Evaporation of Water on Suspended Graphene: Suppressing the

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Evaporation of Water on Suspended Graphene: Suppressing the Effect of Physically Heterogeneous Surfaces Masumeh Foroutan, S. Mahmood Fatemi, Farshad Esmaeilian, and Vahid Fadaei Naeini Langmuir, Just Accepted Manuscript • Publication Date (Web): 26 Oct 2018 Downloaded from http://pubs.acs.org on October 26, 2018

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Evaporation of Water on Suspended Graphene: Suppressing the Effect of Physically Heterogeneous Surfaces Masumeh Foroutan*,a S. Mahmood Fatemi ǂ,a, Farshad Esmaeilian ǂ,a, and Vahid Fadaei Naeiniǂ,b aDepartment

of Physical Chemistry, School of Chemistry, College of Science, University of Tehran, Tehran, Iran

bSchool

of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

Abstract Evaporation of water nano-droplets on a hydrophilically adjusted graphene sheet was studied based on a molecular dynamics approach. Suspended graphene was used as a physically heterogeneous surface, and fixed graphene was considered as an ideally flat surface. State of the triple-phase contact line (TPCL) and shape evolution were addressed at four different temperatures on both substrates. Additionally, contact angle (CA) was studied during 3 ns and 22.5 ns simulations in both closed and opened conditions. The observed constant contact angle regime was predictable for the fixed graphene. However, it was not expected for the suspended system, and was attributed to the oscillations of the substrate atoms. The size of the nano-droplet also affects the CCA mode in both systems, when the number of water molecules decreases to less than 500. The oscillations created a surface on which physical heterogeneities were varying through time. Examination of the evaporation and condensation processes revealed higher rates for the fixed systems. Local mass fluxes were calculated to reveal the contribution of TPCL and meridian surface (MS) of the nano-droplet to evaporation and condensation. The obtained results indicate similar values for the mass flux ratio at the TPCL, which remains twice as large as the MS for both suspended and fixed graphene. The results confirm the assumption that a surface with varying heterogeneities can overwhelm the droplet, and act as an ideally flat surface.

Keywords: Evaporation, Suspended Graphene, Triple-Phase Contact Line, Hydrophilic Surface.

*

Corresponding author: Tel +98 21 61112896; Fax: +98 21 66495291, [email protected] authors contributed equally to this work.

ǂ These

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Introduction Interfacial interactions play an important role in scientific as well as engineering processes, and they are best studied through the wetting phenomenon.1 These interactions most commonly are between a solid and a liquid that are surrounded by a fluid phase. Contact angle (CA) is the thermodynamic characteristic of such a system and is defined with the help of Young’s equation.2-3 Although no mathematical formulation was presented in Young’s original work,4 he tried to illustrate the CA as a local property through the use of the term “angular particles”.4 This idea has forced a decade long debate regarding the effect of the area far from the triple-phase contact line (TPCL) on apparent contact angle (APCA).5-6 Today, the equation that describes the contact angle of a drop with radius, 𝑟, that is resting on an ideal surface can be written as follows:2-3 cos 𝜃 =

𝛾𝑆𝑉 ― 𝛾𝑆𝐿 𝛾𝐿𝑉

𝛤

(1)

― 𝑟𝛾𝐿𝑉

The first part of the equation (1) on the right hand side is the well-known Young’s equation, where 𝛾𝑖𝑗 is the interfacial energy between 𝑖 and 𝑗 phases. The second part takes the effect of line tension, 𝛤, into account and is denoted the Boruvka-Neumann term.7 The TPCL affects APCA through the line tension, which in turn is under the influence of physical/chemical surface heterogeneities.8 In the midst of the above mentioned dispute, characteristics of TPCL were debated in detail by others.9-15 Moreover, simulation studies have validated these theoretical analyses to a great extent.16-18 Many aspects of wetting with regard to its applications especially evaporation, are closely connected to the state of TPCL.19 Evaporation controls fundamental processes in coating20-22 and printing23-25 industries. Recently, it has attracted more attention as an integral part of new technologies such as nanofabrication26-32 and bio-drop33-36 manipulation. Theoretical study of evaporation can be traced to more than a century ago.37 It was observed from early evaporation experiments that both constant-contact-angle (CCA)38-41 and constantcontact-radius (CCR) 38-39, 41-44 modes can be distinguished. A mixed mode is also possible between these two extreme cases, and that is when the drop evaporates through different stages.40-41, 45 Experimental and finite element analyses suggest that TPCL is the main contributor to evaporation particularly on hydrophilic substrates. 46-49 Similar to many aspects of the theory of wetting, TPCL was the first place to look for answers regarding the modes of evaporation. the experimental study of TPCL has not been easy,5-6, 9, 50 nor has its behavior been readily observable through conventional microscopic techniques.11 Because the interaction of TPCL and surface heterogeneities can be neglected only on ideal surfaces,1-3, 51 computational and simulation studies could help in understanding the properties of TPCL. It must be noted that aside from the physiological aspects of these interactions52-58 not much has been discussed. The main challenge of computational studies has been the effect of drop size at nanometer range, since the properties of the TPCL become dominant in small droplets. Zhang et al.59 argued that macroscopic models reach their limit at subnanolitre range. Nonetheless, many characteristics of TPCL can still be analysed. Their recent comprehensive studies16, 59-60 have introduced a new 2 ACS Paragon Plus Environment

