulations when a uniform external electric field is 18 ACS Paragon Plus Environment

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applied to the droplets. Although the free energy curves for the CB-to-W transition were not described, their simulations showed that a higher critical voltage is required to trigger the CB-to-W transition for the surface with a larger groove aspect ratio, which indirectly supports our results. Moreover, in the previous MD studies [49, 50], although different external stimuli such as impingement of droplets on nanotextured surfaces were employed, the same conclusions that the energy barrier separating the CB and W states increases with the groove aspect ratio were also reported. The higher energy barrier ∆E1 for a large groove aspect ratio can be attributed the fact that the water film needs a larger pressure to break through the groove with a smaller width due to the larger Young-Laplace pressure, furthermore, it also needs a long path to touch the groove bottom for a larger groove depth [51]. On basis of the same reason, the energy barrier ∆E2 separating the W and CB states increases with the groove aspect ratio, as shown in Fig. 7. As a result, once the W state is reached, it is more difficult to convert it into the CB states for the groove with a larger aspect ratio. It is widely recognized that the wetting state and apparent contact angle on a textured surface is closely associated with the intrinsic wettability of its material. Therefore, the CB-to-W transition is discussed for various intrinsic wettabilities. Figure 8 shows the free energy variations corresponding to two intrinsic contact angles of θ0=85.6° and 116.9° during the CB-to-W transition. In the two cases, the groove aspect ratio is h/w=0.75 and the surface charge density is qe=0.03 C m-2. As illustrated in Fig. 8, the free energy barrier ∆E1,pho for the hydrophobic groove with the contact angle of θ0=116.9° is higher than ∆E1,phi for the hydrophilic groove with the contact angle of θ0=85.6°. This is because the hydrophobic groove exhibits the weak attractive intermolecular forces between the liquid and solid surface; thus, a larger driving force is required to make the water film intrude into the groove, leading to the higher ∆E1,pho. On the contrary, the free energy barrier ∆E2,phi for the hydrophilic groove 19 ACS Paragon Plus Environment

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is larger than ∆E2,pho for the hydrophobic groove. This can be attributed to the strong attractive intermolecular forces between the liquid and hydrophilic surface, which leads to a larger resistance for the escape of the liquid from the groove. The above results were also reported for the CB-to-W transition of an oil droplet on the nanostructured surfaces [49]. On the basis of the above results, it can be concluded that the CB state is more stable on the surface with hydrophobic grooves, and hence a higher energy barrier needs to be overcome for triggering the CB-to-W transition; on the contrary, the W state is more favorable on the surface with hydrophilic grooves, so that the CB-to-W transition is triggered more easily on such surface.

■ CONCLUSIONS In this work, the electric-field-induced CB-to-W transition is investigated via MD simulations. The simulations are implemented for a water film placed on the surface decorated with a single nanoscale groove at various surface charge densities, groove aspect ratios, and intrinsic contact angles of the groove. The free energy evolution is computed to explore the mechanism behind the CB-to-W transition. The main conclusions are as follows. 1) When there is no external electric field, the water film is in the CB state. When an external electric field with large enough strength is applied to the film, the water intrusion into the groove is observed until the groove is filled with water molecules, indicating the CB-to-W transition is triggered. In the previous experimental studies, only a sharp reduction in the apparent contact angle is employed as a criterion to judge the occurrence of the electric-field-induced CB-to-W transition, which may be inadequate, at least is doubtful. However, the present simulations provide a direct evidence for the CB-to-W transition. 20 ACS Paragon Plus Environment

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2) The free energy variation corresponding to the CB-to-W transition reveals that the free energy first continuously increases with time until it reaches a maximum value, subsequently the free energy starts to reduce and finally keeps a constant value. Owing to the presence of the energy barrier separating the CB and W states, although the CB state has a higher free energy, it cannot spontaneously convert to the W state. Thus, a large enough energy needs to be input to the water film to overcome this energy barrier. When the external energy input exceeds the energy barrier, the wetting transition will be triggered even if the electric field is removed, otherwise the transition will stop, and the water film will return to the CB state. 3) The dependence of the energy barrier separating the CB and W state on the electric field strength, groove aspect ratio, and intrinsic contact angle of the groove are also discussed. The results show that the energy barrier increases as increasing the aspect ratio and intrinsic contact angle; thus, a stronger electric field is required to make the film touch the groove bottom for triggering the CBto-W transition. Therefore, a more stable CB state can be remained for the groove with a larger aspect ratio and/or a stronger hydrophobicity.

