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Coalescence of water films on carbon-based substrates: the role of the interfacial properties and anisotropic surface topography Hongru Ren, Xiongying Li, Hui Li,* Leining Zhang and Weikang Wu Molecular dynamics (MD) simulations are carried out to study the coalescence of identical adjacent and nonadjacent water films on graphene (G), vertically or horizontally stacked carbon nanotube arrays (VCNTA and HCNTA respectively). We highlight the key importance of carbon-based substrates in the growth of the liquid bridge connecting the two water films. This simulation provides reliable evidence to confirm a linear increase of the liquid bridge height, which is sensitive to the surface properties and the
Received 28th December 2014, Accepted 24th March 2015
geometric structure. In the case of nonadjacent water films, the meniscus liquid bridge occurs solely on
DOI: 10.1039/c4cp06081d
provide an available method to tune the coalescence of adjacent or nonadjacent films with alteration
the VCNTA, which is attributed to the spreading of water films driven by the capillary force. Our results of topographically patterned surfaces, which has important implications in the design of condensation,
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ink-jet printing and drop manipulation on a substrate.
1. Introduction Coalescence is a key phenomenon in varieties of natural processes such as raindrop growth, cloud formation, and thunderstorm development,1,2 as so far it has attracted considerable attention of the atmospheric science community. Coalescence is also of great interest in the technological processes involving sprays, inkjet printing,3,4 filtration,5 emulsions6 and dispersions of drops.7 In regard to spray painting and coating, the extent of coalescence plays a vital role in determining the properties of solid coating.8 Furthermore, in microfluidic devices, controlling the coalescence of liquid drops provides a multitude of potential applications in chemistry, physics and materials science.9 Several experimental and theoretical studies have been performed to research drop coalescence in viscous or low-viscosity liquid.10,11 In terms of adjacent drops on a substrate, numerous investigations have been focused on the effect of the droplet geometry or the surface tension gradient on the dynamics of the liquid bridge between droplets.12,13 Coalescence occurring between films placed on solid substrates, however, might differ thoroughly from the coalescence of two free or sessile drops. Generally, there are two stages during the coalescence process on substrates: one is the rapid expansion of the meniscus neck between the contracting thin films, and the other is the change in the combined film shape from elliptical to more circular for a Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials, Ministry of Education, Shandong University, Jinan 250061, People’s Republic of China. E-mail: [email protected]
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long time. Noteworthy is that the dynamics of the first stage is essential for industrial and biochemical processes, such as solidification owing to cooling and liquid imbibition on plant foliage.14,15 To date, some effort has been devoted to study thinfilm coalescence on a wettable substrate at the early-time stage.16 These results reveal that the width of the liquid bridge between two droplets presents power-law behavior, obeying the scaling law with exponent 1/2. However, once water films are located on some hydrophobic substrates,17 films tend to contract and eventually convert into a droplet after a long time. The coalescence behavior of water films at the early time under this circumstance is still obscure. Furthermore, whether and how the wettability of substrate influences the coalescence of two droplets has remained unanswered until now. Carbon-based substrates with outstanding intrinsic properties, especially graphene and carbon nanotubes (CNTs) with promising applications in some practical fields, have captivated much attention for their theoretical and experimental studies.18–20 In recent years, the aligned carbon nanotubes (ACNTs) have created broad scientific interest as some studies have revealed a novel strategy to control the surface wettability by tuning the surface structure without altering the chemical composition.21 Moreover, aligned arrays with carbon tubes parallel to the surface can contribute to anisotropic wetting behavior which is universal in the natural world. To date, there is great interest in exploring the interaction of water with carbon materials, coming from a desire to investigate the phase behavior of water at nanoscale and the function of carbon nanotubes in biological media.22,23 The water–carbon interaction is also important in
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nanoscale hydrophobic objects immersed in aqueous solutions,24,25 which directly influences some of the interfacial properties, such as carrier mobility,26 adhesion27 and wetting.28 In spite of intense research on water–carbon nanotubes, the performance of water films on horizontally placed carbon nanotubes (HCNTs) with a geometrically anisotropic wrinkled surface has rarely been discussed. Herein we report a study to explore the relevance of coalescence behavior and a substrate at nanoscale, and further discover how to regulate the coalescence dynamics by tuning the surface properties.
2. Methods and modeling In this paper, MD simulations are performed to investigate the coalescence of identical water films on graphene (G), horizontally or vertically stacked CNT arrays, denoted as HCNTA and VCNTA, respectively (as shown in Fig. 1). The adjacent water films with 8754 molecules are placed above the carbon-based substrate. The diameter and the thickness of the water film are 135.6 Å and 10 Å, respectively. The periodic boundary conditions are applied in all spatial directions, and the size of the simulation box is 32 18 20 nm3. The MD simulations are performed using the large-scale atomic/molecular massively parallel simulator (LAMMPS) package29,30 in the constant-volume and constant-temperature (NVT) ensemble, where the temperature is held at 300 K, controlled by a Nose–Hoover thermostat. The water model in this study is the four-point TIP4P31 rigid model consisting of a long-range Coulombic potential which is calculated by Hockney’s particle–particle and particle–mesh (PPPM)32 method. The O–H bond and the H–O–H angle are constrained using the SHAKE algorithm.33 The interaction among carbon atoms is modeled by the adaptive intermolecular reactive empirical bond order (AIREBO) potential,34 and the water–carbon interaction is described by the 12-6 Lennard-Jones (LJ) potential with parameters sCO = 3.19 Å and eCO = 0.4389 kJ mol1 and sCH = 0 Å, eCH = 0 kJ mol1 (these parameters have been applied to calculate the water–carbon interaction for the water–graphite system by Werder35). The global LJ cutoff radius and the Coulombic cutoff radius are 10 Å and 12 Å, respectively. The water molecules also interact via the LJ potential
Fig. 1 Schematic plot of the simulated system. The adjacent water films located on the graphene (G), horizontally and vertically stacked carbon nanotubes array (HCNTA and VCNTA respectively) surfaces. The diameter and height of films are defined as D = 135.6 Å and H = 10 Å respectively, and the interval between carbon nanotubes is 3.4 Å (for both VCNTA and HCNTA surfaces). Color code for elements: O, red; H, white; C, gray.