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path to evaporation research through MD simulation. Xie et al.61 chose an almost similar route and studied the contribution of different sections of the droplet’s surface on mass flux as well as evaporation. The mentioned works show that the TPCL is the main contributor to evaporation on hydrophilic surfaces, and the contact line flux on hydrophilic surfaces is comparable 56 or even larger59 than that of the meridian surface (MS) of the droplet. In this paper, suspended graphene was chosen as a physically heterogeneous substrate, on which the location of the heterogeneities can vary through time. In addition, fixed graphene was selected as a flat substrate. The values for non-bonded interactions of both graphene sheets were adjusted to make them hydrophilic. Thus the effect of TPCL can be carefully analyzed on both substrates. After describing the details of the studied systems, a novel approach to the idea of suppressing the effect of physical heterogeneities and occurrence of CCR regime in evaporation is introduced.

Computational Methods A series of MD simulations at different temperatures were performed using LAMMPS62, and structures were visualized using the VMD package63. In order to investigate the evaporation of water, we chose two different systems with a box of water on fixed and suspended graphene substrates – See Figure 1 (a). Carbon atoms of graphene were fixed during the simulation of the fixed systems, and the temperature was applied to the box of water with an NVT ensemble. The suspended graphene, which is a result of oscillating carbon atoms, can be formed by the distortion of C–C bonds following the work of Caturla et al.64 Based on a previous work,65 we considered two regions with a width of 4 Å at the opposite ends of the graphene substrate. The two regions were held fixed, while the NVT ensemble was applied to the carbon atoms between them. The NVE ensemble was applied to the box of water in these systems. There is no prior MD work concerned with both a heating substrate and an evaporating water droplet on suspended graphene to the best of our. In both systems, we utilized an armchair configuration of graphene with (154 × 154) Å2 dimension, which is large enough to ignore the size effect66 and consists of 8928 carbon atoms. It should be noted that an equilibrium molecular dynamics simulation (EMDS) and a non-equilibrium molecular dynamics simulation (NEMDS) were performed for the fixed and suspended, respectively. The SPC/E (extended) water model was used for all simulations.67 2091 water molecules were employed creating a water droplet with a density of 1 g.cm-3 similar to that of the pure water. The starting water cluster was confined to a tetragonal configuration with (50 × 50 × 25) Å3 dimension. The water droplet was placed on the center of the graphene sheet at an initial distance of about 3 Å from the surface as shown in Figure 1 (a). Simulations were performed at (300, 400, 450 and 500) K. The temperature of suspended graphene was fixed with a Nosé-Hoover thermostat68 with a relaxation time of 1 ps. Nonperiodic boundary conditions were applied in the Z-direction of the simulation box while periodic boundary conditions were considered in the other two directions.69 The size of the simulation cell along Z-direction was set equal to 155 Å, and a mirror boundary condition was


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speciﬁed at the edges. The time step was set to 1 fs, and the original simulations were carried out for 3 ns. In addition, 22.5 ns long simulations were also performed to monitor the evaporation modes. In these longer simulations, the system was opened after 2.5 ns, the reason behind which will become apparent in the following sections (see section 2 of Supp. Info. for more detail). The main difference between short and long simulations was the closed and opened characteristic of the system, respectively. In other words, a deleting procedure was carried out in the long, or opened simulations, where 1 water molecule was deleted every 1 ps similar to the work of Zhang et al.16 The simulation method for open systems comprised of three parts. First, locating the water molecules that resided above a certain value along Z direction after the evaporation from the droplet. Second, random selection of one of the aforementioned water molecules, and third, deletion of the chosen molecule. Although the first occurred at the final stage of each simulation step, the second and third were performed outside of the simulation iteration and did not affect its progress. No other conditions were changed for longer simulations. The particle mesh Ewald method with a 12.0 Å real-space cutoff and splines on the order of 1 with a 10-4 tolerance was implemented to compute the electrostatic interactions.70 Non-bonded van-der-Waals interactions were modeled using a cut-off distance of 10 Å, in terms of 12 - 6 Lennard-Jones potential, that is:71 𝑈𝐿𝐽 (𝑟𝑖𝑗) = 4𝜀𝑖𝑗