■ ASSOCIATED CONTENT Supporting Information The equilibrium contact angle of a water droplet on Au surfaces with different εO-Au; the morphology evolution of water film on the groove without surface charge or with surface change; the free energy variation of water films with various thicknesses.


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■ Acknowledgments This study was partially supported by the National Science Fund for Distinguished Young Scholars of China (No. 51525602), Science Fund for Creative Research Groups of the National Natural Science Foundation of China (No. 51821004), and the Fundamental Research Funds for the Central Universities (Nos. JB2018110 and 2017ZZD006).

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[9] Wenzel, R. N. Resistance of solid surfaces to wetting by water. Ind. Eng. Chem. 1936, 28, 988994. [10] Cassie, A. B. D. Contact angles. Discuss. Faraday Soc. 1948, 3, 11-16. [11] Giacomello, A.; Meloni, S.; Chinappi, M.; Casciola, C. M. Cassie-Baxter and Wenzel states on a nanostructured surface: Phase diagram, metastabilities, and transition mechanism by atomistic free energy calculations. Langmuir 2012, 28, 10764-10772. [12] Shahraz, A.; Borhan, A.; Fichthorn, K. A. Wetting on physically patterned solid surfaces: The relevance of molecular dynamics simulations to macroscopic systems. Langmuir 2013, 29, 1163211639. [13] Bormashenko, E. Progress in understanding wetting transitions on rough surfaces. Adv. Colloid Interface Sci. 2015, 222, 92-103. [14] Ren, W. Wetting transition on patterned surfaces: Transition states and energy barriers. Langmuir 2014, 30, 2879-2885. [15] Tsai, P.; Lammertink, R. G. H.; Wessling, M.; Lohse, D. Evaporation-triggered wetting transition for water droplets upon hydrophobic microstructures. Phys. Rev. Lett. 2010, 104, 116102. [16] Bartolo, D.; Bouamrirene, F.; Verneuil, E.; Buguin, A.; Silberzan, P.; Moulinet, S. Bouncing or sticky droplets: Impalement transitions on superhydrophobic micropatterned surfaces. Europhys. Lett. 2006, 74, 299-305. [17] Yoshimitsu, Z.; Nakajima, A.; Watanabe, T.; Hashimoto, K. Effects of surface structure on the hydrophobicity and sliding behavior of water droplets. Langmuir 2002, 18, 5818-5822. [18] Bormashenko, E.; Pogreb, R.; Whyman, G.; Bormashenko, Y.; Erlich, M. Vibration-induced Cassie-Wenzel wetting transition on rough surfaces. Appl. Phys. Lett. 2007, 90, 457-458. 23 ACS Paragon Plus Environment

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[19] Krupenkin, T. N.; Taylor, J. A.; Schneider, T. M.; Yang, S. From rolling ball to complete wetting: The dynamic tuning of liquids on nanostructured surfaces. Langmuir 2004. 20, 3824-3827. [20] Verplanck, N.; Galopin, E.; Camart, J. C.; Thomy, V. Reversible electrowetting on superhydrophobic silicon nanowires. Nano lett. 2007, 7, 813-817. [21] McHale, G.; Herbertson, D. L.; Elliott, S. J.; And N. J. S.; Newton, M. I. Electrowetting of nonwetting liquids and liquid marbles. Langmuir 2007, 23, 918-924. [22] Ahuja, A.; Taylor, J. A.; Lifton, V.; Sidorenko, A.; Salamon, T. R.; Lobaton, E. J.; Kolodner, P.; Krupenkin, T. N. Nanonails: A simple geometrical approach to electrically tunable superlyophobic surfaces. Langmuir 2008, 24, 9-14. [23] Bahadur, V.; Garimella, S. V. Electrowetting-based control of droplet transition and morphology on artificially microstructured surfaces. Langmuir 2008, 24, 8338-8345. [24] Kakade, B.; Mehta, R.; Durge, A.; Kulkarni, S.; Pillai, V. Electric field induced, superhydrophobic to superhydrophilic switching in multiwalled carbon nanotube papers. Nano Lett. 2008, 8, 2693-2696. [25] Brunet, P.; Lapierre, F.; Thomy, V.; Coffinier, Y.; Boukherroub, R. Extreme resistance of superhydrophobic