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with sOO = 3.16435 Å and eOO = 0.16275 kJ mol1. The velocity Verlet algorithm36 with a time step of 1.0 fs is chosen to calculate the time integration of Newton’s equation of motion. To improve the computational efficiency, the substrates are fixed during the simulation process. The water density and hydrogen bond distribution profiles are important to describe the structure of water in the interfacial region. To achieve this goal, the water films are divided into many slabs with a thickness of 0.2 Å along the z direction. We define two water molecules to be hydrogen-bonded by a geometrical criterion37 if the distance between oxygen atoms of water molecules is less or equal to 3.5 Å; furthermore, the bond angle between the O–O direction and the O–H bond of the donor is less than 301.
3. Results and discussion The typical early-time coalescence evolution of identical water films on graphene and CNT arrays is presented in Fig. 2. It is apparent that upon contact, the meniscus bridge between two films expands rapidly in the direction perpendicular to the center lines of the films. As simulation progresses, the two films develop a tendency to coalesce and ultimately combine into one elliptical droplet. Given enough time, the merged elliptical droplet changes into a circular form with a smaller surface area. It must be pointed out that Werder35 has demonstrated that generally once the calculation starts, the water films on graphite contract and then gradually convert into a water drop with a hemispherical configuration after hundreds of picoseconds. Here, we focus on the initial rapid growth of the meniscus bridge between the adjacent films in the first 150 ps. During this period of time, the water films gradually contract and the structure of water films is more like spreading droplets; Ristenpart16 referred to the coalescence of spreading droplets and thought the coalescence of this water structure is just like thin-film coalescence. So we think that during the first time period, the water films still keep their initial form. Considering that water is a low-viscosity liquid, which means that the viscous force can be negligible, a fully inertial regime is applied to describe masses of the dynamics. The driving forces of coalescence can be understood from a balance between surface tension and inertia, which is characterized by the liquid density. On one side, when the liquid interface is curved, the surface tension gives rise to a pressure jump, which induces the capillary pressure (or Laplace pressure). According to the Young–Laplace g equation, the driving pressure is given by Pcap , where Pcap is r the pressure differential across the liquid interface, g is the surface tension, and r is the principal radius of curvature of the liquid bridge surface. On the other side, the rapid liquid flow into the meniscus bridge is attributed to the capillary pressure, yielding a dynamical pressure Piner which is related to the fluid velocity. The scaling law for the bridge expansion with exponent 1/2 or 2/3 on partially wettable substrates has been observed by means of balancing these two pressures.12 To elucidate the growth dynamics of the liquid bridge placed on carbon-based substrates, we plot the height–time curves as
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Fig. 2 Top view of two coalescing water films in contact with three types of substrates. The time periods from the initial of the process are presented in the image in terms of G and HCNTA surfaces. The CNTs with the diameter of 13.56 Å are applied for the CNT array.
shown in Fig. 3(a). The liquid bridge height for the HCNTA or VCNTA substrate is calculated from the top of the surface roughness. It is clear that the height of the liquid bridge displays a linear increasing tendency with simulation time, h0 B t, for all three substrates, additionally, at any given time after 30 ps, the value of height on G is the largest, followed by the one on the HCNTA, implying that the increase in the liquid bridge height on G is higher than that on CNT arrays. Fig. 3(b) presents the evolution of the bridge width as a function of time. The results illustrate that the width of the liquid bridge has a rapid nearly-linear increasing trend with the simulation time on G and HCNTA substrates, whereas on the VCNTA, the width changes slightly over time with small oscillations. The above comparisons of the bridge size-change reveal that the neighboring water films coalesce much faster on the HCNTA than on the VCNTA substrate, indicating that the coalescence rate sensitively depends on the anisotropic surface topography. In order to study the power-law, the width is scaled by the initial radius R of the water film, and time rescaled as the characteristic pffiffiffiffiffiffiffiffiffiffiffiffiffiffi time t, which is defined as t ¼ rR3 =s, where r is the density of water and s is the surface tension of 72 mN m1. The data as displayed in Fig. 3(c) reveal that the expanding liquid bridge obeys the scaling law, yielding the exponents 0.530 and 0.548 for water–G and water–HCNTA systems, respectively, which are close to the proposed exponent 1/2. However, there is a non-linear relationship between the dimensionless width and scaling time when water films are located on VCNTA substrate, suggesting that the power-law scaling is not applicative for the growth of the liquid bridge for the water–VCNTA system. To analyze the structure of the water film on graphene or CNT arrays, we calculate the water density and hydrogen bond distributions along the vertical direction to the surface. The computed average water density profiles are depicted in Fig. 4(a). In the vicinity of the substrate, the mass–density distribution changes remarkably owing to the presence of carbon-based substrates. Obviously, two relatively intense density peaks at equilibrium distances of 3.2 Å and 6.2 Å, respectively, can be observed on the curves for three systems, which is well