𝜎𝑖𝑗 12

𝜎𝑖𝑗 6

𝑟𝑖𝑗

𝑟𝑖𝑗

[( ) ― ( ) ]

(2)

wherein 𝜀𝑖𝑗 and 𝜎𝑖𝑗 are the well depth and collision diameter, respectively. 𝑟𝑖𝑗 refers to the distance between the two interacting atoms i and j. The harmonic potential style was used for bonding based on𝐸bond = 1 2𝐾𝑏𝑜𝑛𝑑(𝑟 ― 𝑟0)2, where 𝑟𝑜 is the equilibrium bond distance and 𝐾𝑏𝑜𝑛𝑑 is the bond coefficient. The harmonic potential style was also used for angling based 𝐸𝑎𝑛𝑔𝑙𝑒 = 1 2𝐾𝑎𝑛𝑔𝑙𝑒(𝜃 ― 𝜃0)2, where 𝜃0 the equilibrium value of angle and 𝐾𝑎𝑛𝑔𝑙𝑒 is the angle coefficient. The parameters used for bonding, nonbonding, and angle interactions for the constituents are given in Tables 1 and 2. It should be noted that the parameters used for bond and angle interactions were taken from refs.72-73 We used the dihedral potential for graphene in the style of OPLS potential, which were described by Watkins and Jorgensen, to achieve the suspended graphene.74 The OPLS potential for dihedral style is:75-76 1

1

1

𝐸𝑑𝑖ℎ𝑒𝑑𝑟𝑎𝑙𝑠 = 2𝐾1[1 + cos (∅)] + 2𝐾2[1 ― cos (2∅)] + 2𝐾3[1 + cos (3∅)] + 1 𝐾 [1 ― cos (4∅)] 2 4

(3)

The dihedral coefficients of graphene are given in Table 3.75-76 Overall, the total potential energy of the system was calculated by adding the contribution of each equation as: (4) 𝐸(𝑟𝑁) = 𝐸𝑏𝑜𝑛𝑑𝑠 + 𝐸𝑎𝑛𝑔𝑙𝑒𝑠 + 𝐸𝑑𝑖ℎ𝑒𝑑𝑟𝑎𝑙𝑠 + 𝐸𝑛𝑜𝑛𝑏𝑜𝑛𝑑𝑒𝑑 4 ACS Paragon Plus Environment

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where Enonbonded can be calculated as follows: Enonbonded = ∑𝑖 > 𝑗𝑓𝑖𝑗

(

𝐴𝑖𝑗 𝑟𝑖𝑗

12

𝐶𝑖𝑗

𝑞𝑖𝑞𝑗𝑒2

― 𝑟 6 + 4𝜋𝜀0𝑟𝑖𝑗 𝑖𝑗

)

(5)

The SHAKE algorithm was used to constrain the bonds and angles of each water molecule.77 Lorentz-Berthelot mixing rules were also used to calculate cross interactions and to adjust the graphene as a hydrophilic substrate.78 Figures 1 (b) and (c) show the final snapshot of the MD simulation for suspended as well as fixed graphene at 400 K, respectively.

Results and Discussion Evaporation of a water nano-droplet in a mainly closed system was studied in this research. In such systems the evaporation and condensation can be studied in more detail, since each molecule can participate in both processes many number of times. This has helped in monitoring the procedure and analyzing the contribution of TPCL as well as MS through many cycles. An intricate part of the presented analysis included the characterization of TPCL through its height. Shape and CA analyses are also presented to follow the conventional experimental studies and identify the evaporation regime. Longer simulations were also performed to monitor the evolution of CA in additional opened systems. The main goal of these simulations was to analyze the behavior of the nano-droplet based on its evaporation regime to observe its complete evaporation. Moreover, the evaporation process does not differ from the opened systems to the closed ones. Rather, it is the deleting of water molecules that is occurring in these systems. In both opened and closed systems, the evaporation can be defined as the separation of one or a group of water molecules from the nanodroplet, which is identified by the utilization of cluster analysis. Therefore, the acquired data from these simulations can act as complementary results relative to the shorter simulations. Finally, evaporation, condensation, and local mass fluxes are analyzed. Fixed and Heated Surfaces In the current research, two different systems were studied based on their heating method. The different heating methods resulted in distinct characteristics. In this section the behavior of the substrate is analyzed based on the interaction energy. Figures 2 (a)-(d) illustrate the distribution of the van der Waals interaction energy of one water molecule at 6.25 Å distance from the surface for both systems. This distance was chosen based on the number density profiles, which will be discussed in another section. Using the values presented in Table 1, one water molecule was scanned on the surface to extract the presented energy contours. Figures 2 (b)-(d) were drawn for three different time steps at 300 K with 5 ps intervals. It should be emphasized that the minimum and maximum position of the carbon atoms, along Z-axis, remains in the range of (-4, 4) angstroms, which is in agreement with the work of Ma et al.79 Based on the work of Bao et al., the temperature affects the morphology of suspended graphene as well.80 It can be observed that the fixed substrate interacts uniformly with the water molecules. However, the oscillations of the graphene sheet lead to changes in the interaction pattern which 5 ACS Paragon Plus Environment