surfaces

to

impalement:

Reversible

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related

to

the

impacting/bouncing drop test. Langmuir 2008, 24, 11203-11208. [26] Vrancken, R. J.; Kusumaatmaja, H.; Hermans, K.; Prenen, A. M.; Olivier Pierre, L. O.; Bastiaansen, C. W. M.; Broer, D. J. Fully reversible transition from Wenzel to Cassie-Baxter states on corrugated superhydrophobic surfaces. Langmuir 2009, 26, 3335-3341.


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[27] Han, Z.; Tay, B.; Tan, C.; Shakerzadeh, M.; Ostrikov, K. Electrowetting control of Cassie-toWenzel transitions in superhydrophobic carbon nanotube-based nanocomposites. ACS Nano. 2009, 3, 3031-3036. [28] Lapierre, F.; Thomy, V.; Coffinier, Y.; Blossey, R.; Boukherroub, R. Reversible electrowetting on superhydrophobic double-nanotextured surfaces. Langmuir 2009, 25, 6551-6558. [29] Manukyan, G.; Oh, J. M.; Ende, V. D. D.; Lammertink, R. G. H.; Mugele, F. Electrical switching of wetting states on superhydrophobic surfaces: A route towards reversible Cassie-to-Wenzel transitions. Phys. Rev. Lett. 2011, 106, 014501-1-014501-4. [30] Bormashenko, E.; Pogreb, R.; Balter, S.; Aurbach, D. Electrically controlled membranes exploiting Cassie-Wenzel wetting transitions. Sci. Rep. 2013, 3, 3028-3024. [31] Laird, E. D.; Bose, R. K.; Qi, H.; Lau, K. K. S.; Li, C. Y.; Electric field-induced, reversible lotusto-rose transition in nanohybrid shish kebab paper with hierarchical roughness. ACS Appl. Mater. Interfaces 2013, 5, 12089-12098. [32] Varilly, P.; Chandler, D. Water evaporation: A transition path sampling study. J. Phys. Chem. B 2013, 117, 1419-1428. [33] Daw, M. S.; Baskes, M. I. Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in Metals. Phys. Rev. B 1984, 29, 6443-6453. [34] Foiles, S.M,; Baskes, M. I.; Daw, M. S. Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys. Rev. B 1986, 33, 7983-7991. [35] Wang, B. B.; Wang, X. D.; Wang, T. H.; Lu, G.; Yan, W. M. Enhancement of boiling heat transfer of thin water film on an electrified solid surface. Int. J. Heat Mass Transf. 2017, 109, 410416. 25 ACS Paragon Plus Environment