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consistent with the result from Werder.35 Based on this finding, we can assuredly validate that configurations of water near G or CNT arrays are ordered, which are ascribed to the two water layers formed close to the surface. Additionally, it is worth noting that the value of the first peak is 2.4 on the G surface, whereas the peak gets higher on CNT array substrates, indicating that a much more ordered and structured first water layer is organized on the CNT array surfaces. The hydrogen bond (HB) distribution along the z direction is shown in Fig. 4(b). It is clear that more than 10 Å away from the surface, per water molecule has an average number of hydrogen bonds of 3.66, which is observed to mutually agree with the previous MD simulation value of 3.7035 and is close to the experimental value of 3.90.38 Intriguingly, near the substrate, two relatively intense density peaks exist in the HB density curves and the first minimum can be identified at the distance of 6.2 Å for the water–G system. To make sense of this peak diversity in the water density curves, we have calculated the carbon–oxygen interaction energy as shown in Fig. 4(c). Apparently, the interaction strength between water and the substrate on the G surface is weaker than that on CNT arrays, which results in the lower peak. While the water–water interaction strength is stronger for the water–G system than the water–CNT group as presented in Fig. 4(d). From the above-mentioned facts, we can conclude that in the direction perpendicular to the substrate, the organization of water close to the surface is primarily dominated by the carbon–oxygen interaction, restricting the water molecules in the ordered-layer structure. The diffusivity of water molecules, considered as one of the physical characteristics to describe the behavior of water at the substrate, is further explored by the mean square displacement (MSD). Fig. 5 displays the MSD curves along the z (left) and x directions (right). Comparing the diffusivity of water molecules in the two directions, we can find that on the same substrate, the diffusion speed in the x-direction is much higher than that in the z-direction, suggesting that the ordered structure layer near the substrate significantly goes against the diffusion of water molecules along the z direction. Furthermore, a striking discovery from Fig. 5(a) is that the diffusion speed of water
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Fig. 3 Coalescence of adjacent films. (a) The height of liquid bridge h0, (b) and its width d0 as a function of simulation time of threeptypes ffiffiffiffiffiffiffiffiffiffiffiffiffiffi of substrates. (c) Width of the meniscus bridge vs. t/t, where t ¼ rR3 =s is the dimensionless time. The dashed lines are fitting data points. The insets present the geometry of water films from front and top views and define the meniscus height h0 and width d0.
molecules perpendicular to the G substrate is the highest, followed by the HCNTA. Notably, the order of the diffusion speed agrees well with the order of the increasing rate of the liquid bridge height, intensely implying the higher peak value in the density distribution curve, the lower diffusion speed of the water molecules along the z direction, and then the lower height increasing rate of the meniscus bridge. In the direction of the x axis, for water–G and water–HCNTA systems, there is no distinct difference in the diffusion speed between these two groups. It is worth noting that in general, the diffusion speed of
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water molecules on the nanotube should be different from that on the graphene due to the curvature effect. This influence can be observed in the local region however we calculate the MSD of all the molecules in the water group. As a result, it is reasonable that there is no distinct difference in the diffusion speed between water–G and water–HCNTA systems on the whole along the x direction. However, in terms of the VCNTA substrate, the diffusivity of water molecules is much lower than that on G and HCNTA substrates. This result provides further evidence of the smallest growth rate of the liquid bridge on the VCNTA substrate, leading to the longest time to complete the early-stage coalescence. Extensive simulations are performed to investigate the effect of surface wettability on the coalescence dynamics of adjacent films on CNT arrays. Diameters of CNTs are chosen as 16.27 Å, 18.98 Å and 21.7 Å, respectively, which are arranged at a fixed interval of 3.4 Å. The contact angle (WCA) of water, which is predominantly employed to characterize the surface wetting properties, is measured. In addition, a detailed description of the measurement of y can be observed in Fig. 6(a), by plotting the liquid/air interface contour. It was found that water has apparent equilibrium WCAs of 61.541, 70.511 and 80.471 for three HCNTA substrates. Due to the wetting anisotropy when water films are placed on CNT arrays, the contact angles referred here are examined in the axial direction of CNTs. From Fig. 6(b), it is obvious that the height of the liquid bridge has a linear increasing tendency with simulation time; moreover, on the rough surface with the smallest WCA, the height is much lower than the others. The inset graph in Fig. 6(b) quantitatively exhibits that the average growth velocity of the liquid bridge height increases monotonously with the increasing WCA. Additionally, the growth speed reaches the maximum sharply when the WCA increases to 80.471, implying that, for a drop with the WCA of less than 901, the expansion rate of the meniscus bridge is sensitive to the surface wettability, and the roughness surface with a large WCA is quite beneficial for enhancing the coalescence rate. To answer the question of why the water films behave so differently on VCNTA and HCNTA substrates, it is necessary to study the effect of the surface structure on the coalescence dynamics of neighboring films. Noteworthy is that the surface of the CNT array presents a sinusoidally wrinkled and grooved surface with the anisotropic texture which induces the diversity of the flow velocity in different directions. Fig. 7(b) shows that the three-phase contact line of the water film placed on the CNT array with a wrinkled surface explicitly presents an elliptic shape, deviating from a circular form on the G substrate in Fig. 7(a). This result implies that the surface geometric anisotropy plays a key role in the movement of the contact line, permitting the water film to preferentially flow perpendicular instead of parallel to the groove. This phenomenon appears to contradict the existing viewpoint that the movement of liquid perpendicular to grooves is less than that along the parallel direction, since the grooves are proposed to act as obstacles to contact-line motion, which could induce pinning. This anomalous phenomenon is explained in Fig. 7(c). It is obvious that a
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Fig. 4 Interface properties. (a) Water density distribution along the z direction perpendicular to the surface. The graphene or the top layer carbon atoms of the CNT array is placed at the plane where z = 0. The equilibrium distance of the first ordered layer and the peak value for the G surface are marked. (b) Average hydrogen bond distribution profile normal to the surface. (c) The variation of water–substrate interaction energy EW–S versus time. (d) The interaction energy between water and water molecules EW–W as a function of time.