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evolve continually. These changes result in the formation of physically heterogeneous regions that interact with the water nano-droplet. Recently, our group has shown the scale of impact of these heterogeneities on CA hysteresis.81 Such heterogeneities can also affect the movement of the nano-droplet, which will be discussed in the next section. The Movement of the Nano-Droplet Center-of-mass (COM) can be used to analyze the movement of a set of molecules. Based on the value of COM along XY-plane, the movement of the nano-droplet on the graphene substrate can be studied. As the first derivative of XY-COM changes sign, the direction of motion (DOM) of the nano-droplet changes as well. These points can be used to determine whether the nanodroplet moves easily or feels more resistance from the graphene substrate (see section 1 of Supp. Info. for more detail). Figure 3 shows the number of changes in the DOM of the nano-droplet during the 3 ns simulations. The droplet was considered moving in a direction only if the derivative of the XYCOM diagram did not change sign for at least 3 ps. It should be noted that only the first 0.5 ns of the simulation was used to extract COM values at 500 K, since the nano-droplet has less than 500 water molecules on the fixed graphene past this time as a result of the evaporation. Based on the presented values in Figure 3, the droplet changes its DOM on suspended graphene more than the fixed substrate. Furthermore, the increase in temperature of the systems has resulted in more changes the droplet’s DOM. The answer to the number of changes in the DOM can be found by a closer look at the oscillations of the carbon atoms, since The only difference between the systems was whether the carbon atoms are fixed or not. Figure 4 illustrates the distribution of the van der Waals interaction energy, while the insets show snap shots of the graphene sheet at t = 2.0, 2.08, 2.2 nanoseconds. The figures were drawn based on the method which was explained in the previous section. The blue and green arrows display the DOM and the occurrence of a revolution in the DOM, respectively. (see section 1 of Supp. Info. for more detail) It can be seen that as the nano-droplet moves from point I to II, the darker section of Figure 4 (a) moves to the location illustrated in Figure 4 (b). This is one of the instantaneous sites which forces the droplet to change its direction at point II. In addition, the dark section of Figure 4 (c) at the lower half of the graphene sheet forces another change in the DOM a few picoseconds past point III – (see section 1 of Supp. Info. for more detail). Therefore, the physical heterogeneities are the reason behind the increase in number of direction changes for the nano-droplet on suspended graphene. State of TPCL Number density of water molecules was studied to extract the height of TPCL. Figure 5 (a) and (b) illustrate the calculated distributions for the final 0.5 ns of the short simulations. The highest peaks are located at 3.25 Å and 6.25 Å from the surface. These two layers of water molecules have stronger interactions with the surface and can be denoted the interfacial and adjacent layers, 6 ACS Paragon Plus Environment

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respectively. It can be observed that the height of the peaks decreases as the temperature increases in both systems. This is related to the simultaneous occurrence of spreading as well as evaporation.82 The only exception to the results occurs for the fixed substrate at 500 K. High temperature has caused the droplet to be completely evaporated even though an interfacial layer of water molecules can still be distinguished. Based on the obtained data, the highest distance from the surface where water molecules are still under significant influence from the graphene was chosen as the height of the adjacent layer and was used in further analyses as the height of TPCL. Shape Evolution and Contact Angle Analysis In this study, the deformation of the droplet was quantified via the sphericity parameter.54, 59 First, a mass-density contour map of the interfacial and adjacent layers was computed through the simulation. Then, the isodensity points where the mass density was equal to 0.2 of the bulk of the drop were extracted. A circle was fitted to the data set to find the center and radius of the drop. Based on the deviation from the fitted radius, the sphericity was calculated through the use of the following equation: 𝑆=

𝑅𝑠𝑚𝑎𝑙𝑙𝑒𝑟

(6)