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[36] Wang, X. D.; Peng, X. F.; Wang, B. X. Contact angle hysteresis and hysteresis tension on rough solid surface. Chinese J. Chem. Eng. 2004, 12, 615-621. [37] Gao, L.; McCarthy, T. J. Contact angle hysteresis explained. Langmuir 2006, 22, 6234-6237 [38] Amabili, M; Giacomello, A; Meloni, S; Casciola, C. M. Intrusion and extrusion of a liquid on nanostructured surfaces. J. Phys. Condens. Mat. 2016, 29, 014003. [39] Kirkwood, J. G. Statistical mechanics of fluid mixtures. J. Chem. Phys. 1935, 3, 300-313. [40] Bonomi, M.; Branduardi, D.; Bussi, G. PLUMED: A portable plugin for free-energy calculations with molecular dynamics. Comput. Phys. Commun. 2009, 180, 1961-1972. [41] Alberti, G.; De Simone, A. Wetting of rough surfaces: A homogenization approach. Proc. R. Soc. London, Ser. A 2005, 461, 79-97. [42] Lobaton, E. J.; Salamon, T. R. Computation of constant mean curvature surfaces: Application to the gas-liquid interface of a pressurized fluid on a superhydrophobic surface. Adv. Colloid Interface Sci. 2007, 314, 184-198. [43] Marmur, A. From hygrophilic to superhygrophobic: theoretical conditions for making highcontact-angle surfaces from low-contact-angle materials. Langmuir 2008, 24, 7573-7579. [44] Lee, S. M.; Kwon, T. H. Mass-producible replication of highly hydrophobic surfaces from plant leaves. Nanotechnology 2006, 17, 3189-3196. [45] Patankar, N. A. Transition between superhydrophobic states on rough surfaces. Langmuir 2004, 20, 7097-7102. [46] Pashos, G.; Kokkoris, G.; Boudouvis A. G. Minimum energy paths of wetting transition on grooved surfaces. Langmuir 2010, 26, 8941-8945.


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[47] Yuan, Q.; Zhao, Y. P. Statics and dynamics of electrowetting on pillar-arrayed surfaces at the nanoscale. Nanoscale 2015, 7, 2561-2567. [48] Bhushan, B.; Jung, Y. C. Wetting study of patterned surfaces for superhydrophobicity. Ultramicroscopy 2007, 107,1033-1041. [49] Savoy, E. S.; Escobedo, F. A. Simulation study of free-energy barriers in the wetting transition of an oily fluid on a rough surface with reentrant geometry. Langmuir 2012, 28, 16080-16090. [50] Koishi, T.; Yasuoka, K.; Fujikawa, S.; et al. Coexistence and transition between Cassie and Wenzel state on pillared hydrophobic surface. Proc. Natl. Acad. Sci. U. S. A. 2009, 106,8435-8440. [51] Kusumaatmaja, H.; Blow, M. L.; Dupuis, A.; Yeomans, J. M. The collapse transition on superhydrophobic surfaces. Europhys. Lett. 2008, 81, 36003.


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Table and Figure Captions

Table 1. Summarization of experimental studies on the wetting transition triggered by an external electric field. Table 2. Values of potential parameters. Figure 1. Initial configuration of the simulated system. Figure 2. The morphology evolution of water film on the groove (a) without surface charge and (b) with surface change. Figure 3. The morphology evolution of water film on the grooves with various surface charge densities: (a) qe=0.003 C m-2; (b) qe=0.01 C m-2; (c) qe=0.02 C m-2. Figure 4. The free energy variation of water film on the grooves with various surface charge densities: (a) qe=0.003 C m-2; (b) qe=0.01 C m-2; (c) qe=0.02 C m-2. Figure 5. The morphology evolution of water film from three different wetting states after the external electric filed is remove. Figure 6. The effect of charge density on the free energy of water film. Figure 7. The effect of groove aspect ratio on the free energy of water film. Figure 8. The effect of groove intrinsic contact angle on the free energy of water film.


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Table 1. Summarization of experimental studies on the wetting transition triggered by an external electric field. Author

Year

Fluids

Structure

Voltage

Contact Angle

Krupenkin et al. [19]

2004

water/methanol-water

silicon posts

20-50 V

80º-110º

Verplanck et al. [20]

2007

water

nanowires

0-150 V

137º-160º

Mchale et al. [21]

2007

water

PTFE

0-100 V

110º-150º

Ahuja et al. [22]

2008

water/ethanol-water

nanowires

0-90 V

66º-134º

Bahadur et al. [23]

2008

water

silicon pillars

0-100 V

40º-120º

Kakade et al. [24]