Fig. 5
Mean square displacements (MSDs) of water molecules on G and CNTs array along (a) z direction and (b) x direction.
wave-shaped contact line appears in the direction parallel to the groove; intriguingly, this local wave feature very much resembles the sinusoidally wrinkled pattern which is observed to mutually agree well with the experimental result.39 This local pinning derives from the inhibition effect of CNTs, when the liquid moves at the top of the surface roughness, the motion of the contact-line is mainly hindered by the interactions between water and CNTs, besides this, a degree of physical adsorption due to the high specific surface of CNTs also contributes to the pinning of the contact-line. From the above-mentioned results, we can speculate that the resulting restraint of the groove is possibly relatively small compared with the local pinning at the crest of the surface feature in our simulation system, eventually enhancing the priority of the movement of the contact line perpendicular to the groove. To some extent, for the water–VCNTA
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system, the local pinning at the crest of the sinusoidal pattern confines the movement of the contact-line along the groove and then further decreases the growth rate of the bridge width. In the previous section, we mainly research how the interfacial properties and the anisotropic surface pattern influence the coalescence rate of adjacent water films located on G and CNT arrays. Next we will reveal the role of the underlying substrate on the coalescence behavior of nonadjacent water films, which are separated at a certain distance of 1 Å. As can be noted in Fig. 8(c), coalescence only occurs on the VCNTA, whereas when placed on the G substrate, it is obvious that the water films are strongly inclined to contract due to surface tension. As the process proceeds, the films gradually change into a hemispherical shape apart from each other as shown in Fig. 8(a). The similar noncoalescence behavior is also observed
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the groove has also attracted our attention, which plays a pivotal part in facilitating the contact of isolated water films. When the contact line moves in the direction perpendicular to the groove, water molecules can permeate into the grooves in a system denoted as the Wenzel regime,40 where the grooves are filled by liquid, and then the coalescence behavior is achieved owing to the advance of the contact line, actuated by the capillary force which is originated from the penetrating liquid. This hypothesis is verified by Fig. 8(d). From the comparison of front view profiles at different times before coalescence, it is clear that the curved liquid surface (near the top) experiences Laplace pressure oriented towards the centre of curvature which is believed to impel the contact line past the wave crest. As this process proceeds progressively across time, an obvious contact point as marked in Fig. 8(d) is produced between water films at a simulation time of up to 36 ps, triggering the formation of a thin liquid bridge, which plays an essential role in the subsequent coalescence process. Based on this finding, we can identify the key factor to determine whether the coalescence of nonadjacent films could occur, which is prevailingly attributed to the initial advance of the contact line.
4. Conclusion Fig. 6 (a) Illustration of the contact angle (y) measurement by plotting the liquid/air interface contour, the red curve marks the fitting interface of the water droplet. y is denoted as the angle between a tangential line of the droplet surface and another line within the substrate. The WCAs are averaged over five measurements. (b) The height of the liquid bridge as a function of time on the HCNTA with various equilibrium contact angles of 61.541, 70.511 and 80.471. And the inserted graph is the average increasing velocity of bridge height n with respect to WCA.
for the water–HCNTA system. Specifically, in this case, the local pinning at the top of surface roughness plays a dominant role in hindering the movement of the contact line along the x-direction and further holds back the contact of two films. To find out the source to generate coalescence behavior in contact with the VCNTA substrate, we have further examined the initial spreading of water films before contact. Apart from the impeditive effect of the groove on the movement of the contact line perpendicular to the axial direction of CNTs, another function of
The coalescence behavior of water films on the carbon-based substrate is affected by both the interfacial properties and the anisotropic surface pattern. The growth of the liquid bridge width can be roughly described by the scaling law, h0 B t1/2, when water films are located on G and HCNTA substrate during the early-time coalescence. There is no doubt that interactions between water and the substrate restrict water molecules in the ordered-layer and further generate changes in the first layer peak. Additionally, the lower diffusion speed of water molecules in the direction perpendicular to the surface arising from the relatively ordered water layer on the CNT array is responsible for the lower coalescence rate. The significant local pinning at the crest of surface roughness, which allows the preferential flow perpendicular to the groove, can significantly produce a variability of the growth rate between HCNTA and VCNTA substrates. Aside from this, the advancing contact line driven by the penetrating liquid urges the occurrence of the contact point of nonadjacent films placed on the VCNTA. These discoveries can
Fig. 7 Top view of water films on flat and wrinkled surfaces. (a) Image of the water film on the G substrate, revealing a circular shape. (b) Snapshot of isolated water on the CNT array, showing an elliptic form. (c) Water film presents pining of the contact line at the crest of surface roughness.
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Fig. 8 Performance of nonadjacent water films. (a and b) Images of isolated water films 1 Å apart from each other on G and HCNTA surfaces. (c) Coalescence process occurred on the VCNTA surface with a rapid expansion of the liquid bridge. (d) Side image of water profiles at different time periods before contact. The inset circle marks the contact point.
provide a better insight into the relevance between coalescence and interfacial properties or structure and aid in the development of an effective method for controlling the coalescence dynamics of water films.
Acknowledgements The authors would like to acknowledge the support from the National Natural Science Foundation of China (Grant No. 51271100). This work is also supported by the National Basic Research Program of China (Grant No. 2012CB825702). This work is also supported by the Special Funding in the Project of the Taishan Scholar Construction Engineering.