𝑅𝑙𝑎𝑟𝑔𝑒𝑟

In Equation 6, 𝑅𝑠𝑚𝑎𝑙𝑙𝑒𝑟 and 𝑅𝑙𝑎𝑟𝑔𝑒𝑟 are separate averages of a collection of smaller and larger radii, respectively. Table 4 holds the acquired data from the shape analysis of the droplet for every system. It was observed that 𝑆 > 0.8 for both fixed and suspended systems during the 3 ns simulations. The only exception was the fixed system at 500 K. In this system, it was impossible to distinguish the layers and the contact area of the droplet after 0.6 ns. The acquired results are in agreement with number density profiles – see Figure 5 – and indicate that the droplet maintains an almost circular contact area as the simulations move forward. Therefore, the spherical cap assumption can be used in characterization of the droplet and its contact angle, which is in line with the work of Zhang et al.59 The CA can be used to determine whether the droplet evaporation occurs in CCA or CCR regime. The mass-density contour map of the droplet was used to determine the CA at different time intervals. A similar procedure to sphericity analysis was used to extract the meridian points of the droplet, where the mass-density ratio of the boundary to the bulk of the drop was 0.2. Two projections of the mass-density contour map were used within 10 ps intervals i.e. XZ and YZ. The CA of each projection was calculated using a simple circle fitting algorithm, although the interfacial and adjacent layers were ignored due to the mass-density fluctuations. Figures 6Figure (a) and (b) illustrate the mass-density contour map of the droplet for XZ and YZ projections on the suspended graphene at 400 K when t = 3 ns. The calculated CAs for the system at different temperatures are shown in Figure 6 (c), where it is evident that the graphene substrate behaves as a hydrophilic surface. The mean value of contact angle after the first 0.5 ns of the simulation is presented in Table 4. It should be noted that the presented values for the 7 ACS Paragon Plus Environment

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fixed system at 500 K are based on the first 0.6 ns of the simulation, since no droplet exists past this time. As previously discussed, additional simulations with opened systems were performed up to the complete evaporation of the nano-droplet to carefully monitor the evolution of CA. Table 4 holds the CA results for the extended simulations on both fixed as well as suspended graphene. It should be noted that no additional data are presented for the fixed system at 500 K, since complete evaporation had occurred in short simulations. These values represent the CA of the nano-droplet before its size reaches 500 molecules. Past this time, it becomes more difficult to extract a uniform mass-density contour map of the nano-droplet. Therefore, large fluctuations occur in the data set, and a trend of decrease can be observed. The CA analysis completely fails, as the evaporation continues, and the size of the nano-droplet reaches ~100 molecules. No massdensity contour map can be acquired further, and the value of the CA can be set to zero. The obtained results prove that size effects can cause a different behavior from the nano-droplet, which is in agreement with Ref.79 (see section 2 of Supp. Info. for more detail) Based on the presented data, the CCA regime is the observed evaporation mode in both 3 ns and 22.5 ns simulations. This mode is active, and the evaporation continues with an almost constant value of the CA until the size of the droplet passes a threshold. The acquired data suggest that this threshold is at ~500 molecules on the hydrophilically adjusted graphene, and the TPCL acts as a dominant contributing factor to CA past this stage. The obtained results also indicate that a second threshold is observable where the collection of the water molecules can no longer be called a nano-droplet. The nano-cluster of water appears at ~100 molecules until the complete evaporation has occurred. Finally, the similar behavior of both fixed and suspended systems, even past the 500 mark, confirms the original idea that these two systems behave almost the same as one another. Further characterization of the effect of TPCL on CA requires separate comprehensive researches. However, the mobility of water molecules, the height of the interfacial as well as adjacent layers, the effect of Lennard-Jones interactions on wettability of the substrate, and other properties of the surface can be contributing factors. In summary, oscillations of the carbon atoms create heterogeneous sites. The effect of fixed physical heterogeneities on CA has been observed.83 However, constant evolution of these sites seem to overwhelm the droplet and to result in a similar behavior to that of an ideal surface. Furthermore, it can be observed that the CA values decrease as temperature rises in both 3 ns and 22.5 ns simulations. A similar behavior on hydrophilic PMMA was recently reported by our team, which is line with the acquired results.82 Following the discussion regarding the TPCL and CA behaviors, evaporation and condensation processes can now be studied further. Evaporation and Condensation A step by step analysis was carried out on each water molecule and its neighbors during the 3 ns simulations to study the evaporation process. Oxygen atoms were used to represent the water molecules. In each specific time step, a cluster analysis was performed in which the minimum 8 ACS Paragon Plus Environment

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distance between two water molecules inside the drop, or rC, was less than 3.7 Å. Simulation data were analyzed from start to finish, and each evaporation and condensation was recorded. Figures 7 (a) and (b) illustrate the number of molecules inside the drop during the 3 ns simulations. In fixed systems the droplet is at the defined temperature from the start of the simulation. Therefore, a sudden decrease in the number of molecules inside the droplet is observed for the fixed systems – Figure 7 (b). In the suspended systems, more time is needed for the nano-droplet to reach the defined temperature. (see section 3 of Supp. Info. for more detail) This is where the size of the nanodroplet reaches an almost constant value – see Figure 7 (a). Thus, the evaporation process can be divided into two stages for these systems. First, acquiring sufficient kinetic energy to reach the isothermal steady state. Second, the steady state where the evaporation and condensation rates become almost equal, and the droplet size plateaus. Table 4. holds the evaporation and condensation rates based on a least-squares fitting with a coefficient of determination of 0.99 for both systems at the steady state. As a result of the different heating methods, small discrepancy can be observed between the evaporation/condensation rates. Local Mass Flux In this section, mass fluxes are studied to determine the contribution of TPCL and MS to the evaporation process during the 3 ns simulations. The two general locations for evaporation of the molecules are the MS and the TPCL - see Figure 8 (a). Following this argument, the local mass flux and mass flux ratio can be estimated.59 Equation 7 was used to calculate the local mass flux: 𝑁𝑖(𝑡)