2008

water

MWCNTS

0-50 V

20º-160º

Brunet et al. [25]

2008

water

nanowires

10-135 V

80º-160º

Vrancken et al. [26]

2009

water

SU-8 grooves

0-150 V

60º-110º

Han et al. [27]

2009

water/NaCl-water

carbon nanotube 18V-43 V

104º-142º

Lapierre et al. [28]

2009

water

nanowires

0-190 V

137º-155º

Manukyan et al. [29]

2011

water

SU-8 grooves

0-250 V

110º-150º

Bormashenko et al. [30]

2013

ethanol-water

PC membrane

0-42 V

68º-81º

Laird et al. [31]

2013

PTFE+CNT

wafer

0-119 V

95º-154º


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Table 2. Values of potential parameters. Particles

σi,j (Å)

εi,j (eV)

q (e)

O-O

3.1660

0.0068

-0.8476

H-H

0.0000

0.0000

+0.4238

O-H

0.0000

0.0000

—

O-Au (1)

2.8675

0.0554

—

85.6

O-Au (2)

2.8675

0.0114

—

116.9

H-Au (1) (2)

0.0000

0.0000

—


θ (º)

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h w

y x

z 9.792nm

1.632nm

Figure 1. Initial configuration of the simulated system.


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(a)

(b) 0 ps

24 ps

34 ps

70 ps

122 ps

180 ps

313 ps

1000 ps

Figure 2. The morphology evolution of water film on the groove (a) without surface charge and (b) with surface change.


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(a)

(b)

(c) 34 ps

85 ps

122 ps

150 ps

200 ps

400 ps

600 ps

1000 ps

Figure 3. The morphology evolution of water film on the grooves with various surface charge densities: (a) qe=0.003 C m-2; (b) qe=0.01 C m-2; (c) qe=0.02 C m-2.


Langmuir

(a)

-16400

-2

qe=0.003 C m

F/kBT

-16600 -16800 -17000 -17200 -17400 0

200

400

600

800

t (ps)

(b)

-16400

1000

q e=0.01 C m -2

F /k B T

-16600 -16800 -17000 -17200 -17400 0

200

(c)

-16600

(1)

400

600

800

t (ps)

1000

q e=0.02 C m -2

(2)

-16800

F /k B T

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

Page 34 of 39

E1

(3)

-17000

E2

-17200 -17400 0

200

400

600

t (ps)

800

1000

Figure 4. The free energy variation of water film on the grooves with various surface charge densities: (a) qe=0.003 C m-2; (b) qe=0.01 C m-2; (c) qe=0.02 C m-2. 34 ACS Paragon Plus Environment

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

Langmuir

(a)

(b)

(c) 0 ps

19 ps

42 ps

64 ps

155 ps

166 ps

470 ps

1000 ps

Figure 5. The morphology evolution of water film from three different wetting states after the external electric filed is remove.


Langmuir

q e=0.02 C m -2

-16600

q e=0.015 C m -2

E1

-16800

F /K B T

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

Page 36 of 39

E2

-17000 -17200 -17400 0

200

400

600

t (ps)

800

1000

Figure 6. The effect of charge density on the free energy of water film.


Page 37 of 39

-16600

E1=464

-16800

F /k B T

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

Langmuir

E1=348

h/w=0.5 h/w=0.75 h/w=1

-17000

E1=232

-17200 -17400 0

200

400

600

t (ps)

800

1000

Figure 7. The effect of groove aspect ratio on the free energy of water film.


Langmuir

-16600 E 1,pho E2,pho

-16800

F /k B T

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

Page 38 of 39

 

-17000 E1,phi

-17200

E2,phi

-17400 0

200

400

600

t (ps)

800

1000

Figure 8. The effect of groove intrinsic contact angle on the free energy of water film.


Page 39 of 39

For Table of Contents Use Only -16600

F/kBT

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

Langmuir

(1)

(2)

-16800

E1

(3)

-17000

E2

-17200 -17400 0

200

400

600

t (ps)

800


1000

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