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Coalescence of water films on carbon-based substrates: the role of the interfacial properties and anisotropic surface topography Hongru Ren, Xiongying Li, Hui Li,* Leining Zhang and Weikang Wu Molecular dynamics (MD) simulations are carried out to study the coalescence of identical adjacent and nonadjacent water films on graphene (G), vertically or horizontally stacked carbon nanotube arrays (VCNTA and HCNTA respectively). We highlight the key importance of carbon-based substrates in the growth of the liquid bridge connecting the two water films. This simulation provides reliable evidence to confirm a linear increase of the liquid bridge height, which is sensitive to the surface properties and the
Received 28th December 2014, Accepted 24th March 2015
geometric structure. In the case of nonadjacent water films, the meniscus liquid bridge occurs solely on
DOI: 10.1039/c4cp06081d
provide an available method to tune the coalescence of adjacent or nonadjacent films with alteration
the VCNTA, which is attributed to the spreading of water films driven by the capillary force. Our results of topographically patterned surfaces, which has important implications in the design of condensation,
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ink-jet printing and drop manipulation on a substrate.
1. Introduction Coalescence is a key phenomenon in varieties of natural processes such as raindrop growth, cloud formation, and thunderstorm development,1,2 as so far it has attracted considerable attention of the atmospheric science community. Coalescence is also of great interest in the technological processes involving sprays, inkjet printing,3,4 filtration,5 emulsions6 and dispersions of drops.7 In regard to spray painting and coating, the extent of coalescence plays a vital role in determining the properties of solid coating.8 Furthermore, in microfluidic devices, controlling the coalescence of liquid drops provides a multitude of potential applications in chemistry, physics and materials science.9 Several experimental and theoretical studies have been performed to research drop coalescence in viscous or low-viscosity liquid.10,11 In terms of adjacent drops on a substrate, numerous investigations have been focused on the effect of the droplet geometry or the surface tension gradient on the dynamics of the liquid bridge between droplets.12,13 Coalescence occurring between films placed on solid substrates, however, might differ thoroughly from the coalescence of two free or sessile drops. Generally, there are two stages during the coalescence process on substrates: one is the rapid expansion of the meniscus neck between the contracting thin films, and the other is the change in the combined film shape from elliptical to more circular for a Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials, Ministry of Education, Shandong University, Jinan 250061, People’s Republic of China. E-mail: [email protected]
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long time. Noteworthy is that the dynamics of the first stage is essential for industrial and biochemical processes, such as solidification owing to cooling and liquid imbibition on plant foliage.14,15 To date, some effort has been devoted to study thinfilm coalescence on a wettable substrate at the early-time stage.16 These results reveal that the width of the liquid bridge between two droplets presents power-law behavior, obeying the scaling law with exponent 1/2. However, once water films are located on some hydrophobic substrates,17 films tend to contract and eventually convert into a droplet after a long time. The coalescence behavior of water films at the early time under this circumstance is still obscure. Furthermore, whether and how the wettability of substrate influences the coalescence of two droplets has remained unanswered until now. Carbon-based substrates with outstanding intrinsic properties, especially graphene and carbon nanotubes (CNTs) with promising applications in some practical fields, have captivated much attention for their theoretical and experimental studies.18–20 In recent years, the aligned carbon nanotubes (ACNTs) have created broad scientific interest as some studies have revealed a novel strategy to control the surface wettability by tuning the surface structure without altering the chemical composition.21 Moreover, aligned arrays with carbon tubes parallel to the surface can contribute to anisotropic wetting behavior which is universal in the natural world. To date, there is great interest in exploring the interaction of water with carbon materials, coming from a desire to investigate the phase behavior of water at nanoscale and the function of carbon nanotubes in biological media.22,23 The water–carbon interaction is also important in
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nanoscale hydrophobic objects immersed in aqueous solutions,24,25 which directly influences some of the interfacial properties, such as carrier mobility,26 adhesion27 and wetting.28 In spite of intense research on water–carbon nanotubes, the performance of water films on horizontally placed carbon nanotubes (HCNTs) with a geometrically anisotropic wrinkled surface has rarely been discussed. Herein we report a study to explore the relevance of coalescence behavior and a substrate at nanoscale, and further discover how to regulate the coalescence dynamics by tuning the surface properties.
2. Methods and modeling In this paper, MD simulations are performed to investigate the coalescence of identical water films on graphene (G), horizontally or vertically stacked CNT arrays, denoted as HCNTA and VCNTA, respectively (as shown in Fig. 1). The adjacent water films with 8754 molecules are placed above the carbon-based substrate. The diameter and the thickness of the water film are 135.6 Å and 10 Å, respectively. The periodic boundary conditions are applied in all spatial directions, and the size of the simulation box is 32 18 20 nm3. The MD simulations are performed using the large-scale atomic/molecular massively parallel simulator (LAMMPS) package29,30 in the constant-volume and constant-temperature (NVT) ensemble, where the temperature is held at 300 K, controlled by a Nose–Hoover thermostat. The water model in this study is the four-point TIP4P31 rigid model consisting of a long-range Coulombic potential which is calculated by Hockney’s particle–particle and particle–mesh (PPPM)32 method. The O–H bond and the H–O–H angle are constrained using the SHAKE algorithm.33 The interaction among carbon atoms is modeled by the adaptive intermolecular reactive empirical bond order (AIREBO) potential,34 and the water–carbon interaction is described by the 12-6 Lennard-Jones (LJ) potential with parameters sCO = 3.19 Å and eCO = 0.4389 kJ mol1 and sCH = 0 Å, eCH = 0 kJ mol1 (these parameters have been applied to calculate the water–carbon interaction for the water–graphite system by Werder35). The global LJ cutoff radius and the Coulombic cutoff radius are 10 Å and 12 Å, respectively. The water molecules also interact via the LJ potential
Fig. 1 Schematic plot of the simulated system. The adjacent water films located on the graphene (G), horizontally and vertically stacked carbon nanotubes array (HCNTA and VCNTA respectively) surfaces. The diameter and height of films are defined as D = 135.6 Å and H = 10 Å respectively, and the interval between carbon nanotubes is 3.4 Å (for both VCNTA and HCNTA surfaces). Color code for elements: O, red; H, white; C, gray.