(7)

𝐽𝑖(t) = 𝐴𝑖(𝑡)

where 𝑁𝑖 is the total number of evaporated molecules from the general i location, and 𝐴𝑖 is its surface area at the time step, t. Thus, local mass flux of the TPCL and MS would be 𝐽𝑇𝑃𝐶𝐿(t) = 𝑁𝑇𝑃𝐶𝐿(t) 𝐴 (t) and 𝐽 (t) = 𝑁𝑀𝑆(t) 𝐴 (t), respectively. 𝑇𝑃𝐶𝐿

𝑀𝑆

𝑀𝑆

The surface areas were calculated based on the shape of each location. TPCL was considered as a cylinder with the height of 6.25 Å. The droplet was also modelled as a spherical cap (SC). The CA of the droplet was used to estimate its total surface area (𝐴𝑆𝐶). Therefore, the 𝐴𝑀𝑆 was calculated as the difference between 𝐴𝑆𝐶 and 𝐴𝑇𝑃𝐶𝐿. The radii of the 𝐴𝑇𝑃𝐶𝐿 and 𝐴𝑆𝐶 were also extracted from the sphericity calculations – see Table 4. Finally, the mass flux ratio was calculated using Equation 8. 𝐽𝑖(𝑡)

(8)

𝐾𝑖(t) = 𝐽𝑡𝑜𝑡(𝑡)

In the above equation, 𝐽𝑖(𝑡) is the evaporation flux from location i, and 𝐽𝑡𝑜𝑡(𝑡) is the total evaporation flux. A similar analysis can be utilized to estimate the local flux and flux ratio for the condensation process. Figures 8 (b) and (c) illustrate the mass flux ratio for the suspended as well as fixed systems at 400 K and 450 K, respectively. The results indicate similar mass flux ratios for TPCL and MS of both systems after 0.5 ns. It can be concluded that the constant oscillation of the hydrophilic 9 ACS Paragon Plus Environment

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graphene sheet has resulted in a similar evaporation behavior to that of an ideally flat surface. On these surfaces TPCL is considered as the main contributor to evaporation. Figures 9 (a) and (b) present the average mass flux ratio during the evaporation as well as condensation processes for both systems. It can be observed that in almost all the cases the TPCL contributes twice as large as MS to evaporation flux. The acquired data for both systems slightly deviates at 300 K , since very few number of molecules evaporate at this temperature, and therefore the data show large uncertainty values. Zhang et al.59 showed that TPCL contributes disproportionately to evaporation mass flux in their hydrophilic system. This clearly indicates that TPCL is controlling the evaporation process on hydrophilic surfaces. Both our results and theirs are in line with experimental data46, 48-49, while our data presents additionally important notions. The oscillations of the surface atoms can form heterogeneities – see Figures 2 and 4. However, the constant oscillations seem to overwhelm the droplet as discussed elsewhere as well.81 This behavior causes the droplet to act as if it is resting on a flat surface. Therefore, CCA regime should be observed on similar surfaces with high number of heterogeneities which are controllable and can vary through time. Only size-effects can alter the evaporation regime, and even then the effect is similar on both substrates. Such surfaces can be achieved using similar methods for controlling wetting transitions.84-85 The authors believe that the acquired results present a novel idea to the wetting theory and show that TPCL as well as its effects could be overwhelmed, while in theory the substrate behavior is far from an ideal surface.

Conclusion Theoretical and computational studies have indicated that local mass flux from TPCL is the main contributor to the evaporation process on hydrophilic surfaces. The presented research follows an MD approach to compare the evaporation process on an ideally flat surface with a physically heterogeneous substrate on which the heterogeneities vary through time i.e. a fixed graphene with a suspended graphene. Number density profile was used to characterize the TPCL. Shape evolution and CA analysis of the nano-droplet revealed a CCA regime for both systems in closed simulations, which was not expected on a heterogeneous surface. Extended opened simulations confirmed the CCA regime up to a threshold at which size-effects become dominant. Evaporation and condensation processes were analyzed. The acquired data signifies that the TPCL is the main contributor to evaporation flux on both surfaces. The average flux ratio for both systems were similar. This suggests that a surface with varying as well as controllable physical heterogeneities can act as a flat surface and suppress the effect of physical heterogeneities while giving rise to CCA regimes. The authors believe that the presented results could introduce a new pathway in tuning the behavior of heterogeneous surfaces and their effect on evaporation.