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with sOO = 3.16435 Å and eOO = 0.16275 kJ mol1. The velocity Verlet algorithm36 with a time step of 1.0 fs is chosen to calculate the time integration of Newton’s equation of motion. To improve the computational efficiency, the substrates are fixed during the simulation process. The water density and hydrogen bond distribution profiles are important to describe the structure of water in the interfacial region. To achieve this goal, the water films are divided into many slabs with a thickness of 0.2 Å along the z direction. We define two water molecules to be hydrogen-bonded by a geometrical criterion37 if the distance between oxygen atoms of water molecules is less or equal to 3.5 Å; furthermore, the bond angle between the O–O direction and the O–H bond of the donor is less than 301.
3. Results and discussion The typical early-time coalescence evolution of identical water films on graphene and CNT arrays is presented in Fig. 2. It is apparent that upon contact, the meniscus bridge between two films expands rapidly in the direction perpendicular to the center lines of the films. As simulation progresses, the two films develop a tendency to coalesce and ultimately combine into one elliptical droplet. Given enough time, the merged elliptical droplet changes into a circular form with a smaller surface area. It must be pointed out that Werder35 has demonstrated that generally once the calculation starts, the water films on graphite contract and then gradually convert into a water drop with a hemispherical configuration after hundreds of picoseconds. Here, we focus on the initial rapid growth of the meniscus bridge between the adjacent films in the first 150 ps. During this period of time, the water films gradually contract and the structure of water films is more like spreading droplets; Ristenpart16 referred to the coalescence of spreading droplets and thought the coalescence of this water structure is just like thin-film coalescence. So we think that during the first time period, the water films still keep their initial form. Considering that water is a low-viscosity liquid, which means that the viscous force can be negligible, a fully inertial regime is applied to describe masses of the dynamics. The driving forces of coalescence can be understood from a balance between surface tension and inertia, which is characterized by the liquid density. On one side, when the liquid interface is curved, the surface tension gives rise to a pressure jump, which induces the capillary pressure (or Laplace pressure). According to the Young–Laplace g equation, the driving pressure is given by Pcap , where Pcap is r the pressure differential across the liquid interface, g is the surface tension, and r is the principal radius of curvature of the liquid bridge surface. On the other side, the rapid liquid flow into the meniscus bridge is attributed to the capillary pressure, yielding a dynamical pressure Piner which is related to the fluid velocity. The scaling law for the bridge expansion with exponent 1/2 or 2/3 on partially wettable substrates has been observed by means of balancing these two pressures.12 To elucidate the growth dynamics of the liquid bridge placed on carbon-based substrates, we plot the height–time curves as
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Fig. 2 Top view of two coalescing water films in contact with three types of substrates. The time periods from the initial of the process are presented in the image in terms of G and HCNTA surfaces. The CNTs with the diameter of 13.56 Å are applied for the CNT array.
shown in Fig. 3(a). The liquid bridge height for the HCNTA or VCNTA substrate is calculated from the top of the surface roughness. It is clear that the height of the liquid bridge displays a linear increasing tendency with simulation time, h0 B t, for all three substrates, additionally, at any given time after 30 ps, the value of height on G is the largest, followed by the one on the HCNTA, implying that the increase in the liquid bridge height on G is higher than that on CNT arrays. Fig. 3(b) presents the evolution of the bridge width as a function of time. The results illustrate that the width of the liquid bridge has a rapid nearly-linear increasing trend with the simulation time on G and HCNTA substrates, whereas on the VCNTA, the width changes slightly over time with small oscillations. The above comparisons of the bridge size-change reveal that the neighboring water films coalesce much faster on the HCNTA than on the VCNTA substrate, indicating that the coalescence rate sensitively depends on the anisotropic surface topography. In order to study the power-law, the width is scaled by the initial radius R of the water film, and time rescaled as the characteristic pffiffiffiffiffiffiffiffiffiffiffiffiffiffi time t, which is defined as t ¼ rR3 =s, where r is the density of water and s is the surface tension of 72 mN m1. The data as displayed in Fig. 3(c) reveal that the expanding liquid bridge obeys the scaling law, yielding the exponents 0.530 and 0.548 for water–G and water–HCNTA systems, respectively, which are close to the proposed exponent 1/2. However, there is a non-linear relationship between the dimensionless width and scaling time when water films are located on VCNTA substrate, suggesting that the power-law scaling is not applicative for the growth of the liquid bridge for the water–VCNTA system. To analyze the structure of the water film on graphene or CNT arrays, we calculate the water density and hydrogen bond distributions along the vertical direction to the surface. The computed average water density profiles are depicted in Fig. 4(a). In the vicinity of the substrate, the mass–density distribution changes remarkably owing to the presence of carbon-based substrates. Obviously, two relatively intense density peaks at equilibrium distances of 3.2 Å and 6.2 Å, respectively, can be observed on the curves for three systems, which is well
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consistent with the result from Werder.35 Based on this finding, we can assuredly validate that configurations of water near G or CNT arrays are ordered, which are ascribed to the two water layers formed close to the surface. Additionally, it is worth noting that the value of the first peak is 2.4 on the G surface, whereas the peak gets higher on CNT array substrates, indicating that a much more ordered and structured first water layer is organized on the CNT array surfaces. The hydrogen bond (HB) distribution along the z direction is shown in Fig. 4(b). It is clear that more than 10 Å away from the surface, per water molecule has an average number of hydrogen bonds of 3.66, which is observed to mutually agree with the previous MD simulation value of 3.7035 and is close to the experimental value of 3.90.38 Intriguingly, near the substrate, two relatively intense density peaks exist in the HB density curves and the first minimum can be identified at the distance of 6.2 Å for the water–G system. To make sense of this peak diversity in the water density curves, we have calculated the carbon–oxygen interaction energy as shown in Fig. 4(c). Apparently, the interaction strength between water and the substrate on the G surface is weaker than that on CNT arrays, which results in the lower peak. While the water–water interaction strength is stronger for the water–G system than the water–CNT group as presented in Fig. 4(d). From the above-mentioned facts, we can conclude that in the direction perpendicular to the substrate, the organization of water close to the surface is primarily dominated by the carbon–oxygen interaction, restricting the water molecules in the ordered-layer structure. The diffusivity of water molecules, considered as one of the physical characteristics to describe the behavior of water at the substrate, is further explored by the mean square displacement (MSD). Fig. 5 displays the MSD curves along the z (left) and x directions (right). Comparing the diffusivity of water molecules in the two directions, we can find that on the same substrate, the diffusion speed in the x-direction is much higher than that in the z-direction, suggesting that the ordered structure layer near the substrate significantly goes against the diffusion of water molecules along the z direction. Furthermore, a striking discovery from Fig. 5(a) is that the diffusion speed of water
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Fig. 3 Coalescence of adjacent films. (a) The height of liquid bridge h0, (b) and its width d0 as a function of simulation time of threeptypes ffiffiffiffiffiffiffiffiffiffiffiffiffiffi of substrates. (c) Width of the meniscus bridge vs. t/t, where t ¼ rR3 =s is the dimensionless time. The dashed lines are fitting data points. The insets present the geometry of water films from front and top views and define the meniscus height h0 and width d0.
molecules perpendicular to the G substrate is the highest, followed by the HCNTA. Notably, the order of the diffusion speed agrees well with the order of the increasing rate of the liquid bridge height, intensely implying the higher peak value in the density distribution curve, the lower diffusion speed of the water molecules along the z direction, and then the lower height increasing rate of the meniscus bridge. In the direction of the x axis, for water–G and water–HCNTA systems, there is no distinct difference in the diffusion speed between these two groups. It is worth noting that in general, the diffusion speed of
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water molecules on the nanotube should be different from that on the graphene due to the curvature effect. This influence can be observed in the local region however we calculate the MSD of all the molecules in the water group. As a result, it is reasonable that there is no distinct difference in the diffusion speed between water–G and water–HCNTA systems on the whole along the x direction. However, in terms of the VCNTA substrate, the diffusivity of water molecules is much lower than that on G and HCNTA substrates. This result provides further evidence of the smallest growth rate of the liquid bridge on the VCNTA substrate, leading to the longest time to complete the early-stage coalescence. Extensive simulations are performed to investigate the effect of surface wettability on the coalescence dynamics of adjacent films on CNT arrays. Diameters of CNTs are chosen as 16.27 Å, 18.98 Å and 21.7 Å, respectively, which are arranged at a fixed interval of 3.4 Å. The contact angle (WCA) of water, which is predominantly employed to characterize the surface wetting properties, is measured. In addition, a detailed description of the measurement of y can be observed in Fig. 6(a), by plotting the liquid/air interface contour. It was found that water has apparent equilibrium WCAs of 61.541, 70.511 and 80.471 for three HCNTA substrates. Due to the wetting anisotropy when water films are placed on CNT arrays, the contact angles referred here are examined in the axial direction of CNTs. From Fig. 6(b), it is obvious that the height of the liquid bridge has a linear increasing tendency with simulation time; moreover, on the rough surface with the smallest WCA, the height is much lower than the others. The inset graph in Fig. 6(b) quantitatively exhibits that the average growth velocity of the liquid bridge height increases monotonously with the increasing WCA. Additionally, the growth speed reaches the maximum sharply when the WCA increases to 80.471, implying that, for a drop with the WCA of less than 901, the expansion rate of the meniscus bridge is sensitive to the surface wettability, and the roughness surface with a large WCA is quite beneficial for enhancing the coalescence rate. To answer the question of why the water films behave so differently on VCNTA and HCNTA substrates, it is necessary to study the effect of the surface structure on the coalescence dynamics of neighboring films. Noteworthy is that the surface of the CNT array presents a sinusoidally wrinkled and grooved surface with the anisotropic texture which induces the diversity of the flow velocity in different directions. Fig. 7(b) shows that the three-phase contact line of the water film placed on the CNT array with a wrinkled surface explicitly presents an elliptic shape, deviating from a circular form on the G substrate in Fig. 7(a). This result implies that the surface geometric anisotropy plays a key role in the movement of the contact line, permitting the water film to preferentially flow perpendicular instead of parallel to the groove. This phenomenon appears to contradict the existing viewpoint that the movement of liquid perpendicular to grooves is less than that along the parallel direction, since the grooves are proposed to act as obstacles to contact-line motion, which could induce pinning. This anomalous phenomenon is explained in Fig. 7(c). It is obvious that a
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Fig. 4 Interface properties. (a) Water density distribution along the z direction perpendicular to the surface. The graphene or the top layer carbon atoms of the CNT array is placed at the plane where z = 0. The equilibrium distance of the first ordered layer and the peak value for the G surface are marked. (b) Average hydrogen bond distribution profile normal to the surface. (c) The variation of water–substrate interaction energy EW–S versus time. (d) The interaction energy between water and water molecules EW–W as a function of time.