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Associated Content Supporting Information Changes in the direction of motion of the nano-droplet, contact angle analysis of extended simulations, and temperature of water molecules are provided to support the main content.

Notes The authors declare no financial competing interest.


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References 1. De Gennes, P.-G.; Brochard-Wyart, F.; Quéré, D., Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves. Springer Science & Business Media: New York, 2013. 2. Adamson, A. W.; Gast, A. P., Physical chemistry of surfaces. 6 ed.; John Wiley & Sons: New York, 1997; p 784. 3. Meier, G. H., Thermodynamics of Surfaces and Interfaces: Concepts in Inorganic Materials. University Press: Cambridge, 2014. 4. Young, T., An Essay on the Cohesion of Fluids. Philosophical Transactions of the Royal Society of London 1805, 65-87. 5. Erbil, H. Y., The debate on the dependence of apparent contact angles on drop contact area or three-phase contact line: a review. Surface Science Reports 2014, 69 (4), 325-365. 6. Esmaeilian, F.; Sahba Yaghmaee, M.; Riahifar, R.; Raissi, B., Comparison of wetting models and geometrical analysis in describing the effect of cavity number, size, and position on apparent contact angle. Journal of Adhesion Science and Technology 2017, 31 (12), 1338-1347. 7. Bormashenko, E., Young, Boruvka–Neumann, Wenzel and Cassie–Baxter equations as the transversality conditions for the variational problem of wetting. Colloids and Surfaces A: Physicochemical and Engineering Aspects 2009, 345 (1), 163-165. 8. Bormashenko, E., Progress in understanding wetting transitions on rough surfaces. Advances in Colloid and Interface Science 2015, 222, 92-103. 9. Amirfazli, A.; Neumann, A. W., Status of the three-phase line tension: a review. Advances in Colloid and Interface Science 2004, 110 (3), 121-141. 10. Nosonovsky, M., On the Range of Applicability of the Wenzel and Cassie Equations. Langmuir 2007, 23 (19), 9919-9920. 11. Bormashenko, E.; Musin, A.; Whyman, G.; Barkay, Z.; Zinigrad, M., Revisiting the Fine Structure of the Triple Line. Langmuir 2013, 29 (46), 14163-14167. 12. Bormashenko, E.; Bormashenko, Y., Wetting of Composite Surfaces: When and Why Is the Area Far from The Triple Line Important? The Journal of Physical Chemistry C 2013, 117 (38), 19552-19557. 13. McHale, G., Cassie and Wenzel: Were They Really So Wrong? Langmuir 2007, 23 (15), 82008205. 14. Extrand, C. W., Origins of Wetting. Langmuir 2016, 32 (31), 7697-7706. 15. Bormashenko, E.; Musin, A.; Whyman, G.; Barkay, Z.; Zinigrad, M., On universality of scaling law describing roughness of triple line. The European Physical Journal E 2015, 38 (1), 1-9. 16. Zhang, J.; Müller-Plathe, F.; Leroy, F., Pinning of the Contact Line during Evaporation on Heterogeneous Surfaces: Slowdown or Temporary Immobilization? Insights from a Nanoscale Study. Langmuir 2015, 31 (27), 7544-7552. 17. Weijs, J. H.; Marchand, A.; Andreotti, B.; Lohse, D.; Snoeijer, J. H., Origin of line tension for a Lennard-Jones nanodroplet. Physics of Fluids (1994-present) 2011, 23 (2), 022001. 18. Li, Y.; Wu, H.-A.; Wang, F.-C., Effect of a single nanoparticle on the contact line motion. Langmuir 2016, 32 (48), 12676-12685 19. Brutin, D.; Sobac, B., Chapter 3 - Triple Line Motion and Evaporation. In Droplet Wetting and Evaporation, Academic Press: Oxford, 2015; pp 25-30. 20. Hurd, A. J., Evaporation and Surface Tension Effects in Dip Coating. In The Colloid Chemistry of Silica, American Chemical Society: 1994; Vol. 234, pp 433-450. 21. Lee, J.; Son, G., Numerical simulation of liquid film formation and evaporation in dip coating. International Communications in Heat and Mass Transfer 2015, 68, 220-227. 22. Berteloot, G.; Daerr, A.; Lequeux, F.; Limat, L., Dip coating with colloids and evaporation. Chemical Engineering and Processing: Process Intensification 2013, 68, 69-73. 23. Belgardt, C.; Sowade, E.; Blaudeck, T.; Baumgartel, T.; Graaf, H.; von Borczyskowski, C.; Baumann, R. R., Inkjet printing as a tool for the patterned deposition of octadecylsiloxane monolayers on silicon oxide surfaces. Physical Chemistry Chemical Physics 2013, 15 (20), 7494-7504.