Fig. 5
Mean square displacements (MSDs) of water molecules on G and CNTs array along (a) z direction and (b) x direction.
wave-shaped contact line appears in the direction parallel to the groove; intriguingly, this local wave feature very much resembles the sinusoidally wrinkled pattern which is observed to mutually agree well with the experimental result.39 This local pinning derives from the inhibition effect of CNTs, when the liquid moves at the top of the surface roughness, the motion of the contact-line is mainly hindered by the interactions between water and CNTs, besides this, a degree of physical adsorption due to the high specific surface of CNTs also contributes to the pinning of the contact-line. From the above-mentioned results, we can speculate that the resulting restraint of the groove is possibly relatively small compared with the local pinning at the crest of the surface feature in our simulation system, eventually enhancing the priority of the movement of the contact line perpendicular to the groove. To some extent, for the water–VCNTA
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system, the local pinning at the crest of the sinusoidal pattern confines the movement of the contact-line along the groove and then further decreases the growth rate of the bridge width. In the previous section, we mainly research how the interfacial properties and the anisotropic surface pattern influence the coalescence rate of adjacent water films located on G and CNT arrays. Next we will reveal the role of the underlying substrate on the coalescence behavior of nonadjacent water films, which are separated at a certain distance of 1 Å. As can be noted in Fig. 8(c), coalescence only occurs on the VCNTA, whereas when placed on the G substrate, it is obvious that the water films are strongly inclined to contract due to surface tension. As the process proceeds, the films gradually change into a hemispherical shape apart from each other as shown in Fig. 8(a). The similar noncoalescence behavior is also observed
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the groove has also attracted our attention, which plays a pivotal part in facilitating the contact of isolated water films. When the contact line moves in the direction perpendicular to the groove, water molecules can permeate into the grooves in a system denoted as the Wenzel regime,40 where the grooves are filled by liquid, and then the coalescence behavior is achieved owing to the advance of the contact line, actuated by the capillary force which is originated from the penetrating liquid. This hypothesis is verified by Fig. 8(d). From the comparison of front view profiles at different times before coalescence, it is clear that the curved liquid surface (near the top) experiences Laplace pressure oriented towards the centre of curvature which is believed to impel the contact line past the wave crest. As this process proceeds progressively across time, an obvious contact point as marked in Fig. 8(d) is produced between water films at a simulation time of up to 36 ps, triggering the formation of a thin liquid bridge, which plays an essential role in the subsequent coalescence process. Based on this finding, we can identify the key factor to determine whether the coalescence of nonadjacent films could occur, which is prevailingly attributed to the initial advance of the contact line.
4. Conclusion Fig. 6 (a) Illustration of the contact angle (y) measurement by plotting the liquid/air interface contour, the red curve marks the fitting interface of the water droplet. y is denoted as the angle between a tangential line of the droplet surface and another line within the substrate. The WCAs are averaged over five measurements. (b) The height of the liquid bridge as a function of time on the HCNTA with various equilibrium contact angles of 61.541, 70.511 and 80.471. And the inserted graph is the average increasing velocity of bridge height n with respect to WCA.
for the water–HCNTA system. Specifically, in this case, the local pinning at the top of surface roughness plays a dominant role in hindering the movement of the contact line along the x-direction and further holds back the contact of two films. To find out the source to generate coalescence behavior in contact with the VCNTA substrate, we have further examined the initial spreading of water films before contact. Apart from the impeditive effect of the groove on the movement of the contact line perpendicular to the axial direction of CNTs, another function of
The coalescence behavior of water films on the carbon-based substrate is affected by both the interfacial properties and the anisotropic surface pattern. The growth of the liquid bridge width can be roughly described by the scaling law, h0 B t1/2, when water films are located on G and HCNTA substrate during the early-time coalescence. There is no doubt that interactions between water and the substrate restrict water molecules in the ordered-layer and further generate changes in the first layer peak. Additionally, the lower diffusion speed of water molecules in the direction perpendicular to the surface arising from the relatively ordered water layer on the CNT array is responsible for the lower coalescence rate. The significant local pinning at the crest of surface roughness, which allows the preferential flow perpendicular to the groove, can significantly produce a variability of the growth rate between HCNTA and VCNTA substrates. Aside from this, the advancing contact line driven by the penetrating liquid urges the occurrence of the contact point of nonadjacent films placed on the VCNTA. These discoveries can
Fig. 7 Top view of water films on flat and wrinkled surfaces. (a) Image of the water film on the G substrate, revealing a circular shape. (b) Snapshot of isolated water on the CNT array, showing an elliptic form. (c) Water film presents pining of the contact line at the crest of surface roughness.
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Fig. 8 Performance of nonadjacent water films. (a and b) Images of isolated water films 1 Å apart from each other on G and HCNTA surfaces. (c) Coalescence process occurred on the VCNTA surface with a rapid expansion of the liquid bridge. (d) Side image of water profiles at different time periods before contact. The inset circle marks the contact point.
provide a better insight into the relevance between coalescence and interfacial properties or structure and aid in the development of an effective method for controlling the coalescence dynamics of water films.
Acknowledgements The authors would like to acknowledge the support from the National Natural Science Foundation of China (Grant No. 51271100). This work is also supported by the National Basic Research Program of China (Grant No. 2012CB825702). This work is also supported by the Special Funding in the Project of the Taishan Scholar Construction Engineering.
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