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Tables Table 1. Parameters used for nonbonding interactions86 Atoms

εi / Kcal.mol-1

σi / Å

q/e

m / au

Carbon

0.0700

3.5500

0.0000

12.0107

Hydrogen Oxygen

0.0000 0.1554

0.0000 0.4238 1.0079 3.1660 -0.8476 15.9994

Table 2. Parameter used for bonding and angling interactions72-73 Molecules

Bonding

Angle

K / kCal.mol-1. Å -2

r0 / Å

K / kCal.mol-1. Å -2

θ0 / deg.

Graphene

469.00

1.4000

63.00

120.00

Water

200.0

1.0000

200.0

109.47

Table 3. Parameters used for the dihedral angle potential75-76 Molecules Graphene

K1 kCal.mol-1. Å -2 0.0

K2 kCal.mol-1. Å -2 7.25

K3 kCal.mol-1. Å -2 0.0

K4 kCal.mol-1. Å -2 0.0

Table 4. Comparison of the acquired data from the systems with suspended and fixed hydrophilic graphene

Suspended⸸

State of Graphene

Fixed

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T/K

Sph.

CA / deg. (3ns)

CA / deg. (22.5 ns)

Evap. Rate/ Molecules.ns-1

Cond. Rate / Molecules.ns-1

300 400 450 500

0.92 ± 0.02 0.92 ± 0.02 0.93 ± 0.02 0.90 ± 0.04

66.1 ± 1.3 62.6 ± 1.1 60.2 ± 2.1 57.6 ± 2.0

65.3 ± 2.2 63.7 ± 1.3 59.9 ± 1.4 57.9 ± 2.7

15 707 1697 3147

15 688 1688 3113

300 400 450 500

0.93 ± 0.01 0.93 ± 0.02 0.90 ± 0.04 0.78 ± 0.10

66.7 ± 0.7 63.8 ± 1.2 55.0 ± 1.3 19.8 ± 5.2

68.0 ± 1.5 64.7 ± 2.1 54.1 ± 2.4 _*

13 899 3645 4637

12 878 3434 4351

⸸ The evaporation and condensation rates for the suspended system are based on the stage II.

* No additional data are presented for the fixed system at 500 K, since complete evaporation has occurred before 2 ns.


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Figure Captions Figure 1. (a) Initial snapshot of the simulation system. Final snapshots of the simulation for (b) suspended and (c) fixed systems at 400 K. Figure 2. Interaction energy contour for water molecules at 6.25 Å from the surface for (a) fixed graphene sheet. (b)-(d) illustrate the same contour for suspended graphene at three random time frames with 5 ps intervals at 300 K. Figure 3. The number of changes in the direction of the motion of the nano-droplet for fixed (blue) and suspended (red) systems. Figure 4. The distribution of the van der Waals interaction energy. The insets show snapshots of the graphene sheet for t= (a) 2.0, (b) 2.08 and, (c) 2.2 nanoseconds at 300 K. The blue arrow shows the direction of motion (DOM), while the green arrow illustrates the point at which a change in the DOM occurs. Figure 5. Number density distribution of atoms with respect to the distance from the substrate at various temperatures for (a) suspended and (b) fixed graphene sheet. Figure 6. (a) and (b) illustrate the mass-density contour map of the drop at time t = 3ns and 400 K projected to XZ and YZ planes, respectively. (c) The CA evolution of the droplet at different temperatures for suspended and fixed systems denoted by S and F, respectively. Figure 7. Time evolution of the size of the droplet for (a) suspended and (b) fixed hydrophilic graphene. The initial number of molecules was 2091. Figure 8. (a) Schematic representation of the droplet and the available locations for evaporation/condensation. Evaporation flux ratio for TPCL in red, and MS in blue, of the droplet at (b) 400 K and (c) 450 K. Figure 9. Bar chart of the average flux ratio for (a) evaporation and (b) condensation process after t = 0.5 ns.


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Figures Figure 1

(a) Z

Z X

X

Y

Y

155 Å

155 Å

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

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154 Å

154 Å

154 Å

(b)

154 Å

(c)


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Figure 2


Langmuir 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

Figure 3


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Figure 4


Langmuir 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

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Figure 5

(a)

(b)


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Figure 6

(a)

(b)

(c)


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Figure 7

(a)

(b)

Figure 8

(a)

(b)

(c)


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Figure 9

(a)

(b)


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Evaporation of Water on Suspended Graphene: Suppressing the

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